Emona tims-analog-communication-part1 2

CommunicationCommunicationCommunicationCommunication

SystemsSystemsSystemsSystems

ModellingModellingModellingModelling

with

Volume A1 Fundamental Analog

Experiments

Tim Hooper

Communication System Modelling with TIMS

Volume A1 - Fundamental Analog Experiments. Author: Tim Hooper

Issue Number: 4.9

Published by:

Emona Instruments Pty Ltd, 86 Parramatta Road Camperdown NSW 2050 AUSTRALIA. web: www.tims.com.au telephone: +61-2-9519-3933 fax: +61-2-9550-1378

Copyright © 2005 Emona Instruments Pty Ltd and its related entities. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, including any network or Web distribution or broadcast for distance learning, or stored in any database or in any network retrieval system, without the prior written consent of Emona Instruments Pty Ltd.

For licensing information, please contact Emona Instruments Pty Ltd.

The TIMS logo is a registered trademark of Emona TIMS Pty Ltd

Printed in Australia

WHAT IS TIMSWHAT IS TIMSWHAT IS TIMSWHAT IS TIMS ????

TIMS is a Telecommunications Instructional Modelling System. It models telecommunication systems.

Text books on telecommunications abound with block diagrams. These diagrams illustrate the subject being discussed by the author. Generally they are small sub-systems of a larger system. Their behaviour is described by the author with the help of mathematical equations, and with drawings or photographs of the signal waveforms expected to be present.

TIMS brings alive the block diagram of the text book with a working model, recreating the waveforms on an oscilloscope.

How can TIMS be expected to accommodate such a large number of models ?

There may be hundreds of block diagrams in a text book, but only a relatively few individual block types. These block diagrams achieve their individuality because of the many ways a relatively few element types can be connected in different combinations.

TIMS contains a collection of these block types, or modules, and there are very few block diagrams which it cannot model.

PURPOSE OF TIMSPURPOSE OF TIMSPURPOSE OF TIMSPURPOSE OF TIMS

TIMS can support courses in Telecommunications at all levels - from Technical Colleges through to graduate degree courses at Universities.

This text is directed towards using TIMS as support for a course given at any level of teaching.

Most early experiments are concerned with illustrating a small part of a larger system. Two or more of these sub-systems can be combined to build up a larger system.

The list of possible experiments is limitless. Each instructor will have his or her own favourite collection - some of them are sure to be found herein.

Naturally, for a full appreciation of the phenomena being investigated, there is no limit to the depth of mathematical analysis that can be undertaken. But most experiments can be performed successfully with little or no mathematical support. It is up to the instructor to decide the level of understanding that is required.

EXPERIMENT AIMSEXPERIMENT AIMSEXPERIMENT AIMSEXPERIMENT AIMS

The experiments in this Volume are concerned with introductory analog communications. Most of them require only the TIMS basic set of modules.

The experiments have been written with the idea that each model examined could eventually become part of a larger telecommunications system, the aim of this large system being to transmit a message from input to output. The origin of this message, for the analog experiments in Volumes A1 and A2, would ultimately be speech. But for test and measurement purposes a sine wave, or perhaps two sinewaves (as in the two-tone test signal) are generally substituted. For the digital experiments (Volumes D1, D2 and D3) the typical message is a pseudo random binary sequence.

The experiments are designed to be completed in about two hours, with say one hour of preparation prior to the laboratory session.

The five Volumes of Communication Systems Modelling with TIMS are:

A1 - Fundamental Analog Experiments

A2 - Further & Advanced Analog Experiments

D1 - Fundamental Digital Experiments

D2 - Further & Advanced Digital Experiments

D3 – Advanced Digital Experiments

Also available as an optional extra is:

TCLM1 – Technical College Lab Manual

ContentsContentsContentsContents

Introduction to modelling with TIMS..........................................A1-01

Modelling an equation.................................................................A1-02

DSBSC generation......................................................................A1-03

Amplitude modulation.................................................................A1-04

Envelopes ...................................................................................A1-05

Envelope recovery.......................................................................A1-06

SSB generation - the phasing method ..........................................A1-07

Product demodulation - synch. & asynchronous ..........................A1-08

SSB demodulation - the phasing method .....................................A1-09

The sampling theorem.................................................................A1-10

PAM & time division multiplex ...................................................A1-11

Power measurements...................................................................A1-12

Appendix A - Filter responses .....................................................A1

Appendix B - Some Useful Expansions........................................B1

Copyright © 2005 Emona Instruments Pty Ltd A1-01-rev 2.0 - 1

INTRODUCTION TO INTRODUCTION TO INTRODUCTION TO INTRODUCTION TO

MODELLING WITH TIMSMODELLING WITH TIMSMODELLING WITH TIMSMODELLING WITH TIMS

model building ..........................................................................2 why have patching diagrams ? ............................................................... 2

organization of experiments.......................................................3

who is running this experiment ?................................................3

early experiments.......................................................................4 modulation ............................................................................................ 4

messages ...................................................................................4 analog messages .................................................................................... 4

digital messages..................................................................................... 5

bandwidths and spectra. ............................................................5 measurement ......................................................................................... 6

graphical conventions ................................................................6 representation of spectra ........................................................................ 6

filters ..................................................................................................... 8

other functions....................................................................................... 9

measuring instruments ...............................................................9 the oscilloscope - time domain ............................................................... 9

the rms voltmeter ................................................................................. 10

the spectrum analyser - frequency domain............................................ 10

oscilloscope - triggering ..........................................................10

what you see, and what you don`t............................................11

overload. .................................................................................11 overload of a narrowband system ......................................................... 12

the two-tone test signal ........................................................................ 12

Fourier series and bandwidth estimation..................................13

multipliers and modulators ......................................................13 multipliers ........................................................................................... 13

modulators........................................................................................... 14

envelopes ................................................................................15

extremes..................................................................................15

analog or digital ?....................................................................15

SIN or COS ?..........................................................................16

the ADDER - G and g ...........................................................16

abbreviations...........................................................................17

list of symbols .........................................................................18

A1-01 - 2 Copyright © 2005 Emona Instruments Pty Ltd


MODELLING WITH TIMSMODELLING WITH TIMSMODELLING WITH TIMSMODELLING WITH TIMS

model buildingmodel buildingmodel buildingmodel building

With TIMS you will be building models. These models will most often be

hardware realizations of the block diagrams you see in a text book, or have

designed yourself. They will also be representations of equations, which

themselves can be depicted in block diagram form.

What ever the origin of the model, it can be patched up in a very short time. The

next step is to adjust the model to perform as expected. It is perfectly true that

you might, on occasions, be experimenting, or just ‘doodling’, not knowing what

to expect. But in most cases your goal will be quite clear, and this is where a

systematic approach is recommended.

If you follow the steps detailed in the first few experiments you will find that the

models are adjusted in a systematic manner, so that each desired result is

obtained via a complete understanding of the purpose and aim of the

intermediate steps leading up to it.

why have patching diagramswhy have patching diagramswhy have patching diagramswhy have patching diagrams ????

Many of the analog experiments, and all of the digital experiments, display

patching diagrams. These give all details of the interconnections between

modules, to implement a model of the system under investigation.

It is not expected that a glance at the patching diagram

will reveal the nature of the system being modelled.

The patching diagram is presented as firm evidence that a model of the system

can be created with TIMS.

The functional purpose of the system is revealed through the

block diagram which precedes the patching diagram.

Introduction to modelling with TIMS

Copyright © 2005 Emona Instruments Pty Ltd A1-01 - 3

It is the block diagram which you should study to gain insight into the workings

of the system.

If you fully understand the block diagram you should not need the patching

diagram, except perhaps to confirm which modules are required for particular

operations, and particular details of functionality. These is available in the

TIMS User Manual.

You may need an occasional glance at the patching diagram for confirmation of

a particular point.

Try to avoid patching up ‘mechanically’,

according to the patching diagram, without

thought to what you are trying to achieve.

organization of experimentsorganization of experimentsorganization of experimentsorganization of experiments

Each of the experiments in this Text is divided into three parts.

1. The first part is generally titled PREPARATION. This part should be studied

before the accompanying laboratory session.

2. The second part describes the experiment proper. Its title will vary. You will

find the experiment a much more satisfying experience if you arrive at the

laboratory well prepared, rather than having to waste time finding out what

has to be done at the last moment. Thus read this part before the laboratory

session.

3. The third part consists of TUTORIAL QUESTIONS. Generally these

questions will be answered after the experimental work is completed, but it is

a good idea to read them before the laboratory session, in case there are

special measurements to be made.

While performing an experiment you should always have access to the TIMS

user manuals - namely the TIMS User Manual (fawn cover) which contains

information about the modules in the TIMS Basic Set of modules, and the TIMS

Advanced Modules and TIMS Special Applications Modules User Manual (red

cover).

who is running this experimentwho is running this experimentwho is running this experimentwho is running this experiment ????

These experiments and their Tasks are merely suggestions as to how you might

go about carrying out certain investigations. In the final assessment it is you who

are running the experiment, and you must make up your mind as to how you are

going to do it. You can do this best if you read about it beforehand.

If you do not understand a particular instruction, consider what it is you have

been trying to achieve up to that point, and then do it your way.


early experimentsearly experimentsearly experimentsearly experiments

The first experiment assumes no prior knowledge of telecommunications - it is

designed to introduce you to TIMS, and to illustrate the previous remarks about

being systematic. The techniques learned will be applied over and over again in

later work.

The next few experiments are concerned with analog modulation and

demodulation.

modulationmodulationmodulationmodulation

One of the many purposes of modulation is to convert a message into a form

more suitable for transmission over a particular medium.

The analog modulation methods to be studied will generally transform the analog

message signal in the audio spectrum to a higher location in the frequency

spectrum.

The digital modulation methods to be studied will generally transform a binary

data stream (the message), at baseband 1 frequencies, to a different format, and

then may or may not translate the new form to a higher location in the frequency

spectrum.

It is much easier to radiate a high frequency (HF) signal than it is a relatively low

frequency (LF) audio signal. In the TIMS environment the particular part of the

spectrum chosen for HF signals is centred at 100 kHz.

It is necessary, of course, that the reverse process, demodulation, can be carried

out - namely, that the message may be recovered from the modulated signal upon

receipt following transmission.

messagesmessagesmessagesmessages

Many models will be concerned with the transmission or reception of a message,

or a signal carrying a message. So TIMS needs suitable messages. These will

vary, depending on the system.

analog messagesanalog messagesanalog messagesanalog messages

The transmission of speech is often the objective in an analog system.

High-fidelity speech covers a wide frequency range, say 50 Hz to 15 kHz, but for

communications purposes it is sufficient to use only those components which lie

in the audio frequency range 300 to 3000 Hz - this is called ‘band limited

speech’. Note that frequency components have been removed from both the low

and the high frequency end of the message spectrum. This is bandpass filtering.

Intelligibility suffers if only the high frequencies are removed.

Speech is not a convenient message signal with which to make simple and

precise measurements. So, initially, a single tone (sine wave) is used. This

signal is more easily accommodated by both the analytical tools and the

instrumentation and measuring facilities.

1 defined later



The frequency of this tone can be chosen to lie within the range expected in the

speech, and its peak amplitude to match that of the speech. The simple tone can

then be replaced by a two-tone test signal, in which case intermodulation tests

can be carried out 2.

When each modulation or demodulation system has been set up quantitatively

using a single tone as a message (or, preferably with a two-tone test signal), a

final qualitative check can be made by replacing the tone with a speech signal.

The peak amplitude of the speech should be adjusted to match that of the tone.

Both listening tests (in the case of demodulation) and visual examination of the

waveforms can be very informative.

digital messagesdigital messagesdigital messagesdigital messages

The transmission of binary sequences is often the objective of a digital

communication system. Of considerable interest is the degree of success with

which this transmission is achieved. An almost universal method of describing

the quality of transmission is by quoting an error rate 3.

If the sequence is one which can take one of two levels, say 0 and 1, then an error

is recorded if a 0 is received when a 1 was sent, or a 1 received when a 0 was

sent. The bit error rate is measured as the number of errors as a proportion of

total bits sent.

To be able to make such a measurement it is necessary to know the exact nature

of the original message. For this purpose a known sequence needs to be

transmitted, a copy of which can be made available at the receiver for

comparison purposes. The known sequence needs to have known, and useful,

statistical properties - for example, a ‘random’ sequence. Rather simple

generators can be implemented using shift registers, and these provide sequences

of adjustable lengths. They are known as pseudo-random binary sequence

(PRBS) generators. TIMS provides you with just such a SEQUENCE

GENERATOR module. You should refer to a suitable text book for more

information on these.

bandwidths and spectrabandwidths and spectrabandwidths and spectrabandwidths and spectra

Most of the signals you will be examining in the experiments to follow have well

defined bandwidths. That is, in most cases it is possible to state quite clearly that

all of the energy of a signal lies between frequencies f1 and f2 Hz, where f1 < f2.

• the absolute bandwidth of such a signal is defined as (f2 - f1) Hz.

It is useful to define the number of octaves a signal occupies. The octave

measure for the above signal is defined as

octaves = log2(f2 / f1)

Note that the octave measure is a function of the ratio of two frequencies; it says

nothing about their absolute values.

• a wideband signal is generally considered to be one which occupies one or

more octaves.

2 the two-tone test signal is introduced in the experiment entitled ‘Amplifier overload’.3 the corresponding measurement in an analog system would be the signal-to-noise ratio (relatively easy to measure with instruments), or, if speech is the message, the ‘intelligibility’; not so easy to define, let

alone to measure.


• a narrowband signal is one which occupies a small fraction of an octave.

Another name, used interchangeably, is a bandpass signal.

An important observation can be made about a narrowband signal; that is, it can

contain no harmonics.

• a baseband signal is one which extends from DC (so f1 = 0) to a finite

frequency f2. It is thus a wideband signal.

Speech, for communications, is generally bandlimited to the range 300 to

3000 Hz. It thus has a bandwidth in excess of 3 octaves. This is considered to be

a wideband signal. After modulation, to a higher part of the spectrum, it

becomes a narrowband signal, but note that its absolute bandwidth remains

unchanged.

This reduction from a wideband to a narrowband signal is a linear process; it

can be reversed. In the context of communications engineering it involves

modulation, or frequency translation.

You will meet all of these signals and phenomena when working with TIMS.

measurementmeasurementmeasurementmeasurement

The bandwidth of a signal can be measured with a SPECTRUM ANALYSER.

Commercially available instruments typically cover a wide frequency range, are

very accurate, and can perform a large number of complex measurements. They

are correspondingly expensive.

TIMS has no spectrum analyser as such, but can model one (with the TIMS320

DSP module), or in the form of a simple WAVE ANALYSER with TIMS analog

modules. See the experiment entitled Spectrum analysis - the WAVE ANALYSER

(within Volume A2 - Further & Advanced Analog Experiments).

Without a spectrum analyser it is still possible to draw conclusions about the

location of a spectrum, by noticing the results when attempting to pass it through

filters of different bandwidths. There are several filters in the TIMS range of

modules. See Appendix A, and also the TIMS User Manual.

graphical conventionsgraphical conventionsgraphical conventionsgraphical conventions

representation of representation of representation of representation of spectraspectraspectraspectra

It is convenient to have a graphical method of depicting spectra. In this work we

do not get involved with the Fourier transform, with its positive and negative

frequencies and double sided spectra. Elementary trigonometrical methods are

used for analysis. Such methods are more than adequate for our purposes.

When dealing with speech the mathematical analysis is dropped, and descriptive

methods used. These are supported by graphical representations of the signals

and their spectra.

In the context of modulation we are constantly dealing with sidebands, generally

derived from a baseband message of finite bandwidth. Such finite bandwidth

signals will be represented by triangles on the spectral diagrams.

The steepness of the slope of the triangle has no special significance, although

when two or more sidebands, from different messages, need to be distinguished,

each can be given a different slope.



frequency

a baseband signal (eg., a message)

Although speech does not have a DC component, the triangle generally extends

down to zero (the origin) of the frequency scale (rather than being truncated just

before it). For the special case in which a baseband signal does have a DC

component the triangle convention is sometimes modified slightly by adding a

vertical line at the zero-frequency end of the triangle.

a DSBSC

The direction of the slope is important. Its significance becomes obvious when

we wish to draw a modulated signal. The figure above shows a double sideband

suppressed carrier (DSBSC) signal.

Note that there are TWO triangles, representing the individual lower and upper

sidebands. They slope towards the same point; this point indicates the location

of the (suppressed) carrier frequency.

an inverted baseband signal

The orientation is important. If the same message was so modulated that it could

be represented in the frequency spectrum as in the figure above, then this means:

• the signal is located in the baseband part of the spectrum

• spectral components have been transposed, or inverted; frequency

components which were originally above others are now below them.

• since the signal is at baseband it would be audible (if converted with an

electric to acoustic transducer - a pair of headphones, for example), but

would be unintelligible. You will be able to listen to this and other such

signals in TIMS experiments to come.

It is common practice to use the terms erect and inverted to describe these bands.


In the Figure above, a message (a) is frequency translated to become an upper

single sideband (b), and a lower single sideband (c). A three-channel frequency

division multiplexed (FDM) signal is also illustrated (d).

Note that these spectral diagrams do not show any phase information.

Despite all the above, be prepared to accept that these diagrams are used for

purposes of illustration, and different authors use their own variations. For

example, some slope their triangles in the opposite sense to that suggested here.

filtersfiltersfiltersfilters

In a block diagram, there is a simple technique for representing filters. The

frequency spectrum is divided into three bands - low, middle, and high - each

represented by part of a sinewave. If a particular band is blocked, then this is

indicated by an oblique stroke through it. The standard responses are

represented as in the Figure below.

block-diagrammatic representations of filter responses

The filters are, respectively, lowpass,

bandpass, highpass, bandstop, and

allpass.

In the case of lowpass and highpass

responses the diagrams are often further

simplified by the removal of one of the

cancelled sinewaves, the result being as

in the figure opposite.



other functionsother functionsother functionsother functions

amplify add multiply amplitudelimit

integrate

some analog functions

measuring instrumentsmeasuring instrumentsmeasuring instrumentsmeasuring instruments

the oscilloscope the oscilloscope the oscilloscope the oscilloscope ---- time domain time domain time domain time domain

The most frequently used measuring facility with TIMS is the oscilloscope. In

fact the vast majority of experiments can be satisfactorily completed with no

other instrument.

Any general purpose oscilloscope is ideal for all TIMS experiments. It is

intended for the display of signals in the time domain 4. It shows their

waveforms - their shapes, and amplitudes

From the display can be obtained information regarding:

• waveform shape

• waveform frequency - by calculation, using time base information

• waveform amplitude - directly from the display

• system linearity - by observing waveform distortion

• an estimate of the bandwidth of a complex signal; eg, from the sharpness of

the corners of a square wave

When concerned with amplitude information it is customary to record either:

• the peak-to-peak amplitude

• the peak amplitude

of the waveform visible on the screen.

Unless the waveform is a simple sinewave it is always important to record the

shape of the waveform also; this can be:

1. as a sketch (with time scale), and annotation to show clearly what amplitude

has been measured.

2. as an analytic expression, in which case the parameter recorded must be

clearly specified.

4 but with adaptive circuitry it can be modified to display frequency-domain information


the rms voltmeterthe rms voltmeterthe rms voltmeterthe rms voltmeter

The TIMS WIDEBAND TRUE RMS METER module is essential for

measurements concerning power, except perhaps for the simple case when the

signal is one or two sinewaves. It is particularly important when the

measurement involves noise.

Its bandwidth is adequate for all of the signals you will meet in the TIMS

environment.

An experiment which introduces the WIDEBAND TRUE RMS METER, is

entitled Power measurements. Although it appears at the end of this Volume, it

could well be attempted at almost any time.

the spectrum analythe spectrum analythe spectrum analythe spectrum analyser serserser ---- frequency domain frequency domain frequency domain frequency domain

The identification of the spectral composition of a signal - its components in the

frequency domain - plays an important part when learning about

communications.

Unfortunately, instruments for displaying spectra tend to be far more expensive

than the general purpose oscilloscope.

It is possible to identify and measure the individual spectral components of a

signal using TIMS modules.

Instruments which identify the spectral components on a component-by-

component basis are generally called wave analysers. A model of such an

instrument is examined in the experiment entitled Spectrum analysis - the WAVE

ANALYSER in Volume A2 - Further & Advanced Analog Experiments.

Instruments which identify the spectral components of a signal and display the

spectrum are generally called spectrum analysers. These instruments tend to be

more expensive than wave analysers. Something more sophisticated is required

for their modelling, but this is still possible with TIMS, using the digital signals

processing (DSP) facilities - the TIMS320 module can be programmed to provide

spectrum analysis facilities.

Alternatively the distributors of TIMS can recommend other affordable methods,

compatible with the TIMS environment.

oscilloscope oscilloscope oscilloscope oscilloscope ---- triggering triggering triggering triggering

synchronizatisynchronizatisynchronizatisynchronizationononon

As is usually the case, to achieve ‘text book like’ displays, it is important to

choose an appropriate signal for oscilloscope triggering. This trigger signal is

almost never the signal being observed ! The recognition of this point is an

important step in achieving stable displays.

This chosen triggering signal should be connected directly to the oscilloscope

sweep synchronizing circuitry. Access to this circuitry of the oscilloscope is

available via an input socket other than the vertical deflection amplifier input(s).

It is typically labelled ‘ext. trig’ (external trigger), ‘ext. synch’ (external

synchronization), or similar.



subsubsubsub----multiple frequenciesmultiple frequenciesmultiple frequenciesmultiple frequencies

If two or more periodic waveforms are involved, they will only remain stationary

with respect to each other if the frequency of one is a sub-multiple of the other.

This is seldom the case in practice, but can be made so in the laboratory. Thus

TIMS provides, at the MASTER SIGNALS module, a signal of 2.083 kHz

(which is 1/48 of the 100 kHz system clock), and another at 8.333 kHz (1/12 of

the system clock).

which channelwhich channelwhich channelwhich channel ????

Much time can be saved if a consistent use of the SCOPE SELECTOR is made.

This enables quick changes from one display to another with the flip of a switch.

In addition, channel identification is simplified if the habit is adopted of

consistently locating the trace for CH1 above the trace for CH2.

Colour coded patching leads can also speed trace identification.

what you see, and what you don`twhat you see, and what you don`twhat you see, and what you don`twhat you see, and what you don`t

Instructions such as ‘adjust the phase until there is no output’, or ‘remove the

unwanted signal with a suitable filter’ will be met from time to time.

These instructions seldom result in the amplitude of the signal in question being

reduced to zero. Instead, what is generally meant is ‘reduce the amplitude of the

signal until it is no longer of any significance’.

Significance here is a relative term, made with respect to the system signal-to-

noise ratio (SNR). All systems have a background noise level (noise threshold,

noise floor), and signals (wanted) within these systems must over-ride this noise

(unwanted).

TIMS is designed to have a ‘working level’, the TIMS ANALOG REFERENCE LEVEL,

of about 4 volts peak-to-peak. The system noise level is claimed to be at least

100 times below this 5.

When using an oscilloscope as a measuring instrument with TIMS, the vertical

sensitivity is typically set to about 1 volt/cm. Signals at the reference level fit

nicely on the screen. If they are too small it is wise to increase them if possible

(and appropriate), to over-ride the system noise; or if larger to reduce them, to

avoid system overload.

When they are attenuated by a factor of 100, and if the oscilloscope sensitivity is

not changed, they appear to be ‘reduced to zero’; and in relative terms this is so.

If the sensitivity of the oscilloscope is increased by 100, however, the screen will

no longer be empty. There will be the system noise, and perhaps the signal of

interest is still visible. Engineering judgement must then be exercised to evaluate

the significance of the signals remaining.

overloadoverloadoverloadoverload

If wanted signal levels within a system fall ‘too low’ in amplitude, then the

signal-to-noise ratio (SNR) will suffer, since internal circuit noise is independent

of signal level.

5 TIMS claims a system signal-to-noise ratio of better than 40 dB


If signal levels within a system rise ‘too high’, then the SNR will suffer, since

the circuitry will overload, and generate extra, unwanted, distortion components;

these distortion components are signal level dependent. In this case the noise is

derived from distortion of the signal, and the degree of distortion is usually

quoted as signal-to-distortion ratio (SDR).

Thus analog circuit design includes the need to maintain signal levels at a pre-

defined working level, being ‘not to high’ and ‘not too low’, to avoid these two

extremes.

These factors are examined in the experiment entitled Amplifier overload within

Volume A2 - Further & Advanced Analog Experiments.

The TIMS working signal level, or TIMS ANALOG REFERENCE LEVEL, has been set

at 4 volts peak-to-peak. Modules will generally run into non-linear operation

when this level is exceeded by say a factor of two. The background noise of the

TIMS system is held below about 10 mV - this is a fairly loose statement, since

this level is dependent upon the bandwidth over which the noise is measured, and

the model being examined at the time. A general statement would be to say that

TIMS endeavours to maintain a SNR of better than 40 dB for all models.

overload of a narrowband systemoverload of a narrowband systemoverload of a narrowband systemoverload of a narrowband system

Suppose a channel is narrowband. This means it is deliberately bandlimited so

that it passes signals in a narrow (typically much less than an octave 6) frequency

range only. There are many such circuits in a communications system.

If this system overloads on a single tone input, there will be unwanted harmonics

generated. But these will not pass to the output, and so the overload may go

unnoticed. With a more complex input - say two or more tones, or a speech-

related signal - there will be, in addition, unwanted intermodulation components

generated. Many of these will pass via the system, thus revealing the existence of

overload. In fact, the two-tone test signal should always be used in a narrowband

system to investigate overload.

the twothe twothe twothe two----tone test signaltone test signaltone test signaltone test signal

A two-tone test signal consists of two sine waves added together ! As discussed

in the previous section, it is a very useful signal for testing systems, especially

those which are of narrow-bandwidth. The properties of the signal depend upon:

• the frequency ratio of the two tones.

• the amplitude ratio of the two tones.

For testing narrowband communication systems the two tones are typically of

near-equal frequency, and of identical amplitude. A special property of this form

of the signal is that its shape, as seen in the time domain, is very well defined

and easily recognisable 7.

After having completed the early experiments you will recognise this shape as

that of the double sideband suppressed carrier (DSBSC) signal.

If the system through which this signal is transmitted has a non-linear

transmission characteristic, then this will generate extra components. The

6 defined above

7 the assumption being that the oscilloscope is set to sweep across the screen over a few periods of the

difference frequency.



presence of even small amounts of these components is revealed by a change of

shape of the test signal.

Fourier series and bFourier series and bFourier series and bFourier series and bandwidth andwidth andwidth andwidth

estimationestimationestimationestimation

Fourier series analysis of periodic signals reveals that:

• it is possible, by studying the symmetry of a signal, to predict the presence or

absence of a DC component.

• if a signal is other than sinusoidal, it will contain more than one harmonic

component of significance.

• if a signal has sharp discontinuities, it is likely to contain many harmonic

components of significance

• some special symmetries result in all (or nearly all) of the ODD (or EVEN)

harmonics being absent.

With these observations, and more, it is generally easy to make an engineering

estimate of the bandwidth of a periodic signal.

multipliersmultipliersmultipliersmultipliers and modulators and modulators and modulators and modulators

The modulation process requires multiplication. But a pure MULTIPLIER is

seldom found in communications equipment. Instead, a device called a

MODULATOR is used.

In the TIMS system we generally use a MULTIPLIER, rather than a

MODULATOR, when multiplication is called for, so as not to become diverted

by the side effects and restrictions imposed by the latter.

In commercial practice, however, the purpose-designed MODULATOR is

generally far superior to the unnecessarily versatile MULTIPLIER.

mmmmultipliersultipliersultipliersultipliers

An ideal multiplier performs as a multiplier should ! That is, if the two time-

domain functions x(t) and y(t) are multiplied together, then we expect the result

to be x(t).y(t), no more and no less, and no matter what the nature of these two

functions. These devices are called four quadrant multipliers.

There are practical multipliers which approach this ideal, with one or two

engineering qualifications. Firstly, there is always a restriction on the bandwidth

of the signals x(t) and y(t).

There will inevitably be extra (unwanted) terms in the output (noise, and

particularly distortion products) due to practical imperfections.

Provided these unwanted terms can be considered ‘insignificant’, with respect to

the magnitude of the wanted terms, then the multiplier is said to be ‘ideal’. In


the TIMS environment this means they are at least 40 dB below the TIMS ANALOG

REFERENCE LEVEL 8.

Such a multiplier is even said to be linear. That is, from an engineering point of

view, it is performing as expected.

In the mathematical sense it is not linear, since the mathematical definition of a

linear circuit includes the requirement that no new frequency components are

generated when it performs its normal function. But, as will be seen,

multiplication always generates new frequency components.

DC offDC offDC offDC off----setssetssetssets

One of the problems associated with analog circuit design is minimization of

unwanted DC off-sets. If the signals to be processed have no DC component

(such as in an audio system) then stages can be AC coupled, and the problem is

overcome. In the TIMS environment module bandwidths must extend to DC, to

cope with all possible conditions; although more often than not signals have no

intentional DC component.

In a complex model DC offsets can accumulate - but in most cases they can be

recognised as such, and accounted for appropriately. There is one situation,

however, where they can cause much more serious problems by generating new

components - and that is when multiplication is involved.

With a MULTIPLIER the presence of an unintentional DC component at one

input will produce new components at the output. Specifically, each component

at the other input will be multiplied by this DC component - a constant - and so

a scaled version will appear at the output 9.

To overcome this problem there is an option for AC coupling in the

MULTIPLIER module. It is suggested that the DC mode be chosen only when

the signals to be processed actually have DC components; otherwise use AC

coupling.

modulatorsmodulatorsmodulatorsmodulators

In communications practice the circuitry used for the purpose of performing the

multiplying function is not always ideal in the four quadrant multiplier sense;

such circuits are generally called modulators.

Modulators generate the wanted sum or difference products but in many cases the

input signals will also be found in the output, along with other unwanted

components at significant levels. Filters are used to remove these unwanted

components from the output (alternatively there are ‘balanced’ modulators.

These have managed to eliminate either one or both of the original signals from

the output).

These modulators are restricted in other senses as well. It is allowed that one of

the inputs can be complex (ie., two or more components) but the other can only

be a single frequency component (or appear so to be - as in the switching

modulator). This restriction is of no disadvantage, since the vast majority of

modulators are required to multiply a complex signal by a single-component

carrier.

Accepting restrictions in some areas generally results in superior performance in

others, so that in practice it is the switching modulator, rather than the idealized

8 defined under ‘what you see and what you don t̀’

9 this is the basis of a voltage controlled amplifier - VCA



four quadrant multiplier, which finds universal use in communications

electronics.

Despite the above, TIMS uses the four quadrant multiplier in most applications

where a modulator might be used in practice. This is made possible by the

relatively low frequency of operation, and modest linearity requirements

envelopesenvelopesenvelopesenvelopes

Every narrowband signal has an envelope, and you probably have an idea of what

this means.

Envelopes will be examined first in the experiment entitled DSB generation in

this Volume.

They will be defined and further investigated in the experiments entitled

Envelopes within this Volume, and Envelope recovery within Volume A2 -

Further & Advanced Analog Experiments.

extremesextremesextremesextremes

Except for a possible frequency scaling effect, most experiments with TIMS will

involve realistic models of the systems they are emulating. Thus message

frequencies will be ‘low’, and carrier frequencies ‘high’. But these conditions

need not be maintained. TIMS is a very flexible environment.

It is always a rewarding intellectual exercise to

imagine what would happen if one or more of

the ‘normal’ conditions was changed severely 10.

It is then even more rewarding to confirm our imaginings by actually modelling

these unusual conditions. TIMS is sufficiently flexible to enable this to be done

in most cases.

For example: it is frequently stated, for such-and-such a requirement to be

satisfied, that it is necessary that ‘x1 >> x2’. Quite often x1 and x2 are

frequencies - say a carrier and a message frequency; or they could be amplitudes.

You are strongly encouraged to expand your horizons by questioning the reasons

for specifying the conditions, or restrictions, within a model, and to consider, and

then examine, the possibilities when they are ignored.

analog or digitalanalog or digitalanalog or digitalanalog or digital ????

What is the difference between a digital signal and an analog signal ?

Sometimes this is not clear or obvious.

10 for an entertaining and enlightening look at the effects of major changes to one or more of the physical

constants, see G. Gamow; Mr Tompkins in Wonderland published in 1940, or easier Mr. Tompkins in

Paperback, Cambridge University Press, 1965.


In TIMS digital signals are generally thought of as those being compatible with

the TTL standards. Thus their amplitudes lie in the range 0 to +5 volts. They

come from, and are processed by, modules having RED output and input sockets.

It is sometimes necessary, however, to use an analog filter to bandlimit these

signals. But their large DC offsets would overload most analog modules, . Some

digital modules (eg, the SEQUENCE GENERATOR) have anticipated this, and

provide an analog as well as a digital (TTL) output. This analog output comes

from a YELLOW socket, and is a TTL signal with the DC component removed

(ie, DC shifted).

SIN or COS ?SIN or COS ?SIN or COS ?SIN or COS ?

Single frequency signals are generally referred to as sinusoids, yet when

manipulating them trigonometrically are often written as cosines. How do we

obtain cosωt from a sinusoidal oscillator !

There is no difference in the shape of a sinusoid and a cosinusoid, as observed

with an oscilloscope. A sinusoidal oscillator can just as easily be used to provide

a cosinusoid. What we call the signal (sin or cos) will depend upon the time

reference chosen.

Remember that cosωt = sin(ωt + π/2)

Often the time reference is of little significance, and so we choose sin or cos, in

any analysis, as is convenient.

the ADDER the ADDER the ADDER the ADDER ---- G and g G and g G and g G and g

Refer to the TIMS User Manual for a description of the ADDER module. Notice

it has two input sockets, labelled ‘A’ and ‘B’.

In many experiments an ADDER is used to make a linear sum of two signals a(t)

and b(t), of amplitudes A and B respectively, connected to the inputs A and B

respectively. The proportions of these signals which appear at the ADDER

output are controlled by the front panel gain controls G and g.

The amplitudes A and B of the two input signals are seldom measured, nor the

magnitudes G and g of the adjustable gains.

Instead it is the magnitudes GA and gB which are of more interest, and these are

measured directly at the ADDER output. The measurement of GA is made when

the patch lead for input B is removed; and that of gB is measured when the

patch lead for input A is removed.

When referring to the two inputs in this text it would be formally correct to name

them as ‘the input A’ and ‘the input B’. This is seldom done. Instead, they are

generally referred to as ‘the input G’ and ‘the input g’ respectively (or sometimes

just G and g). This should never cause any misunderstanding. If it does, then it

is up to you, as the experimenter, to make an intelligent interpretation.



abbreviationsabbreviationsabbreviationsabbreviations

This list is not exhaustive. It includes only those abbreviations used in this Text.

abbreviation meaning AM amplitude modulation

ASK amplitude shift keying (also called OOK)

BPSK binary phase shift keying

CDMA code division multiple access

CRO cathode ray oscilloscope

dB decibel

DPCM differential pulse code modulation

DPSK differential phase shift keying

DSB double sideband (in this text synonymous with DSBSC)

DSBSC double sideband suppressed carrier

DSSS direct sequence spread spectrum

DUT device under test

ext. synch. external synchronization (of oscilloscope). ‘ext. trig.’ preferred

ext. trig. external trigger (of an oscilloscope)

FM frequency modulation

FSK frequency shift keying

FSD full scale deflection (of a meter, for example)

IP intermodulation product

ISB independent sideband

ISI intersymbol interference

LSB analog: lower sideband digital: least significant bit

MSB most significant bit

NBFM narrow band frequency modulation

OOK on-off keying (also called ASK)

PAM pulse amplitude modulation

PCM pulse code modulation

PDM pulse duration modulation (see PWM)

PM phase modulation

PPM pulse position modulation

PRK phase reversal keying (also called PSK)

PSK phase shift keying (also called PRK - see BPSK)

PWM pulse width modulation (see PDM)

SDR signal-to-distortion ratio

SNR signal-to-noise ratio

SSB single sideband (in this text is synonymous with SSBSC)

SSBSC single sideband suppressed carrier

SSR sideband suppression ratio

TDM time division multiplex

THD total harmonic distortion

VCA voltage controlled amplifier

WBFM wide band frequency modulation


list of symbolslist of symbolslist of symbolslist of symbols

The following symbols are used throughout the text, and have the following

meanings

a(t) a time varying amplitude

α, φ, ϕ, phase angles

β deviation, in context of PM and FM

δf a small frequency increment

∆φ peak phase deviation

δt a small time interval

φ(t) a time varying phase

m in the context of envelope modulation, the depth of modulation

µ a low frequency (rad/s); typically that of a message (µ << ω).

ω a high frequency (rad/s); typically that of a carrier (ω >> µ)

y(t) a time varying function


MODELLING AN EQUATIOMODELLING AN EQUATIOMODELLING AN EQUATIOMODELLING AN EQUATIONNNN

PREPARATION................................................................................ 2

an equation to model ................................................................ 2

the ADDER........................................................................................... 3

conditions for a null............................................................................... 4

more insight into the null ...................................................................... 5

TIMS experiment procedures.................................................... 6

EXPERIMENT.................................................................................. 7

signal-to-noise ratio............................................................................. 12

achievements........................................................................... 12

as time permits........................................................................ 13

TUTORIAL QUESTIONS............................................................... 13

TRUNKS................................................................................ 14


MODELLING AN EQUATIOMODELLING AN EQUATIOMODELLING AN EQUATIOMODELLING AN EQUATIONNNN

ACHIEVEMENTS: a familiarity with the TIMS modelling philosophy;

development of modelling and experimental skills for use in future

experiments. Introduction to the ADDER, AUDIO OSCILLATOR,

and PHASE SHIFTER modules; also use of the SCOPE SELECTOR

and FREQUENCY COUNTER.

PREREQUISITES: a desire to enhance one’s knowledge of, and insights into, the

phenomena of telecommunications theory and practice.

PREPARATIONPREPARATIONPREPARATIONPREPARATION

This experiment assumes no prior knowledge of telecommunications. It illustrates

how TIMS is used to model a mathematical equation. You will learn some

experimental techniques. It will serve to introduce you to the TIMS system, and

prepare you for the more serious experiments to follow.

In this experiment you will model a simple trigonometrical equation. That is, you

will demonstrate in hardware something with which you are already familiar

analytically.

an equation to modelan equation to modelan equation to modelan equation to model

You will see that what you are to do experimentally is to demonstrate that two AC

signals of the same frequency, equal amplitude and opposite phase, when added,

will sum to zero.

This process is used frequently in communication electronics as a means of

removing, or at least minimizing, unwanted components in a system. You will

meet it in later experiments.

The equation which you are going to model is:

y(t) = V1 sin(2πf1t) + V2 sin(2πf2t + α) ........ 1

= v1(t) + v2(t) ........ 2

Here y(t) is described as the sum of two sine waves. Every young trigonometrician

knows that, if:

each is of the same frequency: f1 = f2 Hz ........ 3

each is of the same amplitude: V1 = V2 volts ........ 4

Modelling an equation


and they are 180o out of phase: α = 180 degrees ........ 5

then: y(t) = 0 ........ 6

A block diagram to represent eqn.(1) is suggested in Figure 1.

-1

INVERTING

AMPLIFIER

ADDER

OUT v (t)1

v (t)2

y(t)

1πV sin2 f t

SOURCE

Figure 1: block diagram model of Equation 1

Note that we ensure the two signals are of the same frequency (f1 = f2) by obtaining

them from the same source. The 180 degree phase change is achieved with an

inverting amplifier, of unity gain.

In the block diagram of Figure 1 it is assumed, by convention, that the ADDER has

unity gain between each input and the output. Thus the output is y(t) of eqn.(2).

This diagram appears to satisfy the requirements for obtaining a null at the output.

Now see how we could model it with TIMS modules.

A suitable arrangement is illustrated in block diagram form in Figure 2.

v (t)1

v (t)2

OSCILLOSCOPE and

FREQUENCY COUNTER connections

not shown.

y(t) = g.v (t) + G.v (t)1 2

= V sin2 f t + V sin2 f t1 2

π π1 2

Figure 2: the TIMS model of Figure 1.

Before you build this model with TIMS modules let us consider the procedure you

might follow in performing the experiment.

the ADDERthe ADDERthe ADDERthe ADDER

The annotation for the ADDER needs explanation. The symbol ‘G’ near input A

means the signal at this input will appear at the output, amplified by a factor ‘G’.

Similar remarks apply to the input labelled ‘g’. Both ‘G’ and ‘g’ are adjustable by

adjacent controls on the front panel of the ADDER. But note that, like the controls


on all of the other TIMS modules, these controls are not calibrated. You must

adjust these gains for a desired final result by measurement.

Thus the ADDER output is not identical with eqn.(2), but instead:

ADDER output = g.v1(t) + G.v2(t) ........ 7

= V1 sin2πf1t + V2 sin2πf2t........ 8

conditions for a nullconditions for a nullconditions for a nullconditions for a null

For a null at the output, sometimes referred to as a ‘balance’, one would be excused

for thinking that:

if:

1) the PHASE SHIFTER is adjusted to introduce a difference of 180o

between its input and output

and

2) the gains ‘g’ and ‘G’ are adjusted to equality

then

3) the amplitude of the output signal y(t) will be zero.

In practice the above procedure will almost certainly not result in zero output !

Here is the first important observation about the practical modelling of a theoretical

concept.

In a practical system there are inevitably small impairments to be accounted for.

For example, the gain through the PHASE SHIFTER is approximately unity, not

exactly so. It would thus be pointless to set the gains ‘g’ and ‘G’ to be precisely

equal. Likewise it would be a waste of time to use an expensive phase meter to set

the PHASE SHIFTER to exactly 180o, since there are always small phase shifts not

accounted for elsewhere in the model. See Q1, Tutorial Questions, at the end of

this experiment.

These small impairments are unknown, but they are stable.

Once compensated for they produce no further problems.

So we do not make precise adjustments to modules, independently of the system

into which they will be incorporated, and then patch them together and expect the

system to behave. All adjustments are made to the system as a whole to bring about

the desired end result.

The null at the output of the simple system of Figure 2 is achieved by adjusting the

uncalibrated controls of the ADDER and of the PHASE SHIFTER. Although

equations (3), (4), and (5) define the necessary conditions for a null, they do not

give any guidance as to how to achieve these conditions.



more insight into the nullmore insight into the nullmore insight into the nullmore insight into the null

It is instructive to express eqn. (1) in phasor form. Refer to Figure 3.

Figure 3: Equation (1) in phasor form

Figure 3 (a) and (b) shows the phasors V1 and V2 at two different angles α. It is

clear that, to minimise the length of the resultant phasor (V1 + V2), the angle α in

(b) needs to be increased by about 45o.

The resultant having reached a minimum, then V2 must be increased to approach

the magnitude of V1 for an even smaller (finally zero) resultant.

We knew that already. What is clarified is the condition prior to the null being

achieved. Note that, as angle α is rotated through a full 360o, the resultant

(V1 + V2) goes through one minimum and one maximum (refer to the TIMS User

Manual to see what sort of phase range is available from the PHASE SHIFTER).

What is also clear from the phasor diagram is that, when V1 and V2 differ by more

than about 2:1 in magnitude, the minimum will be shallow, and the maximum

broad and not pronounced 1.

Thus we can conclude that, unless the magnitudes V1

and V2 are already reasonably close, it may be difficult

to find the null by rotating the phase control.

So, as a first step towards finding the null, it would be wise to set V2 close to V1.

This will be done in the procedures detailed below.

Note that, for balance, it is the ratio of the magnitudes V1 and V2 , rather than their

absolute magnitudes, which is of importance.

So we will consider V1 of fixed magnitude (the

reference), and make all adjustments to V2.

This assumes V1 is not of zero amplitude !

1 fix V

1 as reference; mentally rotate the phasor for V

2. The dashed circle shows the locus of its extremity.


TIMS experimenTIMS experimenTIMS experimenTIMS experiment procedures.t procedures.t procedures.t procedures.

In each experiment the tasks ‘T’ you are expected to perform, and the questions ‘Q’

you are expected to answer, are printed in italics and in slightly larger characters

than the rest of the text.

In the early experiments there will a large list of tasks, each given in considerable

detail. Later, you will not need such precise instructions, and only the major steps

will be itemised. You are expected to become familiar with the capabilities of your

oscilloscope, and especially with synchronization techniques.



EXPERIMENTEXPERIMENTEXPERIMENTEXPERIMENT

You are now ready to model eqn. (1). The modelling is explained step-by-step as a

series of small tasks.

Take these tasks seriously, now and in later experiments, and TIMS will provide

you with hours of stimulating experiences in telecommunications and beyond. The

tasks are identified with a ‘T’, are numbered sequentially, and should be performed

in the order given.

T1 both channels of the oscilloscope should be permanently connected to the

matching coaxial connectors on the SCOPE SELECTOR. See the

TIMS User Manual for details of this module.

T2 in this experiment you will be using three plug-in modules, namely: an

AUDIO OSCILLATOR, a PHASE SHIFTER, and an ADDER. Obtain

one each of these. Identify their various features as described in the

TIMS User Manual.

Most modules can be controlled entirely from their front panels, but some have

switches mounted on their circuit boards. Set these switches before plugging the

modules into the TIMS SYSTEM UNIT; they will seldom require changing during

the course of an experiment.

T3 set the on-board range switch of the PHASE SHIFTER to ‘LO’. Its circuitry

is designed to give a wide phase shift in either the audio frequency

range (LO), or the 100 kHz range (HI).

Modules can be inserted into any one of the twelve available slots in the TIMS

SYSTEM UNIT. Choose their locations to suit yourself. Typically one would try

to match their relative locations as shown in the block diagram being modelled.

Once plugged in, modules are in an operating condition.

T4 plug the three modules into the TIMS SYSTEM UNIT.

T5 set the front panel switch of the FREQUENCY COUNTER to a GATE TIME of

1s. This is the most common selection for measuring frequency.

When you become more familiar with TIMS you may choose to associate certain

signals with particular patch lead colours. For the present, choose any colour

which takes your fancy.


T6 connect a patch lead from the lower yellow (analog) output of the AUDIO

OSCILLATOR to the ANALOG input of the FREQUENCY COUNTER.

The display will indicate the oscillator frequency f1 in kilohertz (kHz).

T7 set the frequency f1 with the knob on the front panel of the AUDIO

OSCILLATOR, to approximately 1 kHz (any frequency would in fact

be suitable for this experiment).

T8 connect a patch lead from the upper yellow (analog) output of the AUDIO

OSCILLATOR to the ‘ext. trig’ [ or ‘ext. synch’ ] terminal of the

oscilloscope. Make sure the oscilloscope controls are switched so as

to accept this external trigger signal; use the automatic sweep mode

if it is available.

T9 set the sweep speed of the oscilloscope to 0.5 ms/cm.

T10 patch a lead from the lower analog output of the AUDIO OSCILLATOR to

the input of the PHASE SHIFTER.

T11 patch a lead from the output of the PHASE SHIFTER to the input G of the

ADDER 2.

T12 patch a lead from the lower analog output of the AUDIO OSCILLATOR to

the input g of the ADDER.

T13 patch a lead from the input g of the ADDER to CH2-A of the SCOPE

SELECTOR module. Set the lower toggle switch of the SCOPE

SELECTOR to UP.

T14 patch a lead from the input G of the ADDER to CH1-A of the SCOPE

SELECTOR. Set the upper SCOPE SELECTOR toggle switch UP.

T15 patch a lead from the output of the ADDER to CH1-B of the SCOPE

SELECTOR. This signal, y(t), will be examined later on.

Your model should be the same as that shown in Figure 4 below, which is based on

Figure 2. Note that in future experiments the format of Figure 2 will be used for

TIMS models, rather than the more illustrative and informal style of Figure 4,

which depicts the actual flexible patching leads.

You are now ready to set up some signal levels.

2 the input is labelled ‘A’, and the gain is ‘G’. This is often called ‘the input G’; likewise ‘input g’.



v (t)1

v (t)2

Figure 4: the TIMS model.

T16 find the sinewave on CH1-A and, using the oscilloscope controls, place it in

the upper half of the screen.

T17 find the sinewave on CH2-A and, using the oscilloscope controls, place it in

the lower half of the screen. This will display, throughout the

experiment, a constant amplitude sine wave, and act as a monitor on

the signal you are working with.

Two signals will be displayed. These are the signals connected to the two ADDER

inputs. One goes via the PHASE SHIFTER, which has a gain whose nominal value

is unity; the other is a direct connection. They will be of the same nominal

amplitude.

T18 vary the COARSE control of the PHASE SHIFTER, and show that the relative

phases of these two signals may be adjusted. Observe the effect of the

±1800 toggle switch on the front panel of the PHASE SHIFTER.

As part of the plan outlined previously it is now necessary to set the amplitudes of

the two signals at the output of the ADDER to approximate equality.

Comparison of eqn. (1) with Figure 2 will show that the ADDER gain control g

will adjust V1, and G will adjust V2.

You should set both V1 and V2, which are the magnitudes of the two signals at the

ADDER output, at or near the TIMS ANALOG REFERENCE LEVEL, namely

4 volt peak-to-peak.

Now let us look at these two signals at the output of the ADDER.

T19 switch the SCOPE SELECTOR from CH1-A to CH1-B. Channel 1 (upper

trace) is now displaying the ADDER output.

T20 remove the patch cords from the g input of the ADDER. This sets the

amplitude V1 at the ADDER output to zero; it will not influence the

adjustment of G.


T21 adjust the G gain control of the ADDER until the signal at the output of the

ADDER, displayed on CH1-B of the oscilloscope, is about 4 volt

peak-to-peak. This is V2.

T22 remove the patch cord from the G input of the ADDER. This sets the V2

output from the ADDER to zero, and so it will not influence the

adjustment of g.

T23 replace the patch cords previously removed from the g input of the ADDER,

thus restoring V1.

T24 adjust the g gain control of the ADDER until the signal at the output of the

ADDER, displayed on CH1-B of the oscilloscope, is about 4 volt

peak-to-peak. This is V1.

T25 replace the patch cords previously removed from the G input of the ADDER.

Both signals (amplitudes V1 and V2) are now displayed on the upper half of the

screen (CH1-B). Their individual amplitudes have been made approximately equal.

Their algebraic sum may lie anywhere between zero and 8 volt peak-to-peak,

depending on the value of the phase angle α. It is true that 8 volt peak-to-peak

would be in excess of the TIMS ANALOG REFERENCE LEVEL, but it won`t

overload the oscilloscope, and in any case will soon be reduced to a null.

Your task is to adjust the model for a null at the ADDER

output, as displayed on CH1-B of the oscilloscope.

You may be inclined to fiddle, in a haphazard manner, with the few front panel

controls available, and hope that before long a null will be achieved. You may be

successful in a few moments, but this is unlikely. Such an approach is definitely

not recommended if you wish to develop good experimental practices.

Instead, you are advised to remember the plan discussed above. This should lead

you straight to the wanted result with confidence, and the satisfaction that instant

and certain success can give.

There are only three conditions to be met, as defined by equations (3), (4), and (5).

• the first of these is already assured, since the two signals are coming from a

common oscillator.

• the second is approximately met, since the gains ‘g’ and ‘G’ have been

adjusted to make V1 and V2, at the ADDER output, about equal.

• the third is unknown, since the front panel control of the PHASE SHIFTER

is not calibrated 3.

It would thus seem a good idea to start by adjusting the phase angle α. So:

3 TIMS philosophy is not to calibrate any controls. In this case it would not be practical, since the phase

range of the PHASE SHIFTER varies with frequency.



T26 set the FINE control of the PHASE SHIFTER to its central position.

T27 whilst watching the upper trace, y(t) on CH1-B, vary the COARSE control of

the PHASE SHIFTER. Unless the system is at the null or maximum

already, rotation in one direction will increase the amplitude, whilst in

the other will reduce it. Continue in the direction which produces a

decrease, until a minimum is reached. That is, when further rotation

in the same direction changes the reduction to an increase. If such a

minimum can not be found before the full travel of the COARSE control

is reached, then reverse the front panel 180O TOGGLE SWITCH, and

repeat the procedure. Keep increasing the sensitivity of the

oscilloscope CH1 amplifier, as necessary, to maintain a convenient

display of y(t).

Leave the PHASE SHIFTER controls in the position which gives the

minimum.

T28 now select the G control on the ADDER front panel to vary V2, and rotate it

in the direction which produces a deeper null. Since V1 and V2 have

already been made almost equal, only a small change should be

necessary.

T29 repeating the previous two tasks a few times should further improve the

depth of the null. As the null is approached, it will be found easier

to use the FINE control of the PHASE SHIFTER. These adjustments

(of amplitude and phase) are NOT interactive, so you should reach

your final result after only a few such repetitions.

Nulling of the two signals is complete !

You have achieved your first objective

You will note that it is not possible to achieve zero output from the ADDER. This

never happens in a practical system. Although it is possible to reduce y(t) to zero,

this cannot be observed, since it is masked by the inevitable system noise.

T30 reverse the position of the PHASE SHIFTER toggle switch. Record the

amplitude of y(t), which is now the absolute sum of V1 PLUS V2. Set

this signal to fill the upper half of the screen. When the 1800 switch is

flipped back to the null condition, with the oscilloscope gain

unchanged, the null signal which remains will appear to be ‘almost

zero’.


signalsignalsignalsignal----totototo----noise rationoise rationoise rationoise ratio

When y(t) is reduced in amplitude, by nulling to well below the TIMS ANALOG

REFERENCE LEVEL, and the sensitivity of the oscilloscope is increased, the

inevitable noise becomes visible. Here noise is defined as anything we don`t want.

The noise level will not be influenced by the phase cancellation process which

operates on the test signal, so will remain to mask the moment when y(t) vanishes;

see Q2.

It will be at a level considered to be negligible in the TIMS environment - say less

then 10 mV peak-to-peak. How many dB below reference level is this ?

Note that the nature of this noise can reveal many things. See Q3.

achievementsachievementsachievementsachievements

Compared with some of the models you will be examining in later experiments you

have just completed a very simple exercise. Yet many experimental techniques

have been employed, and it is fruitful to consider some of these now, in case they

have escaped your attention.

• to achieve the desired proportions of two signals V1 and V2 at the output of

an ADDER it is necessary to measure first one signal, then the other. Thus

it is necessary to remove the patch cord from one input whilst adjusting the

output from the other. Turning the unwanted signal off with the front panel

gain control is not a satisfactory method, since the original gain setting

would then be lost.

• as the amplitude of the signal y(t) was reduced to a small value (relative to

the remaining noise) it remained stationary on the screen. This was because

the oscilloscope was triggering to a signal related in frequency (the same, in

this case) and of constant amplitude, and was not affected by the nulling

procedure. So the triggering circuits of the oscilloscope, once adjusted,

remained adjusted.

• choice of the oscilloscope trigger signal is important. Since the oscilloscope

remained synchronized, and a copy of y(t) remained on display (CH1)

throughout the procedure, you could distinguish between the signal you were

nulling and the accompanying noise.

• remember that the nulling procedure was focussed on the signal at the

oscillator (fundamental) frequency. Depending on the nature of the

remaining unwanted signals (noise) at the null condition, different

conclusions can be reached.

a) if the AUDIO OSCILLATOR had a significant amount of harmonic

distortion, then the remaining ‘noise’ would be due to the presence of

these harmonic components. It would be unlikely for them to be

simultaneously nulled. The ‘noise’ would be stationary relative to the

wanted signal (on CH1). The waveform of the ‘noise’ would provide

a clue as to the order of the largest unwanted harmonic component

(or components).

b) if the remaining noise is entirely independent of the waveform of the

signal on CH1, then one can make statements about the waveform

purity of the AUDIO OSCILLATOR.



as time permitsas time permitsas time permitsas time permits

At TRUNKS is a speech signal. You can identify it by examining each of the three

TRUNKS outputs with your oscilloscope. You will notice that, during speech

pauses, there remains a constant amplitude sinewave. This represents an

interfering signal.

T31 connect the speech signal at TRUNKS to the input of the HEADPHONE

AMPLIFIER. Plug the headphones into the HEADPHONE

AMPLIFIER, and listen to the speech. Notice that, no matter in which

position the front panel switch labelled ‘LPF Select’ is switched, there

is little change (if any at all) to the sound heard.

There being no significant change to the sound means that the speech was already

bandlimited to about 3 kHz, the LPF cutoff frequency, and that the interfering tone

was within the same bandwidth. What would happen if this corrupted speech

signal was used as the input to your model of Figure 2 ? Would it be possible to

cancel out the interfering tone without losing the speech ?

T32 connect the corrupted speech to your nulling model, and try to remove the

tone from the speech. Report and explain results.

TUTORIAL QUESTIONSTUTORIAL QUESTIONSTUTORIAL QUESTIONSTUTORIAL QUESTIONS

Q1 refer to the phasor diagram of Figure 3. If the amplitudes of the phasors V1

and V2 were within 1% of each other, and the angle α within 1o of

180o, how would you describe the depth of null ? How would you

describe the depth of null you achieved in the experiment ? You must

be able to express the result numerically.

Q2 why was not the noise nulled at the same time as the 1 kHz test signal ?

Q3 describe a method (based on this experiment) which could be used to estimate

the harmonic distortion in the output of an oscillator.

Q4 suppose you have set up the system of Figure 2, and the output has been

successfully minimized. What might happen to this minimum if the

frequency of the AUDIO OSCILLATOR was changed (say by 10%).

Explain.

Q5 Figure 1 shows an INVERTING AMPLIFIER, but Figure 2 has a PHASE

SHIFTER in its place. Could you have used a BUFFER AMPLIFIER

(which inverts the polarity) instead of the PHASE SHIFTER ?

Explain.


TRUNKSTRUNKSTRUNKSTRUNKS

There should be a speech signal, corrupted by one or two tones, at TRUNKS. If

you do not have a TRUNKS system you could generate this signal yourself with a

SPEECH module, an AUDIO OSCILLATOR, and an ADDER.


DSBSC GENERATIONDSBSC GENERATIONDSBSC GENERATIONDSBSC GENERATION

PREPARATION................................................................................ 2

definition of a DSBSC............................................................... 2

block diagram........................................................................................ 4

viewing envelopes ..................................................................... 4

multi-tone message.................................................................... 5

linear modulation .................................................................................. 6

spectrum analysis ...................................................................... 6

EXPERIMENT.................................................................................. 6

the MULTIPLIER..................................................................... 6

preparing the model .................................................................. 6

signal amplitude. ....................................................................... 7

fine detail in the time domain..................................................... 8

overload................................................................................................. 8

bandwidth ................................................................................. 9

alternative spectrum check ...................................................... 12

speech as the message ............................................................. 12


TRUNKS................................................................................ 14

APPENDIX ..................................................................................... 14

TUNEABLE LPF tuning information...................................... 14


DSBSC GENERATIONDSBSC GENERATIONDSBSC GENERATIONDSBSC GENERATION

ACHIEVEMENTS: definition and modelling of a double sideband suppressed

carrier (DSBSC) signal; introduction to the MULTIPLIER, VCO,

60 kHz LPF, and TUNEABLE LPF modules; spectrum estimation;

multipliers and modulators.

PREREQUISITES: completion of the experiment entitled ‘Modelling an equation’

in this Volume.


This experiment will be your introduction to the MULTIPLIER and the double

sideband suppressed carrier signal, or DSBSC. This modulated signal was

probably not the first to appear in an historical context, but it is the easiest to

generate.

You will learn that all of these modulated signals are derived from low frequency

signals, or ‘messages’. They reside in the frequency spectrum at some higher

frequency, being placed there by being multiplied with a higher frequency signal,

usually called ‘the carrier’ 1.

definition of a DSBSCdefinition of a DSBSCdefinition of a DSBSCdefinition of a DSBSC

Consider two sinusoids, or cosinusoids, cosµt and cosωt. A double sideband

suppressed carrier signal, or DSBSC, is defined as their product, namely:

DSBSC = E.cosµt . cosωt ........ 1

Generally, and in the context of this experiment, it is understood that::

ω >> µ ........ 2

Equation (3) can be expanded to give:

cosµt . cosωt = (E/2) cos(ω - µ)t + (E/2) cos(ω + µ)t ...... 3

Equation 3 shows that the product is represented by two new signals, one on the

sum frequency (ω + µ), and one on the difference frequency (ω - µ) - see Figure 1.

1 but remember whilst these low and high qualifiers reflect common practice, they are not mandatory.

DSBSC generation


Remembering the inequality of eqn. (2) the two new components are located close

to the frequency ω rad/s, one just below, and the other just above it. These are

referred to as the lower and upper sidebands 2 respectively.

ω µ ω µ++++ frequency

E2

These two components were

derived from a ‘carrier’ term on

ω rad/s, and a message on

µ rad/s. Because there is no term

at carrier frequency in the

product signal it is described as a

double sideband suppressed

carrier (DSBSC) signal.

Figure 1: spectral components

The term ‘carrier’ comes from the context of ‘double sideband amplitude

modulation' (commonly abbreviated to just AM).

AM is introduced in a later experiment (although, historically, AM preceded

DSBSC).

The time domain appearance of a DSBSC (eqn. 1) in a text book is generally as

shown in Figure 2.

message

E

-E

time

+ 1

- 1

0

DSBSC

Figure 2: eqn.(1) - a DSBSC - seen in the time domain

Notice the waveform of the DSBSC in Figure 2, especially near the times when the

message amplitude is zero. The fine detail differs from period to period of the

message. This is because the ratio of the two frequencies µ and ω has been made

non-integral.

Although the message and the carrier are periodic waveforms (sinusoids), the

DSBSC itself need not necessarily be periodic.

2 when, as here, there is only one component either side of the carrier, they are better described as side

frequencies. With a more complex message there are many components either side of the carrier, from

whence comes the term sidebands.


block diagramblock diagramblock diagramblock diagram

A block diagram, showing how eqn. (1) could be modelled with hardware, is shown

in Figure 3 below.

AUDIO OSC. µµµµ

ωωωωCARRIER

DSBSC A.cos t µµµµ

B.cos ωωωω t

t ωωωω. cos E . µµµµcos t

Figure 3: block diagram to generate eqn. (1) with hardware.

viewing enveviewing enveviewing enveviewing envelopeslopeslopeslopes

This is the first experiment dealing with a narrow band signal. Nearly all

modulated signals in communications are narrow band. The definition of 'narrow

band' has already been discussed in the chapter Introduction to Modelling with

TIMS.

You will have seen pictures of DSB or DSBSC signals (and amplitude modulation -

AM) in your text book, and probably have a good idea of what is meant by their

envelopes 3. You will only be able to reproduce the text book figures if the

oscilloscope is set appropriately - especially with regard to the method of its

synchronization. Any other methods of setting up will still be displaying the same

signal, but not in the familiar form shown in text books. How is the 'correct

method' of synchronization defined ?

With narrow-band signals, and particularly of the type to be examined in this and

the modulation experiments to follow, the following steps are recommended:

1) use a single tone for the message, say 1 kHz.

2) synchronize the oscilloscope to the message generator, which is of fixed

amplitude, using the 'ext trig.' facility.

3) set the sweep speed so as to display one or two periods of this message on

one channel of the oscilloscope.

4) display the modulated signal on another channel of the oscilloscope.

With the recommended scheme the envelope will be stationary on the screen. In all

but the most special cases the actual modulated waveform itself will not be

stationary - since successive sweeps will show it in slightly different positions. So

the display within the envelope - the modulated signal - will be 'filled in', as in

Figure 4, rather than showing the detail of Figure 2.

3 there are later experiments addressed specifically to envelopes, namely those entitled Envelopes, and

Envelope Recovery.

DSBSC generation


Figure 4: typical display of a DSBSC, with the message from

which it was derived, as seen on an oscilloscope. Compare with

Figure 2.

multimultimultimulti----tone messagetone messagetone messagetone message

The DSBSC has been defined in eqn. (1), with the message identified as the low

frequency term. Thus:

message = cosµt ........ 4

For the case of a multi-tone message, m(t), where:

m t a ti i

i

n

( ) cos=

=

∑ µ1 ........ 5

then the corresponding DSBSC signal consists of a band of frequencies below ω,

and a band of frequencies above ω. Each of these bands is of width equal to the

bandwidth of m(t).

The individual spectral components in these sidebands are often called

sidefrequencies.

If the frequency of each term in the expansion is expressed in terms of its difference

from ω, and the terms are grouped in pairs of sum and difference frequencies, then

there will be ‘n’ terms of the form of the right hand side of eqn. (3).

Note it is assumed here that there is no DC term in m(t). The presence of a DC

term in m(t) will result in a term at ω in the DSB signal; that is, a term at ‘carrier’

frequency. It will no longer be a double sideband suppressed carrier signal. A

special case of a DSB with a significant term at carrier frequency is an amplitude

modulated signal, which will be examined in an experiment to follow.

A more general definition still, of a DSBSC, would be:

DSBSC = E.m(t).cosωt ........ 6

where m(t) is any (low frequency) message. By convention m(t) is generally

understood to have a peak amplitude of unity (and typically no DC component).


linear modulationlinear modulationlinear modulationlinear modulation

The DSBSC is a member of a class known as linear modulated signals. Here the

spectrum of the modulated signal, when the message has two or more components,

is the sum of the spectral components which each message component would have

produced if present alone.

For the case of non-linear modulated signals, on the other hand, this linear addition

does not take place. In these cases the whole is more than the sum of the parts. A

frequency modulated (FM) signal is an example. These signals are first examined

in the chapter entitled Analysis of the FM spectrum, within Volume A2 - Further &

Advanced Analog Experiments, and subsequent experiments of that Volume.

spectrum analysisspectrum analysisspectrum analysisspectrum analysis

In the experiment entitled Spectrum analysis - the WAVE ANALYSER, within Volume

A2 - Further & Advanced Analog Experiments, you will model a WAVE ANALYSER.

As part of that experiment you will re-examine the DSBSC spectrum, paying

particular attention to its spectrum.


the MULTIPLIERthe MULTIPLIERthe MULTIPLIERthe MULTIPLIER

This is your introduction to the MULTIPLIER module.

Please read the section in the chapter of this Volume entitled Introduction to

modelling with TIMS headed multipliers and modulators. Particularly note the

comments on DC off-sets.

preparing the modelpreparing the modelpreparing the modelpreparing the model

Figure 3 shows a block diagram of a system suitable for generating DSBSC derived

from a single tone message.

Figure 5 shows how to model this block diagram with TIMS.

DSBSC generation


ext. trig.

SCOPE

Figure 5: pictorial of block diagram of Figure 3

The signal A.cosµt, of fixed amplitude A, from the AUDIO OSCILLATOR,

represents the single tone message. A signal of fixed amplitude from this oscillator

is used to synchronize the oscilloscope.

The signal B.cosωt, of fixed amplitude B and frequency exactly 100 kHz, comes

from the MASTER SIGNALS panel. This is the TIMS high frequency, or radio,

signal. Text books will refer to it as the 'carrier signal'.

The amplitudes A and B are nominally equal, being from TIMS signal sources.

They are suitable as inputs to the MULTIPLIER, being at the TIMS ANALOG

REFERENCE LEVEL. The output from the MULTIPLIER will also be, by design

of the internal circuitry, at this nominal level. There is no need for any amplitude

adjustment. It is a very simple model.

T1 patch up the arrangement of Figure 5. Notice that the oscilloscope is

triggered by the message, not the DSBSC itself (nor, for that matter,

by the carrier).

T2 use the FREQUENCY COUNTER to set the AUDIO OSCILLATOR to about

1 kHz

Figure 2 shows the way most text books would illustrate a DSBSC signal of this

type. But the display you have in front of you is more likely to be similar to that of

Figure 4.

signal amplitude.signal amplitude.signal amplitude.signal amplitude.

T3 measure and record the amplitudes A and B of the message and carrier

signals at the inputs to the MULTIPLIER.

The output of this arrangement is a DSBSC signal, and is given by:

DSBSC = k A.cosµt B.cosωt ...... 7


The peak-to-peak amplitude of the display is:

peak-to-peak = 2 k A B volts ...... 8

Here 'k' is a scaling factor, a property of the MULTIPLIER. One of the purposes of

this experiment is to determine the magnitude of this parameter.

Now:

T4 measure the peak-to-peak amplitude of the DSBSC

Since you have measured both A and B already, you have now obtained the

magnitude of the MULTIPLIER scale factor 'k'; thus:

k = (dsbsc peak-to-peak) / (2 A B) ...... 9

Note that 'k' is not a dimensionless quantity.

fine detail in the time domainfine detail in the time domainfine detail in the time domainfine detail in the time domain

The oscilloscope display will not in general show the fine detail inside the DSBSC,

yet many textbooks will do so, as in Figure 2. Figure 2 would be displayed by a

single sweep across the screen. The normal laboratory oscilloscope cannot retain

and display the picture from a single sweep 4. Subsequent sweeps will all be

slightly different, and will not coincide when superimposed.

To make consecutive sweeps identical, and thus to display the DSBSC as depicted

in Figure 2, it is necessary that ‘µ’ be a sub-multiple of ‘ω’. This special condition

can be arranged with TIMS by choosing the '2 kHz MESSAGE' sinusoid from the

fixed MASTER SIGNALS module. The frequency of this signal is actually

100/48 kHz (approximately 2.08 kHz), an exact sub-multiple of the carrier

frequency. Under these special conditions the fine detail of the DSBSC can be

observed.

T5 obtain a display of the DSBSC similar to that of Figure 2. A sweep speed of,

say, 50µs/cm is a good starting point.

overloadoverloadoverloadoverload

When designing an analog system signal overload must be avoided at all times.

Analog circuits are expected to operate in a linear manner, in order to reduce the

chance of the generation of new frequencies. This would signify non-linear

operation.

4 but note that, since the oscilloscope is synchronized to the message, the envelope of the DSBSC remains in

a fixed relative position over consecutive sweeps. It is the infill - the actual DSBSC itself - which is slightly

different each sweep.

DSBSC generation


A multiplier is intended to generate new frequencies. In this sense it is a non-

linear device. Yet it should only produce those new frequencies which are wanted -

any other frequencies are deemed unwanted.

A quick test for unintended (non-linear) operation is to use it to generate a signal

with a known shape -a DSBSC signal is just such a signal. Presumably so far your

MULTIPLIER module has been behaving ‘linearly’.

T6 insert a BUFFER AMPLIFIER in one or other of the paths to the

MULTIPLIER, and increase the input amplitude of this signal until

overload occurs. Sketch and describe what you see.

bandwidthbandwidthbandwidthbandwidth

Equation (3) shows that the DSBSC signal consists of two components in the

frequency domain, spaced above and below ω by µ rad/s.

With the TIMS BASIC SET of modules, and a DSBSC based on a 100 kHz carrier,

you can make an indirect check on the truth of this statement. Attempting to pass

the DSBSC through a 60 kHz LOWPASS FILTER will result in no output,

evidence that the statement has some truth in it - all components must be above

60 kHz.

A convincing proof can be made with the 100 kHz CHANNEL FILTERS module 5.

Passage through any of these filters will result in no change to the display (see

alternative spectrum check later in this experiment).

Using only the resources of the TIMS BASIC SET of modules a convincing proof is

available if the carrier frequency is changed to, say, 10 kHz. This signal is

available from the analog output of the VCO, and the test setup is illustrated in

Figure 6 below. Lowering the carrier frequency puts the DSBSC in the range of the

TUNEABLE LPF.

AUDIO OSC. DSBSC A.cos t µµµµ

B.cos ωωωω t

oscilloscope trigger

TUNEABLE

vcoωωωω=10kHz

µµµµ =1kHz

LPF

Figure 6: checking the spectrum of a DSBSC signal

T7 read about the VCO module in the TIMS User Manual. Before plugging the

VCO in to the TIMS SYSTEM UNIT set the on-board switch to VCO.

Set the front panel frequency range selection switch to ‘LO’.

5 this is a TIMS ADVANCED MODULE.


T8 read about the TUNEABLE LPF in the TIMS User Manual and the

Appendix A to this text.

T9 set up an arrangement to check out the TUNEABLE LPF module. Use the

VCO as a source of sinewave input signal. Synchronize the

oscilloscope to this signal. Observe input to, and output from, the

TUNEABLE LPF.

T10 set the front panel GAIN control of the TUNEABLE LPF so that the gain

through the filter is unity.

T11 confirm the relationship between VCO frequency and filter cutoff frequency

(refer to the TIMS User Manual for full details, or the Appendix to

this Experiment for abridged details).

T12 set up the arrangement of Figure 6. Your model should look something like

that of Figure 7, where the arrangement is shown modelled by TIMS.

ext. trig

Figure 7: TIMS model of Figure 6

T13 adjust the VCO frequency to about 10 kHz

T14 set the AUDIO OSCILLATOR to about 1 kHz.

T15 confirm that the output from the MULTIPLIER looks like Figures 2

and/or 4.

Analysis predicts that the DSBSC is centred on 10 kHz, with lower and upper

sidefrequencies at 9.0 kHz and 11.0 kHz respectively. Both sidefrequencies should

fit well within the passband of the TUNEABLE LPF, when it is tuned to its widest

passband, and so the shape of the DSBSC should not be altered.

T16 set the front panel toggle switch on the TUNEABLE LPF to WIDE, and the

front panel TUNE knob fully clockwise. This should put the passband

edge above 10 kHz. The passband edge (sometimes called the ‘corner

frequency’) of the filter can be determined by connecting the output

from the TTL CLK socket to the FREQUENCY COUNTER. It is given

by dividing the counter readout by 360 (in the ‘NORMAL’ mode the

dividing factor is 880).

DSBSC generation


T17 note that the passband GAIN of the TUNEABLE LPF is adjustable from the

front panel. Adjust it until the output has a similar amplitude to the

DSBSC from the MULTIPLIER (it will have the same shape). Record

the width of the passband of the TUNEABLE LPF under these

conditions.

Assuming the last Task was performed successfully this confirms that the DSBSC

lies below the passband edge of the TUNEABLE LPF at its widest. You will now

use the TUNEABLE LPF to determine the sideband locations. That this should be

possible is confirmed by Figure 8 below.

0

dB

50

Figure 8: the amplitude response of the TUNEABLE LPF

superimposed on the DSBSC spectrum.

Figure 8 shows the amplitude response of the TUNEABLE LPF superimposed on

the DSBSC, when based on a 1 kHz message. The drawing is approximately to

scale. It is clear that, with the filter tuned as shown (passband edge just above the

lower sidefrequency), it is possible to attenuate the upper sideband by 50 dB and

retain the lower sideband effectively unchanged.

T18 make a sketch to explain the meaning of the transition bandwidth of a

lowpass filter. You should measure the transition bandwidth of your

TUNEABLE LPF, or instead accept the value given in Appendix A to

this text.

T19 lower the filter passband edge until there is a just-noticeable change to the

DSBSC output. Record the filter passband edge as fA. You have

located the upper edge of the DSBSC at (ω + µ) rad/s.

T20 lower the filter passband edge further until there is only a sinewave output.

You have isolated the component on (ω - µ) rad/s. Lower the filter

passband edge still further until the amplitude of this sinewave just

starts to reduce. Record the filter passband edge as fB.


T21 again lower the filter passband edge, just enough so that there is no

significant output. Record the filter passband edge as fC

T22 from a knowledge of the filter transition band ratio, and the measurements

fA and fB , estimate the location of the two sidebands and compare

with expectations. You could use fC as a cross-check.

alternative spectrum checkalternative spectrum checkalternative spectrum checkalternative spectrum check

If you have a 100kHz CHANNEL FILTERS module, or from a SPEECH module,

then, knowing the filter bandwidth, it can be used to verify the theoretical estimate

of the DSBSC bandwidth.

speech as the messagespeech as the messagespeech as the messagespeech as the message

If you have speech available at TRUNKS you might like to observe the appearance

of the DSBSC signal in the time domain.

Figure 9 is a snap-shot of what you might see.

Figure 9: speech derived DSBSC

DSBSC generation



Q1 in TIMS the parameter ‘k’ has been set so that the product of two sinewaves,

each at the TIMS ANALOG REFERENCE LEVEL, will give a

MULTIPLIER peak-to-peak output amplitude also at the TIMS

ANALOG REFERENCE LEVEL. Knowing this, predict the expected

magnitude of 'k'

Q2 how would you answer the question ‘what is the frequency of the signal

y(t) = E.cosµt.cosωt’ ?

Q3 what would the FREQUENCY COUNTER read if connected to the signal

y(t) = E.cosµt.cosωt ?

Q4 is a DSBSC signal periodic ?

Q5 carry out the trigonometry to obtain the spectrum of a DSBSC signal when

the message consists of three tones, namely:

message = A1.cosµ1t + A2.cosµ2t + A3 cosµ3t

Show that it is the linear sum of three DSBSC, one for each of the

individual message components.

Q6 the DSBSC definition of eqn. (1) carried the understanding that the message

frequency µ should be very much less than the carrier frequency ω.

Why was this ? Was it strictly necessary ? You will have an

opportunity to consider this in more detail in the experiment entitled

Envelopes (within Volume A2 - Further & Advanced Analog

Experiments).



If you do not have a TRUNKS system you could obtain a speech signal from a

SPEECH module.

APPENDIXAPPENDIXAPPENDIXAPPENDIX

TUNEABLE LPFTUNEABLE LPFTUNEABLE LPFTUNEABLE LPF tuning information tuning information tuning information tuning information

Filter cutoff frequency is given by:

NORM range: clk / 880

WIDE range: clk / 360

See the TIMS User Manual for full details.


AMPLITUDE MODULATIONAMPLITUDE MODULATIONAMPLITUDE MODULATIONAMPLITUDE MODULATION

PREPARATION ................................................................................2

theory........................................................................................3

depth of modulation ..................................................................4

measurement of ‘m’............................................................................... 5

spectrum................................................................................................ 5

other message shapes. ............................................................................ 5

other generation methods...........................................................6

EXPERIMENT ..................................................................................7

aligning the model .....................................................................7

the low frequency term a(t) .................................................................... 7

the carrier supply c(t)............................................................................. 7

agreement with theory ........................................................................... 9

the significance of ‘m’ .............................................................10

the modulation trapezoid.........................................................11

TUTORIAL QUESTIONS ...............................................................13



ACHIEVEMENTS: modelling of an amplitude modulated (AM) signal; method of

setting and measuring the depth of modulation; waveforms and

spectra; trapezoidal display.

PREREQUISITES: a knowledge of DSBSC generation. Thus completion of the

experiment entitled DSBSC generation would be an advantage.


In the early days of wireless, communication was carried out by telegraphy, the

radiated signal being an interrupted radio wave. Later, the amplitude of this

wave was varied in sympathy with (modulated by) a speech message (rather than

on/off by a telegraph key), and the message was recovered from the envelope of

the received signal. The radio wave was called a ‘carrier’, since it was seen to

carry the speech information with it. The process and the signal was called

amplitude modulation, or ‘AM’ for short.

In the context of radio communications, near the end of the 20th century, few

modulated signals contain a significant component at ‘carrier’ frequency.

However, despite the fact that a carrier is not radiated, the need for such a signal

at the transmitter (where the modulated signal is generated), and also at the

receiver, remains fundamental to the modulation and demodulation process

respectively. The use of the term ‘carrier’ to describe this signal has continued to

the present day.

As distinct from radio communications, present day radio broadcasting

transmissions do have a carrier. By transmitting this carrier the design of the

demodulator, at the receiver, is greatly simplified, and this allows significant cost

savings.

The most common method of AM generation uses a ‘class C modulated

amplifier’; such an amplifier is not available in the BASIC TIMS set of

modules. It is well documented in text books. This is a ‘high level’ method of

generation, in that the AM signal is generated at a power level ready for

radiation. It is still in use in broadcasting stations around the world, ranging in

powers from a few tens of watts to many megawatts.

Unfortunately, text books which describe the operation of the class C modulated

amplifier tend to associate properties of this particular method of generation with

those of AM, and AM generators, in general. This gives rise to many

misconceptions. The worst of these is the belief that it is impossible to generate

an AM signal with a depth of modulation exceeding 100% without giving rise to

serious RF distortion.

Amplitude modulation


You will see in this experiment, and in others to follow, that there is no problem

in generating an AM signal with a depth of modulation exceeding 100%, and

without any RF distortion whatsoever.

But we are getting ahead of ourselves, as we have not yet even defined what AM

is !

theorytheorytheorytheory

The amplitude modulated signal is defined as:

AM = E (1 + m.cosµt) cosωt ........ 1

= A (1 + m.cosµt) . B cosωt ........ 2

= [low frequency term a(t)] x [high frequency term c(t)] ........ 3

Here:

‘E’ is the AM signal amplitude from eqn. (1). For modelling convenience

eqn. (1) has been written into two parts in eqn. (2), where (A.B) = E.

‘m’ is a constant, which, as you will soon see, defines the ‘depth of modulation’.

Typically m < 1. Depth of modulation, expressed as a percentage, is

100.m. There is no inherent restriction upon the size of ‘m’ in eqn. (1).

This point will be discussed later.

‘µµµµ’ and ‘ωωωω’ are angular frequencies in rad/s, where µ/(2.π) is a low, or message

frequency, say in the range 300 Hz to 3000 Hz; and ω/(2.π) is a radio, or

relatively high, ‘carrier’ frequency. In TIMS the carrier frequency is

generally 100 kHz.

Notice that the term a(t) in eqn. (3) contains both a DC component and an AC

component. As will be seen, it is the DC component which gives rise to the term

at ω - the ‘carrier’ - in the AM signal. The AC term ‘m.cosµt’ is generally

thought of as the message, and is sometimes written as m(t). But strictly

speaking, to be compatible with other mathematical derivations, the whole of the

low frequency term a(t) should be considered the message.

Thus:

a(t) = DC + m(t) ........ 4

Figure 1 below illustrates what the oscilloscope will show if displaying the AM

signal.


Figure 1 - AM, with m = 1, as seen on the oscilloscope

A block diagram representation of eqn. (2) is shown in Figure 2 below.

AM message sine wave

µ( )

carrier sine wave

ω( )

m(t)

c(t) g

G

a(t)

voltage DC

Figure 2: generation of equation 2

For the first part of the experiment you will model eqn. (2) by the arrangement of

Figure 2. The depth of modulation will be set to exactly 100% (m = 1). You will

gain an appreciation of the meaning of ‘depth of modulation’, and you will learn

how to set other values of ‘m’, including cases where m > 1.

The signals in eqn. (2) are expressed as voltages in the time domain. You will

model them in two parts, as written in eqn. (3).

depth of modulationdepth of modulationdepth of modulationdepth of modulation

100% amplitude modulation is defined as the condition when m = 1. Just what

this means will soon become apparent. It requires that the amplitude of the DC

(= A) part of a(t) is equal to the amplitude of the AC part (= A.m). This means

that their ratio is unity at the output of the ADDER, which forces ‘m’ to a

magnitude of exactly unity.

By aiming for a ratio of unity it is thus not necessary to

know the absolute magnitude of A at all.



measurement of ‘m’measurement of ‘m’measurement of ‘m’measurement of ‘m’

The magnitude of ‘m’ can be measured directly from the AM display itself.

Thus:

mP Q

P Q=

−

+ ........ 5

where P and Q are as defined in Figure 3.

Figure 3: the oscilloscope display for the case m = 0.5

spectrumspectrumspectrumspectrum

Analysis shows that the sidebands of the AM, when derived from a message of

frequency µ rad/s, are located either side of the carrier frequency, spaced from it

by µ rad/s.

frequencyωω µ ω µ+

E

Em

2

You can see this by expanding eqn. (2). The

spectrum of an AM signal is illustrated in

Figure 4 (for the case m = 0.75). The spectrum

of the DSBSC alone was confirmed in the

experiment entitled DSBSC generation. You

can repeat this measurement for the AM signal.

Figure 4: AM spectrumAs the analysis predicts, even when m > 1, there

is no widening of the spectrum.

This assumes linear operation; that is, that there is no hardware overload.

other message shapes.other message shapes.other message shapes.other message shapes.

Provided m ≤ 1 the envelope of the AM will always be a faithful copy of the

message. For the generation method of Figure 2 the requirement is that:


the peak amplitude of the AC component must not exceed the

magnitude of the DC, measured at the ADDER output

As an example of an AM signal derived from speech, Figure 5 shows a snap-shot

of an AM signal, and separately the speech signal.

There are no amplitude scales shown, but you should be able to deduce the depth

of modulation 1 by inspection.

speech

AMAM

Figure 5: AM derived from speech.

other generation methodsother generation methodsother generation methodsother generation methods

There are many methods of generating AM, and this experiment explores only

one of them. Another method, which introduces more variables into the model,

is explored in the experiment entitled Amplitude modulation - method 2, to be

found in Volume A2 - Further & Advanced Analog Experiments.

It is strongly suggested that you examine your text book for other methods.

Practical circuitry is more likely to use a modulator, rather than the more

idealised multiplier. These two terms are introduced in the Chapter of this

Volume entitled Introduction to modelling with TIMS, in the section entitled

multipliers and modulators.

1 that is, the peak depth



EXPEXPEXPEXPERIMENTERIMENTERIMENTERIMENT

aligning the modelaligning the modelaligning the modelaligning the model

the low frequency term a(t)the low frequency term a(t)the low frequency term a(t)the low frequency term a(t)

To generate a voltage defined by eqn. (2) you need first to generate the term a(t).

a(t) = A.(1 + m.cosµt) ........ 6

Note that this is the addition of two parts, a DC term and an AC term. Each part

may be of any convenient amplitude at the input to an ADDER.

The DC term comes from the VARIABLE DC module, and will be adjusted to

the amplitude ‘A’ at the output of the ADDER.

The AC term m(t) will come from an AUDIO OSCILLATOR, and will be

adjusted to the amplitude ‘A.m’ at the output of the ADDER.

the carrier supply c(t)the carrier supply c(t)the carrier supply c(t)the carrier supply c(t)

The 100 kHz carrier c(t) comes from the MASTER SIGNALS module.

c(t) = B.cosωt ........ 7

The block diagram of Figure 2, which models the AM equation, is shown

modelled by TIMS in Figure 6 below.

CH1-A

CH2-A

ext. trig CH1-B

Figure 6: the TIMS model of the block diagram of Figure 2


To build the model:

T1 first patch up according to Figure 6, but omit the input X and Y connections

to the MULTIPLIER. Connect to the two oscilloscope channels

using the SCOPE SELECTOR, as shown.

T2 use the FREQUENCY COUNTER to set the AUDIO OSCILLATOR to about

1 kHz.

T3 switch the SCOPE SELECTOR to CH1-B, and look at the message from the

AUDIO OSCILLATOR. Adjust the oscilloscope to display two or

three periods of the sine wave in the top half of the screen.

Now start adjustments by setting up a(t), as defined by eqn. (4), and with m = 1.

T4 turn both g and G fully anti-clockwise. This removes both the DC and the

AC parts of the message from the output of the ADDER.

T5 switch the scope selector to CH1-A. This is the ADDER output. Switch the

oscilloscope amplifier to respond to DC if not already so set, and

the sensitivity to about 0.5 volt/cm. Locate the trace on a

convenient grid line towards the bottom of the screen. Call this the

zero reference grid line.

T6 turn the front panel control on the VARIABLE DC module almost fully anti-

clockwise (not critical). This will provide an output voltage of about

minus 2 volts. The ADDER will reverse its polarity, and adjust its

amplitude using the ‘g’ gain control.

T7 whilst noting the oscilloscope reading on CH1-A, rotate the gain ‘g’ of the

ADDER clockwise to adjust the DC term at the output of the

ADDER to exactly 2 cm above the previously set zero reference line.

This is ‘A’ volts.

You have now set the magnitude of the DC part of the message to a known

amount. This is about 1 volt, but exactly 2 cm, on the oscilloscope screen. You

must now make the AC part of the message equal to this, so that the ratio Am/A

will be unity. This is easy:

T8 whilst watching the oscilloscope trace of CH1-A rotate the ADDER gain

control ‘G’ clockwise. Superimposed on the DC output from the

ADDER will appear the message sinewave. Adjust the gain G until

the lower crests of the sinewave are EXACTLY coincident with the

previously selected zero reference grid line.



The sine wave will be centred exactly A volts above the previously-chosen zero

reference, and so its amplitude is A.

Now the DC and AC, each at the ADDER output, are of exactly the same

amplitude A. Thus:

A = A.m ........ 8

and so:

m = 1 ........ 9

You have now modelled A.(1 + m.cosµt), with m = 1. This is connected to one

input of the MULTIPLIER, as required by eqn. (2).

T9 connect the output of the ADDER to input X of the MULTIPLIER. Make

sure the MULTIPLIER is switched to accept DC.

Now prepare the carrier signal:

c(t) = B.cosωt ........ 10

T10 connect a 100 kHz analog signal from the MASTER SIGNALS module to

input Y of the MULTIPLIER.

T11 connect the output of the MULTIPLIER to the CH2-A of the SCOPE

SELECTOR. Adjust the oscilloscope to display the signal

conveniently on the screen.

Since each of the previous steps has been completed successfully, then at the

MULTIPLIER output will be the 100% modulated AM signal. It will be

displayed on CH2-A. It will look like Figure 1.

Notice the systematic manner in which the required outcome was achieved.

Failure to achieve the last step could only indicate a faulty MULTIPLIER ?

agreement with theoryagreement with theoryagreement with theoryagreement with theory

It is now possible to check some theory.

T12 measure the peak-to-peak amplitude of the AM signal, with m = 1, and

confirm that this magnitude is as predicted, knowing the signal

levels into the MULTIPLIER, and its ‘k’ factor.


the significance of ‘m’the significance of ‘m’the significance of ‘m’the significance of ‘m’

First note that the shape of the outline, or envelope, of the AM waveform (lower

trace), is exactly that of the message waveform (upper trace). As mentioned

earlier, the message includes a DC component, although this is often ignored or

forgotten when making these comparisons.

You can shift the upper trace down so that it matches the envelope of the AM

signal on the other trace 2. Now examine the effect of varying the magnitude of

the parameter 'm'. This is done by varying the message amplitude with the

ADDER gain control G 3.

• for all values of ‘m’ less than that already set (m = 1), the envelope of the

AM is the same shape as that of the message.

• for values of m > 1 the envelope is NOT a copy of the message shape.

It is important to note that, for the condition m > 1:

• it should not be considered that there is envelope distortion, since the

resulting shape, whilst not that of the message, is the shape the theory

predicts.

• there need be no AM signal distortion for this method of generation.

Distortion of the AM signal itself, if present, will be due to amplitude

overload of the hardware. But overload should not occur, with the levels

previously recommended, for moderate values of m > 1.

T13 vary the ADDER gain G, and thus ‘m’, and confirm that the envelope of

the AM behaves as expected, including for values of m > 1.

2 comparing phases is not always as simple as it sounds. With a more complex model the additional small

phase shifts within and between modules may be sufficient to introduce a noticeable off-set (left or right) between the two displays. This can be corrected with a PHASE SHIFTER, if necessary.

3 it is possible to vary the depth of modulation with either of the ADDER gain controls. But depth of

modulation ‘m’ is considered to be proportional to the amplitude of the AC component of m(t).



Figure 7: the AM envelope for m < 1 and m > 1

T14 replace the AUDIO OSCILLATOR output with a speech signal available

at the TRUNKS PANEL. How easy is it to set the ADDER gain G to

occasionally reach, but never exceed, 100% amplitude modulation ?

the modulation trapezoidthe modulation trapezoidthe modulation trapezoidthe modulation trapezoid

With the display method already examined, and with a sinusoidal message, it is

easy to set the depth of modulation to any value of ‘m’. This method is less

convenient for other messages, especially speech.

The so-called trapezoidal display is a useful alternative for more complex

messages. The patching arrangement for obtaining this type of display is

illustrated in Figure 8 below, and will now be examined.

Figure 8: the arrangement for producing the TRAPEZOID

T15 patch up the arrangement of Figure 8. Note that the oscilloscope will have

to be switched to the ‘X - Y’ mode; the internal sweep circuits are

not required.


T16 with a sine wave message show that, as m is increased from zero, the

display takes on the shape of a TRAPEZOID (Figure 9).

T17 show that, for m = 1, the TRAPEZOID degenerates into a TRIANGLE

T18 show that, for m > 1, the TRAPEZOID extends beyond the TRIANGLE,

into the dotted region as illustrated in Figure 9

Figure 9: the AM trapezoid for m = .5. The trapezoid extends

into the dotted section as m is increased to 1.2 (120%).

So here is another way of setting m = 1. But this was for a sinewave message,

where you already have a reliable method. The advantage of the trapezoid

technique is that it is especially useful when the message is other than a sine

wave - say speech.

T19 use speech as the message, and show that this also generates a

TRAPEZOID, and that setting the message amplitude so that the

depth of modulation reaches unity on peaks (a TRIANGLE) is

especially easy to do.

practical note: if the outline of the trapezoid is not made up of straight-line sections

then this is a good indicator of some form of distortion. For m < 1 it could be

phase distortion, but for m > 1 it could also be overload distortion. Phase

distortion is not likely with TIMS, but in practice it can be caused by

(electrically) long leads to the oscilloscope, especially at higher carrier

frequencies.




Q1 there is no difficulty in relating the formula of eqn. (5) to the waveforms of

Figure 7 for values of ‘m’ less than unity. But the formula is also

valid for m > 1, provided the magnitudes P and Q are interpreted

correctly. By varying ‘m’, and watching the waveform, can you see

how P and Q are defined for m > 1 ?

Q2 explain how the arrangement of Figure 8 generates the TRAPEZOID of

Figure 9, and the TRIANGLE as a special case.

Q3 derive eqn.(5), which relates the magnitude of the parameter ‘m’ to the

peak-to-peak and trough-to-trough amplitudes of the AM signal.

Q4 if the AC/DC switch on the MULTIPLIER front panel is switched to AC

what will the output of the model of Figure 6 become ?

Q5 an AM signal, depth of modulation 100% from a single tone message, has a

peak-to-peak amplitude of 4 volts. What would an RMS voltmeter

read if connected to this signal ? You can check your answer if you

have a WIDEBAND TRUE RMS METER module.

Q6 in Task T6, when modelling AM, what difference would there have been to

the AM from the MULTIPLIER if the opposite polarity (+ve) had

been taken from the VARIABLE DC module ?


ENVELOPESENVELOPESENVELOPESENVELOPES

PREPARATION................................................................................ 2

envelope definition .................................................................... 2

example 1: 100% AM............................................................................ 3

example 2: 150% AM........................................................................... 4

example 3: DSBSC............................................................................... 4

EXPERIMENT.................................................................................. 5

test signal generation................................................................. 5

envelope examples .................................................................... 6

envelope recovery .................................................................................. 7

envelope visualization for small (ω/µ) ........................................ 7

reduction of the carrier-to-message freq ratio......................................... 8

other examples .......................................................................... 9

unreliable oscilloscope triggering........................................................... 9

synchronization to an off-air signal...................................................... 10

use of phasors ......................................................................... 10



ENVELOPESENVELOPESENVELOPESENVELOPES

ACHIEVEMENTS: definition and examination of envelopes; the envelope of a

wideband signal, although difficult to visualize, is shown to fit the

definition.

PREREQUISITES: completion of the experiments entitled DSBSC generation,

and AM generation, in this Volume, would be an advantage.

PREPARATIPREPARATIPREPARATIPREPARATIONONONON

envelope definitionenvelope definitionenvelope definitionenvelope definition

When we talk of the envelopes of signals we are concerned with the appearance of

signals in the time domain. Text books are full of drawings of modulated signals,

and you already have an idea of what the term ‘envelope’ means. It will now be

given a more formal definition.

Qualitatively, the envelope of a signal y(t) is that boundary within which the signal

is contained, when viewed in the time domain. It is an imaginary line.

This boundary has an upper and lower part. You will see these are mirror images

of each other. In practice, when speaking of the envelope, it is customary to

consider only one of them as ‘the envelope’ (typically the upper boundary).

Although the envelope is imaginary in the sense described above, it is possible to

generate, from y(t), a signal e(t), having the same shape as this imaginary line.

The circuit which does this is commonly called an envelope detector. See the

experiment entitled Envelope recovery in this Volume.

For the purposes of this discussion a narrowband signal will be defined as one

which has a bandwidth very much less than an octave. That is, if it lies within the

frequency range f1 to f2, where f1 < f2, then:

log2(f1/f2) << 1

Another way of expressing this is to say that f1 ≈ f2. so that

Envelopes


(f2 - f1)/(f2 + f1) << 1

A wideband signal will be defined as one which is very much wider than a

narrowband signal !

For further discussion see the chapter , in this Volume, entitled Introduction to

modelling with TIMS, under the heading bandwidth and spectra.

Every signal has an envelope, although, with wideband signals, it is not always

conceptually easy to visualize. To avoid such visualization difficulties the

discussion below will assume we are dealing with narrow band signals. But in fact

there need be no such restriction on the definition, as will be seen later.

Suppose the spectrum of the signal y(t) is located near fo Hz, where:

ωο = 2.π.fo. ........ 1

We state here, without explanation, that if y(t) can be written in the form:

y(t) = a(t).cos[ωot + ϕ(t)] ........ 2

where a(t) and ϕ(t) contain only frequency components much lower than fo (ie., at

message, or related, frequencies), then we define the envelope e(t) of y(t) as the

absolute value of a(t).

That is,

envelope e(t) = | a(t) | ........ 3

Remember that an AM signal has been defined as:

y(t) = A.(1 + m.cosµt).cosωt ........ 4

where µ, ω, and m have their usual meanings (see List Of Symbols at the end of the

chapter Introduction to Modelling with TIMS).

It is common practice to think of the message as being m.cosµt. Strictly the

message should include the DC component; that is (1 + m.cosµt). But the

presence of the DC component is often forgotten or ignored.

example 1: 100% AMexample 1: 100% AMexample 1: 100% AMexample 1: 100% AM

Consider first the case when y(t) is an AM signal.

From the definitions above we see:

a(t) = A.(1 + m.cosµt) ........ 5

ϕ(t) = 0 ........ 6

The requirement that both a(t) and ϕ(t) contain only components at or near the

message frequency are met, and so it follows that the envelope must be e(t), where:

e(t) = | A.(1 + m.cosµt) | ........ 7

For the case m ≤ 1 the absolute sign has no effect, and so there is a linear

relationship between the message and envelope, as desired for AM.


Figure 1: AM, with m = 1

This is clearly shown in Figure 1, which is for 100% AM (m = 1). Both a(t) and its

modulus is shown. They are the same.

example 2: 150% AMexample 2: 150% AMexample 2: 150% AMexample 2: 150% AM

For the case of 150% AM the envelope is still given by e(t) of eqn. 7, but this time

m = 1.5, and the absolute sign does have an effect.

Figure 2: 150% AM

Figure 2 shows the case for m = 1.5. As well as the message (upper trace) the

absolute value of the message is also plotted (centre trace). Notice how it matches

the envelope of the modulated signal (lower trace).

example 3: DSBSCexample 3: DSBSCexample 3: DSBSCexample 3: DSBSC

For a final example look at the DSBSC, where a(t) = cosµt. There is no DC

component here at all. Figure 3 shows the relevant waveforms.

Figure 3: DSBSC

Envelopes



test signal generationtest signal generationtest signal generationtest signal generation

The validity of the envelope definition can be tested experimentally. The

arrangement of Figure 4 will serve to make some envelopes for testing. It has

already been used for AM generation in the earlier experiment Amplitude

Modulation - method 1.

please note: in this experiment you will observing envelopes, but not recovering

them. The recovery of envelopes is the subject of the experiment entitled

Envelope recovery within this Volume.

variable DC voltage

message sine wave

µ( )

carrier sine wave

ω( )

c(t)

ext. trig

g

G

outa(t)

y(t)

m(t)

Figure 4: a test signal generator

T1 patch up the model of Figure 4, to generate 100% AM, with the frequency of

the AUDIO OSCILLATOR about 1 kHz, and the high frequency term

at 100 kHz coming from the MASTER SIGNALS module.

T2 make sure that the oscilloscope display is stable, being triggered from the

message generator. Display a(t) - the message including the DC

component - on the oscilloscope channel (CH1-A), and y(t), the output

signal, on channel (CH2-A). Your patching arrangements are shown

in Figure 5 below.


CH1-A

CH2-A

ext. trig

Figure 5: the generator modelled by TIMS

envelope examplesenvelope examplesenvelope examplesenvelope examples

example 1

The case m ≤ 100% requires the message to have a DC component larger than the

AC component. The signal is illustrated in Figure 1 for m = 1.

T3 confirm that, for the case m ≤ 1 the value of e(t) is the same as that of a(t),

and so the envelope has the same shape as the message.

example 2

The case m > 100% requires the message to have a DC component smaller than the

AC component. The signal is illustrated in Figure 2.

T4 set m = 1.5 and reproduce the traces of Figure 2.

example 3

DSBSC has no carrier component, so the DC part of the message is zero. The

signal is illustrated in Figure 3.

T5 remove the DC term from the ADDER; this makes the output signal a

DSBSC. Confirm that the analysis gives the envelope shape as

| cosµt | and that this is displayed on the oscilloscope.

Envelopes


envelope recoveryenvelope recoveryenvelope recoveryenvelope recovery

In the experiment entitled Envelope recovery you will examine ways of generating

signals, which are exact copies of these envelopes, from the modulated signals

themselves.

envelope visenvelope visenvelope visenvelope visualization for small (ualization for small (ualization for small (ualization for small (ωωωω////µµµµ))))

It has already been confirmed, in all cases so far examined, that there is agreement

between the definition of the envelope, and what the oscilloscope displays. The

conditions have been such that the carrier frequency was always considerably larger

then the message frequency - that is, ω >> µ. In discussions on envelopes this

condition is usually assumed; but is it really necessary ?

For some more insight we will examine the situation as the ratio (ω / µ) is reduced,

so that the relation ω >> µ is no longer satisfied. To do this you will discard the

100 kHz carrier, and use instead a variable source from the VCO.

As a first check, the VCO will be set to the 100 kHz range, and an AM signal

generated, to confirm the performance of the new model.

for all displays to follow, remember to keep the

message waveform (CH1-A) so it just touches the

AM waveform (CH2-A), thus clearly showing the

relationship between the shape of a(t) and e(t).

T6 before plugging in the VCO set it into ‘VCO mode’ with the switch located on

the circuit board. Select the HI frequency range with the front panel

toggle switch. Plug it in, and set the frequency to approximately

100 kHz

T7 set the message frequency from the AUDIO OSCILLATOR to, say, 1 kHz.

T8 remove the patch cord from the 100 kHz sine wave of the MASTER SIGNALS

module, and connect it to the analog output of the VCO.

T9 confirm that the new model can generate AM, and then adjust the depth of

modulation to somewhere between say 50% and 100%,

A clear indication of what we call the envelope will be needed; since this is AM,

with m < 1, this can be provided by the message itself. Do this by shifting the

message, displayed on CH1-A, down to be coincident with the envelope of the

signal on CH2-A. Now prepare for some interesting observations.


T10 slowly vary the VCO frequency over its whole HI range. Most of the time the

display will be similar to that of Figure 1 but it might be possible to

obtain momentary glimpses of the AM signal as it appears in

Figure 6.

If you obtain a momentary display, such as shown in Figure 6, notice how the AM

signal slowly drifts left or right, but always fits within the same boundary, the top

half of which has been simulated by the message on the other trace.

Figure 6: single sweep of a 70% AM

reduction of the carrierreduction of the carrierreduction of the carrierreduction of the carrier----totototo----message freq ratiomessage freq ratiomessage freq ratiomessage freq ratio

The ratio of carrier-to-message frequency so far has been about 100:1.

The mathematical definition of the envelope puts no restraint on the relative size of

ω and µ, except, perhaps, to say that ω ≥ µ.

Can you imagine what would happen to the envelope if this ratio could be reduced

even further ?

To approach this situation, as gently as possible:

T11 rotate the frequency control of the VCO fully clockwise. Change the

frequency range to LO, with the front panel toggle switch.

The AM signal will probably still look like that of Figure 1 But now slowly

decrease the carrier frequency (the VCO), repeating the steps previously taken

when the carrier was 100 kHz.

T12 slowly reduce the VCO frequency, and thus the ratio ( ω /µ). Monitor the

VCO frequency with the FREQUENCY COUNTER, and keep a mental

note of the ratio. Most of the time the display will be similar to that of

Figure 6, although the AM signal will be drifting left and right,

perhaps too fast to see clearly.

Envelopes


As the ratio is lowered, and approaches unity, visualization of the envelope

becomes more difficult (especially if the message is not being displayed as well).

You see that, despite this, the signal is still neatly confined by the same envelope,

represented by the message. For these low ratios of ( ω / µ) the AM signal can no

longer be considered narrowband.

A very interesting case is obtained when ω ≈ 2µ

T13 set the VCO close to 2 kHz. With the 1 kHz message this makes the carrier-

to-message ratio approximately 2. Tune the VCO carefully until the

AM is drifting slowly left or right. The ‘AM’ signal, for such it is by

mathematical definition, will be changing shape all the time. None-

the-less, it will still be asymptotic to the signal which is defined as the

envelope.

Note that the definition of envelope still applies, although it is difficult to visualize

without some help, as has been seen.

It will be worth your while to spend some time exploring the situation.

other examplesother examplesother examplesother examples

These are just a few simple examples of the validity of the envelope definition. In

later experiments you will meet other modulated signals, and be seeing their

envelopes. Interesting examples will be that of the single sideband (SSB) signal,

and Armstrong`s signal (see experiments within Volume A2 - Further & Advanced

Analog Experiments). These, and all others, will verify the definition.

unreliable oscilloscope triggering.unreliable oscilloscope triggering.unreliable oscilloscope triggering.unreliable oscilloscope triggering.

Note that in this experiment the oscilloscope was always triggered externally to the

message. The envelope is related to the message, and we want the envelope

stationary on the screen.

It is bad practice, but common with the inexperienced, to synchronize the

oscilloscope directly to the display being examined, rather than to use an

independent (but well chosen) signal.

To emphasise this point:

T14 restore the carrier to the 100 kHz region, and the depth of modulation to

'100% AM'. Display this, as an AM signal, on CH2-A.

T15 set the oscilloscope trigger control to 'internal, channel 2'.

T16 adjust the oscilloscope controls so that the envelope is stationary. Although

the method is not recommended, this will probably be possible. If not,

then the point is made !

T17 slowly reduce the depth of modulation, until synchronization is lost.


What should be done to restore synchronization ? The inexperienced user generally

tries a few haphazard adjustments of the oscilloscope sweep controls until (with

luck) the display becomes stationary. It is surely an unsatisfactory arrangement to

readjust the oscilloscope every time the depth of modulation is changed.

If you restore the oscilloscope triggering to the previous state (as per Figure 5) then

you will note that no matter what the depth of modulation, synchronism cannot be

lost.

synchrsynchrsynchrsynchronization to an offonization to an offonization to an offonization to an off----air signalair signalair signalair signal

If a modulated signal is received ‘off-air’, then there is no direct access to the

message. This would be the case if you are sent such a signal via TRUNKS. How

then can one trigger the oscilloscope to display a stationary envelope ?

What is required is a copy of the envelope. This can be obtained from an envelope

detector. See the experiment entitled Envelope recovery.

use of phasorsuse of phasorsuse of phasorsuse of phasors

This experiment has introduced you to the definition of the envelope of a

narrowband signal. If you can define a signal analytically then you should be able

to obtain an expression for its envelope. Visualization of the shape of this

expression may not be easy, but you can always model it with TIMS.

You should be able to predict the shape of envelopes without necessarily looking at

them on an oscilloscope. Graphical construction using phasors gives a good idea of

the shape of the envelope, and can give precise values of salient features, such as

amplitudes of troughs and peaks, and the time interval between them.


Q1 use phasors to construct the envelope of (a) an AM signal and (b) a DSBSC

signal.

Q2 use phasors to construct the envelope of the sum of a DSBSC and a large

carrier, when the phase difference between these two is not zero (as it

is for AM). The technique should quickly convince you that the

envelope is no longer a sine wave, although it may be tedious to

obtain an exact shape.

Q3 what is meant by ‘selective fading’ ? How would this affect the envelope of

an envelope modulated signal ?


ENVELOPE RECOVERYENVELOPE RECOVERYENVELOPE RECOVERYENVELOPE RECOVERY

PREPARATION................................................................................ 2

the envelope.............................................................................. 2

the diode detector ..................................................................... 2

the ideal envelope detector........................................................ 3

the ideal rectifier ................................................................................... 3

envelope bandwidth ............................................................................... 3

DSBSC envelope ................................................................................... 4

EXPERIMENT.................................................................................. 5

the ideal model ......................................................................... 5

AM envelope ......................................................................................... 5

DSBSC envelope ................................................................................... 7

speech as the message; m < 1................................................................ 8

speech as the message; m > 1................................................................ 8

the diode detector ..................................................................... 9


APPENDIX A ................................................................................. 11

analysis of the ideal detector ................................................... 11

practical modification .......................................................................... 12


ENVELOPE RECOVERYENVELOPE RECOVERYENVELOPE RECOVERYENVELOPE RECOVERY

ACHIEVEMENTS: The ideal ‘envelope detector’ is defined, and then modelled. It

is shown to perform well in all cases examined. The limitations of the

‘diode detector’, an approximation to the ideal, are examined.

Introduction to the HEADPHONE AMPLIFIER module.

PREREQUISITES: completion of the experiment entitled Envelopes in this

Volume.


the envelopethe envelopethe envelopethe envelope

You have been introduced to the definition of an envelope in the experiment

entitled Envelopes. There you were reminded that the envelope of a signal y(t) is

that boundary within which the signal is contained, when viewed in the time

domain. It is an imaginary line.

Although the envelope is imaginary in the sense described above, it is possible to

generate, from y(t), a signal e(t), having the same shape as this imaginary line.

The circuit which does this is commonly called an envelope detector. A better

word for envelope detector would be envelope generator, since that is what these

circuits do.

It is the purpose of this experiment for you to model circuits which will generate

these envelope signals.

the diode detectorthe diode detectorthe diode detectorthe diode detector

The ubiquitous diode detector is the prime example of an envelope generator. It is

well documented in most textbooks on analog modulation. It is synonymous with

the term ‘envelope demodulator’ in this context.

But remember: the diode detector is an approximation to the ideal. We will first

examine the ideal circuit.

Envelope recovery


the ideal envelope detector.the ideal envelope detector.the ideal envelope detector.the ideal envelope detector.

The ideal envelope detector is a circuit which takes the absolute value of its input,

and then passes the result through a lowpass filter. The output from this lowpass

filter is the required envelope signal. See Figure 1.

Absolute value

operator LPFin

envelope out

Figure 1: the ideal envelope recovery arrangement

The truth of the above statement will be tested for some extreme cases in the work

to follow; you can then make your own conclusions as to its veracity.

The absolute value operation, being non-linear, must generate some new frequency

components. Among them are those of the wanted envelope. Presumably, since the

arrangement actually works, the unwanted components lie above those wanted

components of the envelope.

It is the purpose of the lowpass filter to separate the

wanted from the unwanted components generated by

the absolute value operation.

The analysis of the ideal envelope recovery circuit, for the case of a general input

signal, is not a trivial mathematical exercise, the operation being non-linear. So it

is not easy to define beforehand where the unwanted components lie. See the

Appendix to this experiment for the analysis of a special case.

the ideal rectifierthe ideal rectifierthe ideal rectifierthe ideal rectifier

A circuit which takes an absolute value is a fullwave rectifier. Note carefully that

the operation of rectification is non-linear. The so-called ideal rectifier is a

precision realization of a rectifier, using an operational amplifier and a diode in a

negative feedback arrangement. It is described in text books dealing with the

applications of operational amplifiers to analog circuits. An extension of the

principle produces an ideal fullwave rectifier.

You will find a halfwave rectifier is generally adequate for use in an envelope

recovery circuit. Refer to the Appendix to this experiment for details.

envelope bandwidthenvelope bandwidthenvelope bandwidthenvelope bandwidth

You know what a lowpass filter is, but what should be its cut-off frequency in this

application ? The answer: ‘the cut-off frequency of the lowpass filter should be

high enough to pass all the wanted frequencies in the envelope, but no more’. So

you need to know the envelope bandwidth.


In a particular case you can determine the expression for the envelope from the

definition given in the experiment entitled Envelopes, and the bandwidth by

Fourier series analysis. Alternatively, you can estimate the bandwidth, by

inspecting its shape on an oscilloscope, and then applying rules of thumb which

give quick approximations.

An envelope will always include a constant, or DC, term.

This is inevitable from the definition of an envelope - which includes the operation

of taking the absolute value. It is inevitable also in the output of a practical circuit,

by the very nature of rectification.

The presence of this DC term is often forgotten. For the case of an AM signal,

modulated with music, the DC term is of little interest to the listener. But it is a

direct measure of the strength of the carrier term, and so is used as an automatic

gain control signal in receivers.

It is important to note that it is possible for the bandwidth of the envelope to be

much wider than that of the signal of which it is the envelope. In fact, except for

the special case of the envelope modulated signal, this is generally so. An obvious

example is that of the DSBSC signal derived from a single tone message.

DSBSC envelopeDSBSC envelopeDSBSC envelopeDSBSC envelope

The bandwidth of a DSBSC signal is twice that of the highest modulating

frequency. So, for a single tone message of 1 kHz, the DSBSC bandwidth is 2 kHz.

But the bandwidth of the envelope is many times this.

For example, we know that, analytically:

DSBSC = cosµt.cosωt ........ 1

= a(t).cos[ωot + ϕ(t)] ........ 2

because µ << ω then a(t) = cosµt ........ 3

ϕ(t) = 0 ........ 4

and envelope e(t) = | a(t) | (by definition) ........ 5

So:

• from the mathematical definition the envelope shape is that of the absolute

value of cosµt. This has the shape of a fullwave rectified version of cosµt.

• by looking at it, and from considerations of Fourier series analysis 1, the

envelope must have a wide bandwidth, due to the sharp discontinuities in its

shape. So the lowpass filter will need to have a bandwidth wide enough to

pass at least the first few odd harmonics of the 1 kHz message; say a

passband extending to at least 10 kHz ?

1 see the section on Fourier series and bandwidth estimation in the chapter entitled Introduction to

modelling with TIMS, in this Volume

Envelope recovery



the ideal modelthe ideal modelthe ideal modelthe ideal model

The TIMS model of the ideal envelope detector is shown in block diagram form in

Figure 2.

PRECISION RECTIFIER

within

UTILITIES module

LPFin out

Figure 2: modelling the ideal envelope detector with TIMS

The ‘ideal rectifier’ is easy to build, does in fact approach the ideal for our

purposes, and one is available as the RECTIFIER in the TIMS UTILITIES module.

For purposes of comparison, a diode detector, in the form of ‘DIODE + LPF’, is

also available in the same module; this will be examined later.

The desirable characteristics of the lowpass filter will depend upon the frequency

components in the envelope of the signal as already discussed.

We can easily check the performance of the ideal envelope detector in the

laboratory, by testing it on a variety of signals.

The actual envelope shape of each signal can be displayed by observing the

modulated signal itself with the oscilloscope, suitably triggered.

The output of the envelope detector can be displayed, for comparison, on the other

channel.

AM envelopeAM envelopeAM envelopeAM envelope

For this part of the experiment we will use the generator of Figure 3, and connect

its output to the envelope detector of Figure 2.


c(t)

test signal

g

G

DC voltage

a(t) m(t)

µµµµmessage

( )

100kHz

ωωωω( )

Figure 3: generator for AM and DSBSC

T1 plug in the TUNEABLE LPF module. Set it to its widest bandwidth, which is

about 12 kHz (front panel toggle switch to WIDE, and TUNE control

fully clockwise). Adjust its passband gain to about unity. To do this

you can use a test signal from the AUDIO OSCILLATOR, or perhaps

the 2 kHz message from the MASTER SIGNALS module.

T2 model the generator of Figure 3, and connect its output to an ideal envelope

detector, modelled as per Figure 2. For the lowpass filter use the

TUNEABLE LPF module. Your whole system might look like that

shown modelled in Figure 4 below.

CH1-A ext. trig

GENERATOR

ENVELOPE

RECOVERY

CH2-A

CH1-B spare

CH2-B

Figure 4: modulated signal generator and envelope recovery

T3 set the frequency of the AUDIO OSCILLATOR to about 1 kHz. This is your

message.

T4 adjust the triggering and sweep speed of the oscilloscope to display two

periods of the message (CH2-A).

Envelope recovery


T5 adjust the generator to produce an AM signal, with a depth of modulation less

than 100%. Don`t forget to so adjust the ADDER gains that its output

(DC + AC) will not overload the MULTIPLIER; that is, keep the

MULTIPLIER input within the bounds of the TIMS ANALOG

REFERENCE LEVEL (4 volt peak-to-peak). This signal is not

symmetrical about zero volts; neither excursion should exceed the

2 volt peak level.

T6 for the case m < 1 observe that the output from the filter (the ideal envelope

detector output) is the same shape as the envelope of the AM signal -

a sine wave.

DSBSC envelopeDSBSC envelopeDSBSC envelopeDSBSC envelope

Now let us test the ideal envelope detector on a more complex envelope - that of a

DSBSC signal.

T7 remove the carrier from the AM signal, by turning ‘g’ fully anti-clockwise,

thus generating DSBSC. Alternatively, and to save the DC level just

used, pull out the patch cord from the ‘g’ input of the ADDER (or

switch the MULTIPLIER to AC).

Were you expecting to see the waveforms of Figure 5 ? What did you see ?

Figure 5: a DSBSC signal

You may not have seen the expected waveform. Why not ?

With a message frequency of 2 kHz, a filter bandwidth of about 12 kHz is not wide

enough.

You can check this assertion; for example:

a) lower the message frequency, and note that the recovered envelope shape

approaches more closely the expected shape.

b) change the filter. Try a 60 kHz LOWPASS FILTER.


T8 (a) lower the frequency of the AUDIO OSCILLATOR, and watch the shape

of the recovered envelope. When you think it is a better

approximation to expectations, note the message frequency, and the

filter bandwidth, and compare with predictions of the bandwidth of a

fullwave rectified sinewave.

(b) if you want to stay with the 2 kHz message then replace the TUNEABLE

LPF with a 60 kHz LOWPASS FILTER. Now the detector output

should be a good copy of the envelope.

speech as the mespeech as the mespeech as the mespeech as the message; mssage; mssage; mssage; m <<<< 1111

Now try an AM signal, with speech from a SPEECH module, as the message.

To listen to the recovered speech, use the HEADPHONE AMPLIFIER.

The HEADPHONE AMPLIFIER enables you to listen to an audio signal connected

to its input. This may have come via an external lowpass filter, or via the internal

3 kHz LOWPASS FILTER. The latter is switched in and out by the front panel

switch. Refer to the TIMS User Manual for more information.

Only for the case of envelope modulation, with the depth of modulation 100% or

less, will the speech be intelligible. If you are using a separate lowpass filter,

switching in the 3 kHz LPF of the HEADPHONE AMPLIFIER as well should make

no difference to the quality of the speech as heard in the HEADPHONES, because

the speech at TRUNKS has already been bandlimited to 3 kHz.

speech as the message; mspeech as the message; mspeech as the message; mspeech as the message; m >>>> 1111

Don't forget to listen to the recovered envelope when the depth of modulation is

increased beyond 100%. This will be a distorted version of the speech.

Distortion is usually thought of as having been caused by some circuit imperfection.

There is no circuit imperfection occurring here !

The envelope shape, for all values of m, including m > 1, is as exactly as theory

predicts, using ideal circuitry.

The envelope recovery circuit you are using is close to ideal; this may not be

obvious when listening to speech, but was confirmed earlier when recovering the

wide-band envelope of a DSBSC.

The distortion of the speech arises quite naturally from the fact that there is a non-

linear relationship between the message and the envelope, attributed directly to the

absolute sign in eqn. (5).

Envelope recovery


the diode detectorthe diode detectorthe diode detectorthe diode detector

It is assumed you will have referred to a text book on the subject of the diode

detector. This is an approximation to the ideal rectifier and lowpass filter.

How does it perform on these signals and their envelopes ?

There is a DIODE DETECTOR in the UTILITIES MODULE. The diode has not

been linearized by an active feedback circuit, and the lowpass filter is approximated

by an RC network. Your textbook should tell you that this is a good engineering

compromise in practice, provided:

a) the depth of modulation does not approach 100%

b) the ratio of carrier to message frequency is ‘large’.

You can test these conditions with TIMS. The patching arrangement is simple.

T9 connect the signal, whose envelope you wish to recover, directly to the

ANALOG INPUT of the ‘DIODE + LPF’ in the UTILITIES MODULE,

and the envelope (or its approximation) can be examined at the

ANALOG OUTPUT. You should not add any additional lowpass

filtering, as the true ‘diode detector’ uses only a single RC network

for this purpose, which is already included.

The extreme cases you could try would include:

a) an AM signal with depth of modulation say 50%, and a message of 500 Hz.

What happens when the message frequency is raised ? Is ω >> µ ?

b) a DSBSC. Here the inequality ω >> µ is meaningless. This inequality applies

to the case of AM with m < 1. It would be better expressed, in the present

instance, as ‘he carrier frequency ω must be very much higher than the highest

frequency component expected in the envelope’. This is certainly NOT so here.

T10 repeat the previous Task, but with the RECTIFIER followed by a simple RC

filter. This compromise arrangement will show up the shortcomings

of the RC filter. There is an independent RC LPF in the UTILITIES

MODULE. Check the TIMS User Manual regarding the time

constant.

T11 you can examine various combinations of diode, ideal rectifier, RC and

other lowpass filters, and lower carrier frequencies (use the VCO).

The 60 kHz LPF is a very useful filter for envelope work.

T12 check by observation: is the RECTIFIER in the UTILITIES MODULE a

halfwave or fullwave rectifier ?


TUTORITUTORITUTORITUTORIAL QUESTIONSAL QUESTIONSAL QUESTIONSAL QUESTIONS

Q1 an analysis of the ideal envelope detector is given in the Appendix to this

experiment. What are the conditions for there to be no distortion

components in the recovered envelope ?

Q2 analyse the performance of a square-law device as an envelope detector,

assuming an ideal filter may be used. Are there any distortion

components in the recovered envelope ?

Q3 explain the major difference differences in performance between envelope

detectors with half and fullwave rectifiers.

Q4 define what is meant by ‘selective fading’. If an amplitude modulated signal

is undergoing selective fading, how would this affect the performance

of an envelope detector as a demodulator ?

Envelope recovery


APPENDIX AAPPENDIX AAPPENDIX AAPPENDIX A

analysis of the ideal deanalysis of the ideal deanalysis of the ideal deanalysis of the ideal detectortectortectortector

The aim of the rectifier is to take the absolute value of the signal being rectified.

That is, to multiply it by +1 when it is positive, and -1 when negative.

An analysis of the ideal envelope detector is not a trivial exercise, except in special

cases. Such a special case is when the input signal is an envelope modulated signal

with m < 1.

In this case we can make the following assumption, not proved here, but verified by

practical measurement and observations, namely: the zero crossings of an AM

signal, for m < 1, are uniform, and spaced at half the period of the carrier.

If this is the case, then the action of an ideal rectifier on such a signal is equivalent

to multiplying it by a square wave s(t) as per Figure 1A. It is important to ensure

that the phases of the AM and s(t) are matched correctly in the analysis; in the

practical circuit this is done automatically.

Figure 1A: the function s(t) and its operation upon an AM signal

The Fourier series expansion of s(t), as illustrated, is given by:

s(t) = 4/π [1.cosωt - 1/3.cos3ωt + 1/5.cos5ωt - ..... ] .................... A1

Thus s(t) contains terms in all odd harmonics of the carrier frequency

The input to the lowpass filter will be the rectifier output, which is:

rectifier output = s(t) . AM .................... A2

Note that the AM is centred on ‘ω’, and s(t) is a string of terms on the ODD

harmonics of ω. Remembering also that the product of two sinewaves gives ‘sum

and difference’ terms, then we conclude that:

• the 1st harmonic in s(t) gives a term near DC and another centred at 2ω


• the 3rd harmonic in s(t) gives a term at 2ω and 4ω

• the 5th harmonic in s(t) gives a term at 4ω and 6ω

• and so on

We define the AM signal as:

AM = A [1 + m(t)] cosωt .................... A3

where, for the depth of modulation to be less than 100%, |m(t)| < 1.

From the rectified output we are only interested in any term near DC; this is the

one we can hear. In more detail:

term near DC = (1/2).(4/π).A.m(t) .................... A4

which is an exact, although scaled, copy of the message m(t).

The other terms are copies of the original AM, but on all even multiples of the

carrier, and of decreasing amplitudes. They are easily removed with a lowpass

filter. The nearest unwanted term is a scaled version of the original AM on a

carrier frequency 2ω rad/s.

For the case where the carrier frequency is very much higher than the highest

message frequency, that is when ω >> µ, an inequality which is generally satisfied,

the lowpass filter can be fairly simple. Should the carrier frequency not satisfy this

inequality, we can still see that the message will be recovered UNDISTORTED so

long as the carrier frequency is at least twice the highest message frequency, and a

filter with a steeper transition band is used.

practical modificationpractical modificationpractical modificationpractical modification

In practice it is easier to make a halfwave than a fullwave rectifier. This means

that the expression for s(t) will contain a DC term, and the magnitudes of the other

terms will be halved. The effect of this DC term in s(t) is to create an extra term in

the output, namely a scaled copy of the input signal.

This is an extra unwanted term, centred on ω rad/s, and in fact the lowest frequency

unwanted term. The lowest frequency unwanted term in the fullwave rectified

output is centred on 2ω rad/s.

This has put an extra demand upon the lowpass filter. This is not significant when

ω >> µ, but will become so for lower carrier frequencies.

ω ω2 ω4 frequency

wanted unwanted

present only withhalfwave rectifier

ω6µ

Figure 2A: rectifier output spectrum (approximate scale)


SSB GENERATION SSB GENERATION SSB GENERATION SSB GENERATION ---- THE PHASING THE PHASING THE PHASING THE PHASING

METHODMETHODMETHODMETHOD

PREPARATION ................................................................................2

the filter method .................................................................................... 2

the phasing method................................................................................ 2

Weaver’s method ................................................................................... 3

the SSB signal ...........................................................................3

the envelope........................................................................................... 3

generator characteristics ............................................................4

a phasing generator................................................................................ 4

performance criteria............................................................................... 6

EXPERIMENT ..................................................................................7

the QPS.....................................................................................7

phasing generator model............................................................8

performance measurement.........................................................9

degree of modulation - PEP ....................................................11

determining rated PEP......................................................................... 12

practical observation ...............................................................12



SSB GENERATION SSB GENERATION SSB GENERATION SSB GENERATION ---- THE THE THE THE

PHASING METHODPHASING METHODPHASING METHODPHASING METHOD

ACHIEVEMENTS: introduction to the QUADRATURE PHASE SPLITTER

module (QPS); modelling the phasing method of SSB generation;

estimation of sideband suppression; definition of PEP.

PREREQUISITES: an acquaintance with DSBSC generation, as in the

experiment entitled DSBSC generation, would be an advantage.

PRPRPRPREPARATION EPARATION EPARATION EPARATION

There are three well known methods of SSB generation using analog techniques,

namely the filter method, the phasing method, and Weaver’s method. This

experiment will study the phasing method.

the filter methodthe filter methodthe filter methodthe filter method

You have already modelled a DSBSC signal.

An SSB signal may be derived from this by the use of a suitable bandpass filter -

commonly called, in this application, an SSB sideband filter. This, the filter

method, is probably the most common method of SSB generation. Mass

production has given rise to low cost, yet high performance, filters. But these

filters are generally only available at ‘standard’ frequencies (for example

455 kHz, 10.7 MHz) and SSB generation by the filter method at other

frequencies can be expensive. For this reason TIMS no longer has a 100 kHz

SSB filter module, although a decade ago these were in mass production and

relatively inexpensive 1.

the phasing methodthe phasing methodthe phasing methodthe phasing method

The phasing method of SSB generation, which is the subject of this experiment,

does not require an expensive filter, but instead an accurate phasing network, or

1 analog frequency division multiplex, where these filters were used, has been superseded by time division multiplex

SSB generation - the phasing method


quadrature phase splitter (QPS). It is capable of acceptable performance in

many applications.

The QPS operates at baseband, no matter what the carrier frequency (either

intermediate or final), in contrast to the filter of the filter method.

Weaver’s methodWeaver’s methodWeaver’s methodWeaver’s method

In 1956 Weaver published a paper on what has become known either as ‘the

third method’, or ‘Weaver`s method’, of SSB generation 2.

Weaver’s method can be modelled with TIMS - refer to the experiment entitled

Weaver`s SSB generator (within Volume A2 - Further & Advanced Analog

Experiments).

the SSB signalthe SSB signalthe SSB signalthe SSB signal

Recall that, for a single tone message cosµt, a DSBSC signal is defined by:

DSBSC = A.cosµt.cosωt ......... 1

= A/2.cos(ω - µ)t + A/2.cos(ω + µ)t ......... 2

= lower sideband + upper sideband ......... 3

When, say, the lower sideband (LSB) is removed, by what ever method, then the

upper sideband (USB) remains.

USB = A/2.cos(ω + µ)t ......... 4

This is a single frequency component at frequency (ω + µ)/(2.π) Hz. It is a

(co)sine wave. Viewed on an oscilloscope, with the time base set to a few periods

of ω, it looks like any other sinewave.

What is its envelope ?

the envelopethe envelopethe envelopethe envelope

The USB signal of eqn. (4) can be written in the form introduced in the

experiment on Envelopes in this Volume. Thus:

USB = a(t).cos[(ω + µ)t + ϕ(t)] ........ 5

The envelope has been defined as:

envelope = | a(t) | ........ 6

= A/2 [from eqn. (4)] ........ 7

Thus the envelope is a constant (ie., a straight line) and the oscilloscope,

correctly set up, will show a rectangular band of colour across the screen.

2 Weaver, D.K., “A third method of generation and detection of single sideband signals”, Proc. IRE, Dec.

1956, pp. 1703-1705


This result may seem at first confusing. One tends to ask: ‘where is the message

information’ ?

answer: the message amplitude information is contained in the

amplitude of the SSB, and the message frequency information is

contained in the frequency offset, from ω, of the SSB.

An SSB derived from a single tone message is a very simple example. When the

message contains more components the SSB envelope is no longer a straight line.

Here is an important finding !

An ideal SSB generator, with a single tone message,

should have a straight line for an envelope.

Any deviation from this suggests extra components in the SSB itself. If there is

only one extra component, say some ‘leaking’ carrier, or an unwanted sideband

not completely suppressed, then the amplitude and frequency of the envelope will

identify the amplitude and frequency of the unwanted component.

generator characteristicsgenerator characteristicsgenerator characteristicsgenerator characteristics

A most important characteristic of any SSB generator is the amount of out-of-

band energy it produces, relative to the wanted output. In most cases this is

determined by the degree to which the unwanted sideband is suppressed 3. A

ratio of wanted-to-unwanted output power of 40 dB was once considered

acceptable commercial performance; but current practice is likely to call for a

suppression of 60 dB or more, which is not a trivial result to achieve.

a phasing generator.a phasing generator.a phasing generator.a phasing generator.

The phasing method of SSB generation is based on the addition of two DSBSC

signals, so phased that their upper sidebands (say) are identical in phase and

amplitude, whilst their lower sidebands are of similar amplitude but opposite

phase.

The two out-of-phase sidebands will cancel if added; alternatively the in-phase

sidebands will cancel if subtracted.

The principle of the SSB phasing generator in illustrated in Figure 1.

Notice that there are two 90o phase changers. One operates at carrier frequency,

the other at message frequencies.

The carrier phase changer operates at a single, fixed frequency, ω rad/s.

3 but this is not the case for Weaver's method



The message is shown as a single tone at frequency µ rad/s. But this can lie

anywhere within the frequency range of speech, which covers several octaves. A

network providing a constant 90o phase shift over this frequency range is very

difficult to design. This would be a wideband phase shifter, or Hilbert

transformer.

ωcos t

ΣSSB

DSB

DSBQ

Q

µcos t(message)

π/2π/2

II

Figure 1: principle of the SSB Phasing Generator

In practice a wideband phase splitter is used. This is shown in the arrangement

of Figure 2.

ωcos tµcos t(message)

QPS ΣSSB

DSB

DSBQ

Q

Q

π/2

I

I

I

Figure 2: practical realization of the SSB phasing generator

The wideband phase splitter consists of two complementary networks - say I

(inphase) and Q (quadrature). When each network is fed from the same input

signal the phase difference between the two outputs is maintained at 90o. Note

that the phase difference between the common input and either of the outputs is

not specified; it is not independent of frequency.

Study Figures 1 and 2 to ensure that you appreciate the difference.

At the single frequency µ rad/s the arrangements of Figure 1 and Figure 2 will

generate two DSBSC. These are of such relative phases as to achieve the

cancellation of one sideband, and the reinforcement of the other, at the summing

output.


You should be able to confirm this. You could use graphical methods (phasors)

or trigonometrical analysis.

The QPS may be realized as either an active or passive circuit, and depends for

its performance on the accuracy of the components used. Over a wide band of

audio frequencies, and for a common input, it maintains a phase difference

between the two outputs of 90 degrees, with a small frequency-dependant error

(typically equiripple).

performance criteriaperformance criteriaperformance criteriaperformance criteria

As stated earlier, one of the most important measures of performance of an SSB

generator is its ability to eliminate (suppress) the unwanted sideband. To

measure the ratio of wanted-to-unwanted sideband suppression directly requires a

SPECTRUM ANALYSER. In commercial practice these instruments are very

expensive, and their purchase cannot always be justified merely to measure an

SSB generator performance.

As always, there are indirect methods of measurement. One such method

depends upon a measurement of the SSB envelope, as already hinted.

Suppose that the output of an SSB generator, when the message is a single tone

of frequency µ rad/s, consists only of the wanted sideband W and a small amount

of the unwanted sideband U.

It may be shown that, for U << W, the envelope is nearly sinusoidal and of a

frequency equal to the frequency difference of the two components.

Thus the envelope frequency is (2µ) rad/s.

Figure 3 : measuring sideband suppression via the envelope

It is a simple matter to measure the peak-to-peak and the trough-to-trough

amplitudes, giving twice P, and twice Q, respectively. Then:

P = W + U ................ 6

Q = W - U ................ 7

as seen from the phasor diagram. This leads directly to:

sideband suppression = 20 10log [ ]

P Q

P QdB

+

− ........ 8



If U is in fact the sum of several small components then an estimate of the

wanted to unwanted power ratio can still be made. Note that it would be greater

(better) than for the case where U is a single component.

A third possibility, the most likely in a good design, is that the envelope becomes

quite complex, with little or no stationary component at either µ or µ/2; in this

case the unwanted component(s) are most likely system noise.

Make a rough estimate of the envelope magnitude, complex in shape though it

may well be, and from this can be estimated the wanted to unwanted suppression

ratio, using eqn.(8). This should turn out to be better than 26 dB in TIMS, in

which case the system is working within specification. The TIMS QPS module

does not use precision components, nor is it aligned during manufacture. It gives

only a moderate sideband suppression, but it is ideal for demonstration purposes.

Within the ‘working frequency range’ of the QPS the phase error from 900

between the two outputs will vary with frequency (theoretically in an equi-ripple

manner).


the QPSthe QPSthe QPSthe QPS

Refer to the TIMS User Manual for information about the QUADRATURE

PHASE SPLITTER - the ‘QPS’.

Before patching up an SSB phasing generator system, first examine the

performance of the QUADRATURE PHASE SPLITTER module. This can be

done with the arrangement of Figure 4.

QPS

Q

in

OSCILLOSCOPEI

Figure 4: arrangement to check QPS performance

With the oscilloscope adjusted to give equal gain in each channel it should show

a circle. This will give a quick confirmation that there is a phase difference of

approximately 90 degrees between the two output sinewaves at the measurement

frequency. Phase or amplitude errors should be too small for this to degenerate


visibly into an ellipse. The measurement will also show the bandwidth over

which the QPS is likely to be useful.

T1 set up the arrangement of Figure 4. The oscilloscope should be in X-Y

mode, with equal sensitivity in each channel. For the input signal

source use an AUDIO OSCILLATOR module. For correct QPS

operation the display should be an approximate circle. We will not

attempt to measure phase error from this display.

T2 vary the frequency of the AUDIO OSCILLATOR, and check that the

approximate circle is maintained over at least the speech range of

frequencies.

phasing generator modelphasing generator modelphasing generator modelphasing generator model

When satisfied that the QPS is operating satisfactorily, you are now ready to

model the SSB generator. Once patched up, it will be necessary to adjust

amplitudes and phases to achieve the desired result. A hit-and-miss method can

be used, but a systematic method is recommended, and will be described now.

CH1-A

ext. trig

CH2-A

CH1-B

various

Figure 5: the SSB phasing generator model

T3 patch up a model of the phasing SSB generator, following the arrangement

illustrated in Figure 5. Remember to set the on-board switch of the

PHASE SHIFTER to the ‘HI’ (100 kHz) range before plugging it in.

T4 set the AUDIO OSCILLATOR to about 1 kHz

T5 switch the oscilloscope sweep to ‘auto’ mode, and connect the ‘ext trig’ to

an output from the AUDIO OSCILLATOR. It is now synchronized

to the message.



T6 display one or two periods of the message on the upper channel CH1-A of

the oscilloscope for reference purposes. Note that this signal is

used for external triggering of the oscilloscope. This will maintain

a stationary envelope while balancing takes place. Make sure you

appreciate the convenience of this mode of triggering.

Separate DSBSC signals should already exist at the output of each

MULTIPLIER. These need to be of equal amplitudes at the output of the

ADDER. You will set this up, at first approximately and independently, then

jointly and with precision, to achieve the required output result.

T7 check that out of each MULTIPLIER there is a DSBSC signal.

T8 turn the ADDER gain ‘G’ fully anti-clockwise. Adjust the magnitude of the

other DSBSC, ‘g’, of Figure 5, viewed at the ADDER output on

CH2-A, to about 4 volts peak-to-peak. Line it up to be coincident

with two convenient horizontal lines on the oscilloscope graticule

(say 4 cm apart).

T9 remove the ‘g’ input patch cord from the ADDER. Adjust the ‘G’ input to

give approximately 4 volts peak-to-peak at the ADDER output,

using the same two graticule lines as for the previous adjustment.

T10 replace the ‘g’ input patch cord to the ADDER.

The two DSBSC are now appearing simultaneously at the ADDER output.

Now use the same techniques as were used for balancing in the experiment

entitled Modelling an equation in this Volume. Choose one of the ADDER gain

controls (‘g’ or ‘G’) for the amplitude adjustment, and the PHASE SHIFTER for

the carrier phase adjustment.

The aim of the balancing procedure is to

produce an SSB at the ADDER output.

The amplitude and phase adjustments are non-interactive.

performance measurementperformance measurementperformance measurementperformance measurement

Since the message is a sine wave, the SSB will also be a sine wave when the

system is correctly adjusted. Make sure you agree with this statement before

proceeding.


The oscilloscope sweep speed should be such as to display a few periods of the

message across the full screen. This is so that, when looking at the SSB, a

stationary envelope will be displayed.

Until the system is adjusted the display will look more like a DSBSC, or even an

AM, than an SSB.

Remote from balance the envelope should be stationary, but perhaps not

sinusoidal. As the balance condition is approached the envelope will become

roughly sinusoidal, and its amplitude will reduce. Remember that the pure SSB

is going to be a sinewave 4. As discussed earlier, if viewed with an appropriate

time scale, which you have already set up, this should have a constant (‘flat’)

envelope.

This is what the balancing procedure is aiming to achieve.

T11 balance the SSB generator so as to minimize the envelope amplitude.

During the process it may be necessary to increase the oscilloscope

sensitivity as appropriate, and to shift the display vertically so that

the envelope remains on the screen.

T12 when the best balance has been achieved, record results, using Figure 3 as

a guide. Although you need the magnitudes P and Q, it is more

accurate to measure

a) 2P directly, which is the peak-to-peak of the SSB

b) Q indirectly, by measuring (P-Q), which is the peak-to-

peak of the envelope.

As already stated, the TIMS QPS is not a precision device, and a

sideband suppression of better than 26 dB is unlikely.

You will not achieve a perfectly flat envelope. But its amplitude may be small or

comparable with respect to the noise floor of the TIMS system.

The presence of a residual envelope can be due to any one or more of:

• leakage of a component at carrier frequency (a fault of one or other

MULTIPLIER 5)

• incomplete cancellation of the unwanted sideband due to imperfections of

the QPS 6.

• distortion components generated by the MULTIPLIER modules.

• other factors; can you suggest any ?

Any of the above will give an envelope ripple period comparable with the period

of the message, rather than that of the carrier. Do you agree with this

statement ?

If the envelope shape is sinusoidal, and the frequency is:

4 for the case of a single-tone message, as you have

5 the TIMS user is not able to make adjustments to a MULTIPLIER balance

6 there is no provision for adjustments to the QPS



• twice that of the message, then the largest unwanted component is due to

incomplete cancellation of the unwanted sideband.

• the same as the message, then the largest unwanted component is at carrier

frequency (‘carrier leak’).

If it is difficult to identify the shape of the envelope, then it is probably a

combination of these two; or just the inevitable system noise. An engineering

estimate must then be made of the wanted-to-unwanted power ratio (which could

be a statement of the form ‘better than 45 dB’), and an attempt made to describe

the nature of these residual signals.

T13 if not already done so, use the FREQUENCY COUNTER to identify your

sideband as either upper (USSB) or lower (LSSB). Record also the

exact frequency of the message sine wave from the AUDIO

OSCILLATOR. From a knowledge of carrier and message

frequencies, confirm your sideband is on one or other of the

expected frequencies.

To enable the sideband identification to be confirmed analytically

(see Question below) you will need to make a careful note of the

model configuration, and in particular the sign and magnitude of

the phase shift introduced by the PHASE SHIFTER, and the sign of

the phase difference between the I and Q outputs of the QPS.

Without these you cannot check results against theory.

degree of modulation degree of modulation degree of modulation degree of modulation ---- PEP PEP PEP PEP

The SSB generator, like a DSBSC generator, has no ‘depth of modulation’, as

does, for example, an AM generator 7. Instead, the output of an SSB transmitter

may be increased until some part of the circuitry overloads, giving rise to

unwanted distortion components. In a good practical design it is the output

amplifier which should overload first 8. When operating just below the point of

overload the transmitter output amplifier is said to be producing its maximum

peak output power - commonly referred to as the ‘PEP’ - an abbreviation for

‘peak envelope power’.

Depending upon the nature of the message, the amplifier may already have

exceeded its maximum average power output capability. This is generally so

with tones, or messages with low peak-to-average power waveform, but not so

with speech, which has a relatively high peak-to-average power ratio of

approximately 14 dB.

When setting up an SSB transmitter, the message amplitude must be so adjusted

that the rated PEP is not exceeded. This is not a trivial exercise, and is difficult

to perform without the appropriate equipment.

7 which has a fixed amplitude carrier term for reference.

8 why ?


determining rated PEPdetermining rated PEPdetermining rated PEPdetermining rated PEP

The setting up procedure for an SSB transmitter assumes a knowledge of the

transmitter rated PEP. But how is this determined in the first place ? This

question is discussed further in the experiment Amplifier overload.

practical observationpractical observationpractical observationpractical observation

You might be interested to look at both an SSB and a DSBSC signal when

derived from speech. Use a SPEECH module. You can view these signals

simultaneously since the DSBSC is available within the SSB generator.

Q can you detect any difference, in the time domain, between an SSB and a

DSBSC, each derived from (the same) speech ? If so, could you

decide which was which if you could only see one of them ?




Q1 what simple modification(s) to your model would change the output from

the current to the opposite sideband ?

Q2 with a knowledge of the model configuration, and the individual module

properties, determine analytically which sideband (USSB or LSSB)

the model should generate. Check this against the measured result.

Q3 why are mass produced (and, consequently, affordable) 100 kHz SSB filters

not available in the 1990s ?

Q4 what sort of phase error could the arrangement of Figure 4 detect ?

Q5 is the QPS an approximation to the Hilbert transformer ? Explain.

Q6 suggest a simple test circuit for checking QPS modules on the production

line.

Q7 the phasing generator adds two DSBSC signals so phased that one pair of

sidebands adds and the other subtracts. Show that, if the only

error is one of phasing, due to the QPS, the worst-case ratio of

wanted to unwanted sideband, is given by:

SSR dB= 202

10log [cot( )]α

where α is the phase error of the QPS.

Typically the phase error would vary over the frequency range in an

equi-ripple manner, so α would be the peak phase error.

Evaluate the SSR for the case α = 1 degree.

Q8 obtain an expression for the envelope of an SSB signal (derived from a

single tone message) when the only imperfection is a small amount

of carrier ‘leaking’ through. HINT: refer to the definition of

envelopes in the experiment entitled Envelopes in this Volume. At

what ratio of sideband to carrier leak would you say the envelope

was roughly sinusoidal ? note: expressions for the envelope of an

SSB signal, for the general message m(t), involve the Hilbert

transform, and the analytic signal.

Q9 sketch the output of an SSB transmitter, as seen in the time domain, when

the message is two audio tones of equal amplitude. Discuss.

Q10 devise an application for the QPS not connected with SSB.


PRODUCT DEMODULATIONPRODUCT DEMODULATIONPRODUCT DEMODULATIONPRODUCT DEMODULATION ----

SYNCHRONOUS & SYNCHRONOUS & SYNCHRONOUS & SYNCHRONOUS &

ASYNCHRONOUSASYNCHRONOUSASYNCHRONOUSASYNCHRONOUS

INTRODUCTION..............................................................................2

frequency translation .................................................................2

the process............................................................................................. 2

interpretation ......................................................................................... 3

the demodulator ........................................................................4

synchronous operation: ω0 = ω1 ........................................................... 4

carrier acquisition .................................................................................. 5

asynchronous operation: ω0 =/= ω1 ..................................................... 5

signal identification....................................................................5

demodulation of DSBSC........................................................................ 6

demodulation of SSB ............................................................................. 6

demodulation of ISB.............................................................................. 7

EXPERIMENT ..................................................................................7

synchronous demodulation ........................................................7

asynchronous demodulation ......................................................8

SSB reception ........................................................................................ 9

DSBSC reception ................................................................................... 9


TRUNKS ................................................................................12


PRODUCT DEMODULATIONPRODUCT DEMODULATIONPRODUCT DEMODULATIONPRODUCT DEMODULATION ----

SYNCHRONOUS & SYNCHRONOUS & SYNCHRONOUS & SYNCHRONOUS &

ASYNCHRONOUSASYNCHRONOUSASYNCHRONOUSASYNCHRONOUS

ACHIEVEMENTS: frequency translation; modelling of the product

demodulator in both synchronous and asynchronous mode;

identification, and demodulation, of DSBSC, SSB, and ISB.

PREREQUISITES: familiarity with the properties of DSBSC, SSB, and ISB.

Thus completion of the experiment entitled DSBSC generation in

this Volume would be an advantage.

INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION

frequency translationfrequency translationfrequency translationfrequency translation

All of the modulated signals you have seen so far may be defined as narrow band.

They carry message information. Since they have the capability of being based

on a radio frequency carrier (suppressed or otherwise) they are suitable for

radiation to a remote location. Upon receipt, the object is to recover -

demodulate - the message from which they were derived.

In the discussion to follow the explanations will be based on narrow band

signals. But the findings are in no way restricted to narrow band signals; they

happen to be more convenient for purposes of illustration.

the processthe processthe processthe process

When a narrow band signal y(t) is multiplied with a sine wave, two new signals

are created - on the ‘sum and difference’ frequencies.

Figure 1 illustrates the action for a signal y(t), based on a carrier fc, and a

sinusoidal oscillator on frequency fo.

Product demodulation - synchronous & asynchronous


Figure 1: ‘sum and difference frequencies’

Each of the components of y(t) was moved up an amount fo in frequency, and

down by the same amount, and appear at the output of the multiplier.

Remember, neither y(t), nor the oscillator signal, appears at the multiplier

output. This is not necessarily the case with a ‘modulator’. See Tutorial

Question Q7.

A filter can be used to select the new components at either the sum frequency

(BPF preferred, or an HPF) or difference frequency (LPF preferred, or a BPF).

the combination of MULTIPLIER, OSCILLATOR,

and FILTER is called a frequency translator.

When the frequency translation is down to baseband the frequency translator

becomes a demodulator.

interpretationinterpretationinterpretationinterpretation

The method used for illustrating the process of frequency translation is just that -

illustrative. You should check out, using simple trigonometry, the truth of the

special cases discussed below. Note that this is an amplitude versus frequency

diagram; phase information is generally not shown, although annotations, or a

separate diagram, can be added if this is important.

Individual spectral components are shown by directed lines (phasors), or groups

of these (sidebands) as triangles. The magnitude of the slope of the triangle

generally carries no meaning, but the direction does - the slope is down towards

the carrier to which these are related 1.

When the trigonometrical analysis gives rise to negative frequency components,

these are re-written as positive, and a polarity adjustment made if necessary.

Thus:

V.sin(-ωt) = -V.sin(ωt)

Amplitudes are usually shown as positive, although if important to emphasise a

phase reversal, phasors can point down, or triangles can be drawn under the

horizontal axis.

To interpret a translation result graphically, first draw the signal to be translated

on the frequency/amplitude diagram in its position before translation. Then slide

it (the graphic which represents the signal) both to the left and right by an

amount fo, the frequency of the signal with which it is multiplied.

1 that is the convention used in this text; but some texts put the carrier at the top end of the slope !


If the left movement causes the graphic to cross the zero-frequency axis into the

negative region, then locate this negative frequency (say -fx) and place the

graphic there. Since negative frequencies are not recognised in this context, the

graphic is then reflected into the positive frequency region at +fx. Note that this

places components in the triangle, which were previously above others, now

below them. That is, it reverses their relative positions with respect to frequency.

special case:special case:special case:special case: ffffoooo = f = f = f = fcccc

In this case the down translated components straddle the origin. Those which

fall in the negative frequency region are then reflected into the positive region, as

explained above. They will overlap components already there. The resultant

amplitude will depend upon relative phase; both reinforcement and cancellation

are possible.

If the original signal was a DSBSC, then it is the components from the LSB

which are reflected back onto those from the USB. Their relative phases are

determined by the phase between the original DSBSC (on fc) and the local carrier

(fo).

Remember that the contributions to the output by the USB and LSB are combined

linearly. They will both be erect, and each would be perfectly intelligible if

present alone. Added in-phase, or coherently, they reinforce each other, to give

twice the amplitude of one alone, and so four times the power.

In this experiment the product demodulator is examined, which is based on the

arrangement illustrated in Figure 2. This demodulator is capable of

demodulating SSB 2, DSBSC, and AM. It can be used in two modes, namely

synchronous and asynchronous.

the demodulatorthe demodulatorthe demodulatorthe demodulator

synchronous operation: synchronous operation: synchronous operation: synchronous operation: ωωωω0000 ==== ωωωω1111

For successful demodulation of DSBSC and AM the synchronous demodulator

requires a ‘local carrier’ of exactly the same frequency as the carrier from which

the modulated signal was derived, and of fixed relative phase, which can then be

adjusted, as required, by the phase changer shown.

INPUT OUTPUT

on carrier ωο rad/s

local carrier

on οω rad/s

the message

phase

adjustment

modulated signal

Figure 2: synchronous demodulator; ωωωω1 = ωωωω0

2 but is it an SSB demodulator in the full meaning of the word ?



carrier acquisitioncarrier acquisitioncarrier acquisitioncarrier acquisition

In practice this local carrier must be derived from the modulated signal itself.

There are different means of doing this, depending upon which of the modulated

signals is being received. Two of these carrier acquisition circuits are examined

in the experiments entitled Carrier acquisition and the PLL and The Costas loop.

Both these experiments may be found within Volume A2 - Further & Advanced

Analog Experiments.

stolen carrierstolen carrierstolen carrierstolen carrier

So as not to complicate the study of the synchronous demodulator, it will be

assumed that the carrier has already been acquired. It will be ‘stolen’ from the

same source as was used at the generator; namely, the TIMS 100 kHz clock

available from the MASTER SIGNALS module.

This is known as the stolen carrier technique.

asynchronous operation:asynchronous operation:asynchronous operation:asynchronous operation: ωωωω0000 =/= =/= =/= =/= ωωωω1111

For asynchronous operation - acceptable for SSB - a local carrier is still required,

but it need not be synchronized to the same frequency as was used at the

transmitter. Thus there is no need for carrier acquisition circuitry. A local

signal can be generated, and held as close to the desired frequency as

circumstances require and costs permit. Just how close is ‘close enough’ will be

determined during this experiment.

local asynchronous carrierlocal asynchronous carrierlocal asynchronous carrierlocal asynchronous carrier

For the carrier source you will use a VCO module in place of the stolen carrier

from the MASTER SIGNALS module. There will be no need for the PHASE

SHIFTER. It can be left in circuit if found convenient; its influence will go

unnoticed.

signal identificationsignal identificationsignal identificationsignal identification

The synchronous demodulator is an example of the special case discussed above,

where fo = fc . It can be used for the identification of signals such as DSBSC,

SSB, ISB, and AM.

During this experiment you will be sent SSB, DSBSC, and ISB signals. These

will be found on the TRUNKS panel, and you are asked to identify them.

oscilloscope synchronizationoscilloscope synchronizationoscilloscope synchronizationoscilloscope synchronization

Remember that, when examining the generation of modulated signals, the

oscilloscope was synchronized to the message, in order to display the ‘text book’

pictures associated with each of them. At the receiving end the message is not

available until demodulation has been successfully achieved. So just ‘looking’ at

them at TRUNKS, before using the demodulator, may not be of much use 3. In

the model of Figure 2 (above), there is no recommendation as to how to

synchronize the oscilloscope in the first instance; but keep the need in mind.

3 none the less, synchronization to the envelope is sometimes possible. Perhaps the non-linearities of the

oscilloscope's synchronizing circuitry, plus some filtering, can generate a fair copy of the envelope ?


demodulation of DSBSCdemodulation of DSBSCdemodulation of DSBSCdemodulation of DSBSC

With DSBSC as the input to a synchronous demodulator, there will be a message

at the output of the 3 kHz LPF, visible on the oscilloscope, and audible in the

HEADPHONES.

The magnitude of the message will be dependent upon the adjustment of the

PHASE SHIFTER. Whilst watching the message on the oscilloscope, make a

phase adjustment with the front panel control of the PHASE SHIFTER, and note

that:

a) the message amplitude changes. It may be both maximized AND minimized.

b) the phase of the message will not change; but how can this be observed ? If

you have generated your own DSBSC then you have a copy of the message,

and have synchronized the oscilloscope to it. If the DSBSC has come from

the TIMS TRUNKS then you have perhaps been sent a copy for reference.

Otherwise ..... ?

The process of DSBSC demodulation can be examined graphically using the

technique described earlier.

The upper sideband is shifted down in frequency to just above the zero frequency

origin.

The lower sideband is shifted down in frequency to just below the zero frequency

origin. It is then reflected about the origin, and it will lie coincident with the

contribution from the upper sideband.

These contributions should be identical with respect to amplitude and frequency,

since they came from a matching pair of sidebands.

Now you can see what the phase adjustment will do. The relative phase of these

two contributions can be adjusted until they reinforce to give a maximum

amplitude. A further 180o shift would result in complete cancellation.

demodulation of SSBdemodulation of SSBdemodulation of SSBdemodulation of SSB

With SSB as the input to a synchronous demodulator, there will be a message at

the output of the 3 kHz LPF, visible on the oscilloscope, and audible in the

HEADPHONES.

Whilst watching the message on the oscilloscope, make a phase adjustment with

the front panel control of the PHASE SHIFTER, and note that:

a) the message amplitude does NOT change.

b) the phase of the message will change; but how can this be observed ? If you

have generated your own SSB then you have a copy of the message, and have

synchronized the oscilloscope to it. If the SSB has come from the TIMS

TRUNKS then you have perhaps been sent a copy for reference. But

otherwise ..... ?

Using the graphical interpretation, as was done for the case of the DSBSC, you

can see why the phase adjustment will have no effect upon the output amplitude.



Two identical contributions are needed for a phase

cancellation, but there is only one available.

demodulation of ISBdemodulation of ISBdemodulation of ISBdemodulation of ISB

An ISB signal is a special case of a DSBSC; it has a lower sideband (LSB) and

an upper sideband (USB), but they are not related. It can be generated by adding

two SSB signals, one a lower single sideband (LSSB), the other an upper single

sideband (USSB). These SSB signals have independent messages, but are based

on a common (suppressed, or small amplitude) carrier 4.

With ISB as the input to a synchronous demodulator, there will be a signal at the

output of the 3 kHz LPF, visible on the oscilloscope, and audible in the

HEADPHONES.

This will not be a single message, but the linear sum of the individual messages

on channel 1 and channel 2 of the ISB.

So is it reasonable to call this an SSB demodulator ?

A phase adjustment will have no apparent effect, either visually on the

oscilloscope, or audibly. But it must be doing something ?

query: explain what is happening when the test signal is an ISB, and why

channel separation is not possible.

query: what could be done to separate the messages on the two channels of an

ISB transmission ? hint: it might be easier to wait for the

experiment on SSB demodulation.


synchronous demodulationsynchronous demodulationsynchronous demodulationsynchronous demodulation

The aim of the experiment is to use a synchronous demodulator to identify the

signals at TRUNKS. Initially you do not know which is which, nor what

messages they will be carrying; these must also be identified.

The demodulator of Figure 2 is easily modelled with TIMS.

The carrier source will be the 100 kHz from the MASTER SIGNALS module.

This will be a stolen carrier, phase-locked to, but not necessarily in-phase with,

the transmitter carrier. It will need adjustment with a PHASE SHIFTER module.

4 the small carrier, or ‘pilot’ carrier, is typically about 20 dB below the peak signal level.


For the lowpass filter use the HEADPHONE AMPLIFIER. This has an in-built

3 kHz LPF which may be switched in or out. If this module is new to you, read

about it in the TIMS User Manual.

A suitable TIMS model of the block diagram of Figure 2 is shown below, in

Figure 3.

IN

CH1-A

CH2-A

CH2-B

roving trace

Figure 3: TIMS model of Figure 1

T1 patch up the model of Figure 3 above. This shows ω0 = ω1. Before

plugging in the PHASE SHIFTER, set the on-board switch to HI.

T2 identify SIGNAL 1 at TRUNKS. Explain your reasonings.

T3 identify SIGNAL 2 at TRUNKS Explain your reasonings.

T4 identify SIGNAL 3 at TRUNKS Explain your reasonings.

asynchronous demodulationasynchronous demodulationasynchronous demodulationasynchronous demodulation

We now examine what happens if the local carrier is off-set from the desired

frequency by an adjustable amount δf, where:

δf = |( fc - fo )| ........ 1

The process can be considered using the graphical approach illustrated earlier.

By monitoring the VCO frequency (the source of the local carrier) with the

FREQUENCY COUNTER you will know the magnitude and direction of this

offset by subtracting it from the desired 100 kHz.

VCO fine tuningVCO fine tuningVCO fine tuningVCO fine tuning

Refer to the TIMS User Manual for details on fine tuning of the VCO. It is quite

easy to make small frequency adjustments (fractions of a Hertz) by connecting a

small negative DC voltage into the VCO Vin input, and tuning with the GAIN

control.



SSB receptionSSB receptionSSB receptionSSB reception

Consider first the demodulation of an SSB signal.

You can show either trigonometrically or graphically that the output of the

demodulator filter will be the desired message components, but each displaced in

frequency by an amount δf from the ideal.

If δf is small - say 10 Hz - then you might guess that the speech will be quite

intelligible 5. For larger offsets the frequency shift will eventually be

objectionable. You will now investigate this experimentally. You will find that

the effect upon intelligibility will be dependant upon the direction of the

frequency shift, except perhaps when δf is less than say 10 Hz.

T5 replace the 100 kHz stolen carrier with the analog output of a VCO, set to

operate in the 100 kHz range. Monitor its frequency with the

FREQUENCY COUNTER.

T6 as an optional task you may consider setting up a system of modules to

display the magnitude of δf directly on the FREQUENCY

COUNTER module. But you will find it not as convenient as it

might at first appear - can you anticipate what problem might

arise before trying it ? (hint: 1 second is a long time !). A

recommended method of showing the small frequency difference

between the VCO and the 100 kHz reference is to display each on

separate oscilloscope traces - the speed of drift between the two

gives an immediate and easily recognised indication of the

frequency difference.

T7 connect an SSB signal, derived from speech, to the demodulator input.

Tune the VCO slowly around the 100 kHz region, and listen. Report

results.

DSBSC receptionDSBSC receptionDSBSC receptionDSBSC reception

For the case of a double sideband input signal the contributions from the LSB

and USB will combine linearly, but:

• one will be pitched high in frequency by an amount δf

• one will be pitched low in frequency, by an amount δf

Remember there was no difficulty in understanding the speech from one or the

other of the sidebands alone for small δf (the SSB investigation already

completed), even though it may have sounded unnatural. You will now

investigate this added complication.

5 the error δf is added or subtracted to each frequency component. Thus harmonic relationships are

destroyed. But for small δf (say 10 Hz or less) this may not be noticed.


T8 connect a DSBSC signal, derived from speech, to the demodulator input.

Tune the VCO slowly around the 100 kHz region, and listen. Report

results. Especially compare them with the SSB case.


Your observations made during the above experiment should enable you to

answer the following questions.

Q1 describe any significant differences between the intelligibility of the output

from a product demodulator when receiving DSBSC and SSB, there

being a small frequency off-set δf. Consider the cases:

a) δf = 0.1 Hz

b) δf = 10 Hz

c) δf = 100 Hz

Q2 would you define the synchronous demodulator as an SSB demodulator ?

Explain.

Q3 if a ‘DSBSC’ signal had a small amount of carrier present what effect

would this have as observed at the output of a synchronous

demodulator ?

Q4 consider the two radio receivers demodulating the same AM signal (on a

carrier of ω0 rad/s), as illustrated in the diagram below. The

lowpass filters at each receiver output are identical. Assume the

local oscillator of the top receiver remains synchronized to the

received carrier at all times.

input

( AM on ) ω0

ω0

ideal envelope detector

a) how would you describe each receiver ?



b) do you agree that a listener would be unable to distinguish

between the two audio outputs ?

Now suppose a second AM signal appeared on a nearby channel.

c) how would each receiver respond to the presence of this new

signal, as observed by the listener ?

d) how would you describe the bandwidth of each receiver ?

Q5 suppose, while you were successfully demodulating the DSBSC on

TRUNKS, a second DSBSC based on a 90 kHz carrier was added to

it. Suppose the amplitude of this ‘unwanted’ DSBSC was much

smaller than that of the wanted DSBSC.

a) would this new signal at the demodulator INPUT have any effect

upon the message from the wanted signal as observed at the

demodulator OUTPUT ?

b) what if the unwanted DSBSC was of the same amplitude as the

wanted DSBSC. Would it then have any effect ?

c) what if the unwanted DSBSC was ten times the amplitude of the

wanted DSBSC. Would it then have any effect ?

Explain !

Q6 define what is meant by ‘selective fading’. If an amplitude modulated

signal is undergoing selective fading, how would this affect the

performance of a synchronous demodulator ?

Q7 what are the differences, and similarities, between a multiplier and a

modulator ?



If you do not have a TRUNKS system you could generate your own ‘unknowns’.

These could include a DSBSC, SSB, ISB (independent single sideband), and

CSSB (compatible single sideband).

SSB generation is detailed in the experiment entitled SSB generation - the

phasing method in this Volume.

ISB can be made by combining two SSB signals (a USB and an LSB, based on

the same suppressed carrier, and with different messages) in an ADDER.

CSSB is an SSB plus a large carrier. It has an envelope which is a reasonable

approximation to the message, and so can be demodulated with an envelope

detector. But the CSSB signal occupies half the bandwidth of an AM signal.

Could it be demodulated with a demodulator of the types examined in this

experiment ?


SSB DEMODULATION SSB DEMODULATION SSB DEMODULATION SSB DEMODULATION ---- THE THE THE THE

PHASING METHODPHASING METHODPHASING METHODPHASING METHOD

PREPARATION ................................................................................2

carrier acquisition from SSB .....................................................2

the synchronous demodulator ....................................................3

a true SSB demodulator ............................................................3

principle of operation............................................................................. 4

practical realization ............................................................................... 4

practical considerations.......................................................................... 5

EXPERIMENT ..................................................................................6

outline .......................................................................................6

patching the model ....................................................................6

trimming ............................................................................................... 7

check the I branch.................................................................................. 7

check the Q branch ................................................................................ 7

combine branches .................................................................................. 8

swapping sidebands ............................................................................... 9

identification of signals at TRUNKS..........................................9

asynchronous demodulation of SSB ........................................10



SSB DEMSSB DEMSSB DEMSSB DEMODULATION ODULATION ODULATION ODULATION ----

THE PHASING METHODTHE PHASING METHODTHE PHASING METHODTHE PHASING METHOD

ACHIEVEMENTS: modelling of a phasing-type SSB demodulator; examination

of the sideband selection capabilities of a true SSB demodulator;

synchronous and asynchronous demodulation of SSB; evasion of

DSB sideband interference by sideband selection.

PREREQUISITES: completion of the experiments entitled Product

demodulation - synchronous and asynchronous and SSB

generation - the phasing method in this Volume would be an

advantage.


This experiment is concerned with the demodulation of SSB. Any

trigonometrical analyses that you may need to perform should use a single tone

as the message, knowing that eventually it will be replaced by bandlimited

speech. We will not be considering the transmission of data via SSB. As has

been done in earlier demodulation experiments, a ‘stolen carrier’ will be used

when synchronous operation is required. It will be shown that, when speech is

the message, synchronous demodulation is not strictly necessary; this is

fortunate, since carrier acquisition is a problem with SSB.

carrier acquisition from SSBcarrier acquisition from SSBcarrier acquisition from SSBcarrier acquisition from SSB

A pure SSB signal (without any trace of a carrier) contains no explicit

information about the frequency of the carrier from which it was generated

But, for speech communications, synchronous operation of the demodulator is

not essential; a local carrier within say 10 Hz of the ideal is adequate.

None-the-less, when SSB first came to popularity for mobile voice

communications in the 1950s it was difficult (and, therefore, expensive) to

maintain a local carrier within 10 Hz (or even 100 Hz, for that matter) of that

required. Many techniques were developed for providing a local carrier of the

required tolerance, including sending a trace of the carrier - a ‘pilot’ carrier - to

which the receiver was ‘locked’ to give synchronous operation.

SSB Demodulation - the Phasing Method


In the interim the tolerance problem was overcome by inevitable technological

advances, including the advent of frequency synthesisers, and asynchronous

operation became the norm.

In the 1990s the need for synchronous operation has returned, although for a

different reason. Now it is desired to send data (or digitized speech) and phase

coherence offers some advantages. But methods are still sought to avoid it.

Fortunately, ideal synchronous-type demodulation is not necessary when the

message is speech. An error of up to 10 Hz in the local carrier is quite acceptable

in most cases (see, for example, Hanson, J.V. and Hall, E.A.; ‘Some results

concerning the perception of musical distortion in mis-tuned single sideband

links’, IEEE Trans. on Comm., correspondence pp.299-301, Feb. 1975). For

speech communications an error of up to 100 Hz can be tolerated, although the

speech may sound unnatural. You can make your own assessment in this

experiment.

the sthe sthe sthe synchronous demodulatorynchronous demodulatorynchronous demodulatorynchronous demodulator

INPUT(modulated signal

0ωon carrier )

0ωcarrier source

OUTPUT(message)

bandwidth B Hz.

Figure 1: the synchronous demodulator

SSB demodulation can be carried out with a synchronous demodulator. You

should remember this from the experiment entitled ‘Product demodulation -

synchronous and asynchronous’. Figure 1 will remind you of the basic elements.

Note that for SSB derived from speech there is no need for the phase shifter 1.

But the arrangement of Figure 1 can not be described as an SSB demodulator,

since it is unable to differentiate between the upper and lower sideband of a

DSBSC signal. It responds to signals in a window either side of the carrier to

which it is tuned, yet the wanted SSB signal will be located on one side of this

carrier, not both. The window is too wide - as well as responding to the signal in

the wanted sideband, it will also respond to any signals in the other sideband.

There may be other signals there, and there certainly will be unwanted noise.

Thus the output signal-to-noise ratio will be unnecessarily worsened.

a true SSB demodulatora true SSB demodulatora true SSB demodulatora true SSB demodulator

A true SSB demodulator must have the ability to select sidebands.

All the methods of SSB generation so far discussed have their counterparts as

demodulators. In this experiment you will be examining the phasing-type

demodulator. A block diagram of such a demodulator is illustrated in Figure 2.

1 why ?


inω

0

Q

Σmessage

out

bandwidth B Hz.π/2

π/2

I

Figure 2: the ideal phasing-type SSB demodulator

principle of operationprinciple of operationprinciple of operationprinciple of operation

It is convenient, for the purpose of investigating the operation of this

demodulator, to use for the input signal two components, one ωH rad/s, above ω0,

and the other at ωLrad/s, below ω0. This enables us to follow each sideband

through the system and so to appreciate the principle of operation.

The multipliers produce both sum and difference products. The sum frequencies

are at or about 2ω rad/s, and the difference (wanted) products near DC. The

discussion below is simplified if we assume there are two identical filters, one

each in the I (inphase) and Q (quadrature) paths, which remove the sum

products.

Consider the upper path I: into the ‘I’ input of the summer go two contributions;

the first is that from the component at ωH, the second from the component ωL.

Two more contributions to the summer come from the lower path ‘Q’.

You can show that these four contributions are so phased that those from one

side of ω0 will add, whilst those from the other side will cancel. Thus the

demodulator appears to look at only one side of the carrier.

The purpose of the adjustable phase α is to vary the phase of the local carrier

source ω0 with respect to the incoming signal, also on ω0.

practical realizationpractical realizationpractical realizationpractical realization

As was discussed in the experiment entitled ‘SSB generation - the phasing

method’, the physical realization of a two-terminal wide-band 90o phase shifter

network (in the Q arm) presents great difficulties. So the four-terminal

quadrature phase splitter - the QPS - is used instead. This necessitates a slight

rearrangement of the scheme of Figure 2 to that illustrated in Figure 3.



Q

Σ

QPS

QPS

Q

ω0

message

OUTIN

π/2

II

Figure 3: the practical phasing-type SSB demodulator

practical considerationspractical considerationspractical considerationspractical considerations

Figure 3 is a practical arrangement of a phasing-type SSB demodulator.

The π/2 phase shifter needs to introduce a 900 phase shift at a single frequency,

so is a narrowband device, and presents no realization problems.

The QPS, on the other hand, needs to perform over the full message bandwidth,

so is a wideband device.

Remember that the outputs from the multipliers contain the sum and difference

frequencies of the product; the difference frequencies are those of interest, being

in the message frequency band.

The sum frequencies are at twice the carrier frequency, and are of no interest. It

is tempting to remove them with two filters, one at the output of each multiplier,

because their presence will increase the chances of overload of the QPS. But the

transfer functions of these filters would need to be identical across the message

bandwidth, so as not to upset the balance of the system, and this would be a

difficult practical requirement.

Being a linear system in the region of the QPS and the summing block, two

filters in the I and Q arms (the inputs to the summing block) can be replaced by a

single filter in output of the summing block.

The lowpass filter in the summing block output determines the bandwidth of the

demodulator in the 100 kHz part of the spectrum; that is, the width of the

window located either above or below the frequency ω0. Its bandwidth must be

equal to or less than the frequency range over which the QPS is designed to

operate, since, outside that range, cancellation of the unwanted sideband will

deteriorate.



outlineoutlineoutlineoutline

For this experiment you will be sent three signals via the trunks; an SSB, an

ISB, and a DSBSC (with superimposed interference on one sideband).

Generally speaking, if the messages are speech, or of unknown waveform, it

would be very difficult (impossible ?) to differentiate between these three by

viewing with an oscilloscope. For single tone messages it would easier -

consider this !

You may be advised of the nature of the messages, but not at which TRUNKS

outlet each signal will appear.

The aim of the experiment will be to identify each signal by using an SSB

demodulator.

The unknown signals will be in the vicinity of 100 kHz, as arranged by your

Laboratory Manager. They may or may not be based on a 100 kHz carrier locked

to yours.

You should start the experiment using the 100 kHz sinewave from the MASTER

SIGNALS module for the local carrier; but any stable carrier near 100 kHz

would suffice. This will need to be split into two paths in quadrature. If you use

the 100 kHz carriers from the MASTER SIGNALS module you might feel

tempted to use the sine and cosine outputs. But fine trimming will be needed for

precise balance of the demodulator, so a PHASE SHIFTER will be used instead.

This has been included in the patching diagram of Figure 4.

patching the modelpatching the modelpatching the modelpatching the model

T1 patch up a model to realize the arrangement of Figure 3. A possible

method is shown in Figure 4. The VCO serves as the test input

signal.

CH1-A

IN

100kHz signals

LOCALCARRIER

QUADRATURE

PHASE

TRANSMITTER SSB RECEIVER

Figure 4: model of an SSB demodulator



Before the demodulator can be used it must be aligned. A suitable test input

signal is required. A single component near 100 kHz is suitable; this can come

from a VCO, set to one or two kilohertz above or below 100 kHz, where the

unknown signals will be located, and so where your demodulator will be

operating. Make sure, after demodulation, it will be able to pass through the

3 kHz LPF of the HEADPHONE AMPLIFIER module.

For example, a 98 kHz single frequency component is simulating an SSB signal,

derived from a 2 kHz message, and based on a 100 kHz (suppressed) carrier.

trimmtrimmtrimmtrimminginginging

After patching up the model the balancing procedure can commence.

T2 set the VCO to, say, the upper sideband of 100 kHz, at 102 kHz or

thereabouts.

T3 check that there is a signal of much the same shape and amplitude from

each MULTIPLIER. These signals should be about 4 volts peak-to-

peak. Their appearance will be dependent upon the oscilloscope

sweep speed, and method of synchronization. They will probably

appear unfamiliar to you, and unlike text book pictures of

modulated signals. Do you understand why ?

You will now examine the performance of the upper, ‘P’, branch and the lower,

‘Q’, branch, independently.

Remember that each branch is like a normal (asynchronous) SSB demodulator.

Phasing has no influence on the output amplitude. It is only when the outputs

from the two branches are combined that something special happens.

check the I branchcheck the I branchcheck the I branchcheck the I branch

T4 remove input Q from the ADDER. Adjust the output of the filter, due to I,

to about 2 volts peak-to-peak with the appropriate ADDER gain

control. It will be a sine wave. Confirm it is of the correct

frequency. Confirm that adjustment of the PHASE SHIFTER has no

significant effect upon its amplitude.

check the Q branchcheck the Q branchcheck the Q branchcheck the Q branch

T5 remove input I from the ADDER, and replace input Q. Adjust the output of

the filter, due to I, to about 2 volts peak-to-peak with the

appropriate ADDER gain control. It will be a sine wave. Confirm

it is of the correct frequency. Confirm that adjustment of the

PHASE SHIFTER has no significant effect upon the amplitude.


combine branchescombine branchescombine branchescombine branches

T6 replace input Q to the ADDER. What would you expect to see ? Merely the

addition of two sinewaves, of the same frequency, similar amplitude,

and unknown relative phase. The resultant is also a sine wave, of

same frequency, and amplitude anywhere between about zero volt,

and 4 volt peak-to-peak. What would we like it to be ?

T7 rotate the PHASE SHIFTER front panel control. Depending upon the state

of the 1800 toggle switch you may achieve either a maximum or a

minimum amplitude output from the filter. Choose the minimum.

T8 adjust one or other (not both) of the ADDER gain controls until there is a

better minimum.

T9 alternate between adjustments of the PHASE control and the ADDER gain

control, for the best obtainable minimum. These adjustments will

not be interactive, so the procedure should converge fast.

When the above adjustments are completed to your satisfaction you have a true

SSB receiver. It has been adjusted to ignore any input on the sideband in which

your test signal was located. If this was the lower sideband, then you have an

upper sideband receiver. If it had been in the upper sideband, then you have a

lower sideband receiver.

Note that you were advised to null the unwanted sideband, rather than maximise

the wanted.

But you could have, in principle, chosen to adjust for a maximum. In that case, if

the test signal had been in the lower sideband, then you have a lower sideband

receiver. Had it been in the upper sideband, then you have an upper sideband

receiver.

In practice it is customary to choose the nulling method. Think about it !

To convince yourself that what was stated above about which sideband will be

selected, you should sweep the VCO from say 90 kHz to 110 kHz, while

watching the output from the receiver - that is, from the 3 kHz LPF output. You

will be looking for the extent of the ‘window’ through which the receiver looks at

the RF spectrum.

T10 do a quick sweep of the VCO over its full frequency range (or say 90 to

110 kHz). Notice that there is a ‘window’ about 3 kHz wide on one

side only of 100 kHz from which there is an output from the

receiver. Elsewhere there is very little.

T11 repeat the previous Task, this time more carefully, noting precisely the

VCO and audio output frequencies involved, their relationship to

each other, and to the 3 kHz LPF response. Sketch the approximate

response of the SSB receiver.



swapping sidebandsswapping sidebandsswapping sidebandsswapping sidebands

It is a simple matter to change the sideband to which the demodulator responds

by flipping the ±1800 toggle switch of the PHASE SHIFTER.

T12 flip the ±1800 toggle switch of the PHASE SHIFTER. Did this reverse the

sideband to which the demodulator responds ? How did you prove

this ? Was (slight) realignment necessary ?

There are other methods which are often suggested for changing from one

sideband to the other with the arrangement of Figure 3. Which of the following

would be successful ?

1. swap inputs to the QPS.

2. swap outputs from the QPS.

3. interchange the I and Q paths of the QPS (ie, inputs and outputs).

4. swap signal inputs to the two MULTIPLIERS.

5. swap carrier inputs to the two MULTIPLIERS.

6. any more suggestions ?

identificatioidentificatioidentificatioidentification of signals at TRUNKSn of signals at TRUNKSn of signals at TRUNKSn of signals at TRUNKS

There are three signals at TRUNKS, all based on a 100 kHz carrier. They are:

• an SSB derived from speech.

• an ISB, at least one channel being derived from speech

• a DSBSC, derived from speech, but with added interference.

T13 use your SSB demodulator to identify and discover as much about the

signals at TRUNKS as you can.

You should have been able to:

• verify that either sideband may be selected from the ISB

• show that the interference is on one sideband of the DSBSC, and that the

other sideband may be demodulated interference-free

• identify which sideband of the DSBSC contained the interference.


asynchronous demodulation of SSBasynchronous demodulation of SSBasynchronous demodulation of SSBasynchronous demodulation of SSB

So far you have been demodulating SSB and other signals with a stolen (and

therefore synchronous) carrier.

There was no provision for varying the phase of the stolen carrier before it was

split into an inphase and quadrature pair. This would have required another

PHASE SHIFTER module in the arrangement of Figure 3. However, it was

observed in an earlier experiment (and may be confirmed analytically) that this

would change the phase of the received message, but not its amplitude, and so

would go unnoticed with speech as the message.

But what if the local carrier is not synchronous - that is, if there is a small

frequency error between the SSB carrier (suppressed at the transmitter), and the

local carrier (supplied at the receiver) ? You can check the effect by using the

analog output from a VCO in place of the 100 kHz carrier from the MASTER

SIGNALS module.

T14 replace the 100 kHz carrier from the MASTER SIGNALS module with the

analog output from a VCO. Set the VCO frequency close to

100 kHz, and monitor it with the FREQUENCY COUNTER.

Remember the preferred method of fine tuning the VCO is to use a

small, negative DC voltage in the CONTROL VOLTAGE socket, and fine

tune with the GAIN control. (refer to the TIMS User Manual).

T15 connect the SSB at TRUNKS to the input of the demodulator, and listen to

the speech as the VCO is tuned slowly through 100 kHz. Report

your findings. In particular, comment on the intelligibility and

recognisability of the speech message when the frequency error δf is

about 0.1 Hz, 10 Hz, and say 100 Hz.




Q1 confirm analytically that the RF window width of the arrangement of

Figure 1 is twice the bandwidth of the LPF.

Q2 confirm analytically that the RF window width of the arrangement of

Figure 2 is equal to the bandwidth of the LPF.

Q3 the trimming procedure of the phasing-type demodulator could have chosen

to maximize or minimize the filter output. Explain the difference

between these two possible methods. Which would you recommend,

and why ?

Q4 when would a true SSB demodulator (Figure 2) give superior performance

to a ‘normal’ product (synchronous) demodulator (Figure 1), when

demodulating a DSBSC. How superior ? Explain.

Q5 you have met all the elements of the SSB demodulator of Figure 3 in earlier

experiments, so should know their characteristics. If not, measure

those you require, and predict, analytically, which sideband it is

‘looking at’. Check that this agrees with experiment.

Q6 why use a PHASE SHIFTER module for the quadrature carrier, instead of

using the inphase and quadrature outputs already available from the

MASTER SIGNALS module ?

Q7 do you think it is essential for an SSB demodulator to be synchronous when

the message is speech ? What sort of frequency error do you think

is acceptable ? What would be the tolerance requirements of the

receiver carrier source (assuming no fine tuning control) if the SSB

was radiated at 20 MHz ? Answer this questions from your own

observations. See what your text book says.


THE SAMPLING THEOREMTHE SAMPLING THEOREMTHE SAMPLING THEOREMTHE SAMPLING THEOREM

PREPARATION................................................................................ 2

EXPERIMENT.................................................................................. 3

taking samples .......................................................................... 3

reconstruction / interpolation .................................................... 5

sample width ......................................................................................... 6

reconstruction filter bandwidth .............................................................. 6

pulse shape ............................................................................................ 7

to find the minimum sampling rate............................................ 7

preparation ............................................................................................ 8

MDSDR........................................................................................... 8

use of MDSDR................................................................................. 9

minimum sampling rate measurement ................................................... 9

further measurements.............................................................. 10

the two-tone test message..................................................................... 11

summing up ............................................................................ 11


APPENDIX A ................................................................................. 13

analysis of sampling ................................................................ 13

sampling a cosine wave ....................................................................... 13

practical issues .................................................................................... 14

aliasing distortion. ............................................................................... 15

anti-alias filter ..................................................................................... 15

APPENDIX B.................................................................................. 16

3 kHz LPF response................................................................ 16


THETHETHETHE SAMPLING THEOREMSAMPLING THEOREMSAMPLING THEOREMSAMPLING THEOREM

ACHIEVEMENTS: experimental verification of the sampling theorem; sampling

and message reconstruction (interpolation)

PREREQUISITES: completion of the experiment entitled Modelling an equation.


A sample is part of something. How many samples of something does one need, in

order to be able to deduce what the something is ? If the something was an

electrical signal, say a message, then the samples could be obtained by looking at it

for short periods on a regular basis. For how long must one look, and how often, in

order to be able to work out the nature of the message whose samples we have - to

be able to reconstruct the message from its samples ?

This could be considered as merely an academic question, but of course there are

practical applications of sampling and reconstruction.

Suppose it was convenient to transmit these samples down a channel. If the

samples were short, compared with the time between them, and made on a regular

basis - periodically - there would be lots of time during which nothing was being

sent. This time could be used for sending something else, including a set of

samples taken of another message, at the same rate, but at slightly different times.

And if the samples were narrow enough, further messages could be sampled, and

sandwiched in between those already present. Just how many messages could be

packed into the channel ?

The answers to many of these questions will be discovered during the course of this

experiment. It is first necessary to show that sampling and reconstruction are,

indeed, possible !

The sampling theorem defines the conditions for successful sampling, of particular

interest being the minimum rate at which samples must be taken. You should be

reading about it in a suitable text book. A simple analysis is presented in

Appendix A to this experiment.

This experiment is designed to introduce you to some of the fundamentals,

including determination of the minimum sampling rate for distortion-less

reconstruction.

The sampling theorem



taking samptaking samptaking samptaking samplesleslesles

In the first part of the experiment you will set up the arrangement illustrated in

Figure 1. Conditions will be such that the requirements of the Sampling Theorem,

not yet given, are met. The message will be a single audio tone.

Figure 1: sampling a sine wave

To model the arrangement of Figure 1 with TIMS the modules required are a

TWIN PULSE GENERATOR (only one pulse is used), to produce s(t) from a clock

signal, and a DUAL ANALOG SWITCH (only one of the switches is used). The

TIMS model is shown in Figure 2 below.

ext. trig CH1-A CH2-A

CH1-B

CH2-B

roving trace

Figure 2: the TIMS model of Figure 1


T1 patch up the model shown in Figure 2 above. Include the oscilloscope

connections. Note the oscilloscope is externally triggered from the

message.

note: the oscilloscope is shown synchronized to the message. Since the message

frequency is a sub-multiple of the sample clock, the sample clock could

also have been used for this purpose. However, later in the experiment the

message and clock are not so related. In that case the choice of

synchronization signal will be determined by just what details of the

displayed signals are of interest. Check out this assertion as the

experiment proceeds.

T2 view CH1-A and CH2-A, which are the message to be sampled, and the

samples themselves. The sweep speed should be set to show two or

three periods of the message on CH1-A

T3 adjust the width of the pulse from the TWIN PULSE GENERATOR with the

pulse width control. The pulse is the switching function s(t), and its

width is δt. You should be able to reproduce the sampled waveform of

Figure 3.

Your oscilloscope display will not show the message in dashed form (!), but you

could use the oscilloscope shift controls to superimpose the two traces for

comparison.

Figure 3: four samples per period of a sine wave.

Please remember that this oscilloscope display is that of a VERY SPECIAL CASE,

and is typical of that illustrated in text books.

The message and the samples are stationary on the screen

This is because the frequency of the message is an exact sub-multiple of the

sampling frequency. This has been achieved with a message of (100/48) kHz, and

a sampling rate of (100/12) kHz.



In general, if the oscilloscope is synchronized to the sample clock, successive views

of the message samples would not overlap in amplitude. Individual samples would

appear at the same location on the time axis, but samples from successive sweeps

would be of different amplitudes. You will soon see this more general case.

Note that, for the sampling method being examined, the shape of the top of each

sample is the same as that of the message. This is often called natural sampling.

reconstruction / interpolationreconstruction / interpolationreconstruction / interpolationreconstruction / interpolation

Having generated a train of samples, now observe that it is possible to recover, or

reconstruct (or interpolate) the message from these samples.

From Fourier series analysis, and consideration of the nature of the sampled signal,

you can already conclude that the spectrum of the sampled signal will contain

components at and around harmonics of the switching signal, and hopefully the

message itself. If this is so, then a lowpass filter would seem the obvious choice to

extract the message. This can be checked by experiment.

Later in this experiment you will discover the properties this filter is required to

have, but for the moment use the 3 kHz LPF from the HEADPHONE AMPLIFIER.

The reconstruction circuitry is illustrated in Figure 4.

LOWPASS

FILTER

original message

OUTsamples IN

Figure 4: reconstruction circuit.

You can confirm that it recovers the message from the samples by connecting the

output of the DUAL ANALOG SWITCH to the input of the 3 kHz LPF in the

HEADPHONE AMPLIFIER module, and displaying the output on the oscilloscope.

T4 connect the message samples, from the output of the DUAL ANALOG

SWITCH, to the input of the 3 kHz LPF in the HEADPHONE

AMPLIFIER module, as shown in the patching diagram of Figure 2.

T5 switch to CH2-B and there is the message. Its amplitude may be a little small,

so use the oscilloscope CH2 gain control. If you choose to use a

BUFFER AMPLIFIER, place it at the output of the LPF. Why not

at the input ?

The sample width selected for the above measurements was set arbitrarily at about

20% of the sampling period. What are the consequences of selecting a different

width ?


sample widthsample widthsample widthsample width

Apart from varying the time interval between samples, what effect upon the

message reconstruction does the sample width have ? This can be determined

experimentally.

T6 vary the width of the samples, and report the consequences as observed at the

filter output

reconstruction filter bandwidthreconstruction filter bandwidthreconstruction filter bandwidthreconstruction filter bandwidth

Demonstrating that reconstruction is possible by using the 3 kHz LPF within the

HEADPHONE AMPLIFIER was perhaps cheating slightly ? Had the reconstructed

message been distorted, the distortion components would have been removed by

this filter, since the message frequency is not far below 3 kHz itself. Refer to the

experiment entitled Amplifier overload (within Volume A2 - Further & Advanced

Analog Experiments), and the precautions to be taken when measuring a narrow

band system. The situation is similar here. As a check, you should lower the

message frequency. This will also show some other effects. Carry out the next

Task.

T7 replace the 2 kHz message from the MASTER SIGNALS module with one

from an AUDIO OSCILLATOR. In the first instance set the audio

oscillator to about 2 kHz, and observe CH1-A and CH2-A

simultaneously as you did in an earlier Task. You will see that the

display is quite different.

The individual samples are no longer visible - the display on CH2-A is not

stationary.

T8 change the oscilloscope triggering to the sample clock. Report results.

T9 return the oscilloscope triggering to the message source. Try fine

adjustments to the message frequency (sub-multiples of the sampling

rate).

This time you have a different picture again - the message is stationary, but the

samples are not. You can see how the text book display is just a snap shot over a

few samples, and not a typical oscilloscope display unless there is a relationship

between the message and sampling rate 1.

It is possible, as the message frequency is fine tuned, to achieve a stationary

display, but only for a moment or two.

1 or you have a special purpose oscilloscope



Now that you have a variable frequency message, it might be worthwhile to re-

check the message reconstruction.

T10 look again at the reconstructed message on CH2-B. Lower the message

frequency, so that if any distortion products are present (harmonics of

the message) they will pass via the 3 kHz LPF.

pulse shapepulse shapepulse shapepulse shape

You have been looking at a form of pulse amplitude modulated (PAM) signal. If

this sampling is the first step in the conversion of the message to digital form, the

next step would be to convert the pulse amplitude to a digital number. This would

be pulse code modulation (PCM) 2.

The importance of the pulse shape will not be considered in this experiment. We

will continue to consider the samples as retaining their shapes (as shown in the

Figure 3, for example). Your measurements should show that the amplitude of the

reconstituted message is directly proportional to the width of the samples.

to find the minimum sampling rateto find the minimum sampling rateto find the minimum sampling rateto find the minimum sampling rate

Now that you have seen that an analog signal can be recovered from a train of

periodic samples, you may be asking:

what is the slowest practical sampling rate for

the recovery process to be successful ?

The sampling theorem was discovered in answer to this question. You are invited

now to re-enact the discovery:

• use the 3 kHz LPF as the reconstruction filter. The highest frequency

message that this will pass is determined by the filter passband edge fc,

nominally 3 kHz. You will need to measure this yourself. See Appendix B

to this experiment.

• set the message frequency to fc.

• use the VCO to provide a variable sampling rate, and reduce it until the

message can no longer be reconstructed without visible distortion.

• use, in the first instance, a fixed sample width δt, say 20% of the sampling

period.

The above procedure will be followed soon; but first there is a preparatory

measurement to be performed.

2 if the pulse is wide, with a sloping top, what is its amplitude ?


preparationpreparationpreparationpreparation

MDSDRMDSDRMDSDRMDSDR

In the procedure to follow you are going to report when it is just visibly obvious, in

the time domain, when a single sinewave has been corrupted by the presence of

another. You will use frequencies which will approximate those present during a

later part of the experiment.

The frequencies are:

• wanted component - 3 kHz

• unwanted component - 4 kHz

Suppose initially the amplitude of the unwanted signal is zero volt. While

observing the wanted signal, in the time domain, how large an amplitude would the

unwanted signal have to become for its presence to be (just) noticed ?

A knowledge of this phenomenon will be useful to you throughout your career. An

estimate of this amplitude ratio will now be made with the model illustrated in

Figure 5.

wanted sinewave

unwanted sinewave

output

Figure 5: corruption measurement

T11 obtain a VCO module. Set the ‘FSK - VCO’ switch, located on the circuit

board, to 'VCO'. Set the front panel ‘HI - LO’ switch to ‘LO’. Then

plug the module into a convenient slot in the TIMS unit.

T12 model the block diagram of Figure 5. Use a VCO and an AUDIO

OSCILLATOR for the two sinewaves. Reduce the unwanted signal to

zero at the ADDER output. Set up the wanted signal output amplitude

to say 4 volt peak-to-peak. Trigger the oscilloscope to the source of

this signal. Increase the amplitude of the unwanted signal until its

presence is just obvious on the oscilloscope. Measure the relative

amplitudes of the two signals at the ADDER output. This is your

MDSDR - the maximum detectable signal-to-distortion ratio. It would

typically be quoted in decibels.



use of MDSDRuse of MDSDRuse of MDSDRuse of MDSDR

Consider the spectrum of the signal samples. Refer to Appendix A of this

experiment if necessary.

Components in the lower end of the spectrum of the sampled signal are shown in

Figure 6 below. It is the job of the LPF to extract the very lowest component,

which is the message (here represented by a single tone at frequency µ rad/s).

ωωωωµµµµ

LPFlowest unwanted component

ω−µω−µω−µω−µ ω+µω+µω+µω+µfrequency

attenuation = MDSDRfrequency at which

Figure 6: lower end of the spectrum of the sampled signal

During the measurement to follow, the frequency ‘ω’ will be gradually reduced, so

that the unwanted components move lower in frequency towards the filter

passband.

You will be observing the wanted component as it appears at the output of the LPF.

The closest unwanted component is the one at frequency (ω - µ) rad/s.

Depending on the magnitude of ‘ω’, this component will be either:

1. outside the filter passband, and not visible in the LPF output (as in Figure 6)

2. in the transition band, and perhaps visible in the LPF output

3. within the filter passband, and certainly visible in the LPF output

Assuming both the wanted and unwanted components have the same amplitudes,

the presence of the unwanted component will first be noticed when ‘ω’ falls to the

frequency marked on the transition band of the LPF. This equals, in decibels, the

MDSDR.

T13 measure the frequency of your LPF at which the attenuation, relative to the

passband attenuation, is equal to the MDSDR. Call this fMDSDR.

minimum sampling rate measurementminimum sampling rate measurementminimum sampling rate measurementminimum sampling rate measurement

T14 remove the patch lead from the 8.333 kHz SAMPLE CLOCK source on the

MASTER SIGNALS module, and connect it instead to the VCO TTL

OUTPUT socket. The VCO is now the sample clock source.

T15 use the FREQUENCY COUNTER to set the VCO to 10 kHz or above.


T16 use the FREQUENCY COUNTER to set the AUDIO OSCILLATOR to fc, the

edge of the 3 kHz LPF passband.

T17 synchronize the oscilloscope to the sample clock. Whilst observing the

samples, set the sample width δt to about 20% of the sampling period.

The sampling theorem states, inter alia, that the minimum sampling rate is twice

the frequency of the message.

Under the above experimental conditions, the sampling rate is well above this

minimum.

T18 synchronize the oscilloscope to the message, direct from the AUDIO

OSCILLATOR, and confirm that the message being sampled, and the

reconstructed message, are identical in shape and frequency (the

difference in amplitudes is of no consequence here).

It is now time to determine the minimum sampling rate for undistorted message

reconstruction.

T19 whilst continuing to monitor both the message and the reconstructed

message, slowly reduce the sampling rate (the VCO frequency). As

soon as the message shows signs of distortion (aliasing distortion),

increase the sampling rate until it just disappears. The sampling rate

will now be the minimum possible.

T20 calculate the frequency of the unwanted component. It will be the just-

measured minimum sampling rate, minus the message frequency.

How does this compare with fMDSDR measured in Task 13 ?

T21 compare your result with that declared by the sampling theorem. Explain

discrepancies !

further measurementsfurther measurementsfurther measurementsfurther measurements

A good engineer would not stop here. Whilst agreeing that it is possible to sample

and reconstruct a single sinewave, he would call for a more demanding test.

Qualitatively he might try a speech message. Quantitatively he would probably try

a two-tone test signal.

What ever method he tries, he would make sure he used a band-limited message.

He will then know the highest frequency contained in the message, and adjust his

sampling rate with respect to this.

If you have bandlimited speech available at TRUNKS, or a SPEECH MODULE,

you should repeat the measurements of the previous section.



the twothe twothe twothe two----tone test messagetone test messagetone test messagetone test message

A two-tone test message consists of two audio tones added together.

The special properties of this test signal are discussed in the chapter entitled

Introduction to modelling with TIMS (of this Volume) in the section headed The

two tone test signal, to which you should refer. You should also refer to the

experiment entitled Amplifier overload (within Volume A2 - Further & Advanced

Analog Experiments).

You can make a two-tone test signal by adding the output of an AUDIO

OSCILLATOR to the 2 kHz message from the MASTER SIGNALS module.

There may be a two-tone test signal at TRUNKS, or use a SPEECH Module.

summing summing summing summing upupupup

You have been introduced to the principles of sampling and reconstruction.

The penalty for selecting too low a sampling rate was seen as distortion of the

recovered message. This is known as aliasing distortion; the filter has allowed

some of the unwanted components in the spectrum of the sampled signal to reach

the output. Analysis of the spectrum can tell you where these have come from, and

so how to re-configure the system - more appropriate filter, or faster sampling rate ?

In the laboratory you can make some independent measurements to reach much the

same conclusions.

In a practical situation it is necessary to:

1. select a filter with a passband edge at the highest message frequency, and a

stopband attenuation to give the required signal to noise-plus-distortion

ratio.

2. sample at a rate at least equal to the filter slot 3 band width plus the highest

message frequency. This will be higher than the theoretical minimum rate.

Can you see how this rate was arrived at ?

An application of sampling can be seen in the experiment entitled Time division

multiplexing - PAM (within this Volume).


Q1 even if the signal to be sampled is already bandlimited, why is it good

practice to include an anti-aliasing filter ?

3 the ‘slot band’ is defined in Appendix A at the rear of this Volume.


Q2 in the experiment the patching diagram shows that the non-delayed pulse was

taken from the TWIN PULSE GENERATOR to model the switching

function s(t). What differences would there have been if the delayed

pulse had been selected ? Explain.

note: both pulses are of the same nominal width.

Q3 consider a sampling scheme as illustrated in Figure 1. The sampling rate is

determined by the distance between the pulses of the switching

function s(t). Assume the message was reconstructed using the scheme

of Figure 4.

Suppose the pulse rate was slowly increased, whilst keeping the pulse width

fixed. Describe and explain what would be observed at the lowpass

filter output.



APPENDIXAPPENDIXAPPENDIXAPPENDIX AAAA

analysis of samplinganalysis of samplinganalysis of samplinganalysis of sampling

sampling a cosine wavesampling a cosine wavesampling a cosine wavesampling a cosine wave

Using elementary trigonometry it is possible to derive an expression for the

spectrum of the sampled signal. Consider the simple case where the message is a

single cosine wave, thus:

m(t) = V.cosµt ........ A-1

Let this message be the input to a switch, which is opened and closed periodically.

When closed, any input signal is passed on to the output.

The switch is controlled by a switching function s(t). When s(t) has the value ‘1’

the switch is closed, and when ‘0’ the switch is open. This is a periodic function,

of period T, where:

T = ( 2.π ) / ω sec ........ A-2

and is expressed analytically by the Fourier series expansion of eqn. A-3 below.

s(t) = ao + a1.cosωt + a2.cos2ωt + a3.cos3ωt + ... ........ A-3

The coefficients ai in this expression are a function of (δt/T) of the pulses in s(t),

which is illustrated in Figure A-1 below.

δδδδ tTt i m e t

+ 1

0

Figure A-1: the switching function s(t)

The sampled signal is given by:

sampled signal y(t) = m(t). s(t) ........ A-4

Expansion of y(t), using eqns. A-1 and A-3, shows it to be a series of DSBSC

signals located on harmonics of the switching frequency ω, including the zeroeth

harmonic, which is at DC, or baseband. The magnitude of each of the coefficients

ai will determine the amplitude of each DSBSC term.

The frequency spectrum of this signal is illustrated in graphical form in Figure A-2.


2ω2ω2ω2ω 3ω3ω3ω3ω 4ω4ω4ω4ωωωωω

2µ2µ2µ2µ 2µ2µ2µ2µ 2µ2µ2µ2µ 2µ2µ2µ2µ

frequencyµµµµ

Figure A-2: the sampled signal in the frequency domain

Figure A-2 is representative of the case when the ratio (δt / T) is very small,

making adjacent DSBSC amplitudes almost equal, as shown.

A special case occurs when (δt / T) = 0.5 which makes s(t) a square wave. It is well

known for this case that the even ai are all zero, and the odd terms are

monotonically decreasing in amplitude.

The important thing to notice is that:

1. the DSBSC are spaced apart, in the frequency domain, by the sampling

frequency ω rad/s.

2. the bandwidth of each DSBSC extends either side of its centre frequency by

an amount equal to the message frequency µ rad/s.

3. the lowest frequency term - the baseband triangle - is the message itself.

Inspection of Figure A-2 reveals that, provided:

ω ≥ 2.µ ........ A-5

there will be no overlapping of the DSBSC, and, specifically, the message can be

separated from the remaining spectral components by a lowpass filter.

That is what the sampling theorem says.

practical issuespractical issuespractical issuespractical issues

When the sampling theorem says that the slowest useable sampling rate is twice the

highest message frequency, it assumes that:

1. the message is truly bandlimited to the highest message frequency µ rad/s.

2. the lowpass filter which separates the message from the lowest DSBSC

signal is brick wall.

Neither of these requirements can be met in practice.

If the message is bandlimited with a practical lowpass filter, account must be taken

of the finite transition bandwidth in assessing that frequency beyond which there is

no significant message energy.

The reconstruction filter will also have a finite transition bandwidth, and so

account must be taken of its ability to suppress the low frequency component of the

lowest frequency DSBSC signal.



aliasing distortion.aliasing distortion.aliasing distortion.aliasing distortion.

If the reconstruction filter does not remove all of the unwanted components -

specifically the lower sideband of the nearest DSBSC, then these will be added to

the message. Note that the unwanted DSBSC was derived from the original

message. It will be a frequency inverted version of the message, shifted from its

original position in the spectrum. The distortion introduced by these components,

if present in the reconstructed message, is known as aliasing distortion.

antiantiantianti----alias filteralias filteralias filteralias filter

No matter how good the reconstruction filter is, it cannot compensate for a non-

bandlimited message. So as a first step to eliminate aliasing distortion the message

must be bandlimited. The band limiting is performed by an anti-aliasing filter.


APPENDIX BAPPENDIX BAPPENDIX BAPPENDIX B

3333 kHz LPF responsekHz LPF responsekHz LPF responsekHz LPF response

For this experiment it is necessary to know the frequency response of the 3 kHz

LPF in your HEADPHONE AMPLIFIER.

If this is not available, then you must measure it yourself.

Take enough readings in order to plot the filter frequency response over the full

range of the AUDIO OSCILLATOR. Voltage readings accurate to 10% will be

adequate.

A measurement such as this is simplified if the generator acts as a pure voltage

source; this means, in effect, that its amplitude should remain constant (say within

a few percent) over the frequency range of interest. It is then only necessary to

record the filter output voltage versus frequency. Check that the AUDIO

OSCILLATOR meets this requirement.

Select an in-band frequency as reference - say 1 kHz. Call the output voltage at this

frequency Vref. Output voltage measurements over the full frequency range should

then be recorded, and from them the normalized response, in dB, can be plotted.

Thus, for an output of Vo, the normalized response, in dB, is:

response = 20 log10 (Vo / Vref) dB

Plot the response, in dB, versus log frequency. Prepare a table similar to that of

Table B-1, and complete the entries.

The transition band lies between

the edge of the passband fo and the

start of the stop band fs. The

transition band ratio is ( fs / fo ).

The slot band is defined as the sum

of the passband and the transition

band.

For comparison, the theoretical

response of a 5th order elliptic filter is shown in Figure B-1. This has a passband

edge at 3 kHz, passband ripple of 0.2 dB, and a stopband attenuation of 50 dB.

Figure B-1: theoretical amplitude response of the 5th order elliptic

Characteristic Magnitudepassband width kHz

transition band ratio

stopband attenuation dB

slot band width

Table B-1: LPF filter characteristic


PAM AND TIME DIVISIOPAM AND TIME DIVISIOPAM AND TIME DIVISIOPAM AND TIME DIVISION NNN

MULTIPLEXINGMULTIPLEXINGMULTIPLEXINGMULTIPLEXING

PREPARATION................................................................................ 2

at the transmitter ................................................................................... 2

at the receiver ........................................................................................ 3

EXPERIMENT.................................................................................. 4

clock acquisition ....................................................................... 4

a single-channel demultiplexer model........................................ 4

frame identification ............................................................................... 5

de-multiplexing ..................................................................................... 6

TUTORIAL QUESTIONS................................................................. 7


PAM AND TIME DIVISIOPAM AND TIME DIVISIOPAM AND TIME DIVISIOPAM AND TIME DIVISION NNN

MULTIPLEXINGMULTIPLEXINGMULTIPLEXINGMULTIPLEXING

ACHIEVEMENTS: channel selection from a multi-channel PAM/TDM signal.

PREREQUISITES: completion of the experiment entitled The sampling theorem.


In the experiment entitled The sampling theorem you saw that a band limited

message can be converted to a train of pulses, which are samples of the message

taken periodically in time, and then reconstituted from these samples.

The train of samples is a form of a pulse amplitude modulated - PAM - signal. If

these pulses were converted to digital numbers, then the train of numbers so

generated would be called a pulse code modulated signal - PCM. PCM signals are

examined in Communication Systems Modelling with TIMS, Volume D1 -

Fundamental digital experiments.

In this PAM experiment several messages have been sampled, and their samples

interlaced to form a composite, or time division multiplexed (TDM), signal

(PAM/TDM). You will extract the samples belonging to individual channels, and

then reconstruct their messages.

at the transmitterat the transmitterat the transmitterat the transmitter

Consider the conditions at a transmitter, where two messages are to be sampled and

combined into a two-channel PAM/TDM signal.

If two such messages were sampled, at the same rate but at slightly different times,

then the two trains of samples could be added without mutual interaction. This is

illustrated in Figure 1.

PAM and time division multiplexing


Figure 1: composition of a 2-channel PAM/TDM

The width of these samples is δt, and the time between samples is T. The sampling

thus occurs at the rate (1/T) Hz.

Figure 1 is illustrative only. To save cluttering of the diagram, there are fewer

samples than necessary to meet the requirements of the sampling theorem.

This is a two-channel time division multiplexed, or PAM/TDM, signal.

One sample from each channel is contained in a frame, and this is of length T

seconds.

In principle, for a given frame width T, any number of channels could be

interleaved into a frame, provided the sample width δt was small enough.

at the receiverat the receiverat the receiverat the receiver

Provided the timing information was available - a knowledge of the frame period T

and the sampling width δt - then it is conceptually easy to see how the samples

from one or the other channel could be separated from the PAM/TDM signal.

An arrangement for doing this is called a de-multiplexer. An example is illustrated

in Figure 2.

Figure 2: principle of the PAM/TDM demultiplexer


The switching function s(t) has a period T. It is aligned under the samples from the

desired channel. The switch is closed during the time the samples from the desired

channel are at its input. Consequently, at the switch output appear only the

samples of the desired channel. From these the message can be reconstructed.


At the TRUNKS PANEL is a PAM/TDM signal.

T1 use your oscilloscope to find and display the TDM signal at TRUNKS.

clock acquisitionclock acquisitionclock acquisitionclock acquisition

To recover individual channels it is necessary to have a copy of the sampling clock.

In a commercial system this is generally derived from the PAM/TDM signal itself.

In this experiment you will use the ‘stolen carrier’ technique already met in earlier

experiments.

The PAM/TDM signal at TRUNKS is based on a sampling rate supplied by the

8.333 kHz TTL sample clock at the MASTER SIGNALS module. You have a copy

of this signal, and it will be your stolen carrier.

The PAM/TDM signal contains no explicit information to indicate the start of a

frame. Channel identification is of course vital in a commercial system, but you

can dispense with it for this experiment.

a singlea singlea singlea single----channel demultiplexer modelchannel demultiplexer modelchannel demultiplexer modelchannel demultiplexer model

ANALOGSWITCH

PULSE

GEN.SAMPLECLOCK

message

PAM/TDM in

Figure 3: PAM/TDM demultiplexer block diagram



You are required to model a demultiplexer for this PAM/TDM signal, based on the

ideas illustrated in Figure 2. You will need a TWIN PULSE GENERATOR and a

DUAL ANALOG SWITCH.

T2 patch up a PAM/TDM demultiplexer using the scheme suggested in Figure 3.

Only one switch of the DUAL ANALOG SWITCH will be required.

Use the DELAYED PULSE OUTPUT from the TWIN PULSE

GENERATOR (set the on-board MODE switch to TWIN). Your model

may look like that of Figure 4 below.

CH1-A

CH2-A

CH1-B

CH2-B

ext. trig

Figure 4: TDM demultiplexer

T3 switch the oscilloscope to CH1-A and CH2-A, with triggering from the sample

clock. Set the gains of the oscilloscope channels to 1 volt/cm. Use the

oscilloscope shift controls to place CH1 in the upper half of the

screen, and CH2 in the lower half.

frame identificationframe identificationframe identificationframe identification

A knowledge of the sampling frequency provides information about the frame

width. This, together with intelligent setting of the oscilloscope sweep speed and

triggering, and a little imagination, will enable you to determine how many pulses

are in each frame, and then to obtain a stable display of two or three frames on the

screen.

You cannot identify which samples represent which channel, since there is no

specific marker pulse to indicate the start of a frame.

You will be able to identify which channels carry speech, and which tones. From

their different appearances you can then arbitrarily nominate a particular channel

as number 1.


dededede----multiplexingmultiplexingmultiplexingmultiplexing

T4 measure the frequency of the SAMPLE CLOCK. From this calculate the

FRAME PERIOD. Then set the oscilloscope sweep speed and

triggering so as to display, on CH1-A, two or three frames of the

PAM/TDM signal across the screen.

T5 make a sketch of one frame of the TDM signal. Annotate the time and

amplitude scales.

T6 set up the switching signal s(t), which is the delayed pulse train from the

TWIN PULSE GENERATOR. Whilst observing the display on CH2-

A, adjust the pulse width to approximately the same as the width of the

pulses in the PAM/TDM signal at TRUNKS.

T7 with the DELAY TIME CONTROL on the TWIN PULSE GENERATOR move

the pulse left or right until it is located under the samples of your

nominated channel 1.

T8 switch the oscilloscope display from CH1-A to CH1-B. This should change

the display from the PAM/TDM signal, showing samples from all

channels, to just those samples from the channel you have nominated

as number 1.

T9 switch back and forth between CH1-A and CH1-B and make sure you

appreciate the action of the DUAL ANALOG SWITCH.

T10 move the position of the pulse from the TWIN PULSE GENERATOR with the

DELAY TIME CONTROL, and show how it is possible to select the

samples of other channels.

Having shown that it is possible to isolate the samples of individual channels, it is

now time to reconstruct the messages from individual channels.

Whilst using the oscilloscope switched to CH1-A and CH2-A as an aid in the

selection of different channels, carry out the next two tasks.

T11 listen in the HEADPHONES to the reconstructed messages from each

channel, and report results.

T12 vary the width of the pulse in s(t), and its location in the vicinity of the

pulses of a particular channel, and report results as observed at the

LPF output.




Q1 what is the effect of (a) widening, (b) decreasing the width of the switching

pulse in the PAM/TDM receiver ?

Q2 if the sampling width δt of the channels at the PAM/TDM transmitter was

reduced, more channels could be fitted into the same frame. Is there

an upper limit to the number of channels which could be fitted into a

PAM/TDM system made from an infinite supply of TIMS modules ?

Discuss.

Q3 in practice there is often a ‘guard band’ interposed between the channel

samples at the transmitter. This means that the maximum number of

channels in a frame would be less than (T/δt). Suggest some reasons

for the guard band.

Q4 what would you hear in the HEADPHONES if the PAM/TDM was connected

direct to the HEADPHONE AMPLIFIER, with the 3 kHz LPF in

series ? This could be done by placing a TTL high at the TTL

CONTROL INPUT of the DUAL ANALOG SWITCH you have used in

the DUAL ANALOG SWITCH module.

Q5 draw a block diagram, using TIMS modules, showing how to model a two-

channel PAM/TDM signal.

Power measurementsVol A1, ch 12, rev 1.0 - 145

POWER MEASUREMENTSPOWER MEASUREMENTSPOWER MEASUREMENTSPOWER MEASUREMENTS

PREPARATION............................................................................... 146

definitions................................................................................ 146

measurement methods ............................................................. 147

cross checking ......................................................................... 147

calculating rms values ............................................................. 148

EXPERIMENT................................................................................. 149

single tone ............................................................................... 149

two-tone................................................................................... 149

100% amplitude modulation ................................................... 150

Armstrong`s signal .................................................................. 150

wideband FM........................................................................... 150

speech ...................................................................................... 151

SSB.......................................................................................... 151

TUTORIAL QUESTIONS ............................................................... 152

summary: ................................................................................. 152

146 - A1Power measurements

POWER MEASUREMENTSPOWER MEASUREMENTSPOWER MEASUREMENTSPOWER MEASUREMENTS

ACHIEVEMENTS: this experiment is concerned with the measurement of the

power in modulated signals. It uses the WIDEBAND TRUE RMS

VOLTMETER to make the measurements, each of which can be

confirmed by independent calculation, and indirect measurement

using the oscilloscope.

PREREQUISITES: familiarity with AM, DSB, and SSB signals; relationships

between peak, mean, and ‘rms’ power.


definitionsdefinitionsdefinitionsdefinitions

The measurement of absolute power is seldom required when working with TIMS.

More often than not you will be interested in measuring power ratios, or power

changes. In this case an rms volt meter is very useful, and is available in the

WIDEBAND TRUE RMS VOLTMETER module. You will find that the accuracy

of this meter is more than adequate for measurements of all signals met in the TIMS

environment.

If the magnitude of the voltage V appearing across a resistor of ‘R’ ohms is known to

be Vrms volts, then the power being dissipated in that resistor is, by definition:

powerV

Rwattrms=

2

mean power: is used when one is referring to the power dissipated by a signal in a

given resistive load, averaged over time (or one period, if periodic). It can be

measured unambiguously and directly by an instrument which converts the

electrical power to heat, and then measuring a temperature rise (say). The

addition of the qualifier ‘rms’ (eg, ‘rms power’), as is sometimes seen, is

redundant.

peak power: refers to the maximum instantaneous power level reached by a signal.

It is generally derived from a peak voltage measurement, and then the power,

which would be dissipated by such a voltage, is calculated (for a given load

resistor). The oscilloscope is an ideal instrument for measuring peak voltage,

provided it has an adequate bandwidth.

Power measurementsA1 - 147

Peak power is quoted often in the context of SSB transmitters, where what is

really wanted, and what is generally measured, is peak amplitude (since one is

interested in knowing at what peak amplitude the power amplifier will run

into non-linear operation). To give it the sound of respectability (?) the

measured peak amplitude is squared, divided by the load resistance, and

called peak envelope power (PEP).

measurement methodsmeasurement methodsmeasurement methodsmeasurement methods

Not all communications establishments possess power meters ! They often attempt

to measure power, and especially peak power, indirectly.

This can be a cause of great misunderstanding and error.

The measurements are often made with voltmeters. Some of these voltmeters are

average reading, others peak reading, and others ..... who knows ? These

instruments are generally intended for the measurement of a single sinewave. A

conversion factor (either supplied by the manufacturer, or the head guru of the

establishment) is often applied, to ‘correct’ the reading, when a more complex

waveform is to be measured (eg, speech). These ‘corrections’, if they must be used

at all, need to be applied with great care and understanding of their limitations.

We will not discuss these short cuts any further, but you have been warned of their

existence. It is advisable to enquire as to the method of power measurement when

others perform it for you.

cross checkingcross checkingcross checkingcross checking

The TIMS WIDEBAND TRUE RMS VOLTMETER can be used for the indirect

measurement of power. There are no correction factors to be applied for any of the

waveforms you are likely to meet in the TIMS environment.

What does an rms voltmeter display when connected to a signal ?

For the periodic waveform V cosµt it indicates the rms value (V/√2), which is what

would be expected. It is the rms value which is used to calculate the power

dissipated by a sinewave in a resistive load, in the formula:

power dissipated in R ohms = (rms amplitude)2/R........ 1

Table 1 give some examples which you should check analytically. During the

experiment you can confirm them with TIMS models and instrumentation.


input rms reading peak volts

1 V.cosµtV

2V

2 V1.cosµ1t + V2

.cosµ2t

2 2

1 2

2 2

V V

+

V1 + V2

3 V.cosµt.cosωt

2 2

2

2

2

2 2

V VV

+

= V

4 V.(1 + m.cosµt).cosωt

+2

12

2

mV V.(1 + m)

5 V.m.cosµt.cosωt + V.sinωt

+2

12

2

mV ( )mV 21 +

6 V.cos(ωt + β.cosµt)V

2V

7 speechV

5 2V

Table 1. as usual, assume ω >> µω >> µω >> µω >> µ

calculating rms valuescalculating rms valuescalculating rms valuescalculating rms values

From first principles you will agree that, for the sinewave y(t), where:

y(t) = V.sinµt volt ........ 2

peak amplitude = V volt ........ 3

rms amplitude (by definition) = (V/√2) volt ........ 4

power in 1 ohm = (V2/2) watt ........ 5

To calculate the power that a more complex periodic signal will dissipate in a 1 ohm

resistor the method is:

1. break up the signal into its individual frequency components.

2. if two or more components fall on a single frequency, determine their resultant

amplitude (use phasors, for example)

3. calculate the power dissipated at each frequency

4. add individual powers to obtain the total power dissipated

5. the rms amplitude is obtained by taking the square root of the total power



You will now model the signals in Table 1, and make some measurements to confirm

the calculations shown there.

For each signal it will be possible to measure the individual component amplitudes

with the oscilloscope, by conveniently removing all the others, and then to calculate

the expected rms value of the composite signal.

Then the rms value of the signal itself can be measured, using the TRUE RMS

VOLTMETER. In this way you can check the performance of the voltmeter against

predictions.

single tonesingle tonesingle tonesingle tone

T1 model the signal #1 of Table 1. It is assumed that you can measure the

amplitude ‘V’ on your oscilloscope. It is also assumed that you agree

with the calculated magnitude of the rms voltage as given in the Table.

Check the TRUE RMS VOLTMETER reading.

The two readings should be in the ratio √2 : 1. If this is not so you should either

determine a calibration constant to apply to this (and subsequent) oscilloscope

reading, or adjust the oscilloscope sensitivity. This correction (or adjustment) will

ensure that subsequent readings should have the expected relative magnitudes. But

note that their absolute magnitudes have not been checked. This is not of interest in

this experiment.

two-tonetwo-tonetwo-tonetwo-tone

T2 model the two-tone signal #2 of Table 1. You can combine the two in an

ADDER, and thus examine and measure each one independently at the

ADDER output (as per the previous task). Compare the reading of the

TRUE RMS VOLTMETER with predictions.

T3 adjust the amplitudes of the signal examined in the previous Task to equality.

Confirm that the peak-to-peak amplitude, as measured on the

oscilloscope, can lead directly to a knowledge of the individual

amplitudes V1 and V2. This is needed for the next Task.


100% amplitude modulation100% amplitude modulation100% amplitude modulation100% amplitude modulation

T4 model the AM signal #4 of Table 1. Use the method of generation introduced

in the experiment entitled Amplitude modulation - method 2 ( within

Volume A2 - Further & Advanced Analog Experiments), as it will be

convenient for the next Task. First set up for 100% depth of

modulation (m = 1). Then:

a) remove the DSBSC, leaving the carrier only. Measure its amplitude,

predict its rms value (!), and confirm with the rms meter.

b) remove the carrier, and add the DSBSC. Measure all you can think of,

as per the previous Task for the two-tones of equal amplitude

signal.

c) replace the carrier, making a 100% AM signal. Measure everything you

think you need to predict the rms value of the AM signal. Measure

the rms value with the rms meter. Compare results with

predictions.

T5 use a two-tone signal for the message (2 kHz message from MASTER

SIGNALS and an AUDIO OSCILLATOR, combined in an ADDER).

Set up 100% AM; calculate the expected change of total power

transmitted between no and 100% modulation ? Compare with a

measurement, using the rms meter.

Armstrong`s signalArmstrong`s signalArmstrong`s signalArmstrong`s signal

T6 use the same model as for the previous Task to model Armstrong`s signal -

signal #5 of Table 1. Changing the phase between the DSBSC and

carrier will change the peak amplitude, but confirm that it makes no

difference to the power dissipated.

wideband FMwideband FMwideband FMwideband FM

T7 model the signal #6 of Table 1. You can use the VCO on the ‘HI’ frequency

range. Connect an AUDIO OSCILLATOR to the Vin socket, and use

the GAIN control to vary the degree of modulation. Confirm that

modulation is taking place by viewing the VCO output, with a sweep

speed of say 10µs/cm, and triggering the oscilloscope to the signal

itself. Confirm that there is no change of peak or rms amplitude with

or without modulation. If there is a change then non-linear circuit

operation is indicated.


speechspeechspeechspeech

T8 examine a speech signal available at TRUNKS or from a SPEECH module.

Compare what you consider to be its peak amplitude (oscilloscope)

with its rms amplitude (rms meter). Determine a figure for the peak-

to-average power ratio of a speech signal.

T9 use speech as the message to an AM transmitter. Use a trapezoid to set up

100% AM. Measure the change of output power between no and full

modulation.

SSBSSBSSBSSB

T10 model an SSB transmitter. Measure the peak output amplitude when the

message is a single tone (a VCO could provide such a single).

Measure the rms output voltage. Replace the tone with speech (now

you would need a genuine SSB generator; perhaps there is such a

signal at TRUNKS ?), and set up for the same peak output amplitude.

Measure the rms output amplitude. Any comments ? Compare with

the same measurement upon speech itself.



Q1 name the signals listed in Table 1.

Q2 draw the waveforms of the signals in Table 1.

Q3 show how each of the signals listed in Table 1 can be modelled

Q4 confirm, by analysis, the results recorded in the final column of Table 1.

Q5 confirm, by measurement, the results recorded in the final column of Table 1.

Q6 how does the true rms power meter work ?

summary:summary:summary:summary:

This whole experiment has been tutorial in nature.

Hopefully you observed, or might have concluded, that:

• the oscilloscope is an excellent instrument for measuring peak amplitudes.

• the true rms meter is ideal (in principle and in practice) for (indirect) power

measurements. No corrections at all need be made for particular waveforms.

copyright © 2005 Emona Instruments Pty Ltd A1-appendix A-rev 1.0 - 1

APPENDIX A

to VOLUME A1

TIMS FILTER

RESPONSES

Appendix A to Volume A1

copyright © 2005 Emona Instruments Pty Ltd A1-appendix A - 3

TABLE OF

CONTENTS

TIMS filter responses ......................................................................................................5

Filter Specifications.........................................................................................................7

3 kHz LPF (within the HEADPHONE AMPLIFIER) ......................................................8

TUNEABLE LPF............................................................................................................9

BASEBAND CHANNEL FILTERS - #2 Butterworth 7th order lowpass ......................10

BASEBAND CHANNEL FILTERS - #3 Bessel 7th order lowpass...............................11

BASEBAND CHANNEL FILTERS - #4 ‘flat’ group delay 7th order lowpass...............12

60 kHz LOWPASS FILTER .........................................................................................13

100 kHz CHANNEL FILTERS - #2 7th order lowpass .................................................14

100 kHz CHANNEL FILTERS - #3 6th order bandpass (type - 1) ................................15

100 kHz CHANNEL FILTERS - #3 8th order bandpass (type - 2) ................................16



TIMS filter responses

There are several filters in the TIMS system.

In this appendix will be found the theoretical responses on which these

filters are based.

Except in the most critical of applications - and the TIMS philosophy is

to avoid such situations - these responses can be taken as

representative of the particular filter you are using.



Filter Specifications

A knowledge of filter terminology is essential for the telecommunications engineer. Here are some

useful definitions.

approximation: a formula, or transfer function, which attempts to match a desired filter

response in mathematical form.

order: the ‘size’ of the filter, in terms of the number of poles in the transfer function.

passband: a frequency range in which signal energy should be passed.

passband ripple: the peak-to-peak gain variation within a passband. Usually expressed in

decibels (dB).

realization: a physical circuit whose response matches as closely as possible that of the

approximation.

slotband: regulatory organizations such as CCITT, Austel, FCC, etc, provide their clients with

spectrum ‘slots’. The regulatory definition of a slot may be fairly involved, but, in simple

terms, it is equivalent to specifying an allowed band for transmission, within which the

user is free to exploit the resource as s/he wishes, and to ensure extremely low levels of

leakage outside the limits. In terms of specifying a filter characteristic it means the band

limit is determined by the stop frequencies for a bandpass filter, or from DC to the start of

the stopband for a lowpass filter. Thus it is the sum of the passband plus transition band

(or bands).

stopband: a frequency range in which signal energy should be strongly attenuated.

stopband attenuation: the minimum attenuation of signal energy in the stopband, relative to

that in the passband. Usually expressed in decibels (dB).

transition band: a frequency region between a passband and a stopband.

transition band ratio: the ratio of frequencies at either end of the transition band; generally

expressed as a number greater than unity.

Specification mask

Filters are often specified in terms of a specification mask. Any filter whose response will fit within the

mask is deemed to meet the specification. Typical specification masks are shown in the Figures below.

a lowpass specification mask a bandpass specification mask


3 kHz LPF (within the HEADPHONE AMPLIFIER)

This is an elliptic lowpass, of order 5.

passband ripple 0.2 dB

passband edge 3.0 kHz

stopband attenuation 50 dB

slotband DC to 4.78 kHz

transition band ratio 1.59



TUNEABLE LPF


It is shown plotted with a slotband of 4.0 kHz




slotband DC to 4.0 kHz


Filter cutoff frequency is given by:

NORM range: clk / 880

WIDE range: clk / 360

For more detail see the TIMS User Manual.


BASEBAND CHANNEL FILTERS - #2

Butterworth 7th order lowpass

This filter is selected with the front panel switch in position 2

response monotonic falling

passband -1 dB at 1.88 kHz

stopband -40 dB at 4.0 kHz



BASEBAND CHANNEL FILTERS - #3

Bessel 7th order lowpass


response monotonic falling

passband edge -1 dB at 620 Hz

stopband -40 dB at 4.0 kHz


BASEBAND CHANNEL

FILTERS - #4

‘flat’ group delay 7th order

lowpass


It exhibits an equiripple (‘flat’) group delay response over the complete passband and into the transition

band.




slotband DC to 4 kHz

delay ripple 10 µs peak-to-peak

delay bandwidth DC to 1.92 kHz



60 kHz LOWPASS FILTER



passband edge 60 kHz


slotband DC to 71.4 kHz.



100 kHz CHANNEL FILTERS - #2

7th order lowpass


An inverse-Chebyshev lowpass filter, of order 7.


passband edge 120 kHz


slotband DC to 190 kHz.




6th order bandpass(type - 1)


There are two version of this filter, type 1 and type 2. The characteristic below is that of type 1. This

filter was delivered before mid-1993. The board bears no indication of type.

Type 1 is an inverse Chebyshev bandpass filter, of order 6.


lower passband edge 85 kHz

upper passband edge 115 kHz


slotband 52 kHz to 187 kHz



8th order bandpass(type - 2)


There are two version of this filter, type 1 and type 2. The characteristic below is that of type 2. This

filter was not delivered before mid-1993. The inscription type 2 will be found on the circuit board.

Type 2 is an inverse Chebyshev bandpass filter, of order 8.

100 kHz, order_8, BPF

passband ripple 1 dB

lower passband edge 90 kHz

upper passband edge 110 kHz


slotband 76 kHz to 130 kHz

A1 Copyright © 2004 Emona Instruments Pty Ltd. All rights reserved. Some useful expansions

APPENDIX B

to VOLUME A1

SOME USEFUL EXPANSIONS

Appendix to Volume A1

B- 2 Some useful expansions


Some useful expansions B - 3

SOME USEFUL EXPANSIONS

cosA.cosB = 1/2 [ cos(A-B) + cos(A+B) ]

sinA.sinB = 1/2 [ cos(A-B) - cos(A+B) ]

sinA.cosB = 1/2 [ sin(A-B) + sin(A+B) ]

sin(A+B) = sinA cosB + cosA sinB

sin(A-B) = sinA cosB - cosA sinB

cos(A+B) = cosA cosB - sinA sinB

cos(A-B) = cosA cosB + sinA sinB

cos2Α = 1/2 + 1/2 cos2Α

cos3Α = 3/4 cosΑ + 1/4 cos3Α

cos4Α = 3/8 + 1/2 cos2Α + 1/8 cos4Α

cos5Α = 5/8 cosΑ + 5/16 cos3Α + 1/16 cos5Α

cos6Α = 5/16 + 15/32 cos2Α + 3/16 cos4Α + 1/32 cos6Α

sin2Α = 1/2 - 1/2 cos2Α

sin3Α = 3/4 sinΑ - 1/4 sin3Α

sin4Α = 3/8 - 1/2 cos2Α + 1/8 cos4Α

sin5Α = 5/8 sinΑ - 5/16 sin3Α + 1/16 sin5Α

sin6Α = 5/16 - 15/32 cos2Α + 3/16 cos4Α - 1/32 cos6Α

• During envelope waveform evaluations one or other of the following expansions is often

needed:

arctan [sin

( ) cos] sin sin sin sin .. . .. .

r z

r zr z r z r z r z

1

1

22

1

33

1

442 3 4

−= + + + +

1

2

2

1

1

33

1

55

23 5arctan [

sin] sin sin sin . .. . .

r z

rr z r z r z

−= + + +

1

1 21 2 3

22 3−

− += + + + +

r z

r z rr z r z r z

cos

coscos cos cos . . ..

arctan . . .. . | |x xx x

for x= − + − <3 5

3 51


B- 4 Some useful expansions

• The binomial expansion, for x < 1:

( )( )

!

( )( )

!. .. . .1 1

1

2

1 2

3

2 3

+ = + +−

+− −

+x nxn n x n n n xn

is especially useful for the case n = ½ and n = -½

• A zero-mean square wave, peak-to-peak amplitude 2E, period ( )2π

ω, time axis chosen to

make it an even function:

square waveE

t t t= − + −4 1

33

1

55

πω ω ω[cos cos cos . . .. .

• Required for FM spectral analysis are the following:

cos(β sinφ) = J0(β) + 2 [ J2(β) cos2φ + J4(β) cos4φ + ..................]

sin(β sinφ) = 2 [ J1(β) sinφ + J3(β) sin3φ + J5(β) sin5φ + ............]

cos(β cosφ) = J0(β) - 2 [ J2(β) cos2φ - J4(β) cos4φ + ....................]

sin(β cosφ) = 2 [ J1(β) cosφ - J3(β) cos3φ + J5(β) cos5φ - ..............]

where Jn(β) is a Bessel function of the first kind, argument β, and order n.

• You will also need to know that:

J Jnn

n− = −( ) ( ) ( )β β1


Some useful expansions B - 5




with

Volume A2 Further & Advanced Analog Experiments

Tim Hooper


Volume A2 - Further & Advanced Analog Experiments. Author: Tim Hooper

Issue Number: 4.9

Published by:






EXPERIMEXPERIMEXPERIMEXPERIMENT AIMSENT AIMSENT AIMSENT AIMS


The experiments have been written with the idea that each model examined could eventually become part of a larger telecommunications system, the aim of this large system being to transmit a message from input to output. The origin of this message, for the analog experiments in Volumes A1 and A2, would ultimately be speech. But for test and measurement purposes a sine wave, or perhaps two sinewaves (as in the two-tone test signal) are generally substituted. For the digital experiments (Volumes D1, D2, and D3) the typical message is a pseudo random binary sequence.











Amplitude modulation - method 2 ...............................................A2-01

Weaver`s SSB generator .............................................................A2-02

Weaver`s demodulator ................................................................A2-03

Carrier acquisition and the PLL...................................................A2-04

Spectrum analysis - the WAVE ANALYSER .........................................A2-05

Amplifier overload ......................................................................A2-06

Frequency division multiplex .......................................................A2-07

Phase division multiplex ..............................................................A2-08

Analysis of the FM spectrum.......................................................A2-09

Introduction to FM using a VCO.................................................A2-10

FM and the synchronous demodulator .........................................A2-11

Armstrong`s phase modulator......................................................A2-12

FM deviation multiplication.........................................................A2-13

FM and Bessel zeros ...................................................................A2-14

FM demodulation with the PLL...................................................A2-15

The Costas loop ..........................................................................A2-16

Appendix A - Tables of Bessel Coefficients .................................A2-A



---- METHOD 2 METHOD 2 METHOD 2 METHOD 2

PREPARATION ................................................................................2

AM as DSBSC + carrier ............................................................2

phase requirement ................................................................................. 3

the equation model ....................................................................3

EXPERIMENT..................................................................................4

the TIMS model........................................................................4

adjusting the model ............................................................................... 4

phase adjustment ................................................................................... 5

TUTORIAL QUESTIONS.................................................................8


AMPLITUAMPLITUAMPLITUAMPLITUDE MODULATION DE MODULATION DE MODULATION DE MODULATION

---- METHOD 2 METHOD 2 METHOD 2 METHOD 2

ACHIEVEMENTS: another method of modelling an amplitude modulated

(AM) signal (see the experiment entitled Amplitude modulation

in Volume A1); indirect method of phase measurement.

PREREQUISITES: completion of the experiment entitled Amplitude

modulation in Volume A1 would be an advantage.


AM as DSBSC + carrierAM as DSBSC + carrierAM as DSBSC + carrierAM as DSBSC + carrier

There are many ways of generating an amplitude modulated (AM) signal.

Refer to a text book for some of them. The class C modulated amplifier is a

popular circuit. If the prime requirement of a transmitter is to generate AM,

then this (or variations of it) is probably the best choice. But sometimes it is a

secondary requirement. For example, a transmitter might primarily be

designed for DSBSC generation. An ability to synthesise AM might be a

secondary requirement; a suitable method is examined in this experiment.

In the experiment entitled Amplitude modulation (in Volume A1), you have

already modelled the AM equation in the form of:

AM = E.(1 + m.cosµt).cosωt ........ 1

There are other methods of writing this equation; for example, by expansion, it

becomes:

AM = E.m.cosµt.cosωt + E.cosωt ........ 2

= DSBSC + carrier ........ 3

The depth of modulation ‘m’ is determined by the ratio of the DSBSC and

carrier amplitudes, since, from eqns.(2) and (3):

ratio (DSBSC/carrier) = (E.m) / E = m ........ 4

Amplitude modulation - method 2


phase requirementphase requirementphase requirementphase requirement

The important practical detail here is the need to adjust the relative phase

between the DSBSC and the carrier. This is not shown explicitly in eqn. (2),

but is made clear by rewriting this as:

AM = E.m.cosµt.cosωt + E.cos(ωt + α) ........ 5

Here α is the above mentioned phase, which, for AM, must be set to:

α = 0o ........ 6

Any attempt to model eqn. (2) by adding a DSBSC to a carrier cannot assume

the correct relative phases will be achieved automatically.

It is eqn. (5) which will be achieved in the first instance, with the need for

adjustment of the phase angle α to zero.

the equation modelthe equation modelthe equation modelthe equation model

A block diagram of the arrangement for modelling eqn. (2) is shown in

Figure 1.

100 kHz (sine wave)

DSBSC

carrier

adjust phase

g

G

CH1-A

message (sine wave)

CH2-A

ext. trig

AMout

Figure 1: block diagram of AM generator



the TIMS modelthe TIMS modelthe TIMS modelthe TIMS model

The block diagram of Figure 1 can be modelled by the arrangement of Figure 2.

CH1-A

CH2-A

ext. trig

note use of quadrature carriers

Figure 2: the AM generator model

adjusting the moadjusting the moadjusting the moadjusting the modeldeldeldel

You will now set up a 100% amplitude modulated signal using the model of

Figure 2.

The DSBSC and the carrier from which it is derived are required to be in phase

for the generation of AM.

Examination of Figure 1 might suggest that no

phase adjustment is required, since the DSBSC

and carrier should be already in phase.

But the DSBSC and carrier are taken via separate paths to the ADDER, and

these paths, and the ADDER, can introduce small and unknown (but stable)

phase shifts. Thus at the adding point the two may not be in exact phase. A

correction may be necessary. It is the purpose of the PHASE SHIFTER to

make this small correction. The PHASE SHIFTER itself cannot introduce a

small phase shift, even if the front panel control is fully anti-clockwise. This

may, in any case, be in the wrong direction. To overcome this possible problem

the carriers to the PHASE SHIFTER and to the MULTIPLIER (for the DSBSC

generation) have already been shifted by 900 by using the quadrature outputs

from the MASTER SIGNALS module. Thus the PHASE SHIFTER is required



to introduce a further small adjustment either side of ±900, which is in its mid-

range of control, rather than at one end.

T1 patch up the model of Figure 2. Remember to set the on-board switch of

the PHASE SHIFTER to the ‘HI’ (100 kHz) range before plugging

it in.

T2 set the gain controls g and G of the ADDER fully anti-clockwise.

T3 set the oscilloscope to accept the ‘ext. trig’ signal, and adjust sweep and

gain controls so that the message is displayed on CH1-A, filling

about the top half of the screen.

T4 set the gain control of the oscilloscope CH2 to the same as that of CH1.

T5 without touching the sweep speed of the oscilloscope adjust the amplitude

of the carrier signal, using the G control on the ADDER, so it is

about 2 volts peak-to-peak, but exactly aligned between two

horizontal lines of the oscilloscope graticule.

T6 temporarily remove the carrier signal from the G input of the ADDER

T7 advance the ADDER gain control g until the DSBSC is displayed on

CH2-A of the oscilloscope between the same two graticule lines as

was the carrier.

T8 replace the carrier term into the G input of the ADDER.

You have now set up the signal of eqn. (4), except for the phase angle α.

The output of the ADDER is expected to be a 100% amplitude modulated AM

signal, but only if the relative phase is correct; that is, α = 0.

It is an easy matter to adjust the phase:

T9 vary the front panel control of the PHASE SHIFTER until, watching the

display for CH2-A of the oscilloscope, a 100% AM is achieved.

Q although no instruction was given about how you might recognise the

required phase condition, did you find this self evident ? Explain.

phase adjustmentphase adjustmentphase adjustmentphase adjustment

The above instruction offers no advice as to how the correct phase adjustment

is to be achieved. But if you try it, there will be little doubt as to what to do.


You will notice that there is only one position of the PHASE SHIFTER control

when the troughs of the signal will exactly ‘kiss’, as is expected for 100% AM.

The ‘kiss’ occurs when α = 0. This is clearly illustrated in Figure 3.

Figure 3: showing envelope for small phase errors

From a practical point of view the ‘kiss’ test is adequate as a method of phase

adjustment. But remember it must be made under conditions for m = 1 - that

is, with equal amplitude DSBSC and carrier signals at the ADDER output, and

a sinusoidal message.

For an error of 5 degrees Figure 3 shows clearly that the troughs will not kiss;

this is even more obvious for an error of 10 degrees.

phase = 0 phase = αααα

α

Am

2

Am

2

A

ωω µ−−−− ω µ++++

Amplitude Spectrum

frequency

Phasor Form

Am2

A

Figure 4: DSBSC + carrier, with m = 1

Representation of the DSBSC and carrier in phasor form is shown in Figure 4.

This is another way of looking at the signal. It is clear that, when the phase

angle is other than zero, no matter what the sideband amplitude, they could

never add with the carrier to produce a resultant of zero amplitude, which is

required for the ‘kiss’. When the sidebands are in phase with the carrier, this

can clearly only happen when m = 1 (as it is in the diagram).



Figure 4 also shows the amplitude spectrum. This is not affected as the phase

changes.

There are other methods of phase adjustment. One would be to recover the

envelope in an envelope detector (see earlier experiments) and adjust the phase

until the distortion of the recovered envelope is a minimum. This is a practical

method which achieves directly what is desired - without ever having to

measure relative phase. In this way there may be some compensation for the

inevitable distortion introduced both by the transmitter, at high depths of

modulation, and the receiver.


TUTORIAL TUTORIAL TUTORIAL TUTORIAL

QUESTIONSQUESTIONSQUESTIONSQUESTIONS

Q1 show, with the aid of a phasor diagram, that, when the DSBSC and the

carrier are of the same amplitude (the condition for 100% AM),

the only way for them to periodically sum to zero is for their

relative phase to be zero. This is the condition for the troughs to

‘kiss’. As an extension of this, show that, for m < 1, they could

never kiss.

Q2 how could you use a commercial phase meter to measure the relative

phase between a carrier and a DSBSC ?

Q3 there was no need to make an explicit phase adjustment when modelling

eqn. (1), whereas this was necessary when modelling eqn. (3).

These two equations model the same signal. Comment.

Q4 if an AM signal was connected to the FREQUENCY COUNTER, would it

read:

a) the carrier frequency ?

b) the envelope frequency ?

c) what ?

Explain !


WEAVER`S SSB WEAVER`S SSB WEAVER`S SSB WEAVER`S SSB

GENERATORGENERATORGENERATORGENERATOR

PREPARATION................................................................................ 2

principles .................................................................................. 2

EXPERIMENT.................................................................................. 4

the model.................................................................................. 4

alignment .................................................................................. 4




GENERATORGENERATORGENERATORGENERATOR

ACHIEVEMENTS: exposure to Weaver`s SSB generator, and its alignment

procedure.

PREREQUISITES: completion of some previous experiments involving linear

modulated signal generation, especially SSB generation - the

phasing method.

EXTRA MODULES: a total of four MULTIPLIERS, two PHASE SHIFTERS, and

two TUNEABLE LPF modules is required. This is twice as many of

these modules as are in the TIMS Basic Set.


princprincprincprinciplesiplesiplesiples

You should refer to a Text book for more detail on Weaver`s method of SSB

generation 1. This experiment will introduce you to some of its properties, and

methods of alignment.

You are well advised to try the Tutorial Questions (especially Q1) before attempting

the experiment, but after reading these preparatory notes..

Weaver`s method of SSB generation, like the phasing method, depends for its

operation upon phase cancellation of two DSBSC-like signals. But:

1. it does not require wideband phasing networks, like the phasing method of SSB

generation.

2. it does not require sharp cut-off filters, operating away from baseband, as does

the filter method of SSB generation.

3. its unwanted components - those which are not fully removed (by phasing, as in

the phasing method, or by imperfect filtering, as in the filter method) - do not

1 Weaver, D.K., “A third method of generation and detection of single sideband signals”, Proc. IRE, Dec.

1956, pp. 1703-1705

Weaver`s SSB generator


cause interference to adjacent channels, since they fall inside the SSB channel

itself.

Figure 1 shows a block diagram of the method.

There are two pairs of multipliers. These are referred to as quadrature multipliers,

since they use ‘carriers’ phased relatively at 900. This configuration is found in

many communications circuits.

The message bandwidth is defined as B Hz. It is shown as extending down to DC,

but in practice (speech messages) this is not necessary - even undesirable. The DC

requirement would introduce some complications, including the need for the first

pair of quadrature multipliers to be DC coupled.

Two filters are required, but they are at baseband, where design and realization is

simplified. They must, however, be matched (amplitude and phase responses) as

closely as possible.

There are two phase shifters, but they are required to produce a 900 phase shift at a

single frequency only.

Note that the second pair of quadrature multipliers should, ideally, be DC coupled.

Think about it ! In practice DC coupling is not often provided, since it introduces

DC-offset problems. As a result there can be a small gap in the message, as

received, in the vicinity of (B/2) Hz. See Tutorial Question 6.

SSB out

+-0fB

2 Hz B2

Hz (bandwidth B Hz,

suppressed carrier f Hz)0B2DC to Hz

B

2DC to Hz

IN

message

DC to B Hz

ΣΣΣΣπ

/2 π/2

Figure 1: block diagram of Weaver`s SSB generator

Note that the input lowpass filter shown in the block diagram is not included in the

patching diagram to follow (Figure 2). Its presence is recognised by not allowing

the message source to be tuned above B Hz.

Tracing the message through either the upper arm or the lower arm alone is

insufficient to deduce unambiguously what the frequency of the output signal will

be. This is because of the cancellations which will take place in the summing

block. Until the actual signals and their phases are known it is not possible to

deduce which will cancel and which will add.

The analysis can be performed trigonometrically, using a single tone message.


Note that, what ever the output, the carrier frequency is not that of the second

oscillator.


the modelthe modelthe modelthe model

A suggested model of Weavers SSB generator is shown in Figure 2 below. It is best

patched up stage-by-stage, from the input, checking operation until the output is

reached.

( B/2 = 2.083 kHz )this is the B/2 carrier

#2#1( < B Hz )message

the high frequency term, but NOT the SSB (suppressed) carrier

ext. trig

CH2-A

CH1-A

CH2-B

roving trace

CH1-B

Figure 2: model of Weaver`s SSB generator

Please note: the ‘2 kHz message’ from the MASTER SIGNALS module is not

Weaver`s message, but is being used as the source of a stable, low frequency

carrier, on B/2 Hz (refer the block diagram of Figure 1). Thus the message

bandwidth must not exceed B Hz. A bandlimiting filter for the message is

not included in the model (Figure 2), so the AUDIO OSCILLATOR

message source is kept below 4 kHz for correct performance. But you

should investigate what happens if this restriction is not adhered to - as it

would not be if the message was not strictly bandlimited.

alignmentalignmentalignmentalignment

The alignment of Weaver`s SSB generator is quite straightforward, and will not be

given in any great detail.

T1 before plugging in the PHASE SHIFTER modules, set their on-board range

switches; #1 module to ‘LO’, and #2 module to ‘HI’ (refer Figure 2).



T2 use the ‘2 kHz message’ from the MASTER SIGNALS module to set the

PHASE SHIFTER #1 to about 900. This is achieved to sufficient

accuracy by displaying the input and output to the PHASE SHIFTER

on two oscilloscope traces. Adjust the PHASE SHIFTER front panel

control until one sinewave is delayed 1/4 period with respect to the

other. Fine trimming cannot be carried out until the generator is near

completion.

T3 set the TUNEABLE LPF modules to the same bandwidth, ‘B/2’, namely

2.083 kHz. With the front panel switch set to ‘NORM’, this makes the

‘CLK’ frequency 2.083 x 880 = 1833 kHz.

T4 set the message AUDIO OSCILLATOR to say 1 kHz. Call this fm Hz, and

make a record of it.

T5 now patch up according to Figure 2.

T6 trigger the oscilloscope externally to the message on fm Hz. Use the roving

trace CH1-B to confirm that the waveforms at the output of each of

the low frequency MULTIPLIER modules is a DSBSC. There are no

adjustments you can make if this is not so - check patching !

T7 trigger the oscilloscope to the ‘roving trace’ (CH1-B), and use it to confirm

that the waveform at the output of each of the TUNEABLE LPF

modules is a sine wave. There are no adjustments you can make if

this is not so - check patching ! Its frequency will be (B/2 - fm) Hz -

confirm this.

T8 adjust the gain of each of the TUNEABLE LPF modules filter to make the

amplitude of each output sinewave about 4 volt peak-to-peak (TIMS

ANALOG REFERENCE LEVEL).

T9 confirm with the ‘roving trace’ that the waveform at the output of each of the

high frequency MULTIPLIER modules is a DSBSC. There are no

adjustments you can make if this is not so - check patching ! Its

‘message’ will be the sinewave from the TUNEABLE LPF; use this

for external oscilloscope triggering.

When you reach this point all is ready for the final

amplitude and phase adjustments, which will achieve the

required result at the output of the ADDER.

T10 switch the oscilloscope to CH1-A. Remove the patch lead from the upper

input of the ADDER. Adjust the lower gain control until the output is

a DSBSC of about 4 volt peak-to-peak amplitude. Replace the upper

patch lead.


T11 remove the patch lead from the lower input of the ADDER. Adjust the upper

gain control until the output is a DSBSC of about 4 volt peak-to-peak

amplitude. Replace the lower patch lead.

You are aiming for an ADDER output of a single sinewave.

Although you have adjusted the amplitudes of the signals at the

summing point to approximate equality, their relative phases

have not been set.

T12 while watching the ADDER output, vary the phase of the phase shifter #2,

aiming for a sinewave.

T13 fine trim one (only) of the ADDER gain controls for a better result.

Remember: a perfect SSB (sinewave message) has a straight line

envelope. Synchronise to its ‘message’ - in this case the output from

either TUNEABLE LPF module. Think about it !

Repeat this, and the previous Task, until the best result is achieved.

The two high frequency MULTIPLIER modules, as shown in Figure 2, are set to

accept DC. This is a requirement of the Weaver modulator. But in practice it is a

problem, since DC offsets, preceding the two high-frequency multipliers, will

degrade performance. You can check this by flipping the toggle switches to AC.

T14 change the input coupling of the two high frequency MULTIPLIER modules

to AC, and check if a superior performance can be obtained (a flatter

envelope).

T15 with the two high frequency MULTIPLIER modules still AC coupled, vary

the message frequency through the frequency B/2 (namely, the low

frequency carrier frequency of 2.083 kHz) and demonstrate the gap in

the response. Message frequencies near 2.083 kHz will be missing.

But this imperfection is generally acceptable in practice, and AC

coupling is used.

T16 is there any point to checking the adjustment of the PHASE SHIFTER #1 ?

Alignment of the Weaver SSB generator is complete



T17 measure the frequency of the output. From the details of Figure 1 confirm

that this is a possible outcome. What is the carrier frequency ? This

means ‘with what frequency sinewave would this SSB need to be

multiplied to recover the correct message frequency in a convnetional

demodulator ?’ There will be two answers, only one of which is

correct. Which one ? Why ?

T18 vary the message frequency over its allowed range of B Hz. Remember there

is no message bandlimiting filter installed. Demonstrate that the

generator performs satisfactorily over this range (except for the ‘gap’

previously identified).

T19 measure the sideband suppression ratio (SSR). Refer to the experiment

entitled SSB generation - the phasing method, in Volume A1, for

details.


Q1 perform a trigonometrical analysis of Weaver`s method of SSB generation.

Use a single tone for the message. Assume the ‘B/2’ filters are ideal

(and matched). Assume the only impairments are small phase errors

α1 and α2 in each of the 900 phase shifters. Obtain an expression for

the sideband suppression ratio in decibels, as a function of these two

phase errors.

Q2 from a knowledge of the properties of all of the modules you have used,

predict from the previous calculation which sideband (upper or lower)

your model will generate. Confirm by measurement.

Q3 use any method to determine the (suppressed) carrier frequency of the SSB

generator, in terms of B and fo , both defined in Figure 1. Confirm

from measurement.

Q4 use any method to determine the frequency of the SSB output from the

generator, when:

a) the ‘B/2’ oscillator is on 2.083 kHz

b) the message frequency is 500 Hz

c) the second oscillator frequency is 100 kHz

d) the phasing resulted in an UPPER sideband.

Confirm by measurement.

Q5 when the generator was aligned you measured the output frequency. From

this single measurement can you state:

a) if you have an upper or lower sideband ?

This question cannot be answered without


i) knowing something about the internal arrangement of the

generator

or

ii) increasing the message frequency, and observing if the sideband

frequency increases or decreases.

b) what was the SSB suppressed carrier frequency ?

Q6 the first pair of quadrature multipliers (Figure 1) need to be DC coupled only

if the message contains a DC component. Circuit designers try to

avoid DC coupling, as this requires care in minimizing DC offsets.

AC coupling is preferred, and this is acceptable for speech. The

second pair of quadrature multipliers must be DC coupled, unless one

is prepared to accept a small gap in the message (as received) in the

region of (B/2) Hz. Explain.

Q7 the amplitude of the individual outputs from the ADDER were set to about

4 volts peak-to-peak before final trimming. These were DSBSC-style

signals. When they were present together, and the system aligned,

about what amplitude would you expect for the final SSB signal ?

Show your reasoning. Check by measurement.



DEMODULATORDEMODULATORDEMODULATORDEMODULATOR

PREPARATION................................................................................ 2

EXPERIMENT.................................................................................. 3





ACHIEVEMENTS: alignment of Weaver`s SSB receiver

PREREQUISITES: completion of experiment entitled Weaver`s SSB generator in

this Volume.

EXTRA MODULES: a total of four MULTIPLIERS, two PHASE SHIFTERS, and

two TUNEABLE LPF modules is required. This is twice as many of

these modules as are in the TIMS Basic Set.


It is assumed that you have completed the experiment entitled Weaver`s SSB

generator, where the general principles of Weaver`s method were met.

The demodulator employs the same principles, although ‘in reverse’, as it were.

Its block diagram is shown in Figure 1.

+-0fB

2 HzB2

Hz

B2DC to Hz

B2DC to Hz

INOUT

message, bandwidth B

SSB on carrier f 0

π/2 π

2

Figure 1: model of Weaver`s SSB demodulator

As in the case of the phasing method of SSB generation, two lowpass filters are

shown at the inputs to the second pair of quadrature multipliers. In practice these

two are replaced by a single lowpass filter, of bandwidth B Hz, at the output of the

summing block. Similar comments apply here as were made when describing the

phasing-type SSB demodulator.

Weaver`s SSB demodulator



If you have completed the experiment entitled Weaver`s SSB generator you should

have no difficulty in modelling Weaver`s demodulator !

Your low frequency carrier will be the nominal 2 kHz ‘message’ available from the

MASTER SIGNALS module.

When aligned, you should demonstrate that the receiver looks out at the RF

spectrum on one side only of the carrier to which it is tuned. You should confirm

that this window is B Hz wide 1.

[ Refer to the technique of testing used in the experiment entitled SSB

demodulation – the phasing method in Volume A1. This used a VCO to simulate

an SSB signal derived from a single tone message. Thus, with the VCO tuned to

102 kHz, it simulates the USB of a 100 kHz SSB transmitter, derived from a 2 kHz

message.

When the receiver is tuned to receive the VCO on the high side (USB) of the

100 kHz carrier (say at 102 kHz) then there should be no output from the receiver

when the VCO is tuned to 98 kHz (the LSB) ].


Q1 analyse the system illustrated in Figure 1, and show that it has a window on

the frequency spectrum of bandwidth B/2 Hz. Show exactly where this

is located in the spectrum.

Q2 describe the practical problems associated with placing the two filters at the

inputs to the second pair of multipliers, and the different set of

problems encountered when they are replaced by a single filter at the

summing block output.

1 where B is defined in Figure 1


CARRIER ACQUISITION CARRIER ACQUISITION CARRIER ACQUISITION CARRIER ACQUISITION

AND THE PLLAND THE PLLAND THE PLLAND THE PLL

PREPARATION................................................................................ 2

carrier acquisition methods........................................................ 2

bandpass filter ....................................................................................... 2

the phase locked loop (PLL). ................................................................. 3

squaring ................................................................................................ 4

squarer plus PLL ................................................................................... 6

the Costas loop ...................................................................................... 6

EXPERIMENT.................................................................................. 7

the pilot carrier and BPF ........................................................... 7

the PLL..................................................................................... 7

the squaring multiplier............................................................... 8

the PLL + squarer ..................................................................... 9



CARRIER ACQUISITION CARRIER ACQUISITION CARRIER ACQUISITION CARRIER ACQUISITION

AND THE PLLAND THE PLLAND THE PLLAND THE PLL

ACHIEVEMENTS: introduction to a method of carrier acquisition using the phase

locked loop (PLL)

PREREQUISITES: familiarity with the generation and demodulation of DSBSC -

completion of the experiments entitled DSBSC generation and

Product demodulation - synchronous & asynchronous (both in

Volume A1)

ADVANCED MODULES: 100 kHz CHANNEL FILTERS

EXTRA MODULES: a third MULTIPLIER module would be an advantage


carrier acquisition methodscarrier acquisition methodscarrier acquisition methodscarrier acquisition methods

As you will know there is often a need, at the receiver, to have a copy of the carrier

which was used at the transmitter. See, for example, the experiment entitled

Product demodulation -synchronous & asynchronous in Volume A1.

This need is often satisfied, in a laboratory situation, by using a stolen carrier.

This is easily done with TIMS. But in commercial practice, where the receiver is

remote from the transmitter, this local carrier must be derived from the received

signal itself.

The use of a stolen carrier in the TIMS environment is justified by the fact that it

enables the investigator (you) to concentrate on the main aim of the experiment,

and not be side-tracked by complications which might be introduced by the carrier

acquisition scheme.

bandpass filterbandpass filterbandpass filterbandpass filter

There have been many schemes proposed for the purpose of deriving carrier

information from the received signal. Many of these depend for their operation on

the existence of a component, however small, at carrier frequency, in the

Carrier acquisition and the PLL


transmitted signal itself. This is often called a ‘pilot carrier’. Commercial practice

was to set the pilot carrier at a level of about 20 dB below the major sidebands 1.

Modern practice is to omit pilot carriers completely.

A signal with pilot carrier is illustrated in Figure 1. It is a DSBSC, derived from a

single tone, with a small amount of carrier added. See Tutorial Question Q2.

time

Figure 1: DSB with small carrier leak

To extract a term at carrier frequency from this signal one could use a narrowband

bandpass filter. Unfortunately this scheme, as simple as it appears to be, has its

problems. For example, in practice the frequency stability of the transmitted carrier

may be such that the receiver filter would need either to track it, or be wide enough

to encompass it under all conditions. In this latter case the filter may allow some

sidebands to pass as well, thus impairing the purity of the recovered carrier. So

generally something more sophisticated is required.

the phase locked loop (PLL).the phase locked loop (PLL).the phase locked loop (PLL).the phase locked loop (PLL).

The PLL configuration includes a non-linear feedback loop. See Figure 2. To

analyse its performance to any degree of accuracy is a non-trivial exercise. To

illustrate it in simplified block diagram form is a simple matter.

VCO

inout

control voltage

Figure 2: the basic PLL

To describe its behaviour in elementary terms is also a simple matter.

If there is a component at the desired frequency at the input, it will appear at the

output in filtered and amplitude stabilised form. In addition, if the frequency of the

input changes, the PLL output is capable of following it.

1 typically defined relative to the transmitter peak envelope power (PEP).


The PLL behaves like a narowband tracking filter.

Of course, there are conditions upon this happening.

The principle of operation is simple - or so it would appear.

Consider the arrangement of Figure 2 in open loop form. That is, the connection

between the filter output and VCO control voltage input is broken.

Suppose there is an unmodulated carrier at the input.

The arrangement is reminiscent of a product demodulator. If the VCO was tuned

precisely to the frequency of the incoming carrier, ω0 say, then the output would be

a DC voltage, of magnitude depending on the phase difference between itself and

the incoming carrier.

For two angles within the 3600 range the output would be precisely zero volts DC.

Now suppose the VCO started to drift slowly off in frequency. Depending upon

which way it drifted, the output voltage would be a slowly varying AC, which if

slow enough looks like a varying amplitude DC. The sign of this DC voltage would

depend upon the direction of drift.

Suppose now that the loop of Figure 2 is closed. If the sign of the slowly varying

DC voltage, now a VCO control voltage, is so arranged that it is in the direction to

urge the VCO back to the incoming carrier frequency ω0, then the VCO would be

encouraged to ‘lock on’ to the incoming carrier. The carrier has been ‘acquired’.

Notice that, at lock, the phase difference between

the VCO and the incoming carrier will be 900.

Matters become a little more complicated if the incoming signal is now modulated.

Suppose it was an AM signal. There is always a carrier, and the sidebands are

always symmetrically displaced about it. Qualitatively you may tend to agree that,

if the sidebands were not too large, the PLL would still lock on to the carrier, which

is the largest component present; and so it does.

Being a non-linear arrangement, as analysis will show, it is not so much the largest

component present as the central component to which the PLL will lock. In fact,

the amplitude of the central component need not be large (under some conditions it

can even be zero ! Non-linearities will generate energy at the carrier frequency).

Rather than attempt to justify this statement analytically (it is a non-trivial exercise)

you will make a model of the PLL, and demonstrate that it is able to derive a carrier

from a DSB signal which contains a pilot carrier.

squaringsquaringsquaringsquaring

What happens if the received signal has no pilot carrier ?

This is the general case in modern practice. The solution is to subject the signal to

a non-linear operation. This will generate new spectral components. A popular

non-linear characteristic is that of squaring.



Such a signal processing block is illustrated in block diagram form in Figure 3

below:

divideby

two

in out

Figure 3: the squaring circuit

The divide-by-two block is shown with an analog input. An analog output is

implied. Internally the circuitry may be digital.

This arrangement will generate a component at carrier frequency from a true

DSBSC signal.

It is easy to show, in a simple case, that this is so. For example.

DSBSC = a(t).cosωt ........ 1

DSBSC squared = a2(t) [½ + ½ cos(2ω)t ........ 2

= ½.a2(t) + ½.a2(t).cos2ωt ........ 3

= low frequency term + DSB at 2ω........ 4

Here a(t) is the message. After squaring it must have a DC term, together with

some other low frequency terms.

Since there is a large DC term in a2(t), then there must

be a large term at 2ω in the product a2(t).cos2ωt.

A bandpass filter will extract this. It may be amplitude limited (to stabilise the

amplitude) and then halved in frequency. This may be sufficient processing for

some applications.

The purpose of the BPF is to separate the terms in a2(t) from those around the

frequency of 2ω. For the case where these are widely separated then an RC

highpass filter would probably be adequate. It is assumed that the original DSBSC

is reasonably free of noise and interference.

However, if improved properties are required (see Tutorial Question Q7.), a phase

locked loop (PLL) may replace the bandpass filter 2.

2 or at least ease the requirements of this BPF


squarer plus PLLsquarer plus PLLsquarer plus PLLsquarer plus PLL

For the case where a component at carrier frequency is definitely not present, and

the advantages of a dynamic tracking bandpass filter are desired, then the squarer

plus PLL is recommended. This is illustrated in Figure 4 below.

squarerdivide

bytwo

PLL

Figure 4: squarer-plus-PLL

The squaring arrangement ensures that a component at the desired (carrier)

frequency will be present at the input to the PLL. The PLL operates at 2ω.

So the combination of a squarer and PLL, together with a third multiplier in a

product demodulator arrangement, constitutes a popular, basic synchronous

receiver.

An alternative arrangement of three multipliers and associated operational blocks

constitutes the Costas loop.

the Costas loopthe Costas loopthe Costas loopthe Costas loop

A Costas loop is another well known arrangement which is capable of extracting a

carrier from a received signal.

This arrangement is examined in the experiment entitled The Costas loop (this

Volume).




During this experiment you will consider in turn:

1. a bandpass filter (BPF)

2. the PLL

3. the squarer

4. the squarer plus PLL

5. as time permits, a complete synchronous receiver

the pilot carrier and BPFthe pilot carrier and BPFthe pilot carrier and BPFthe pilot carrier and BPF

When a small but constant amplitude component at carrier frequency (a pilot

carrier) accompanies the transmitted signal it can be extracted with a bandpass

filter. This technique is reasonably self evident and will not be examined. See

Tutorial Question Q1.

the PLLthe PLLthe PLLthe PLL

You will now model the PLL of Figure 2, and use a DSB plus small carrier

(Figure 1) as its input. The arrangement is shown modelled in Figure 5.

IN

Figure 5: a model of the PLL of Figure 2

T1 patch up the model of Figure 5 above. The VCO is in ‘VCO mode’ (check

SW2 on the circuit board). The input signal, a DSB based on a

100 kHz carrier (locked to the TIMS 100 kHz MASTER), is available

at TRUNKS (or you could model it yourself). Initially set the GAIN of

the VCO fully anti-clockwise.

T2 tune the VCO close to 100 kHz. Observe the 100 kHz signal from MASTER

SIGNALS on CH1-A, and the VCO output on CH2-A. Synchronize the

oscilloscope to CH1-A. The VCO signal will not be stationary on the

screen.


T3 slowly advance the GAIN of the VCO until lock is indicated by the VCO signal

(CH2-A) becoming stationary on the screen. If this is not achieved

then reduce the GAIN to near-zero (advanced say 5% to 10% of full

travel) and tune the VCO closer to 100 kHz, while watching the

oscilloscope. Then slowly increase the GAIN again until lock is

achieved.

T4 while watching the phase between the two 100 kHz signals, tune the VCO from

outside lock on the low frequency side, to outside lock on the high

frequency side. Whilst in lock, note (and record) the phase between

the two signals as the VCO is tuned through the lock condition.

Theory suggests (?) they should be 900 apart in the centre of the in-

lock tuning range. See Tutorial Question Q5.

the squaring multiplierthe squaring multiplierthe squaring multiplierthe squaring multiplier

Even without spectrum analysis facilities it is possible to give a convincing

demonstration of the truth of eqn.(4) above, which revealed the generation of a

DSB with carrier (at 2ω) from a DSB without carrier (at ω).

This is achieved by modelling the arrangement of Figure 3, as illustrated in

Figure 6.

#1 : a 50 kHz sinusoid

#2 : a DSBSC

INPUTS from TRUNKS:

CH1-A

ext trig

Figure 6: squaring. The model of Figure 3 without divide-by-2

First check the operation of squaring on a sinusoidal input.

T5 patch up the model of Figure 6. Select the input #1 from TRUNKS (Check

the waveform, and measure its frequency, to confirm it is the 50 kHz

signal).

T6 select CHANNEL #1 on the 100 kHz CHANNEL FILTERS module. This is a

straight through connection. Toggle to select DC.

T7 examine the output of the 100 kHz CHANNEL FILTERS module on CH1-A.

Observe and record the waveform, and the envelope shape. This is

the output from the MULTIPLIER as a squarer. Confirm the presence

of a DC component. note: the MULTIPLIER is switched to ‘AC’.

This means any DC at either input will be blocked, but not any DC at

the output.



T8 switch the 100 kHz CHANNEL FILTERS module to its CHANNEL #3. This is a

100 kHz bandpass filter (BPF).

T9 observe the change of waveform from the 100 kHz CHANNEL FILTERS

module. Confirm it is twice the frequency of the first input, and is

sinusoidal.

Now replace the sinusoidal input with a DSBSC based on a 50 kHz carrier.

T10 change the input from the nominal 50 kHz sinusoid to the 50 kHz DSBSC.

Confirm, at least from all appearances, and expectations, that this is

the DSBSC based on a 50 kHz carrier.

T11 select the straight through connection, CHANNEL #1, on the 100 kHz

CHANNEL FILTERS module. Toggle to pass DC. Observe the

output. Since there is no filtering this is the square of a DSBSC. You

may not have anticipated what it would look like, but at least confirm

that there is a significant DC component present. It is this component

which will produce the desired double frequency carrier term - refer

eqns.(3).

T12 whilst still observing the 100 kHz CHANNEL FILTERS output, select

CHANNEL #3 - the bandpass filter. Confirm that the signal does

indeed now look like a DSB plus carrier, as per eqn.(4). It must be in

the vicinity of 100 kHz, since it passed through the bandpass filter.

See Tutorial Question Q6.

You have now confirmed that the squaring circuit has produced a significant

component at twice the frequency of the suppressed carrier of a DSBSC signal.

A narrowband BPF filter could extract this from the other spectral components.

TIMS does not have a 100 kHz narrowband bandpass filter.

But a PLL can do the job. A PLL behaves like a bandpass filter, although it is built

around a lowpass filter - the lowpass filter in the feedback loop. See Tutorial

Question Q4.

the PLL + squarerthe PLL + squarerthe PLL + squarerthe PLL + squarer

You will now combine squarer (modelled in Figure 6) and the PLL (modelled in

Figure 5), using the output of the squarer as the input to the PLL.

The input to the squarer will be the DSBSC based on a 50 kHz carrier.

The full model is shown in Figure 7.


to divideby two

SQUARING PLL

DSBSC in

(50 kHz carrier)

100 kHz

Figure 7. model of the squarer plus PLL

The divide-by-two would add nothing to the demonstration, so it has been omitted.

T13 combine the models of Figures 5 and 6. Use as input to the squaring circuit

the nominal 50 kHz DSBSC.

T14 go through the procedure to lock the PLL to the 100 kHz output from the

squarer. Describe the setting up, and locking procedure, in your

notes.

T15 refer to Tutorial Question Q8.

So far you have locked the PLL to a signal of constant amplitude. But in practice it

would be required to lock on to a modulated signal whose message was varying.

What would happen, for a speech message, during significant pauses ?

If you have a third MULTIPLIER module you can examine your carrier acquisition

circuit - squarer plus PLL - as the source of local carrier for a product demodulator,

and receiving such a signal.

The product demodulator was examined in the experiment entitled Product

demodulation - synchronous and asynchronous in Volume A1.

A DSBSC, based on a 50 kHz carrier, and with a speech message, will be available

at TRUNKS during the latter part of the experiment.

For further details see your Laboratory Manager.




Q1 suppose a signal has a pilot carrier. This can be used to produce a local

carrier by bandpass filtering, or with a PLL. Compare the two

methods.

Q2 draw an approximate amplitude spectrum of the signal of Figure 1, knowing

that it is a DSBSC plus small carrier term, and explain how this was

done. How would you then define the level of the pilot carrier ?

Q3 compare the advantages of a bandpass filter based on a lowpass filter - the

PLL - with a ‘conventional’ bandpass filter.

Q4 explain how you are able to confirm that the VCO of a PLL has locked on to

the input signal, whose exact carrier frequency is unknown, when the

signal is:

a) an unmodulated carrier

b) an envelope modulated signal

Q5 in Task T4 the two signals may not have been close to 900 apart at the centre

of lock. How could this be, when theory suggests otherwise - or does

it ?

Q6 from the observed DSB plus carrier from the 100 kHz CHANNEL FILTERS

module of Task T12, and knowing the model configuration, draw an

amplitude/frequency spectrum of this signal. Confirm, by

trigonometrical analysis, the relative amplitudes of the spectral

components.

Q7 name some of the improved features of the squarer-plus-PLL compared with

the squarer alone.

Q8 there are many parameters associated with a phase locked loop which are of

interest, and their measurement could form the basis of another

experiment (or an extension of this one). Two properties of interest

are CAPTURE RANGE and LOCK RANGE. You should find out about

these. Of what importance was the setting of the VCO GAIN

(sensitivity) control, and of the VCO frequency control ?


SPECTRUM ANALYSIS SPECTRUM ANALYSIS SPECTRUM ANALYSIS SPECTRUM ANALYSIS ----

THE WAVE ANALYSERTHE WAVE ANALYSERTHE WAVE ANALYSERTHE WAVE ANALYSER

PREPARATION................................................................................ 2

the SPECTRUM ANALYSER.................................................. 2

principle of operation............................................................................. 2

practical variation.................................................................................. 3

the WAVE ANALYSER........................................................... 4

the model............................................................................................... 4

spectrum measurement - single component input ................................... 4

spectral measurement - two component input......................................... 5

practical considerations ............................................................. 6

precautions ............................................................................................ 6

searching methods ................................................................................. 6

where ? ............................................................................................ 6

how large ?....................................................................................... 6

EXPERIMENT.................................................................................. 7

SPECTRUM UTILITIES module ............................................. 7

VCO fine tuning........................................................................ 7

The WAVE ANALYSER model ............................................... 7

test and calibration .................................................................... 8


DSBSC spectrum................................................................................... 9

spectra of unknown signals.................................................................... 9

practical hints .................................................................................. 9

future spectral measurements .................................................... 9



SPECTRUM ANALYSIS SPECTRUM ANALYSIS SPECTRUM ANALYSIS SPECTRUM ANALYSIS ----

THE WAVE ANALYSERTHE WAVE ANALYSERTHE WAVE ANALYSERTHE WAVE ANALYSER

ACHIEVEMENTS: to examine the basic spectrum analyser model; modelling a

WAVE ANALYSER; to consider the effects of non-linearities upon

performance.

PREREQUISITES: completion of the experiment entitled Product demodulation -

synchronous and asynchronous in Volume A1.

EXTRA MODULES: the SPECTRUM UTILITIES module (not in the TIMS Basic

Set of modules).


the SPECTRUM ANALYSERthe SPECTRUM ANALYSERthe SPECTRUM ANALYSERthe SPECTRUM ANALYSER

Spectrum analysers are found in most homes. They are the domestic radio receiver

and TV set. These devices are capable of examining parts of the radio spectrum,

and they report what they find either aurally or visually. From their front panel

controls we can deduce the frequency from the channel to which they are tuned,

and the nature of the spectrum within that channel from the sound and/or picture.

A professional spectrum analyser is an instrument for identifying the amplitude

spectrum of an electrical signal (typically one whose spectrum does not vary with

time). The majority of commercially available instruments cover a very wide

frequency spectrum (Hz to GHz), are extremely accurate, and expensive. They

generally provide a visual display of the amplitude-frequency spectrum.

principrinciprinciprinciple of operationple of operationple of operationple of operation

The principle of a spectrum analyser is represented by a tuneable filter, as shown in

Figure 1.

Spectrum analysis - the WAVE ANALYSER


Figure 1: principle of the spectrum analyser.

The arrow through the bandpass filter (BPF) shown in Figure 1 implies that the

centre frequency to which it is tuned may be changed. The filter bandwidth will

determine the frequency resolution of the instrument. The internal noise generated

in the circuitry, and the gain of the amplifier, will set a limit to its sensitivity.

The symbol of circle-plus-central-arrow represents a voltage indicator of some sort.

For the moment we will disregard its response characteristic (RMS, peak,

average ?), but agree that it will indicate in some way the presence of an output

from the filter.

The frequency of the signal to which the analyser responds is that of the centre

frequency of the BPF.

Instruments which require the user to make a manual search, one component at a

time, are generally called wave analysers; those which perform the frequency

sweep automatically and show the complete amplitude-frequency response on some

sort of visual display are called spectrum analysers.

practical variationpractical variationpractical variationpractical variation

Tuneable bandpass filters are difficult to manufacture. Thus the arrangement of

Figure 1 is not used in an instrument covering a wide frequency range. Figure 2

shows a practical compromise. Although this circuit behaves as a tuneable

bandpass filter, it uses a fixed lowpass filter.

Figure 2: practical spectrum (wave) analyser

The arrangement of Figure 1 is a tuned radio frequency receiver (TRF), and that of

Figure 2 is based on the principle of the superheterodyne receiver (‘superhet’).

Refer to the literature circa 1920 to learn about the historical development of these

two configurations. The practical difficulties of the former, and the advantages of

the latter, are discussed.


The frequency to which the analyser responds is that of the sinusoidal, tuneable,

‘local’ oscillator.

the WAVE ANALYSERthe WAVE ANALYSERthe WAVE ANALYSERthe WAVE ANALYSER

This experiment will be concerned with a wave analyser, which was defined above.


We would like to model a wave analyser that would be of use for future experiments

with TIMS. Its tuning range must cover the audio spectrum from say 300 Hz to

10 kHz, as well as say 10 kHz either side of our standard carrier frequency of

100 kHz.

Its frequency resolution requirements are modest, determined principally by the

fact that we would like to examine the individual spectral components in the

sidebands either side of 100 kHz modulated signals. In TIMS these are seldom

closer than say 250 Hz. A resolution of 100 Hz would be adequate; this is a very

modest requirement.

We cannot model the arrangement of Figure 1, since we do not have a tuneable

BPF with a bandwidth of 100 Hz, covering such a wide range as 250 Hz to

110 kHz.

The problems associated with the realization of the

scheme of Figure 1 are now apparent.

The scheme of Figure 2, meeting the above specification, would require a LPF with

a cut-off of around 50 Hz. In addition a tuneable oscillator is required; this will

need to cover the audio as well as the 100 kHz range.

TIMS provides the tuneable oscillator in the form of the VCO module.

Although a 50 Hz lowpass filter is not difficult to design, there is no such electronic

filter in the TIMS BASIC SET of modules. But a moving coil volt meter will serve

as the output indicator. Due to the inertia of the mechanical movement it will only

respond to DC and very low-frequency signals. It will therefore also serve as the

lowpass filter.

The SPECTRUM UTILITIES module has been designed for the purpose.

spectrum measurement spectrum measurement spectrum measurement spectrum measurement ---- single component input single component input single component input single component input

To make a spectral component measurement it is necessary to understand the

principle of the analyser. For a simple first example, suppose the signal v(t)

appears at the input, where:

v(t) = V1 cos(2πf1t) ........ 1

and that:

VCO output = Vvco.cos(2πf2t) ........ 2



Then:

multiplier output = ½.k.V1.Vvco [cos2π(f1 - f2)t + cos2π(f1 + f2)t] ........ 3

where ‘k’ is a constant of the multiplier.

The LPF filter built into the meter-module will remove the term at frequency

(f1 + f2), and the meter will respond to the term at frequency |(f1 - f2)| = δf. Let the

amplitude of this signal be Vm.

Vm = (½.k.Vvco) V1

........ 4

Since the amplitude of the VCO output is a constant, the magnitude of the meter

reading Vm will be proportional to the amplitude of the input component V1. We

will call the constant of proportionality S, the conversion sensitivity 1, so we have:

S = 2/(k.Vvco.) ........ 5

V1 = S.Vm........ 6

Since V1 is the amplitude of the unknown signal, this last equation gives the

scaling factor to be applied to the meter reading.

The frequency of the input component must lie within ± δf Hz of the VCO

frequency f2.

The inertia of the moving coil meter prevents it responding to signals of more than

a few Hz. For this the VCO frequency must be set close to the frequency of the

unknown component at the input. As the frequency difference δf is slowly reduced

to zero, the meter will at first ‘quiver’ (say δf is 10 Hz or less); then start to

oscillate with greater and greater swings as δf approaches zero.

The peak amplitude of the swing will be Vm, reached as δf approaches zero.

Despite the last statement, setting the frequency error to precisely zero is not

desirable. Should δf = 0 then the term of interest becomes a constant DC voltage,

and its amplitude would depend upon the phase angle between the unknown

component at the input, and the VCO signal. This phase is unknown, and so would

introduce an unnecessary complication.

So to measure the amplitude of the unknown component we set δf to one or two Hz,

and make a note of the peak reading of the meter and the frequency of the VCO.

From this, and the last equation, the unknown amplitude V1 can be derived.

spectral measurement spectral measurement spectral measurement spectral measurement ---- two component input two component input two component input two component input

Suppose there are two components at the input. Provided they are separated by at

least the frequency resolution of the analyser, only one will produce an output from

the filter at any time 2.

1 conversion, because of the frequency change between input and output

2 this assumes linear operation of all circuits


practical considerationspractical considerationspractical considerationspractical considerations

precautionsprecautionsprecautionsprecautions

A moving coil volt meter will not respond to signals of more than 10 Hz or so, due

to its mechanical inertia. This does not prevent its moving coil from being burned

out by other AC signals of excessive amplitude. So, as a practical precaution, the

meter in the SPECTRUM UTILITIES module is protected by a low-order LPF.

This will also remove the component(s) from the MULTIPLIER at the sum

frequency (f1 + f2).

There is a sample-and-hold facility, for capturing the peak swing of the meter.

This should be used with care, and its reading not mis-interpreted, since it bypasses

the filtering effect of the mechanical inertia of the meter, and will capture all and

any signals which reach the meter. Consequently you should have some idea of the

relative amplitudes and location of components before using this facility, and an

appreciation of the response of the built-in LPF. For further information refer to

the TIMS User Manual.

searching methodssearching methodssearching methodssearching methods

Searching for spectral components takes a certain amount of practice. If the VCO

frequency is changed at too great a rate the meter will not have time to respond,

and components of significant amplitude will be missed. If and when the meter

does respond, adjust the VCO frequency carefully until the meter is oscillating very

slowly, and record the peak meter reading. Use the sample-and-hold facility if

appropriate.

wherewherewherewhere ????

In practice one usually has a good idea of where the unknowns are going to be -

what is sought is their relative amplitude. Thus the searching process is not as

difficult as it might at first appear.

how large ?how large ?how large ?how large ?

No great significance is placed on the measurement of absolute amplitudes -

relative amplitudes are what we really want. So pre-calibration is seldom

necessary.

It is often convenient to tune to the largest component of interest, and then to adjust

the meter to full scale deflection (FSD) using the on-board variable resistor RV1,

labelled GAIN. This reading becomes the reference.




SPECTRUM UTILITIES moduleSPECTRUM UTILITIES moduleSPECTRUM UTILITIES moduleSPECTRUM UTILITIES module

The SPECTRUM UTILITIES module contains a centre-reading moving coil meter,

with lowpass filtering, and a sample-and-hold facility. Read about it in the TIMS

User Manual. Pay particular attention to the precautions necessary if you use the

sample-and-hold facility.

VCO fine tuningVCO fine tuningVCO fine tuningVCO fine tuning

Read about the VCO module in the TIMS User Manual. In the present application

it is important to know the techniques of coarse and fine tuning.

• coarse tuning is done with the front panel fo control (typically with no input

connected to Vin).

• for fine tuning it is convenient to set the GAIN control of the VCO to some small

value. Then fine tuning is then done by varying the DC voltage, from the

VARIABLE DC module, which is conected to the Vin input. The smaller the

GAIN setting the finer is the tuning.

The WAVE ANALYSER modelThe WAVE ANALYSER modelThe WAVE ANALYSER modelThe WAVE ANALYSER model

A wave analyser is shown modelled in Figure 3 below.

IN

VCO fine tune

Figure 3: the WAVE ANALYSER model

T1 patch up a model of the block diagram of Figure 2. A suggested scheme is

illustrated in Figure 3. Before plugging in the VCO set the on-board

switch SW2 to select the VCO mode. Remember the LPF is simulated

by the inertia of the moving coil meter movement in the SPECTRUM

UTILITIES module.


test and calibrationtest and calibrationtest and calibrationtest and calibration

Before using the WAVE ANALYSER to measure some unknown signals it needs to

be tested and calibrated in both the audio and 100 kHz regions. You can use the

output from an AUDIO OSCILLATOR as a source of test signal for the former (say

at 1 kHz and 10 kHz)), and the 100 kHz sinewave from the MASTER SIGNALS

module for the latter.

T2 select a 1 kHz sinewave from an AUDIO OSCILLATOR as your source of test

signal. Measure its amplitude V1 at the input to the WAVE

ANALYSER, using the oscilloscope.

T3 connect the VCO output to the FREQUENCY COUNTER, and tune the VCO

to the expected vicinity of the test signal, until the volt meter reading

oscillates slowly. Record the peak reading Vm of the meter.

There is a variable SCALING resistor RV1 on the circuit board of the SPECTRUM

UTILITIES module. You may find it convenient, when measuring spectra, to

adjust this so the meter reads full scale deflection (FSD) on a reference component -

typically the largest to be encountered.

T4 check the operation of the on-board SCALING adjustment of the SPECTRUM

UTILITIES module.

T5 calculate the conversion sensitivity V1 / Vm of your WAVE ANALYSER.

T6 repeat the last three tasks for a 100 kHz test input.

You will now have three determinations of the sensitivity S of the WAVE

ANALYSER. Ideally they should all be the same. This assumes:

• the VCO output amplitude is constant over the full LO and HI frequency ranges

• the k factor of the MULTIPLIER is independent of frequency

• probably the k factor of the MULTIPLIER will vary slightly between the LO and

HI frequency ranges, and so you may need both an SLO and an SHI.

T7 derive an expression for the ‘1 kHz conversion sensitivity’ of the WAVE

ANALYSER in terms of its circuit constants (including the VCO output

voltage, multiplier k factor, meter sensitivity). If you do not know the

value of ‘k’, then set up a temporary arrangement, and measure it.

Compare this conversion sensitivity with the direct measurement.




It is now time to use the WAVE ANALYSER to examine the spectrum of a DSBSC

signal - this was promised in the experiment entitled DSBSC generation in Volume

A1.

DSBSC spectrumDSBSC spectrumDSBSC spectrumDSBSC spectrum

T8 set up a DSBSC signal using an AUDIO OSCILLATOR, MULTIPLIER, and

the 100 kHz sine wave from the MASTER SIGNALS module.

T9 use the oscilloscope to measure the amplitude of the DSBSC (in the time

domain). From this, and a knowledge of the frequency of the AUDIO

OSCILLATOR, sketch the amplitude spectrum of the DSBSC (in the

frequency domain). Show clearly the amplitude and frequency scales.

T10 connect the DSBSC to your WAVE ANALYSER, and search for spectral

components in the range 90 kHz to 110 kHz. Sketch the measured

amplitude spectrum. Show clearly the amplitude and frequency

scales.

T11 compare the last two spectra, and account for any discrepancies.

spectra of unknown signalsspectra of unknown signalsspectra of unknown signalsspectra of unknown signals

When happy with the results of the DSBSC spectrum measurement, have a look at

the signals at TRUNKS. These have been sent to you for analysis.

practical hintspractical hintspractical hintspractical hints

In practice it is relative amplitudes which are of interest. Thus one seldom needs to

carry out an amplitude calibration. This saves time in setting up the model. Also,

one usually knows where the components are, so searching is simplified. It is

convenient to find the largest component, and then to set the sensitivity of the meter

(with the on-board SCALING adjustment) to indicate full scale on this component.

T12 use your WAVE ANALYSER to determine the amplitude/frequency spectra of

the signals at TRUNKS. Note that the sensitivity of the SPECTRUM

UTILITIES meter can be adjusted with an on-board control.

future spectral measurementsfuture spectral measurementsfuture spectral measurementsfuture spectral measurements

In future experiments you will find this inexpensive WAVE ANALYSER is a

useful measurement tool. The model just examined will be found adequate for your

purposes. But remember: its circuits must never be overloaded. In practice this


means that the signal at the analyser input must not overload the input

MULTIPLIER.

Overload - meaning peak amplitude overload - will mean spurious readings. Use

the oscilloscope to ensure that the peak amplitude of the input signal never exceeds

the TIMS ANALOG REFERENCE LEVEL. See the Tutorial Question below.


Q1 the resolution of a wave analyser relates to the width of the ‘window’ through

which it looks at the input spectrum. If the BPF of Figure 1 is ‘brick

wall’ with a passband 2 Hz wide, how would you describe the

frequency resolution of the instrument ? (note: a filter response even

approaching this would be difficult to realize in analog form).

Q2 if the LPF of Figure 2 is ‘brick wall’, and passes frequencies from DC to

1 Hz, how would you describe the frequency resolution of the

instrument ? (note: a reasonable approximation to this filter

response, in analog form, would not be impossible to implement).

In answering the above two questions it was assumed the circuits were linear. Any

non-linearity in the circuitry can degrade performance, as is illustrated by

answering the next question.

Q3 what happens if the amplitude of the input signal is ‘too high’ ? Suppose that

there is an amplifier between the input terminal and the BPF of

Figure 1, which is ‘brick wall’, with a 2 Hz bandwidth. Suppose the

amplifier has a non-linear gain characteristic given by:

e a e a eout in in= +1 33

where a1 = 1 and a3 = -0.1 and the input signal ein is a DSBSC.

Derive an expression for the spectrum reported by the output meter, in

the vicinity of 100 kHz, when the input is a DSBSC on a 100 kHz

carrier, and derived from a 1 kHz sinusoidal message.

The above question is an exercise in trigonometry. It will illustrate

one of the phenomena of intermodulation distortion.

hint: give the DSBSC an amplitude V, and look for sum and/or

difference (‘intermodulation’) components in the vicinity of the

sidebands. Show that these are related in a non-linear way to V, and

discuss the consequences.

Q4 explain the reason for the precautions necessary when using the sample-and-

hold facility of the SPECTRUM UTILITY module.


AMPLIFIER OVERLOADAMPLIFIER OVERLOADAMPLIFIER OVERLOADAMPLIFIER OVERLOAD

PREPARATION................................................................................ 2

not too little - not too much ...................................................... 2

amplifier ‘gain’.......................................................................... 3

ideal amplifier ‘gain’. ............................................................................ 3

real amplifiers ....................................................................................... 3

harmonic distortion ................................................................... 4

calculation of harmonic distortion components ...................................... 4

definition of harmonic distortion - THD ................................................ 5

measurement of THD............................................................................. 5

narrow band systems................................................................. 6

measurement of a narrow band system................................................... 6

the two-tone test signal ............................................................. 7

short cuts............................................................................................... 7

signal-to-distortion ratio - SDR.............................................................. 8

two-tone example .................................................................................. 8

noise ......................................................................................... 9

two-tone test signal generation.................................................. 9

the two-tone seen as a DSBSC ............................................................... 9

EXPERIMENT................................................................................ 10

experimental set-up ................................................................. 10

single tone testing ................................................................... 11

measurement of THD........................................................................... 11

two-tone testing ...................................................................... 13

measurement of SDR........................................................................... 13

conclusions ............................................................................. 16


APPENDIX ..................................................................................... 17

some useful expansions. .......................................................... 17


AMPLIFIER OVERLOADAMPLIFIER OVERLOADAMPLIFIER OVERLOADAMPLIFIER OVERLOAD

ACHIEVEMENTS: an introduction to the definition and measurement of

distortion in wideband and narrowband systems.

PREREQUISITES: completion of the experiment entitled Spectrum analysis - the

WAVE ANALYSER in this Volume.

EXTRA MODULES: SPECTRUM UTILITIES.


not too little not too little not too little not too little ---- not too much not too much not too much not too much

One of the aims of an analog transmission system, such as an audio amplifier or a

long-distance telephone circuit, is to present at the output a faithful reproduction of

the signal at the input. Analog systems will always introduce some signal

degradation, however defined, but it is the aim of the analog design engineer to

keep the amount of degradation to a minimum.

As you are probably already aware, if signal levels within a system rise ‘too high’,

then the circuitry will overload; it is no longer operating in a linear manner. As

will be seen later in this experiment, extra, unwanted, distortion components will

be generated. These distortion, or noise 1, components, are signal-level dependent.

In this case the noise components arise due to the presence of the signal itself.

Conversely, if signal levels within a system fall ‘too low’, then the internal circuit

noise, which is independent of signal level, will eventually swamp the small,

wanted, output. The background noise of the TIMS system is held below about

10 mV peak - this is a fairly loose statement, since this level is dependent upon the

bandwidth over which the noise is measured, and the model being examined at the

time. A general statement would be to say that TIMS endeavours to maintain a

SNR of better than 40 dB for all models.

Thus analog circuit design includes the need to maintain signal levels at a level 'not

to high' and 'not too low', to avoid these two extremes.

The TIMS working level, or ANALOG REFERENCE LEVEL has been set at

4 volts peak-to-peak. Modules will generally overload if this level is exceeded by

say a factor of two.

1 noise is here considered to be anything that is not wanted.

Amplifier overload


It is the purpose of this experiment to introduce you to the phenomenon of circuit

overload, and to offer some means of defining and measuring its effects.

amplifier ‘gain’amplifier ‘gain’amplifier ‘gain’amplifier ‘gain’

ideal amplifier ‘gain’.ideal amplifier ‘gain’.ideal amplifier ‘gain’.ideal amplifier ‘gain’.

Consider an amplifier which is said to have a gain of ‘g’. This is understood to

mean that, if vi is the input signal voltage, then the output vo is given by:

vo = g . vi........ 1

This would be described as an ideal amplifier. Its input/output (i/o) characteristic

would be a straight line, with a slope of g volts/volt.

In simple terms, g is a dimensionless constant. More generally it can be complex,

and frequency dependent; but such complications will be ignored in the work to

follow.

real amplifiersreal amplifiersreal amplifiersreal amplifiers

Unfortunately, a real amplifier does not have an ideal straight-line input/output

characteristic. It is more likely to look like that of Figure 1.

It is obvious to the eye that the

characteristic shown in Figure 1 could

not be considered straight, or linear,

except perhaps for input signal

amplitudes in the range say ± ½ volt.

In this range the slope of the

characteristic is 10 volts/volt.

The amplifier is said to have a small

signal gain of 10. Input signal

amplitudes in the range say ± ½ volt

would be considered small signals for this

amplifier.

A typical amplifier characteristic is likely

to flatten off and become parallel to the Fig 1: typical characteristic

horizontal axis, whereas this characteristic, as defined by eqn. (2) below, will

approach and finally cross the input-axis for larger input amplitudes.

So this approximation to an amplifier characteristic should be used for input

amplitudes restricted to the range 0 to say ±1½ volts.

Its actual input/output relationship is given by:

vo = g1.vi + g3.vi3 ........ 2

where vi and vo are the input and output voltages, respectively, and

g1 = 10 ........ 3


g3 = - 1.5 ........ 4

Note that the range of the so-called linear part of the characteristic is not obvious

from a cursory examination of eqn. (2) alone. We shall later obtain a method of

defining an acceptable operating input signal range.

harmonic distortionharmonic distortionharmonic distortionharmonic distortion

calculation of harmonic distortion componentscalculation of harmonic distortion componentscalculation of harmonic distortion componentscalculation of harmonic distortion components

Intuition tells us that an amplifier with the input-output characteristic of Figure 1

will introduce distortion, but what sort of distortion ? This can be checked

analytically by nominating a test input signal, and then determining the

corresponding output.

Let the test signal be a single tone, vi, where:

vi = V.cosµt ........ 5

Substituting this into eqn. (2), and expanding, gives:

vo = g1 V cosµt + g3 V3 (3/4 cosµt + 1/4 cos3µt) ........ 6

Notice that the cubic term has given rise to two new components; one on the same

frequency as the input signal, and the other on its third harmonic.

After combining like harmonic terms the last equation can be rewritten as:

vo = [g1 V + (3/4) g3 V3] cosµt + (1/4) g3 V3 cos3µt ........ 7

Notice that, at the output:

1) the amplitude of the wanted term cosµt is no longer simply g1 times the input

amplitude (as suggested by eqn. (1)).

2) there is an extra, unwanted term, on the third harmonic of the input.

The original signal has been distorted.

This can be observed in the time domain, using an oscilloscope. For the example

under discussion, the output, for an input of amplitude V = 1 volt, is shown in

Figure 2.

Figure 2: the output voltage waveform of eqn. (7),

for an input amplitude of V = 1 volt

Amplifier overload


definition of harmonic distortion definition of harmonic distortion definition of harmonic distortion definition of harmonic distortion ---- THD THD THD THD

Notice that the analysis has been performed so as to describe the output in terms of

harmonic components of the input. The fundamental, or first harmonic, is the

wanted term, and all higher harmonic terms (in this example there is only one) are

unwanted.

The wanted and unwanted harmonic terms can be compared, and some measure

defined, to describe the amount of harmonic distortion.

The comparison is usually made on a power basis, described as the ‘total harmonic

distortion’, or THD, and defined as:

THDH

H

dB

j

j

n=

=

10 10

1

2

2

2

log........ 8

where H1 is the amplitude of the output signal on the same frequency as the input

test signal, and the Hj are the amplitudes of the 2nd and higher harmonics, or

unwanted, terms.

Figure 3: THD versus input amplitude

for the response of eqn. (2)

For the example above, where the input amplitude V was 1 volt peak, this evaluates

to a THD of 27.48 dB.

Figure 3 shows the THD plotted for input amplitudes in the range 0 to 1½ volts.

Having decided on an acceptable THD for this amplifier (say 40 dB), the user can

now specify a maximum input level (½ volt) from Figure 3.

measurement of THDmeasurement of THDmeasurement of THDmeasurement of THD

There are instruments available which measure THD directly. They supply their

own test input signal to the device under test, measure the total AC power output,

subtract the power due to the wanted signal, and present the THD expressed in

decibels.


You will make your own measurements with TIMS by modelling a WAVE

ANALYSER 2, measuring the amplitudes of the individual output components, and

then applying the THD formula.

Note that this THD is specific to the actual input signal amplitude used for the

measurement. There is no subsequent simple step to enable:

1. prediction of the THD for another input signal amplitude.

2. determination of the non-linear characteristic of the amplifier.

This is because of the non-linear relationship between the input signal amplitude

and the corresponding output THD.

narrow band systemsnarrow band systemsnarrow band systemsnarrow band systems

The previous discussion requires some modification if the system being examined is

narrow band 3.

There are many circuits in an analog communications system which are

narrowband, since many communications signals themselves are narrow band. A

narrowband system is one which has had its frequency response intentionally

restricted. This generally simplifies the circuit design, and eliminates out-of-band

noise.

To simplify the discussion, suppose there is a bandpass filter at the system output,

so that only frequencies over a narrow range either side of the measurement

frequency, µ rad/s, will pass to the output. Let the non-linearities be in the circuitry

preceding the filter.

If this were the case for the example already discussed, the output waveform would

show no sign of distortion, but instead be a pure sinewave ! No distortion would be

visible on an oscilloscope connected to the output, because the distorting third

harmonic signal would not reach the output. An instrument for measuring THD

with a single tone input would register no distortion at all !

Is the system linear or not ? It is definitely non-linear. This can be demonstrated

by observing that the relationship between input amplitude and output amplitude is

not linear.

Using the methods so far employed, this does not

show up as waveform distortion, and would not be

revealed by a spectrum analysis of the output

measurement of a narrow band systemmeasurement of a narrow band systemmeasurement of a narrow band systemmeasurement of a narrow band system

The single-tone test signal we have been using so far is inappropriate for the

measurement of THD in a narrow-band system. What is needed is a more

demanding test signal, which will reveal the non-linearity, and which is more

representative of the signals to be found in most systems. The non-linearity is

2 see the experiment entitled Spectrum Analysis - the Wave Analyser, or model a spectrum analyser using

the TIMS320 module.

3 ‘wideband’ and ‘narrowband’ signals are defined in the chapter entitled Introduction to Modelling with

TIMS.

Amplifier overload


revealed by the transmission of two signals simultaneously, namely the two tone

test signal.

the twothe twothe twothe two----tone test signaltone test signaltone test signaltone test signal

The two-tone test signal consists of two equal amplitude sinusoids, of comparable

frequency. Thus:

v(t) = V (cosµ1t + cosµ2t) where say µ1 < µ2........ 9

Let us use this as the input to the non-linear amplifier previously examined with a

single tone input.

The amplitudes of the various output terms, from trigonometrical expansion of v(t)

when substituted into eqn. (2), are shown below:

cos(µ1).t ==> g1.V + (3/4).g3.V3 + (3/2).g3.V3 ........ 10

cos(µ2).t ==> g1.V + (3/4).g3.V3 + (3/2).g3.V3 ........ 11

cos(3µ1).t ==> (1/4).g3.V3 ........ 12

cos(3µ2).t ==> (1/4).g3.V3 ........ 13

cos(2µ1 - µ2) t ==> (3/4).g3.V3 ........ 14

cos(µ1 - 2µ2) t ==> (3/4).g3.V3 ........ 15

cos(2µ1 + µ2) t ==> (3/4).g3.V3 ........ 16

cos(µ1 + 2µ2) t ==>(3/4).g3.V3 ........ 17

short cutsshort cutsshort cutsshort cuts

The calculation of these amplitude coefficients can be very tedious. But one soon

observes certain phenomena involved, and with a narrowband system applies short

cuts to avoid unnecessary work. Remember that the two frequencies µ1 and µ2 are

close together.

Some observations are:

• The trigonometrical expansions can only generate terms on harmonics of the

original frequencies, and on sum and difference frequencies of the form

(n.µ1 + m.µ2) and (n.µ1 - m.µ2), where n and m are positive integers.

• Components with frequencies µ1 and µ2 will pass through the system, but

none of their higher harmonics.

• Of the sum and difference frequencies (n.µ1 + m.µ2) and (n.µ1 - m.µ2), it is

agreed that only those of the difference group, where n and m differ by

unity, will pass through the system.

• When n is odd, the expansion of (cosµt)n gives rise to all odd harmonics

counting down from the nth.


• When n is even, the expansion of (cosµt)n gives rise to all even harmonics

counting down from the nth. Note that the count goes down to the zeroeth

term, which is DC.

Taking these observations into account when dealing with a narrowband system,

the number of necessary calculations can be reduced.

signalsignalsignalsignal----totototo----distortion ratio distortion ratio distortion ratio distortion ratio ---- SDR SDR SDR SDR

We have seen that when the test input is a single tone, the distortion components

are restricted to being harmonics of this signal. But with a more complex test

signal other distortion products are possible. As has just been seen, a two-tone test

input gives rise to harmonics of each of these signals, as well as intermodulation

products. Intermodulation products (IPs) arise from the products of two or more

signals, and fall on frequencies which are the sums and differences of multiples of

their harmonics.

The measure of distortion can no longer be called THD, since the sum and

difference frequencies are present in addition to the harmonic terms, so the term

signal-to-distortion ratio, or SDR, is used. It is evaluated using the same principle

as THD, namely:

SDR

W

U

dBi

i

n

j

j

m= =

=

10 10

2

1

2

1

log ........ 18

where the amplitude of the n wanted terms is Wi and of the m unwanted terms is Uj.

These are the terms which actually reach the output. In a narrow band system

many others will be generated which will not reach the output.

twotwotwotwo----tone exampletone exampletone exampletone example

We will now apply eqn. (18) to calculate the SDR for the characteristic of Figure 1.

The input signal is defined by eqn. (9), with V = 0.5 volts. This makes the peak

amplitude of the two-tone signal equal to 1 volt, which is comparable with the

amplitude used earlier for the single tone testing. First we will include all

unwanted components in the calculation, making this a wideband result.

wideband SDR = 27.01 dB ........ 19

For the narrowband case the terms to be neglected, in this example, are those on the

third harmonics of µ1 and µ2 and the intermodulation products on the sum

frequencies. The result is then:

narrowband SDR = 30.25 dB ........ 20

Remember that, had a single tone been used for this narrowband system, there

would have been no signal-dependent distortion products found at the output, and

the amplifier would have appeared ideal.

The noise output would not, in fact, have been zero. We have been dealing with

large-signal operation, and so have ignored the existence of random noise.

Amplifier overload


noisenoisenoisenoise

In the work above we have divided the output signal into wanted and unwanted

components. All the unwanted components so far had magnitudes which were

directly dependent upon the amplitude of the input signal. Such unwanted

components are referred to as signal dependent noise.

Also to be considered in any system is random noise, or system noise. This arises

naturally in all circuitry, and its magnitude is independent of any input signal 4.

In the work above we have made no mention of such noise. This is because it has

been assumed insignificant with respect to signal dependent noise. This was a

reasonable assumption, since, in a well designed system, signal dependent noise

only occurs for large input signal magnitudes.

twotwotwotwo----tone test signal generationtone test signal generationtone test signal generationtone test signal generation

The two-tone signal can be made from any two signals of suitable frequencies; a

convenient pair of signals for TIMS is the nominal 2 kHz message at the MASTER

SIGNALS module and an AUDIO OSCILLATOR. Refer to the block diagram of

Figure 4 below.

A lot can be learned about the two tone signal if it can be displayed in a convenient

manner. Recognising it as a form of DSBSC makes this an easy matter.

TWO TONETEST

SIGNAL

µ1

µ2

ENVELOPE DETECTOR ext. trig

Figure 4: two-tone test signal generation

the twothe twothe twothe two----tone seen as a DSBSCtone seen as a DSBSCtone seen as a DSBSCtone seen as a DSBSC

Recall that a two-tone test signal has been defined earlier as in eqn. (9). The

spectrum of this signal is identical with that of a DSBSC, defined as:

DSBSC = 2.V.cosµt.cosωt ........ 21

= V [cos(ω - µ)t + cos(ω + µ)t ] ........ 22

To force the signal of eqn. (21) to match that of eqn. (9), it is necessary that:

ω - µ = µ1........ 23

4 although it can be dependent on the presence of an input generator, the output impedance of which can

influence the system noise.


ω + µ = µ2........ 24

From these two equations the DSBSC frequencies are:

µ = ( | µ2 - µ1 | ) / 2 rad/s ........ 25

ω = ( µ1 + µ2 ) / 2 rad/s ........ 26

To display a DSBSC stationary on the screen a triggering signal is required that is

related to its envelope. The envelope of the DSBSC of eqn. (21) is a full wave

rectified version of cosµt, but there is no signal at this frequency [ eqn. (25) ] if the

two-tone signal is made by the addition of two tones as per eqn. (9).

The appropriate triggering signal can be generated with an envelope detector acting

on the two-tone signal. Remember this is a rectifier followed by lowpass filter

which will pass a few harmonics (ideally the first only) of the difference frequency

of eqn. (25), but not the sum frequency eqn. (26).


experimental setexperimental setexperimental setexperimental set----upupupup

For this experiment you will need a WAVE ANALYSER. We suggest you use the

model examined in the experiment entitled Spectrum analysis - the WAVE

ANALYSER.

For the non-linear amplifier you will use the COMPARATOR within the

UTILITIES module. Please refer to the TIMS User Manual. The

COMPARATOR has an analog (YELLOW) output socket, which you will use, and

in this application it is called a CLIPPER. The CLIPPER has a non-linear

input/output characteristic. That is, it will overload with input signal amplitudes

comparable with the TIMS ANALOG REFERENCE LEVEL of 4 volts peak-to-

peak. The overload characteristic can be varied by means of two on-board DIP

switches. For the present application you will use the ‘soft clipping’ characteristic;

this is set with SW1 switched to ‘ON/ON’, and SW2 switched to ‘OFF/OFF’. The

REF input socket, used for the COMPARATOR, is not used for CLIPPER

applications.

From now on the CLIPPER will be referred to as the

‘DUT’, namely the ‘device-under-test’.

For the purpose of the experiment you could consider it to be an amplifier in an

audio system, where it is required to amplify speech signals. Thus it is a wideband

device.

Amplifier overload


You should base your experimental set up on the block diagram of Figure 5.

test signal

OUT

undertest

device

DUT

to OSCILLOSCOPE and WAVE

ANALYSER

Figure 5: test setup

The WAVE ANALYSER model is shown in Figure 6

UNKNOWN

IN

Figure 6: the WAVE ANALYSER model.

single tone testingsingle tone testingsingle tone testingsingle tone testing

measurement of THDmeasurement of THDmeasurement of THDmeasurement of THD

T1 set the DIP switches on the DUT to the low gain (soft limiting) position,

before inserting the module into the TIMS SYSTEM UNIT. This is the

device under test (‘DUT’). Include the patchings to the SCOPE

SELECTOR inputs.

T2 patch up the model as in Figure 7 below.


CH1-A CH2-A ext. trig

SINGLE TONE

TEST SIGNAL

#1

#2

ANALYSER to WAVE

UNDER TEST

DEVICE

CH1-B

rovinglead

Figure 7: the single tone test model

The ADDER, in cascade with BUFFER #2, will be used later in the two-tone test

set up. BUFFER #2 will be used for test signal amplitude control. The other

BUFFER, #1, is used for polarity reversal and level adjustment of the oscilloscope

display of the input test signal.

T3 set the gain of the ADDER to about ½, and that of BUFFER #2 to about

unity.

T4 use the ‘ext. trig’ from a constant amplitude version of the test source, as

shown, to trigger the oscilloscope. Set the sweep speed to show one or

two periods of the test signal.

T5 switch to CH1-A and CH2-A. Set both channels to the same gain, say

½ volt/cm. You are looking at both the input and output signals of

the DUT.

T6 use the oscilloscope shift controls to superimpose the two traces. Use

BUFFER #1 to equalize their amplitudes.

T7 notice that BUFFER #2 varies the amplitude of both traces, so they stay

superimposed at low input amplitudes, before distortion sets in.

Adjust the gain of BUFFER #2 until the output signal indicates the

onset of moderate distortion; that is, when its shape is obviously

different from the input waveform, which is also being displayed on

the oscilloscope. A ratio of about 5:6 for the distorted and

undistorted peak-to-peak amplitudes gives a measurable amount of

distortion.

You have duplicated Figure 2.

Record the amplitude of the signal at the input to the DUT.

Amplifier overload


You are now set up moderate overload of the DUT. You are ready to measure the

distortion components.

T8 without disturbing the arrangement already patched up, model a WAVE

ANALYSER. For example, use the one examined in the experiment

entitled Spectrum analysis - the WAVE ANALYSER. This is shown

in Figure 6.

T9 use the WAVE ANALYSER to search for, and record, the presence of all

significant components at the output of the DUT for the conditions of

the previous Task. Theory suggests that these will be at 2.084 kHz (set

by the nominal 2 kHz test signal from the MASTER SIGNALS module)

and its odd multiples (odd, because of the approximate cubic shape of

the transfer function of the DUT).

T10 from your measurements of the previous Task calculate the amount of

harmonic distortion ( THD) under the above conditions.

T11 now reduce the level of the input signal to the DUT by (say) 50% (using the

gain control of BUFFER #2).

T12 measure the amplitude of the largest unwanted component - the third

harmonic of the input.

You should have observed that:

whereas the amplitude of the input was reduced by 50%, that

of the largest unwanted component fell by more than this.

This is a phenomenon of non-linear distortion.

Now try a two-tone test, looking for intermodulation products as well as harmonics.

You will work on the same amplifier (DUT) as before.

twotwotwotwo----tone testingtone testingtone testingtone testing

measurement of SDRmeasurement of SDRmeasurement of SDRmeasurement of SDR

If you built the model of Figure 7, then you are almost ready. The new test set-up is

illustrated in Figure 8 below.

The ADDER combines the two signals in equal proportions. The tones should be

of ‘comparable frequency’; say within 10% or less of each other. BUFFER #2 at

the ADDER output is used as a joint level control. As before, BUFFER #1 enables

the ‘before’ and ‘after’ signals, displayed on CH1-A and CH2-A respectively, to be

matched in amplitude.


T13 patch up the model of Figure 8 below. Include the patchings to the SCOPE

SELECTOR inputs.

T14 the two tones are the nominal 2 kHz message from the MASTER SIGNALS

module, and a second from an AUDIO OSCILLATOR. Set the second

tone close to the first, say 1.8 kHz.

TWO-TONE GENERATOR

CH2-A

ANALYSER to WAVE

UNDER

TEST

DEVICE

ext. trig

recovery of the envelope of the two-tonesignal for oscilloscope triggering

INSTRUMENTATION

(WAVE ANALYSER not shown)

CH1-A

rovinglead

CH1-B

DUT input DUT output

Figure 8: two-tone test setup

The two-tone signal necessitates new oscilloscope triggering arrangements. As

already explained, an envelope recovery circuit is needed, and this is shown

modelled with a RECTIFIER in the UTILITIES module, and a TUNEABLE LPF.

Three of the four SCOPE SELECTOR positions are shown permanently connected.

The fourth, CH1-B, can be used as a roving lead, for various waveform inspections,

including the next task.

T15 adjust the two tones at the ADDER output to equal amplitudes (say 2 volt

peak-to-peak each). Adjust the gain of BUFFER #2 to about unity.

T16 check the envelope detector output, using CH1-B. What is wanted is a

periodic signal at envelope frequency, suitable for oscilloscope

triggering. Its shape is not critical. Tune the filter to its lowest

bandwidth; set the front panel passband GAIN control to its mid

range.

Amplifier overload


T17 when satisfied with the previous Task, use the output of the envelope detector

to trigger the oscilloscope, and check on CH1-A (with BUFFER #1 set

to mid-gain) that the envelope of the two-tone signal is stationary on

the screen (showing one or two periods of the envelope). Note that

this display will show up any imperfection in the equality of the

amplitudes of the two tones (or could have been used to set them equal

in the first place).

T18 switch to CH1-A and CH2-A. Set both these oscilloscope channels to the

same gain. You are now observing the input and output of the DUT.

Adjust the gain of BUFFER #2 so that the output (CH2-A) is not

distorted - that is, the same waveform as CH1-A.

T19 use the oscilloscope shift controls to overlay the two waveforms. Adjust the

gain of BUFFER #1 until they are of exactly the same amplitude, and

so appear as a single trace on the screen.

T20 now slowly increase the gain of BUFFER #2. Both traces will get larger,

but remain overlaid, until the signal level into the DUT exceeds its

linear operating range, and the output begins to show distortion. The

two waveforms will no longer be identical, and the difference should

be clearly visible.

T21 familiarize yourself with the overloading process by covering the full gain

range of BUFFER #2. Then set the gain to the point where distortion

of the DUT output waveform is ‘moderate’ 5. A ratio of output to

input signal amplitudes of about 5:6 is suggested as a start. This is

the condition under which you will be making some distortion

measurements. Record the input amplitude to the DUT; sketch the

input and output waveforms.

Remember the DUT has a cubic non-linearity. This suggests it will generate odd

order harmonic and intermodulation products. If the two test signals are f1 and f2,

then the largest unwanted components are likely to be on frequencies 3f1, 3f2,

(2f1±f2) and (2f2±f1).

T22 use the WAVE ANALYSER to search for, and record, the presence of all

significant components in the output of the DUT for the conditions of

the previous Task. Record clearly the frequency of each component

found, and relate it to the frequencies of the two-tone signal.

T23 from your measurements of the previous Task calculate the SDR, using

eqn. (18).

5 if you make it too slight the distortion components will be hard to find !


In the above calculation you might have included all components which you

measured.

But suppose the output signal DUT had then been transmitted via a channel with a

bandpass characteristic. Then many of the distortion components would have been

removed. But distortion would still have been measured, since those

intermodulation products close to the two wanted tones would have been passed.

T24 re-calculate the SDR, assuming transmission was via a bandpass filter.

conclusionsconclusionsconclusionsconclusions

During the experiment you might have taken the opportunity to listen to the signals

with and without distortion, to gain a qualitative idea and appreciation of what

level of distortion - with these types of signals - is detectable by ear.

This experiment has served as an introduction to the methods of measuring and

describing the non-linear performance of an analog circuit. A problem associated

with the measurement of a narrowband system has been demonstrated, together

with a method of overcoming it.


Q1 why were the two tones, in the two-tone test signal, set relatively close in

frequency to each other ?

Q2 equation (19) suggests an alternative method of making a two-tone test

signal. It has the particular advantage of providing a synchronizing

signal (from the low frequency source), the two tones are

automatically of equal amplitude, and the whole signal can be swept

across the spectrum with one control - that of the high frequency

oscillator. What are some disadvantages of this method of

generation ?

Q3 explain qualitatively how the display of the two added tones, as a DSBSC

signal, can be used to equalize the amplitudes of the two tones. Use a

phasor diagram or other method to explain the process quantitatively.

Q4 two businesses advertise the same amplifier, one saying it is a 50 watt

amplifier, and the other a 60 watt amplifier. There is no dishonesty.

How could this be ?

Amplifier overload



some useful expansions.some useful expansions.some useful expansions.some useful expansions.

In analysing a non-linear system in terms of sinusoidal signals as in the above

work, the aim is to convert expressions in terms of powers of sinusoidal signals to

expressions in terms of harmonics of the fundamental frequencies involved.

Some useful expansions are:

cos2Α = 1/2 + 1/2.cos2Α

cos3Α = 3/4.cosΑ + 1/4.cos3Α

cos4Α = 3/8 + 1/2.cos2Α + 1/8.cos4Α

cos5Α = 5/8.cosΑ + 5/16.cos3Α + 1/16.cos5Α

cos6Α = 5/16 + 15/32.cos2Α + 3/16.cos4Α + 1/32.cos6Α

Perhaps you can see the pattern developing ? It is clear that:

• when n is odd, the expansion of (cosmt)n gives rise to all odd harmonics

counting down from the nth.

• when n is even, the expansion of (cosµt)n gives rise to all even harmonics

counting down from the nth. Note that the count goes down to the zeroeth

term, which is DC.

After an expression has been reduced to the sum of harmonic terms, those of

similar frequency must be combined, taking into account their relative phases.

Thus:

V1.cosµ1t + V2.cosµ1t = ( V1 + V2 ).cosµ1t

but

V1.cosµ1t + V2.sinµ1t = V.cos(µ1t + α)

where

V V V= +( )1

2

2

2

and

α = −tan ( )1 2

1

V

V

As an exercise, develop the above expansions in terms of sin functions. There must

be some obvious similarities, but just as importantly there must be differences.

Explain !

Further useful expansions may be found in Appendix B to this Text.


FREQUENCY DIVISION FREQUENCY DIVISION FREQUENCY DIVISION FREQUENCY DIVISION

MULTIPLEXMULTIPLEXMULTIPLEXMULTIPLEX

PREPARATION................................................................................ 2

the application........................................................................... 2

multi-channel tape recorder ....................................................... 2

scheme 1 ............................................................................................... 3

scheme 2 ............................................................................................... 4

avoid crosstalk .......................................................................... 4

EXPERIMENT.................................................................................. 5



FREQUENCY DIVISION FREQUENCY DIVISION FREQUENCY DIVISION FREQUENCY DIVISION


ACHIEVEMENTS: principle of FDM; appreciation that more than one channel

can be recorded on a single track of a domestic tape recorder;

demodulation of FDM.

PREREQUISITES: completion of experiments on DSBSC and SSB demodulation

eg, Product demodulation - synchronous and asynchronous.


The principle of frequency division multiplexing - FDM - should be familiar to

everyone, since every domestic radio or TV receiver is a frequency de-multiplexer.

You are aware that there are many local radio stations operating without mutual

interference. They occupy their own allocated frequency channels without overlap.

They have been frequency multiplexed into the radio spectrum.

A de-multiplexer is merely a device which can select one station (channel) from all

others. It is a frequency selective device.

the applicationthe applicationthe applicationthe application

Although the above description was indeed of FDM, it is not a typical example of

an FDM system. The principle is generally applied when it is required to transmit,

simultaneously, more than one message via a particular communications channel,

such as a transmission line (say twisted pair or coaxial), and all channels emanate

from the same location. Such a medium is thought of as being basically a single

channel, but FDM techniques enable it to carry multiple channels simultaneously.

The motivation comes from the observation that a particular transmission medium,

say twisted pair, or coaxial cable, has a bandwidth much wider than that of a single

voice channel, and so it seems wasteful to use it for one voice channel only.

multimultimultimulti----channel channel channel channel tape recordertape recordertape recordertape recorder

In this experiment the principle of FDM has been used to place several channels on

a single track of an audio tape recorder.

Frequency division multiplex


The bandwidth of a good quality domestic audio tape recorder is at least 16 kHz,

and so is adequate for the purpose of accepting four 3 kHz audio channels side by

side, with spaces between to act as ‘guard bands’.

Two schemes are suggested, namely scheme 1 and scheme 2.

schemeschemeschemescheme 1111

A possible spectrum is shown in Figure 1.

Figure 1: FDM scheme 1

There are four channels in the FDM spectrum of Figure 1, each based on

independent messages of 3 kHz bandwidth.

Channel A is located in its normal position in the frequency spectrum.

Channels B, C and D have been translated in frequency by individual USSB

generators, based on carriers of 4, 8, and 12 kHz respectively.

To recover channel A, a 3 Hz lowpass filter would be sufficient. For the other three

channels, SSB receivers would be required. A de-multiplexing scheme is


S S BD e m o d u la to r



F D M

A

B

C

D

4 k H z

8 k H z

1 2 k H z

Figure 2: de-multiplexer for scheme 1

Notice that the three carrier sources might, in practice, be derived, by division, on a

master clock of, say, 24 kHz. This is typical of FDM systems.

If only one channel is required at a time, then only one SSB demodulator need be

supplied.


scheme 2scheme 2scheme 2scheme 2

A less ambitious scheme, but which none-the-less illustrates the principle, is shown

in Figure 3.

Figure 3: FDM scheme 2

This system has only three channels, but requires a less complex de-multiplexer.

Instead of SSB demodulators, DSBSC demodulators are adequate.

A suitable de-multiplexer is illustrated in Figure 4.

C

D

FDM

8kHz

12kHz

A

Figure 4: demodulation scheme for Figure 3

Unless announced otherwise, it will be assumed below that Scheme 2 is in

operation.

avoid crosstalkavoid crosstalkavoid crosstalkavoid crosstalk

During the experiment it is important to avoid crosstalk.

In an analog system it is essential to operate in a linear manner to avoid the

generation of harmonic and intermodulation distortion. This is especially

important in a multi-channel system if interference between channels - crosstalk -

is to be avoided.

If the crosstalk was introduced at the transmitter there is nothing you can do about

it at the receiver 1. It is your responsibility to avoid circuit overload at the receiver.

If at any time you observe intrusion of the message from another channel into the

channel to which you are tuned, check that it is not your circuitry overloading.

1 do you agree ?



The most likely place for intermodulation to occur is in the MULTIPLIER. Check

this by reducing the amplitude of the FDM from TRUNKS. This can be done by

using a BUFFER AMPLIFIER.

It is the ratio of unwanted-to-wanted signal power that you are trying to reduce.

In a typical overloaded system it can be shown that a 6 dB

reduction of signal level should result in a reduction of the

unwanted signal power by more than 6 dB

This phenomenon is demonstrated in the experiment entitled Amplifier overload in

this Volume.


An FDM signal is available at your TRUNKS panel.

You will note that the demodulators of Figure 4 are not true SSB demodulators.

This is not necessary, since, although each channel is in fact an SSB signal, there is

no signal on the opposite sideband. Secondly, not being DSBSC there is no need to

include a phase changer in the carrier paths.

The two carrier signals can be obtained from an AUDIO OSCILLATOR and VCO

modules. Note that, in both schemes, the receiver for channel A is in principle the

same as that for the other channels, with a local oscillator on zero kHz. This can be

simulated by replacing the oscillator signal with a 2 volt DC signal from the

VARIABLE DC module. Alternatively, for channel A, dispense with the

MULTIPLIER altogether, and use the LOWPASS FILTER only (as in Figures 2

and 4).

Since you have only one HEADPHONE AMPLIFIER you will only be able to listen

to one channel at a time, by connecting the input of the HEADPHONE

AMPLIFIER to the appropriate MULTIPLIER output (for channel B and C), or the

FDM itself (for channel A).

T1 patch up the de-multiplexer scheme of Figure 4. For the two carriers use an

AUDIO OSCILLATOR and a VCO. You will have to share the

HEADPHONE AMPLIFIER (with its 3 kHz LPF) between channels.

T2 locate the FDM signal at the TRUNKS panel.

T3 initially set the peak amplitude of the FDM signal into your demultiplexer at

the TIMS ANALOG REFERENCE LEVEL.


T4 show that it is possible to separate the individual channels with your de-

multiplexer. Record their carrier frequencies (nominally 0, 8, and

12 kHz in the scheme of Figure 3, but the signal at TRUNKS could

differ from this). Remember that, if there is significant crosstalk,

check the effect of a reduction of the amplitude of the FDM signal

from TRUNKS by using a BUFFER AMPLIFIER.

T5 make sure you investigate both methods of recovering channel A. That is,

without the MULTIPLIER, or with the MULTIPLIER and a zero

frequency local oscillator signal.

T6 from your results draw the spectrum, in the format of Figure 3, of the FDM

signal you have been sent.

T7 introduce crosstalk. This can be done by connecting, if not already done so, a

BUFFER AMPLIFIER between TRUNKS and the input to your de-

multiplexer. Initially set the gain of the BUFFER AMPLIFIER to

unity, and re-confirm that crosstalk is low (or non-existent). Then

increase the BUFFER AMPLIFIER gain, by say a factor of two, and

check the crosstalk. This crosstalk ‘measurement’ can only be an

estimate whilst all channels are carrying speech. You should make

some comments on how this estimate was made and recorded.

Record the peak amplitude of the FDM signal into your demultiplexer

when it is set just below the onset of crosstalk.




Q1 draw a block diagram and describe its use to make a tape recording of the

FDM signal you have been sent.

Q2 assuming you have a DSBSC demodulator only (not an SSB demodulator)

could you separate the channels of the scheme illustrated below ?

Q3 you have shown that a true SSB demodulator is not necessary in order to

recover each channel from the scheme of Figure 3. In principle,

however, there is an advantage in using a true SSB demodulator.

Explain.

Q4 to avoid the need for SSB generators to make the FDM signals, an alternative

scheme could generate the spectrum shown below. Could a DSBSC

demodulator be used in principle to recover the three channels

independently ? Can you suggest a possible practical problem(s) with

this scheme ?

Q5 discuss the meaning and significance of the term ‘guard band’ in the present

context.

Q6 in the last Task, was the peak amplitude of the FDM signal above or below

the TIMS ANALOG REFERENCE LEVEL when the crosstalk became

unacceptable (this will have to be a qualitative judgement). Comment.


PHASE DIVISION PHASE DIVISION PHASE DIVISION PHASE DIVISION


PREPARATION................................................................................ 2

the transmitter ........................................................................... 2

the receiver ............................................................................... 3

EXPERIMENT.................................................................................. 4

a single-channel receiver............................................................ 4

a two-channel receiver .............................................................. 5



PHASE DIVISION PHASE DIVISION PHASE DIVISION PHASE DIVISION


ACHIEVEMENTS: phase division multiplex (PDM) demodulation; significance

of the exact quadrature condition; cross-talk estimation

PREREQUISITES: DSBSC generation; synchronous demodulation


Phase division multiplex 1, PDM, is a modulation technique which allows two

DSBSC channels, sharing a common, suppressed carrier, to occupy the same

spectrum space. It is possible to separate the channels, upon reception, by phase

discrimination. Apart from communications applications, especially in digital

communications, the technique is also used for colour difference signals in some

TV systems.

the transmitterthe transmitterthe transmitterthe transmitter

Figure 1 shows a block diagram of the arrangements at the transmitter.

Q

ω0

IN

IN

message

message

out

DSB

DSB

Q

π/2

II

Figure 1: The PDM Generator

1 also known as quadrature phase division multiplexing, or quadrature-carrier multiplexing, or

quadrature amplitude modulation (QAM), or orthogonal multiplexing

Phase division multiplex


There are two message channels, I (in-phase) and Q (quadrature) and these are

converted to DSBSC signals - DSBI and DSBQ. The messages should be

bandlimited (not shown) to the same bandwidth, say 3 kHz if they are speech. Each

DSBSC will therefore occupy a 6 kHz bandwidth. The two DSBSC signals are

added together. They will overlap in frequency, since they share a common carrier

of ω rad/s. So the bandwidth of the PDM will also be 6 kHz.

The key to the system lies in the fact that there is a 90 degree - quadrature - phase

difference between the carriers supplied to the two DSBSC generators.

ththththe receivere receivere receivere receiver

Consider a single DSBSC demodulator as studied in an earlier experiment. It was

learned there that, when receiving a DSBSC signal, it was possible to adjust the

phasing of the local carrier such that the received message amplitude was reduced

to zero.

Suppose now a second DSBSC was added at the transmitter, as has been done in

Figure 1. Since both the transmitter and receiver are operating in a linear manner,

this should make no difference, at the receiver, to the null, already achieved (of

channel I, say). Consequently, if the second DSBSC, channel Q, is of a different

relative phase, it will NOT be nulled, and will appear at the demodulator output.

To listen to the message from channel I, it is merely a matter of changing the

receiver phasing to null channel Q.

In principle the two channels at the transmitter need not

be in exact phase quadrature. So long as there is a finite

phase difference, no matter how small, one of the channels

at the receiver can be nulled, leaving the other.

The disadvantage of a phase difference other than 90 degrees is that this results in a

degradation of signal to noise ratio, as observed at the demodulator output.

Whereas the output noise level is not sensitive to the phase of the local carrier, the

amplitude of the recovered message is. You can show that, for a null of one

channel, the output amplitude from the other is a maximum when the two channels

are in phase quadrature. However, this maximum is fairly broad. An error of 45

degrees from quadrature at the transmitter will result in a 3 dB degradation from

the maximum possible amplitude at the receiver.

What is important is not so much the accuracy of the channel phase difference, but

its stability. It is also assumed that, what ever the phase difference at the

transmitter may be, the receiver will be adjusted appropriately.

In practice, to simplify carrier acquisition by the receiver, a small amount of ‘pilot’

carrier, typically about 20 dB below the peak DSB level, may be inserted at the

transmitter.


EXEXEXEXPERIMENTPERIMENTPERIMENTPERIMENT

At one of the TRUNKS outputs there is PDM signal. It carries two channels,

which will be arbitrarily named as ‘I’ and ‘Q’. They carry independent messages,

one speech (I), the other a single tone (Q).

Locate the PDM signal with your oscilloscope.

With two independent messages, as there are, there is no ‘text book’ type of

stationary display which can be reproduced on your oscilloscope. However,

knowing the message on one channel is a single tone, the PDM will take on the

appearance of a text book 2 DSBSC during speech pauses on the other channel.

The envelope of this DSBSC will not remain stationary, but it may remain so for

periods long enough to verify this statement.

A two-channel demodulator, capable of selecting channels from this PDM signal, is


Error! Objects cannot be created from editing field codes.

Figure 2: a demodulator for PDM.

a singlea singlea singlea single----channel receiverchannel receiverchannel receiverchannel receiver

You may decide to omit those modules in the dotted box required for channel Q. In

this case you will be able to receive either channel, but only one at a time. To do

this:

T1 patch up a TIMS model of the block diagram of Figure 2, omitting that part

in the dotted box. Steal the carrier from the MASTER SIGNALS

module. Use the 3 kHz LPF in the HEADPHONE AMPLIFIER.

T2 use the oscilloscope to select the PDM signal from TRUNKS.

T3 connect the oscilloscope to monitor the output from channel I of the

demodulator. Switch the ‘trig’ to ‘channel A’, in auto mode (if

available). Start with a sweep speed of say 1 ms/cm. There is no

appropriate signal for oscilloscope synchronization.

The oscilloscope will now be displaying the output of Channel I of the demodulator.

This will most likely show contributions from both transmitter channels. You can

listen with HEADPHONES, as well as view on the oscilloscope. The display will

not be stationary during the nulling process, but when the tone channel is isolated

you can synchronize the oscilloscope to it.

2 a DSBSC derived from a single tone

Phase division multiplex


The nulling procedure is best performed by concentrating the ear, if using

headphones, or the eye, if using the oscilloscope, on the message from the

unwanted channel. It is up to you to decide which this unwanted channel should

be, but you may find it easier to null the channel carrying the tone rather than the

speech.

T4 adjust the phase (front panel control on the PHASE SHIFTER #1) until the

unwanted channel is nulled out.

If both channels are carrying speech the visual method of nulling would be very

difficult. When the channels are carrying quite different types of messages, as they

are here, it is less difficult. Could you automate either of these procedures ?

a twoa twoa twoa two----channel receiverchannel receiverchannel receiverchannel receiver

To model a receiver which is capable of demodulating both transmitter channels

simultaneously it is necessary to add the modules within the dotted box of Figure 2.

T5 add the modules for channel Q recovery.

T6 listen to the output of Channel I of your receiver, and null out one channel

from the transmitter with PHASE SHIFTER #1

T7 listen to the output of Channel Q of your receiver, and null out the other

channel from the transmitter with PHASE SHIFTER #2



Q1 obtain an expression for the degradation of SNR at the receiver, as a result of

a phase difference from the ideal 90 at the transmitter, and confirm

that it is 3 dB for a 45 degree error. It is assumed that the receiver

has been (re)adjusted to accommodate what ever phasing is in use at

the transmitter

Q2 since it is not necessary that the two DSBSC of a two-channel PDM signal be

phased exactly 90 degrees apart, why not use three channels, and put

them at 60 degrees apart ? or four channels at 45 degrees apart ?

Discuss the possibilities of such a system.

Q3 if there is a small phase error α in a PDM receiver a listener to one channel

will hear a low-level copy of the message on the other channel; this is

called ‘cross-talk’. Obtain an expression for the level of cross-talk as

a function of phase error.

Q4 there are two PHASE SHIFTER modules in Figure 2. An alternative

connection would be to place PHASE SHIFTER #1 between the

carrier source and the top MULTIPLIER, and PHASE SHIFTER #2

between the carrier source and the lower MULTIPLIER. Can you see

any advantages in this ?


ANALYSIS OF THE FM ANALYSIS OF THE FM ANALYSIS OF THE FM ANALYSIS OF THE FM

SPECTRUMSPECTRUMSPECTRUMSPECTRUM

introduction .............................................................................. 2

definition of modulation ............................................................ 2

phase modulation (PM) - definition ....................................................... 3

frequency modulation (FM) definition ................................................... 3

angle modulation - general form............................................................ 3

receivers ................................................................................... 4


spectral properties.................................................................................. 5

bandwidth ................................................................................. 6

significant sideband criterion................................................................. 6

example ........................................................................................... 7

bandwidth on a power basis ................................................................... 7

bandwidth restriction ............................................................................. 8

amplitude limiting...................................................................... 8

properties of the harmonic terms............................................................ 9

frequency deviation multiplication ............................................. 9

tutorial questions..................................................................... 10


ANALYSIS OF THE FM ANALYSIS OF THE FM ANALYSIS OF THE FM ANALYSIS OF THE FM

SPECTRUSPECTRUSPECTRUSPECTRUMMMM

introductionintroductionintroductionintroduction

To understand the next few experiments it is necessary to have a basic

understanding of the nature of phase modulated (PM) and frequency modulated

(FM) signals. These notes define the angle modulated signal, of which PM and FM

are special cases.

FM, under well defined conditions, offers certain features, including a method of

trading bandwidth for signal-to-noise ratio. These notes will not discuss signal-to-

noise properties, but instead will concentrate on an analysis of the spectral

properties of the signal.

definition of modulationdefinition of modulationdefinition of modulationdefinition of modulation

Consider the signal:

y(t) = E.cos(ωt + φ) ........ 1

This signal possesses, by definition:

• an amplitude ‘E’

• a total phase (ωt + φ)

• an instantaneous frequency defined as the time rate of change of total phase.

Any one of these three parameters may be modulated by a message A.cosµt. Which

ever parameter is chosen, then, by definition:

• the rate of variation of the chosen parameter should be directly proportional to

the rate of variation of the message alone (µ)

• the amount of variation of the chosen parameter should be directly proportional

to the amplitude of the message alone (A)

Other parameters may vary at the same time, as will be seen in what follows, but

these variations will not be strictly in accordance with the above definitions.

Analysis of the FM spectrum


phase modulation (PM) phase modulation (PM) phase modulation (PM) phase modulation (PM) ---- definition definition definition definition

According to the above requirements a signal will be phase modulated, by the

message A.cosµt, if:

total phase = ωt + k1.cosµt ........ 2

and provided k1 is linearly proportional to A, the message amplitude.

Hence:

PM E t k t= +cos( cos )ω µ1........ 3

is a phase modulated signal.

Note that, for PM:

instantaneous frequency = ω - k1.µ.sinµt ........ 4

Although the frequency is also varying with the message, the variation is not

directly proportional to the message amplitude alone. Hence, by definition, this is

not frequency modulation.

frequency modulation (FM) definitionfrequency modulation (FM) definitionfrequency modulation (FM) definitionfrequency modulation (FM) definition

According to the above requirements a signal will be frequency modulated, by the

message A.cosµt, if:

instantaneous frequency = ω + k2.cosµt ........ 5

and provided k2 is linearly proportional to A, the message amplitude.

The total phase is obtained by integration of the instantaneous frequency, and thus

the signal itself must be:

FM E tk

t= +. cos( sin )ωµ

µ2

........ 6

Although the phase is also varying with the message, the variation is not directly

proportional to the message amplitude alone. Hence, by definition, this is not phase

modulation.

angle modulation angle modulation angle modulation angle modulation ---- general form general form general form general form

The defining equation, for both PM and FM, can be written in the form:

y(t) = E.cos(ωt + β.sinµt) ........ 7

One can choose β to represent either PM or FM as the case may be, and according

to the definitions above. Thus:

for PM β = ∆φ, the peak phase deviation ........ 8

and for FM β = ∆φ / µ ........ 9

The parameter β is often called the deviation.

Both PM and FM fall into a class known as angle modulated signals.


receiversreceiversreceiversreceivers

There are demodulators for these signals.

The demodulator in a PM receiver responds in a linear manner to the variations in

phase of the PM signal, and the receiver output is a copy of the original message.

Likewise the demodulator in an FM receiver responds in a linear manner to the

instantaneous frequency variations of the FM signal.

There is an output from a PM receiver if the input is an FM signal, and from an FM

receiver if the input is a PM signal. But these outputs will not be related to the

message in a linear manner.

In the experiment entitled Envelopes (in volume A1) a general expression is

defined for a modulated signal, namely:

y(t) = a(t).cos[ωt + φ(t)] ........ 10

where a(t) and φ(t) were defined as involving components at or near the message

frequency only.

The envelope was defined as being |a(t)|.

Phase variations are described by φ(t).

By definition, the output from both a PM and an FM

receiver will be φ(t), provided a(t) is a constant.


The spectrum of the angle modulated signal y(t) of eqn.(7) above can be obtained

by trigonometrical expansion.

This is an interesting exercise, and you should do it yourself, since it is instructive

to see where the various terms in the expansion come from.

Firstly you will need to know that:

cos(β.sinφ) = J0(β) + 2 [ J2(β).cos2φ + J4(β).cos4φ + ..................] ........ 11

sin(β.sinφ) = 2 [ J1(β).sinφ + J3(β).sin3φ + J5(β).sin5φ + ............] ........ 12

cos(β.cosφ) = J0(β) - 2 [ J2(β).cos2φ - J4(β).cos4φ + ....................] ........ 13

sin(β.cosφ) = 2 [ J1(β).cosφ - J3(β).cos3φ + J5(β).cos5φ - ..............] ........ 14

Here Jn(β) is a Bessel function of the first kind, argument β, and order n.

You will also need to know that:

J Jnn

n− = −( ) ( ) ( )β β1 ........ 15



Using the above formulae, y(t) of eqn.(7) can be expanded into two infinite series.

These can be combined, and then condensed, into the compact form:

y t E J n tn

n

n

( ) . ( ). cos( )= +=−∞

=∞

β ω µ0

........ 16

Notice that the choice of +cos() and +sin() in the defining equation (7) leads to

+cos() in the compact version of eqn.(16). A different combination of cos and sin

in the defining equation will produce a different looking compact version. Whilst

the frequency and amplitudes in each must be the same (why ?) the phases will

inevitably be different. It is difficult and unnecessary to memorise the exact form of

any of these expansions of the defining equation.

spectral propertiesspectral propertiesspectral propertiesspectral properties

Despite the apparent complexity of eqn.(16), which describes the spectrum of the

signal, it is a surprisingly easy matter to make and remember many general

observations about the nature of this spectrum.

What you should commit to memory is the general trends of the Bessel functions,

which are illustrated in Figure 1 below.

Figure 1: Plots of Bessel Functions

Notice that, as a function of β, all the curves are damped oscillatory. Except for

J0(β), they start from zero, rise to a positive maximum, then oscillate about zero

with ever decreasing amplitudes (damped). The exception, J0(β), starts from an

amplitude of unity. Their zero crossings are not uniform, so the functions are not

periodic. If you remember these general trends you will be able to make many

qualitative observations about the behaviour of the FM spectrum.

By a careful examination of eqn.(16), and the plots of the Bessel functions in

Figure 1, the following properties can be deduced. It is useful to retain an

understanding of them all:

0

1.0

0 5 10 15

argument ββββ

0.4-

J ( )ββββ0( )ββββJ

1 ( )ββββJ2


• spectral components are numbered left and right (±) counting from the central

component at ω (number n = 0).

• the spectral lines are spaced µ/(2π) Hz apart

• amplitude of the ±nth component from the centre is E.Jn(β). Because of

eqn.(15) these two components are of equal amplitudes. Thus the spectrum is

symmetrical about the central component at ω.

• the bandwidth is mathematically infinite, but in engineering terms the signal is

considered confined within limits which contain all ‘significant components’.

• you should have an understanding of the term ‘significant sidebands’ (or

spectral components). This is discussed below.

• as β increases, the bandwidth, however defined, increases

• as β increases, individual spectral lines do not increase in amplitude

monotonically. Their amplitudes are determined by Jn(β), plots of which appear

in Figure 1.

• for particular values of β the amplitude of particular sidefrequency pairs

becomes zero (these are the ‘Bessel zeros’).

• the total power in the spectrum is constant, and independent of β. This can be

deduced in more than one way. It is easy if you know that:

Jn

n

n2 1

=−∞

=∞=( )β

• the largest ever component is the one at ω rad/s (often called the ‘carrier’), for

the special case when β = 0

• sidefrequency pairs are alternately in phase-quadrature, and in-phase, with the

term at ω (perhaps this is less obvious)

bandwidthbandwidthbandwidthbandwidth

As engineers we should always know the bandwidth of the signals with which we

are dealing. In many cases bandwidth estimation is not difficult. But for an angle

modulated signal there is no single, closed form formula.

Mathematically the bandwidth of the angle modulated signal of eqn.(7) is infinite,

since the amplitude of the component nµ rad/s from the central component is

E.Jn(β), and this only approaches zero as n approaches infinity.

significant sideband criterionsignificant sideband criterionsignificant sideband criterionsignificant sideband criterion

Fortunately, as engineers, practical concerns enable us to overcome this apparent

problem.

Firstly, we only require a component to be relatively small for us to be able to

ignore it. This requires some sort of reference. For this we use the amplitude of

the unmodulated carrier, which is E.J0(0) (which is equal to E, since J0(0) = 1).

Insignificance is then defined as some fraction of the reference. Thus we have the

‘1% significant sideband criterion’, which declares a component insignificant if it

is 1% or less of the reference.

Secondly, if we can define a minimum width window in the frequency spectrum

outside of which there are no components of significance, then this window will



define its bandwidth. There is no simple formula for evaluating the width of this

window, although there are several well known ‘rules of thumb’.

exampleexampleexampleexample

Let us examine the spectrum of the angle modulated signal, defined by eqn.(7),

with:

β = 5,

and

µ / (2π) = 3 kHz

Reference to the Bessel tables will give the relative amplitudes of the spectral

components. It is usual to draw the normalized amplitude spectrum. This is for the

case E = 1.

Go to the column in the tables for β = 5. Using the 1% significant sideband

criterion search upwards from the bottom 1 of the column until the first entry is

found whose magnitude exceeds 0.01 (1% of 1). The order of the Bessel function is

given in the left-most column; this is ‘n’, and this gives the number of significant

sidebands either side of the carrier. The Tables give n = 8. Thus the bandwidth is

2x8x3 = 48 kHz.

+1

(n = +5)

Figure 2: Amplitude Spectrum for β β β β = 5

bandwidth on a power basisbandwidth on a power basisbandwidth on a power basisbandwidth on a power basis

Another method of defining the bandwidth is on a power basis - it is that window

which contains x% of the total power in the signal. The power of successive

components is added, counting outwards from the carrier, until the required

proportion is accumulated. The reference is the power in the unmodulated carrier.

The two methods converge to the same estimate as the window widens. Depending

on instrumentation available, or mathematical techniques being used, one may be

more convenient than the other.

1 you have to make an engineering judgement that there are no entries in the column below this point !


bandwidth restrictionbandwidth restrictionbandwidth restrictionbandwidth restriction

If an FM signal is passed through a bandpass filter of insufficient bandwidth to pass

all sidebands of significance, then the output from an ideal receiver will be

distorted. The search for an exact analysis of this distortion has occupied

mathematicians since well before the days of Armstrong and the introduction of FM

commercially.

It is common practice to refer to tables of measured results for particular situations.

amplitude limitingamplitude limitingamplitude limitingamplitude limiting

Amplitude limiters are used extensively in angle modulated systems.

It is an easy matter to describe the function of an amplitude limiter:

an amplitude limiter removes variations

in the envelope of a signal.

The input in the present context is a narrow band modulated signal defined by

y(t) = a(t).cos[ωt + φ(t)] ........ 17

where both a(t) and φ(t) contain components at or near the message frequency only.

Some properties of this signal were discussed in the experiment entitled Envelopes.

Vout

Vin

Figure 3: limiter characteristic

An amplitude limiter can be imagined as an amplifier with a characteristic such as

that of Figure 3.

Being a non-linear device it is not an easy matter to analyse its operation on a

general signal. It will be sufficient for our purposes to declare that:

the amplitude limiter will convert a(t)

of eqn.(10) to a constant.

This requires qualification of the nature of a(t). If y(t) is an amplitude modulated

signal, the amplitude limiter can remove moderate amounts of amplitude

modulation; but it would require infinite gain to remove the envelope of a 100%



amplitude modulated signal. Practical considerations need to be taken into account

when assessing the capabilities of the amplitude limiter in each application.

Further, it should be obvious that there will be groups of components (bands)

located around the harmonics of ω.

These bands have useful properties. Thus the amplitude limiter is followed by a

bandpass filter to select one of these wanted bands.

properties of the harmonic termsproperties of the harmonic termsproperties of the harmonic termsproperties of the harmonic terms

The harmonic terms have properties which are useful in angle modulation systems.

These can be examined by a study of the limiter characteristic. Its transfer function

can be described in many ways, one being:

output = a1.(ein) + a3.(ein)3 + a5.(ein)5 + ....... ........ 18

where ein is the input signal.

For the case:

ein = E.cosϕ(t) ........ 19

then eqn.(18) can be re-written as:

output = E1.cosϕ(t) + E3.cos3ϕ(t) + E5.cos5ϕ(t) + ......... ........ 20

Mathematicians may object to the next claim without proof, but as an engineer you

can check experimentally that, if:

ϕ(t) = [ωt + β.cosµt] ........ 21

then substitution into eqn.(20) will lead to:

output = E1.cos(ωt + β.cosµt) + E3.cos(3ωt + 3β.cosµt)

+E5.cos(5ωt + 5β.cosµt) + ......... ........ 22

Note carefully what has and has not happened:

• the limiter output has bands of spectral components centred on odd harmonics

of the original carrier at ω rad/s

• each of these bands of components is an angle modulated signal

• the degree of angle modulation of the input signal was β. The degree of angle

modulation of the nth harmonic has been increased to nβ.

• the rate of angle modulation of the input signal was µ rad/s. The rate of angle

modulation in the harmonics is still µ rad/s, which is as wanted. There has

been no multiplication of the rate.

• typically En+1 < En.

frequency deviation multiplicationfrequency deviation multiplicationfrequency deviation multiplicationfrequency deviation multiplication

In the context of angle modulation the combination of amplitude limiter and

bandpass filter is called a frequency multiplier.

Suppose there is an angle modulated signal, carrier ω rad/s, at the input to the

amplitude limiter. If the output of the amplitude limiter is passed to the bandpass


filter, centred on nω, then this output is an angle modulated signal with n times the

frequency deviation of the input. The fact that this new signal is on a carrier

frequency of n times the input frequency is of secondary importance.

The frequency multiplier would have been better called a deviation multiplier, since

this is its application in the context of angle modulation.

You will meet the amplitude-limiter-plus-bandpass-filter combination in the

experiment entitled FM and deviation multiplication (this Volume).

tutorial questionstutorial questionstutorial questionstutorial questions

Q1 suppose you are given the amplitudes of three adjacent side frequencies in the

spectrum of a PM signal. Knowing ‘n’, can you use the relationship:

ββ

β β=

++ −

2

1 1

. . ( )

( ) ( )

n J

J J

n

n n

to determine the value of β at the transmitter output ?

Q2 the signal of eqn.(7) appears across a 50 ohm resistor. What power is

dissipated in the resistor for the case E = 5 volts and β = 5 ?

Q3 calculate the number of sideband pairs required in the signal y t E t t( ) . cos( . cos )= +ω β µso that it contains 95% of the power in the unmodulated carrier.

Consider the cases:

β = 1, and

β = 5

Q4 a 100 MHz FM signal appears across a 50 ohm load resistor. The amplitude

spectrum, based on a 100 MHz carrier, is recorded as in the table:

a. what was the message

frequency ?

b. what was the power dissipated

in the 50 ohm load ?

c. what would be the bandwidth on

the 5% significant sideband

criterion ?

d. what was the peak phase

deviation of the transmitted

signal ?

e. what was the peak frequency

deviation of the transmitted

signal ?

f. compare the peak frequency

deviation and the signal bandwidth. Any comments ?

freq

MHz

amplitude

volts 100.0000 1.7461

100.0020 0.4101

100.0040 1.6330

100.0060 1.3111

100.0080 0.5480

100.0100 1.9157

100.0120 2.0944

100.0140 1.5509

100.0160 0.9004

100.0180 0.4362

100.0200 0.1826

100.0220 0.0676

100.0240 0.0225

100.0260 0.0068

100.0340 0.0000

100.0360 0.0000



Q5 in the Tables of Bessel Coefficients you will see some entries are negative. Of

what significance is this with relation to the spectrum of an FM

signal ?

Q6 a phase modulated transmitter radiates a signal at 100 MHz, derived from a

2.5 kHz single tone message. The transmitter output peak phase

deviation is ∆φ. Draw the amplitude spectrum for the cases:

∆φ = 1

∆φ = 5

∆φ = 10

Q7 what is the bandwidth of each of the signals of the previous Question, based

on the 2% significant sideband criterion ? Are these bandwidths in

the ratio 1:5:10 ? Comment.

Q8 a frequency modulated transmitter radiates a signal at 100 MHz, derived

from a 2.5 kHz single tone message. The transmitter output peak

frequency deviation is ∆φ = 10 kHz. What is the bandwidth of the FM

signal on the 1% significant sideband criterion ?

If the message frequency is changed to 10 kHz, what now is the

bandwidth on the same criterion ?

Q9 an FM signal with a peak frequency deviation of 20 kHz on a 160 MHz

carrier is multiplied with a 100 MHz sinewave, and the products at

260 MHz selected with a bandpass filter. What is the frequency

deviation of the 260 MHz signal ?



FM USING A VCOFM USING A VCOFM USING A VCOFM USING A VCO

INTRODUCTION ............................................................................. 2

spectrum................................................................................... 3

first Bessel zero ..................................................................................... 3

special case - β = 1.45 .......................................................................... 3

the zero-crossing-counter demodulator ..................................... 3

EXPERIMENT.................................................................................. 4

deviation sensitivity................................................................... 5

deviation linearity...................................................................... 5

the FM spectrum....................................................................... 6

the WAVE ANALYSER........................................................................ 6

first Bessel zero ..................................................................................... 7

special case - β = 1.45 ........................................................................... 7

FM demodulation...................................................................... 8

conclusions ............................................................................... 9



INTRODUCTION TO FM INTRODUCTION TO FM INTRODUCTION TO FM INTRODUCTION TO FM

USING A VCOUSING A VCOUSING A VCOUSING A VCO

ACHIEVEMENTS: FM generation using a VCO. Confirmation of selected

aspects of the FM spectrum. Demodulation using a zero crossing

counter demodulator.

PREREQUISITES: familiarity with the contents of the chapter entitled Analysis of

the FM spectrum; completion of the experiment entitled Spectrum

analysis - the WAVE ANALYSER, both in this Volume.

EXTRA MODULES: SPECTRUM UTILITIES. A second VCO is required for

spectral measurements.

INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION

This experiment has been written to satisfy those who are familiar with the

existence of the ubiquitous VCO integrated circuit, and wish to explore it as a

source of FM.

The VCO - voltage controlled oscillator - is available as a low-cost integrated

circuit (IC), and its performance is remarkable. The VCO IC is generally based on

a bi-stable ‘flip-flop’, or ‘multi-vibrator’ type of circuit. Thus its output waveform

is a rectangular wave. However, ICs are available with this converted to a

sinusoid. The mean frequency of these oscillators is determined by an RC circuit.

The controllable part of the VCO is its frequency, which may be varied about a

mean by an external control voltage.

The variation of frequency is remarkably linear, with respect to the control voltage,

over a large percentage range of the mean frequency. This then suggests that it

would be ideal as an FM generator for communications purposes.

Unfortunately such is not the case.

The relative instability of the centre frequency of these VCOs renders them

unacceptable for modern day communication purposes. The uncertainty of the

centre frequency does not give rise to problems at the receiver, which may be taught

to track the drifting carrier (see this Volume for the experiment entitled Carrier

acquisition and the PLL, which introduces the phase locked loop - PLL). The

problem is that spectrum regulatory authorities insist, and with good reason, that

Introduction to FM using a VCO


communication transmitters maintain their (mean) carrier frequencies within close

limits 1.

It is possible to stabilise the frequency of an oscillator, relative to some fixed

reference, with automatic frequency control circuitry. But in the case of a VCO

which is being frequency modulated there is a conflict, with the result that the

control circuitry is complex, and consequently expensive.

For applications where close frequency control is not mandatory, the VCO is used

to good effect 2.

This experiment is an introduction to the FM signal. The wideband FM signal is

very convenient for studying some of the properties of the FM spectrum.

spectrumspectrumspectrumspectrum

Examination of the spectrum will be carried out by modelling a WAVE ANALYSER.

This instrumentation was introduced in the experiment entitled Spectrum analysis -

the WAVE ANALYSER (in this Volume).

Specifically, two properties of an FM signal will be examined:

first Bessel zerofirst Bessel zerofirst Bessel zerofirst Bessel zero

Check your Bessel tables and confirm that J0(β) = 0 when β = 2.45

This Bessel coefficient controls the amplitude of the spectral component at carrier

frequency, so with β = 2.45 there should be a carrier null.

You will be able to set β = 2.45 and so check this result.

special case special case special case special case ---- β β β β = 1.45 = 1.45 = 1.45 = 1.45

For β = 1.45 the amplitude of the first pair of sidebands is equal to that of the

carrier; and this will be J0(1.45) times the amplitude of the unmodulated carrier

(always available as a reference).

You should confirm this result from Tables of Bessel functions (see, for example,

the Appendix C to this volume).

This is one of the many special cases one can examine, to further verify the

predictions of theory.

the zerothe zerothe zerothe zero----crossingcrossingcrossingcrossing----counter counter counter counter

demodulatordemodulatordemodulatordemodulator

A simple yet effective FM demodulator is one which takes a time average of the

zero crossings of the FM signal. Figure 1 suggests the principle.

1 typically within a few parts per million (ppm) or less, or a few Hertz, which ever is the smaller.

2 suggest such an application


Figure 1: an FM signal, and a train of zero-crossing pulses

Each pulse in the pulse train is of fixed width, and is located at a zero crossing of

the FM signal 3. This is a pulse-repetition-rate modulated signal. If the pulse train

is passed through a lowpass filter, the filter will perform an averaging operation.

The rate of change of this average value is related to the message frequency, and

the magnitude of the change to the depth of modulation at the generator.

This zero-crossing-counter demodulator 4 will be modelled in the latter part of the

experiment. The phase locked loop (PLL) as a demodulator is studied in the

experiment entitled FM demodulation and the PLL in this Volume.


A suitable set-up for measuring some properties of a VCO is illustrated in Figure 2.

Figure 2: the FM generator

For this experiment you will need to measure the sensitivity of the frequency of the

VCO to an external control voltage, so that the frequency deviation can be set as

desired.

The mean frequency of the VCO is set with the front panel control labelled fo.

The mean frequency can as well be varied by a DC control voltage connected to the

Vin socket. Internally this control voltage can be amplified by an amount

determined by the setting of the front panel GAIN control. Thus the frequency

sensitivity to the external control voltage is determined by the GAIN setting of the

VCO.

A convenient way to set the sensitivity (and thus the GAIN control, which is not

calibrated), to a definable value, is described below.

3 only positive going zero crossings have been selected

4 also called the zero crosssing detector



T1 before plugging in the VCO, set the mode of operation to ‘VCO’ with the on-

board switch SW2. Set the front panel switch to ‘LO’. Set the front

panel GAIN control fully anti-clockwise.

T2 patch up the model of Figure 2.

T3 use the FREQUENCY COUNTER to monitor the VCO frequency. Use the

front panel control fo to set the frequency to 10 kHz.

deviation sensitivitydeviation sensitivitydeviation sensitivitydeviation sensitivity

T4 set the VARIABLE DC module output to about +2 volt. Connect this DC

voltage, via BUFFER #2, to the Vin socket of the VCO.

T5 with the BUFFER #2 gain control, set the DC at the VCO Vin socket to exactly

-1.0 volt. With the VCO GAIN set fully anti-clockwise, this will have

no effect on f0.

T6 increase the VCO GAIN control from zero until the frequency changes by

1 kHz. Note that the direction of change will depend upon the polarity

of the DC voltage.

The GAIN control of the VCO is now set to give a 1 kHz peak

frequency deviation for a modulating signal at Vin of 1 volt peak.

The gain control setting will now remain unchanged.

For this setting you have calibrated the sensitivity, S, of the VCO for the purposes

of the work to follow.

Here:

S = 1000 Hz/volt ........ 1

deviation linearitydeviation linearitydeviation linearitydeviation linearity

The linearity of the modulation characteristic can be measured by continuing the

above measurement over a range of input DC voltages. If a curve is plotted of DC

volts versus frequency deviation the linear region can be easily identified.

A second, dynamic, method would be to use a demodulator, using an audio

frequency message. This will be done later. In the meantime:


T7 take a range of readings of frequency versus DC voltage at Vin of the VCO,

sufficient to reveal the onset of non-linearity of the characteristic.

This is best done by producing a plot as the readings are taken.

the FM spectrumthe FM spectrumthe FM spectrumthe FM spectrum

So far you have a theoretical knowledge of the spectrum of the signal from the

VCO, but have made no measurement to confirm this.

The instrumentation to be modelled is the WAVE ANALYSER, introduced in the

experiment entitled Spectrum analysis - the WAVE ANALYSER. It is assumed you have

completed that experiment.


IN

VCO fine tune

Figure 3: the WAVE ANALYSER model.

The VARIABLE DC voltage, with a moderate setting of the VCO GAIN control, is

used as a fine tuning control.

Remember that one is generally not interested in absolute amplitudes - what is

sought are relative amplitudes of spectral components.

Two such spectra will now be studied.

1. the first Bessel zero of the carrier term will be set up.

2. the amplitude of the carrier will be made equal to that of each of the first pair of

sidebands.

The VCO will be set up with a sinusoidal message of 500 Hz.

T8 in the FM generator model of Figure 2 replace the variable DC module with

an AUDIO OSCILLATOR, tuned to 500 Hz.

T9 patch up the WAVE ANALYSER of Figure 3.



T10 revise your skills with the WAVE ANALYSER. Set the frequency deviation of

the FM VCO to zero, with the BUFFER amplifier #2, and search for

the carrier component. Set the on-board SCALING resistor of the

SPECTRUM UTILITIES module to obtain a full scale deflection

(FSD) on the carrier.

first Bessel zerofirst Bessel zerofirst Bessel zerofirst Bessel zero

Refer to the work, under this heading, which was done preparatory to starting the

experiment.

Since

β = ∆f / fm

and

∆f = Vin S

then set

Vin = β.fm / S ≅ 1.22 peak volt

T11 adjust, with the AUDIO OSCILLATOR supplying the message, via the

BUFFER amplifier, for β = 2.45

T12 use the WAVE ANALYSER to confirm the amplitude of the carrier has fallen

very low. Fine trim of the BUFFER amplifier gain control should find

the null. Check that β is still close to 2.45.

T13 find one of the adjacent sidebands. Its amplitude should be J1(β) times the

amplitude of the unmodulated carrier (measured previously).

since J1(2.54) ≅ 0.5

then each of the first pair of sideband should be of amplitude half that of

the unmodulated carrier.

special case special case special case special case ---- ββββ = 1.45 = 1.45 = 1.45 = 1.45

Refer to the work, under this heading, which was done preparatory to starting the

experiment.

T14 set β = 1.45 and confirm that the carrier component, and either or both of

the first pair of sideband, are of similar amplitude.

T15 check that each of the components just measured is J1(1.45) times the

amplitude of the unmodulated carrier.


There are many more special cases, of a similar nature, which you could

investigate. The most obvious would be the Bessel zeros of some of the side-

frequencies.

You will now use this generator to provide an input to a demodulator.

FFFFM demodulationM demodulationM demodulationM demodulation

A simple FM demodulator, if it reproduces the message without distortion, will

provide further confirmation that the VCO output is indeed an FM signal.

A scheme for achieving this result was introduced earlier - the zero-crossing-

counter demodulator - and is shown modelled in Figure 4.

Message

out

FM input

Figure 4: an FM demodulator using a zero-crossing demodulator

The TWIN PULSE GENERATOR is required to produce a pulse at each positive

going zero crossing of the FM signal. To achieve this the FM signal is converted to

a TTL signal by the COMPARATOR, and this drives the TWIN PULSE

GENERATOR.

note: the input signal to the HEADPHONE AMPLIFIER filter is at TTL level. It is

TIMS practice, in order to avoid overload, not to connect a TTL signal to an

analog input. Check for overload. If you prefer you can use the yellow

analog output from the TWIN PULSE GENERATOR. This is an AC

coupled version of the TTL signal.

T16 before plugging in the TWIN PULSE GENERATOR set the on-board MODE

switch SW1 to SINGLE. Patch up the demodulator of Figure 4.

T17 set the frequency deviation of the FM generator to zero, and connect the

VCO output to the demodulator input.

T18 using the WIDTH control of the TWIN PULSE GENERATOR adjust the

output pulses to say a mark/space ratio of 1:1.

T19 observe the demodulator output. If you have chosen to take the TTL output

from the TWIN PULSE GENERATOR there should be a DC voltage

present. Why ? Notice that it is proportional to the width of the

pulses into the LPF of the HEADPHONE AMPLIFIER.



T20 introduce some modulation at the VCO with the BUFFER amplifier gain

control. Observe the output from the LPF of the HEADPHONE

AMPLIFIER using the oscilloscope. Measure its frequency (and

compare with the message source at the transmitter).

T21 show that the amplitude of the message output from the demodulator:

a) varies with the message amplitude into the VCO. Is this a linear

variation ?

b) varies with the pulse width from the TWIN PULSE GENERATOR.

Is this a linear variation ?

c) is constant with the frequency of the message to the VCO. Does

this confirm the VCO is producing FM, and not PM ?

T22 increase the message amplitude into the VCO until distortion is observed at

the receiver output. Can you identify the source of this distortion ?

Record the amplitude of the message at the VCO. You may need to

increase the GAIN of the VCO.

conclusionsconclusionsconclusionsconclusions

There are many other observations you could make.

• have you checked (by calculation) the bandwidth of the FM signal under all

conditions ? Could it ever extend ‘below DC’ and cause wrap-around (fold-

back) problems ?

• do you think there is any conflict with the nearness of the message frequency to

the carrier frequency ? Why not increase the carrier frequency to the limit of

the VCO on the ‘LO’ range - about 15 kHz

• why not avoid possible problems caused by the relatively large ratio µ/ω and

change to the 100 kHz region ?

• try a more demanding distortion test with a two-tone message.



Q1 name some applications where moderate carrier instability of an FM system

is acceptable.

Q2 draw the amplitude/frequency spectrum of the signal generated in task T14.

Q3 how would you define the bandwidth of the signal you generated in Task

T14 ?

Q4 what will the FREQUENCY COUNTER indicate when connected to the FM

signal from the VCO ? Discuss possibilities.

Q5 derive an expression for the sensitivity of the demodulator of Figure 4, and

compare with measurements.

sensitivityoutput message amplitude

input FM frequency deviation=

( )

( )

Q6 what is a magnitude for β, in Jn(β), for a Bessel zero, if:

a) n = 1

b) n = 3


FM AND THE FM AND THE FM AND THE FM AND THE

SYNCHRONOUS SYNCHRONOUS SYNCHRONOUS SYNCHRONOUS


PREPARATION................................................................................ 2

synchronous demodulation - linear modulation .......................... 2

synchronous demod of non-linear modulation............................ 3

FM - spectral properties to be verified....................................... 3

EXPERIMENT.................................................................................. 4

FM spectrum determination at baseband.................................... 5

alternative spectrum analysis ..................................................... 6



FM AND THE FM AND THE FM AND THE FM AND THE

SYNCHRONOUS SYNCHRONOUS SYNCHRONOUS SYNCHRONOUS


ACHIEVEMENTS: confirmation of some properties of the spectrum of an angle

modulated (FM) signal; action of a synchronous demodulator on this

signal; appreciation of the relative phases between the sidefrequency

pairs.

PREREQUISITES: familiarity with the contents of the Chapter entitled Analysis

of the FM spectrum in this Volume; completion of the experiment

entitled Product demodulation - synchronous & asynchronous in

Volume A1.

EXTRA MODULES: SPECTRUM UTILITIES


You are going to look at the operation of the synchronous demodulator on the angle

modulated signal:

y(t) = E.cos[ωt + ϕ(t)] ........ 1

For brevity this angle modulated signal will be referred to as being ‘FM’.

synchronous demodulation synchronous demodulation synchronous demodulation synchronous demodulation ---- linear linear linear linear

modulationmodulationmodulationmodulation

In earlier experiments the term ‘synchronous demodulator’ was used to describe the

arrangement of Figure 1.

This arrangement (also known as a synchronous product demodulator) has been

used to recover the message from AM, DSBSC, and SSB. Since the message was

recovered from the modulated signal input in each case, it was not unreasonable to

call it a demodulator.

FM and the synchronous demodulator


INPUT OUTPUT

local carrier

modulated signalon carrier ωο rad/s

οωon rad/s

phase

adjustment

Figure 1: the synchronous demodulator

This was true because these signals were undergoing linear modulation. This class

of signal was defined in the experiment entitled DSBSC generation.

Recall that, for a double sideband signal, as the phase angle α is adjusted, the

output amplitude from a synchronous demodulator will vary, including reduction to

zero. Zero output results when the local carrier, and the input DSB, are in phase-

quadrature.

synchronous demod of nonsynchronous demod of nonsynchronous demod of nonsynchronous demod of non----linear linear linear linear

modmodmodmodulationulationulationulation

An FM signal is a member of the class defined as undergoing non-linear

modulation. These were defined in the chapter entitled Analysis of the FM

spectrum.

What will happen when the input to the synchronous demodulator is an FM

signal ? Will it recover the message ϕ(t) of eqn.(1) ? The answer is a definite

‘no’ ! None-the-less, what happens is of interest, and forms the subject of this

experiment.

The arrangement of Figure 1 in this application is best thought of as a frequency

translator, for the special case where the translation is back to baseband.

FM FM FM FM ---- spectral properties to be verified spectral properties to be verified spectral properties to be verified spectral properties to be verified

The arrangement illustrated in the above Figure 1 is operating synchronously - this

means that the incoming and local carriers are on exactly the same frequency.

Their relative phases are not yet defined, but may be adjusted by varying the phase

angle α.

Remember that the amplitude spectrum of an FM signal, derived from a single tone

message, is symmetrical about the central (carrier) term on ωo. The spectrum

consists of pairs of sidefrequencies (DSBSC) alternately in phase-quadrature, and

in-phase, with the carrier term. Spectral lines are spaced apart by the message

frequency.

From the experiment entitled Product demodulation - synchronousand

asynchronous you will recall that the upper and lower sidebands of the input signal

will be frequency translated down to the baseband (audio) region where their


respective contributions will now overlap in frequency. The amplitude of the single

resultant from each pair of sidefrequencies will depend upon the relative phases of

the two components being combined. These in turn will be determined by the

phase angle α.

The ‘demodulator’ will give an output of many frequency components, one from

each of the sidefrequency pairs. These will be on exact harmonics of the original

message. The output will thus not be a copy of the message.

An FM demodulator would need to (re)combine all the

sidefrequencies of an FM signal into a single component at

message frequency. So strictly the arrangement of Figure 1 is

not a demodulator in this context.

Since the pairs of DSBSC in the FM spectrum are alternately in-phase, and in

phase-quadrature, their resultants will not maximise simultaneously as the phase

angle α is rotated. Thus the amplitudes of odd harmonics of the message will be

maximised when the even harmonics fall to zero, and vice versa.

All of the above properties will be verified in the experiment to follow.

You will not make measurements with a WAVE ANALYSER at 100 kHz. You

will make baseband measurements to confirm this.


At TRUNKS is an FM signal. It is based on a 100 kHz carrier (of which you have

a copy at the MASTER SIGNALS module) and a single tone message near 1 kHz.

The frequency deviation is sufficient to ensure several pairs of significant

sidefrequencies.

T1 look at the TRUNKS #1 signal with your oscilloscope. By choice of a sweep

speed of, say 1 ms/cm, confirm that its envelope is of constant

amplitude, so, if indeed it is modulated, it probably is an FM signal.

Use a faster sweep speed and see if you can detect any non-uniformity

of the zero-crossings (the compressed and expanded spring analog),

thus further confirming the possibility of its being FM.



FM spectrum determination at FM spectrum determination at FM spectrum determination at FM spectrum determination at

basebandbasebandbasebandbaseband

You will use the ‘synchronous demodulator’ to determine the nature of the FM

spectrum. Note that this method makes the measurements at baseband frequencies.

Error! Objects cannot be created from editing field codes.

Figure 2: synchronous ‘demodulation’ of the FM signal.

T2 patch up the arrangement of Figure 2, which is a 100 kHz SYNCHRONOUS

DEMODULATOR and a baseband WAVE ANALYSER. Before

plugging in the VCO set the on-board switch to ‘VCO’. The front

panel frequency range switch will be set to ‘LO’.

You will now have the opportunity to check the observation made in the chapter

entitled Analysis of the FM spectrum that:

• sidefrequency pairs are alternately in quadrature and in phase with the carrier

term at ω.

This means that the first pair of sidefrequencies are in phase-quadrature with the

carrier.

If the local carrier is set in-phase with the received carrier by means of the PHASE

SHIFTER then any carrier component present in the FM signal will show up as a

DC component at the ‘demodulator’ filter output.

By maximising the DC output from the filter you are

putting the receiver local oscillator in-phase with

the received carrier.

Under this condition there will be no output from the odd sidefrequency pairs.

Conversely there will be no output from the even sidefrequency pairs when the

carrier is in phase-quadrature.

Thus, with a little ingenuity, you can use the WAVE ANALYSER

to identify the nature of the spectrum at 100 kHz, by making

measurements at audio frequencies.


T3 set the oscilloscope to respond to DC, and adjust the PHASE SHIFTER to

maximise the amplitude of the DC output from the 60 kHz LPF. The

local carrier is now in-phase with the received carrier.

T4 use the WAVE ANALYSER to measure the relative amplitudes of all

significant components from the 60 kHz LPF. These will be present

due to the even-order sidefrequency pairs in the 100 kHz spectrum.

Call them V2, V4, etc. You cannot measure V0 (the DC component)

since the VCO does not tune down to DC. You could replace the VCO

signal with a fixed voltage from the VARIABLE DC module, but if you

do this you will need to be sure about what amplitude to use.

It is now necessary to put the local oscillator into the phase-quadrature condition.

T5 swap from the sin to cos output of the 100 kHz signal from the MASTER

SIGNALS module.

T6 use the WAVE ANALYSER to measure the amplitude of all significant

components from the filter. These will be present due to the odd-order

sidefrequency pairs in the 100 kHz spectrum. Call them V1, V3, V5etc.

Make sure you appreciate how you are now in a position to reconstruct the 100 kHz

relative amplitude spectrum from the baseband measurements just completed. Do

not forget that there is a ‘factor-of-two’ correction to be applied to the

sidefrequencies, but not to the carrier 1.

T7 use your baseband measurements to construct an amplitude spectrum of the

100 kHz signal. Compare results with the direct measurement made

earlier (or the amplitude spectrum supplied).

alternative spectrum analysisalternative spectrum analysisalternative spectrum analysisalternative spectrum analysis

The assertion that the sidefrequencies are alternately in-phase and in phase-

quadrature can be checked 2 without the aid of the WAVE ANALYSER. Instead

use the TUNEABLE LPF at the output of the synchronous demodulator.

This filter can be narrowed to pass only the message frequency at µ rad/s (and DC).

By adjusting the phase α the DC output can be maximised, while the AC output

(the signal at message frequency) is simultaneously reduced to zero. If the filter is

then widened to put the passband edge just above 2µ the component at twice the

1 each baseband component came from a sidefrequency pair.

2 strictly the check is valid only for the first two pairs.



message frequency will observed at the output, since this component is maximised

with the DC.

T8 use the TUNEABLE LPF in place of the WAVE ANALYSER and isolate

separately the DC, the component at µ rad/s, and the component at 2µ rad/s. Record their amplitudes.

T9 compare the (relative) amplitudes measured in the previous task with the

corresponding results obtained using the baseband WAVE

ANALYSER. Comment.



Q1 in Task 1, why pick a sweep speed of 1 ms/cm when looking for an envelope ?

Q2 would it be of serious consequence if the phase, when transferring from the

cos to sin outputs of the MASTER SIGNALS module (Task T5), was a

few degrees off a true 90ophase shift ?

Q3 for the final Task you were able to isolate the single component at µ rad/s.

This is the message frequency. Why could not the SYNCHRONOUS

DEMODULATOR, with the filter tuned as it is, then be called an FM

demodulator ?

Q4 did you confirm that the sidefrequency pairs of the FM signal are alternately

in-phase and in phase-quadrature ? Explain.

Q5 did you confirm that the sidefrequency pairs of the FM signal are spaced

apart by the message frequency ? Explain.

Q6 show how the measurements made at baseband were used to determine the

amplitude spectrum of the FM signal at 100 kHz. Draw the amplitude

spectrum of the FM signal.

Q7 the FM signal at TRUNKS is represented by y(t), where:

y(t) = E.cos[ωt + β cosµt]

Can you determine, from the amplitude spectrum of the previous

Question, the magnitude of ‘β’ ?

Q8 what is the ‘factor-of-two’ correction which was referred to when mapping

from the baseband amplitude spectrum (measured with the

synchronous demodulator) to the 100 kHz spectrum ?


ARMSTRONG'S PHASE ARMSTRONG'S PHASE ARMSTRONG'S PHASE ARMSTRONG'S PHASE

MODULATORMODULATORMODULATORMODULATOR

PREPARATION................................................................................ 2

FM generation........................................................................... 2

Armstrong`s modulator ............................................................. 3

theory ....................................................................................... 3

phase deviation ......................................................................... 4

practical realization of Armstrong`s modulator .......................... 5

EXPERIMENT.................................................................................. 6

patching up ............................................................................... 6

model adjustment ...................................................................... 6

Armstrong's phase adjustment ................................................... 8

phase adjustment using the envelope...................................................... 8

phase adjustment using ‘psycho-acoustics’............................................. 9

practical applications................................................................. 9

spectral components.................................................................. 9


APPENDIX ..................................................................................... 13

Analysis of Armstrong`s signal ................................................ 13

the amplitude limiter ........................................................................... 13

Armstrong`s spectrum after amplitude limiting.................................... 14


ARMSTRONG'S PHASE ARMSTRONG'S PHASE ARMSTRONG'S PHASE ARMSTRONG'S PHASE

MODULATORMODULATORMODULATORMODULATOR

ACHIEVEMENTS: modelling Armstrong's modulator; quadrature phase

adjustment; deviation calibration; introduction to the amplitude

limiter.

PREREQUISITES: earlier modulation experiments; an understanding of the

contents of the Chapter entitled Analysis of the FM spectrum in this

Volume.

EXTRA MODULES: SPECTRUM UTILITIES; 100 kHz CHANNEL FILTERS

(optional).


FM generationFM generationFM generationFM generation

As its name implies, an FM signal carries its information in its frequency

variations. Thus the message must vary the frequency of the carrier.

Spectrum space being at a premium, radio communication channels need to be

conserved, and users must keep to their allocated slots to avoid mutual interference.

There is a conflict with FM - the carrier must be maintained at its designated centre

frequency with close tolerance, yet it must also be moved (modulated) by the

message.

A well know source of FM signals is a voltage controlled oscillator (VCO). These

are available cheaply as integrated circuits. It is a simple matter to vary their

frequency over a wide frequency range; but their frequency stability is quite

unsatisfactory for today`s communication systems. Refer to the experiment entitled

Introduction to FM using a VCO in this Volume.

Armstrong`s modulation scheme 1 overcomes the problem 2. It does not change the

frequency of the source from which the carrier is derived, yet achieves the objective

by an indirect method. It forms the subject of this experiment.

1 Armstrong`s system is well described by D.L. Jaffe ‘Armstrong`s Frequency Modulator’, Proc.IRE,

Vol.26, No.4, April 1938, pp475-481.

Armstrong's phase modulator


Armstrong`s modulatorArmstrong`s modulatorArmstrong`s modulatorArmstrong`s modulator

Armstrong's modulator is basically a phase modulator; it can be given a frequency

modulation characteristic by an integrator inserted between the message source and

the modulator. For a single tone message, at one frequency, it is not possible to

tell, by what ever measurement, if the integrator is present (so it is an FM signal) or

not (a PM signal). Only with a change of message frequency can one then make

the decision - by noting the change to the spectral components, for example.

theorytheorytheorytheory

You are already familiar with amplitude modulation, defined as:

AM = E.(1 + m.sinµt).sinωt ...... 1

This expression can be expanded trigonometrically into the sum of two terms:

AM = E.sinωt + E.m.sinµt.sinωt ...... 2

In eqn.(2) the two terms involved with 'ω' are in phase. Now this relation can

easily be changed so that the two are at 90 degrees, or 'in quadrature'. This is done

by changing one of the sinωt terms to cosωt. The signal then becomes what is

sometimes called a quadrature modulated signal. It is Armstrong`s signal.

Thus:

Armstrong`s signal = E.cosωt + E.m.sinµt.sinωt ...... 3

Em

2

Em

2

Em

2

Em

2

(a) (b)

E E

Em

2

Em

2

E

ωµ( ) ω- ω µ+( )

Phasor Form Amplitude Spectrum

m = 1

m = 1

α = 90o

= 0α

frequency

Figure 1: DSBSC + carrier

The signals described by both eqn. (2) and eqn. (3) are shown in phasor form in

Figure 1 (a) and (b) above. The amplitude spectrum is also shown; it is the same

for both cases (a) and (b).

Each diagram shows the signals for the case m = 1. That is to say, the amplitude of

each side frequency component is half that of the carrier.

In the phasor diagram the side frequencies are rotating in opposite directions, so

their resultant stays in the same direction - co-linear with the carrier for (a), and in

phase-quadrature for (b).

2 but introduces another- it is not capable of wide frequency deviations


Both eqn. (2) and eqn. (3) can be modelled by the arrangement of Figure 2 below.

100 kHz (sine wave)

DSBSC

carrier

adjust phase

g

G

message (sine wave)

Armstrong`s signal

Figure 2: Armstrong`s phase modulator

phase deviationphase deviationphase deviationphase deviation

Having defined Armstrong`s signal it is now time to examine its potential for

producing PM.

But first: we have been using the symbol ‘m’ for the ratio of DSBSC to carrier

amplitude, because our starting point was an amplitude modulated signal, and ‘m’

has been traditionally the symbol for depth of amplitude modulation.. The

amplitude modulation was converted to quadrature modulation. We will

acknowledge this in the work to follow by making the change from ‘m’ to ‘∆φ’.

Thus:

∆φ = m ........ 4

Analysis shows (see the Appendix to this experiment) that the carrier of

Armstrong`s signal is undergoing phase modulation.

The peak phase deviation is proportional to the ratio of DSBSC to CARRIER peak

amplitudes at the ADDER output; but it is not a linear relationship. The peak

phase deviation, ∆φ, is given by:

∆φ = arctan [ ]DSBSC

CARRIERradians ...... 5

Remember that the amplitude of the DSBSC is directly proportional to that of the

message, so the message amplitude will determine the amount of phase variation.

For small arguments, arctan(arg) ≈ arg

Thus to minimize distortion at the receiver the ratio of DSBSC to carrier must be

kept small.

A receiver to demodulate a phase modulated signal is sensitive to these phase

deviations.

To keep the received signal distortion to acceptable limits the peak phase deviation

at Armstrong`s modulator should be restricted to a fraction of a radian, according

to distortion requirements as per Figure 3. The analysis of distortion is discussed in

the Appendix to this experiment.



Figure 3: distortion from Armstrong`s modulator

practical realization of Armstrong`s practical realization of Armstrong`s practical realization of Armstrong`s practical realization of Armstrong`s

modulatormodulatormodulatormodulator

The principle of Armstrong's method of phase modulation, or his frequency

modulator (with the added integrator as described earlier), is used in commercial

practice. But the circuitry employed to generate this signal is often not as

straightforward as the arrangement of Figure 2. It is not always possible to isolate,

and so measure separately, the amplitudes of the DSBSC and the CARRIER. So it

is not possible to calculate the phase deviation, in such a simple, straight forward

manner.

Amplitude limiters are also incorporated in the circuitry. These intentionally

remove the envelope, which otherwise could be used as a basis for measurement.

In these cases other methods must be used to set up and calibrate the phase

deviation of the modulator. These include, for example, the use of a calibrated

demodulator. There is also the method of 'Bessel zeros'. This is an elegant and

exact method, and is examined in the experiment entitled FM and Bessel zeros in

this Volume.



patching uppatching uppatching uppatching up

In this experiment you will learn how to set up Armstrong`s modulator for a

specified phase deviation, and a unique method of phase adjustment.

Armstrong`s generator, in block diagram form in Figure 2, is shown modelled in

Figure 4 below.

CH1-A

CH2-A

ext. trig

Figure 4: the model for Armstrong`s modulator

T1 patch up the model in Figure 4. You will notice it is exactly the same

arrangement as was used for modelling AM. The major difference for

the present application will be the magnitude of the phase angle α -

zero degrees for AM, but 900 for Armstrong.

T2 choose a message frequency of about 1 kHz from the AUDIO OSCILLATOR.

model adjustmentmodel adjustmentmodel adjustmentmodel adjustment

T3 check that the oscilloscope has triggered correctly, using the external trigger

facility connected to the message source. Set the sweep speed so that

it is displaying two or three periods of the message, on CH1-A, at the

top of the screen.

Now pay attention to the setting up of the modulator. The signal levels into the

ADDER are at TIMS ANALOG REFERENCE LEVEL, but their relative

magnitudes (and phases) will need to be adjusted at the ADDER output.

To do this:



T4 rotate both g and G fully anti-clockwise.

T5 rotate g clockwise. Watch the trace on CH2-A. A DSBSC will appear.

Increase its amplitude to about 3 volts peak-to-peak. Adjust the trace

so its peaks just touch grid lines exactly a whole number of

centimetres apart. This is for experimental convenience; it will be

matched by a similar adjustment below.

T6 remove the patching cord from input g of the ADDER

T7 rotate G clockwise. The CARRIER will appear as a band across the screen.

Increase its amplitude until its peaks touch the same grid lines as did

the peaks of the DSBSC (the time base is too slow to give a hint of the

fine detail of the CARRIER; in any case, the synchronization is not

suitable).

T8 replace the patch cord to g of the ADDER.

At the ADDER output there is now a DSBSC and a CARRIER, each of exactly the

same peak-to-peak amplitude, but of unknown relative phase.

Observe the envelope of this signal (CH2-A), and compare its shape with that of the

message (CH1-A), also being displayed.

T9 vary the phasing with the front panel control on the PHASE SHIFTER until

the almost sinusoidal envelope (CH2-A) is of twice the frequency as

that of the message (CH1-A). The phase adjustment is complete when

alternate envelope peaks are of the same amplitude.

As a guide, Figure 5 shows three views of Armstrong’s signal, all with equal

amplitudes of DSBSC and carrier, but with different phase errors (ie, errors from

the required 900 phase difference between DSBSC and carrier).


Figure 5: Armstrong’s signal, with ∆∆∆∆φφφφ = 1, and phase errors of

45 deg (lower), 20 deg,(centre) and zero (upper).

Armstrong's phase adjustmentArmstrong's phase adjustmentArmstrong's phase adjustmentArmstrong's phase adjustment

An error from quadrature at the transmitter will show up as distortion of the

recovered message at the receiver. This will be in ‘addition’ to the inherent

distortion introduced by the approximation arctan(arg) ≈ (arg). The ‘addition’

would be anything but linear, and difficult to evaluate, but easy to measure for a

particular case.

How can the phase of the DSBSC and the added carrier be adjusted to be in exact

quadrature ?

An analysis of the envelope of Armstrong`s signal is given in the Appendix to this

experiment. There it is shown that:

1. when in phase quadrature, the envelope is sinusoidal-like in shape (Figure 5

above) with adjacent peaks of equal amplitude.

2. the envelope waveform is periodic, with the fundamental frequency being twice

that of the message from which the DSBSC was derived.

Each of these two findings suggests a different method of phase adjustment.

phase adjustment using the envelopephase adjustment using the envelopephase adjustment using the envelopephase adjustment using the envelope

T10 trim the front panel control of the PHASE SHIFTER until adjacent peaks of

the envelope are of equal amplitude. To improve accuracy you can

increase the sensitivity of the oscilloscope to display the peaks only.

Equating heights of adjacent envelope peaks with the aid of an oscilloscope is an

acceptable method of achieving the quadrature condition. For communication

purposes the message distortion, as observed at the receiver, due to any such phase

error, will be found to be negligible compared with the inherent distortion

introduced by an ideal Armstrong modulator.



phase adjustphase adjustphase adjustphase adjustment using ‘psychoment using ‘psychoment using ‘psychoment using ‘psycho----acoustics’acoustics’acoustics’acoustics’

There is another fascinating method of phase adjustment, first pointed out to the

author by M.O. Felix.

The envelope of Armstrong`s signal is recovered, using an envelope detector, and is

monitored with a pair of headphones. For the in-phase condition this would be a

pure tone at message frequency. As the phase is rotated towards the wanted

90 degrees difference it is very easy to detect, by ear, when the fundamental

component disappears (at µ rad/s, and initially of large amplitude), leaving the

component at 2µ rad/s, initially small, but now large. This is the quadrature

condition.

T11 model an envelope detector, using the RECTIFIER in the UTILITIES

module, and the 3 kHz LPF in the HEADPHONE AMPLIFIER

module. Connect Armstrong`s signal to the input of the envelope

detector. Listen to the filter output (the envelope) with headphones.

Set the PHASE SHIFTER as far off the quadrature condition as

possible, and concentrate your mind on the fundamental. Slowly vary

the phase. You will hear the fundamental amplitude reduce to zero,

while the second harmonic of the message appears. Notice how

sensitive is the point at which the fundamental disappears ! This is

the quadrature condition.

Note that you have been able to detect the presence of a low (finally zero) amplitude

tone in the presence of a much stronger one. This was only possible because the

low amplitude term was a sub-harmonic of the higher amplitude term. The

opposite is extremely difficult. This is a phenomenon of psycho-acoustics.

practical applicationspractical applicationspractical applicationspractical applications

Remember: Armstrong`s modulator generates phase, or frequency, modulation, by

an indirect method. It does not disturb the frequency stability of the carrier source,

as happens in the case of modulators using the direct method - eg, the VCO.

But, to keep the distortion to acceptable limits, Armstrong`s modulator is capable of

small phase deviations only - see the Appendix to this experiment. This is

insufficient for typical communications applications. The deviation can be

increased by additional processing, namely by frequency multipliers.

The frequency multiplier has been discussed in this Volume entitled Analysis of the

FM spectrum. You can learn about them in the experiment entitled FM deviation

multiplication (this Volume). Refer also to the Appendix to this experiment.

spectral componentsspectral componentsspectral componentsspectral components

In later experiments you will be measuring the spectral components of wideband

FM signals. In this experiment all we have is Armstrong`s signal, which, after

amplitude limiting, has relatively few components of any significance. But they are

there, and you can find them.


So now you will model the WAVE ANALYSER, which was introduced in the

experiment entitled Spectral analysis - the WAVE ANALYSER (this Volume), and

look for them.

Table A-1 in the appendix to this experiment shows you what to expect. Notice it

will be possible to find only three, possibly five, components (including the carrier)

with any confidence (the simple WAVE ANALYSER you will be using has its

limitations), but confirming their amplitude ratios as predicted is a satisfying

exercise.

Remember: there are only three components at the output of Armstrong`s

modulator (as modelled by you already).

To create the FM sidebands Armstrong`s signal must first be:

1. amplitude limited, to produce a narrowband FM signal (NBFM)

and then

2. frequency multiplied, to generate a wideband FM signal (WBFM).

You will take step (1) in this experiment, and then step (2) in a later experiment.

The amplitude limiting is performed by the CLIPPER in the UTILITIES module 3

(with gain set to ‘hard limit’; refer to the TIMS User Manual).

Although, for the experiment, there is no need to add a filter following the

amplitude limiter (it won`t change the spectral components in the region of

100 kHz), in practice this would be done, and so in the block diagram of Figure 6

below this is shown. If you have a 100 kHz CHANNEL FILTERS module you

should use it in this position.

Armstrong`s signal(100kHz carrier) NBFM

limiter100kHz

BPF

(to WAVE ANALYSER)

amplitude

Figure 6: Armstrong`s NBFM signal

T12 set up for equal amplitudes of DSBSC and carrier into the ADDER of the

modulator (β = 1), and confirm you have the quadrature condition. A

message frequency of about 1 kHz will be convenient for spectral

measurements.

Although a ratio of DSBSC to carrier of unity will result in significant distortion at

the output from a demodulator (refer Figure 3) one can still predict the amplitude

spectrum and confirm it by measurement.

3 version V2 or later



T13 at the output of your Armstrong modulator add the AMPLITUDE LIMITER

(the CLIPPER in the UTILITIES module) and filter (in the 100 kHz

CHANNEL FILTERS module) as shown in block diagram form in

Figure 6.

T14 model a WAVE ANALYSER, and connect it to the filter output. There is no

need to calibrate it; you are interested in relative amplitudes.

T15 set the phase deviation to zero (by removing the DSBSC from the ADDER of

the modulator). Observe and sketch the waveform of the signals into

and out of the channel filter. Find the 100 kHz carrier component

with the WAVE ANALYSER. This, the unmodulated carrier, is your

reference. For convenience adjust the sensitivity of the SPECTRUM

UTILITIES module so the meter reads full scale.

T16 replace the DSBSC to the ADDER of the modulator. The carrier amplitude

should drop to 84% of the previous reading (if you leave the meter

switch on HOLD nothing will happen !). This amplitude change is

displayed in Table A-1 of the appendix to this experiment.

T17 search for the first pair of sidebands. They should be at amplitudes of 38%

of the unmodulated carrier.

T18 there are further sideband pairs, but they are rather small, and will take

care to find.

T19 you could repeat the spectral measurements for β = 0.5 (which are also

listed in Table A-1).

T20 you were advised to look at the signal from the filter when there was no

modulation. Do this again. Synchronize to the signal itself, and

display ten or twenty periods. Then add the modulation. You will see

the right hand end of the now modulated sinewave move in and out

(the ‘oscillating spring’ analogy), confirming the presence of

frequency modulation (there is no change to the amplitude).



Q1 by writing eqn.(3) in the general form of a(t).cos[ωt + φ(t)], obtain

approximate expressions for both a(t) and φ(t) as functions of ‘m’ (or

the equivalent, ∆φ).

Q2 can a conventional phase meter be used to set the DSBSC and carrier in

quadrature ? Explain.

Q3 a 4 volt peak-to-peak DSBSC is added to a 5 volt peak-to-peak carrier, in

phase-quadrature. Calculate:

a) the peak to peak and the trough-to-trough amplitudes of the

resultant signal.

b) the phase deviation of the carrier, after amplitude limiting.

Q4 suppose the phasing in an Armstrong modulator is adjusted by equating

adjacent envelope maxima. Obtain an approximate expression for the

phase error α, from the ideal quadrature, as a function of a small

error in this amplitude adjustment.

Q5 if there is an error in the phasing of an Armstrong modulator, the output

could be written as

y(t) = E.cosωt + E.cosµt.sin(ωt + α)

Obtain an approximate expression for the phase deviation, following

amplitude limiting, for small α, the phase error from quadrature.

Q6 the phasing in an Armstrong modulator is adjusted by listening for the null of

the message in the envelope (the psycho-acoustic method). If during

this adjustment the fundamental amplitude is reduced to 40 dB below

the amplitude of the second harmonic of the message, what would be

the resulting phase error ?




Analysis of Armstrong`s signalAnalysis of Armstrong`s signalAnalysis of Armstrong`s signalAnalysis of Armstrong`s signal

If we define Armstrong`s signal as:

Armstrong`s signal = cosωt + ∆φ.sinµt.sinωt ...... A.1

and then write this in the general form of a narrowband modulated signal we have:

Armstrong`s signal = a(t).cos[ωt + φ(t)] ...... A.2

where:

a(t) = ( ( ) sin )1 2 2+ ∆φ µt ...... A.3

φ(t) = arctan (-∆φ.sinµt) ...... A.4

where ∆φ = (DSBSC / carrier) ........ A.5.

The expressions for both a(t) and φ(t) can be expanded into infinite series. For

small values of ∆φ, say (∆φ < 0.5), they approximate to:

approx. a(t) = (( )

) (( )

sin )14 4

22 2

+ +∆ ∆φ φ

µt...... A.6

approx. φ(t) = (( )

) cos( )

cos∆∆ ∆

φφ

µφ

µ− −3 3

4 123t t

...... A.7

Equation A.6 confirms that, to a first approximation, the Armstrong envelope is

sinusoidal and of twice the message frequency. There will be higher order even

harmonics of the message, but, as you will have observed in the psycho-acoustic test

earlier, no component at message frequency.

Equation A.7 shows that the phase modulation is proportional to ∆φ, as wanted, but

that there is odd harmonic distortion in the received message. The need to keep the

distortion to an acceptable value puts an upper limit on the size of ∆φ. Figure 3,

shown previously, graphs the expected signal-to-distortion ratio to a better

approximation.

Remember that eqn.A.7 gives the distortion from an ideal demodulator - it gives no

clue as to the spectrum of the Armstrong signal.

the amplitude limiterthe amplitude limiterthe amplitude limiterthe amplitude limiter

From your work on angle modulated signals you will appreciate that the signal

y(t) = cos[ωt + φ(t)] ...... A.8

has the potential for many spectral components.


This is an angle modulated signal, which is what is expected from Armstrong`s

modulator.

But Armstrong`s signal, as defined by eqn.(A.1), has only three components ! We

know this since it is the linear sum of a DSBSC (two components) and a carrier

(one component).

Then where are all the spectral components suggested by eqn.(A.7) ?

The signal of the form of eqn.(A.8) is what we want, but we have one of the form of

eqn.(A.2). The difference is the multiplying term a(t).

We would like a(t) to become a constant.

This is the function of the amplitude limiter. It is required to remove envelope

variations.

The amplitude limiter has been discussed in the Chapter entitled Analysis of the

FM spectrum.

Armstrong`s sArmstrong`s sArmstrong`s sArmstrong`s spectrum after amplitude limitingpectrum after amplitude limitingpectrum after amplitude limitingpectrum after amplitude limiting

Obtaining the spectrum of the amplitude-limited Armstrong signal whilst taking

into account the inevitable distortion involves an expansion of eqn.(A.8) with:

φ(t) = arctan(β.cosµt) ...... A.9

The phase function can be expanded into an odd harmonic series of µ.

φ(t) = β1.cosµt + β3.cos3µt + β5.cos5µt + ....... ........ A.10

This expansion is then substituted in eqn.(A.8). Taking any more than two terms

makes the expansion of eqn.(A.8) extremely tedious, and so this means that the

approximation is only valid for say the range

0 < β < 1

Even with two terms in φ(t) the expansion of eqn.(A.8), to obtain the spectrum, is a

tiresome exercise. But when finished one has an analytic expression for the

spectrum for small β.

An alternative is to use a fast Fourier transform and evaluate the spectrum for

specific values of β. This has been done, and Table A-1 below lists the amplitude

spectrum for β = 0.5 and β = 1

Component amplitude

ββββ = 0

amplitude

ββββ = 0.5

amplitude

ββββ = 1

carrier ω 1.0 0.945 0.835

ω ± 1 µ 0.000 0.23 0.381

ω ± 2 µ 0.000 0.026 0.072

ω ± 3 µ 0.000 0.006 0.031

ω ± 4 µ 0.000 0.001 0.009

ω ± 5 µ 0.000 0.000 0.004

ω ± 6 µ 0.000 0.000 0.001

Table A-1



What would happen if this signal, for β = 1, was processed by a frequency

multiplier ? The deviation would be increased. What would be the new spectrum ?

The analytic derivation of the new spectrum is decidedly non-trivial 4. The easy

way to find the answer is to generate it, and then measure it !

Although not specifically suggested, there will be an opportunity for this in the

experiment entitled FM deviation multiplication in this Volume.

4 remember, this is Armstrong`s signal, involving the arctan function. Derivation of the spectrum of a pure

FM signal, with β = 1, is relatively straight forward (see Analysis of the FM Spectrum)..


FM DEVIATION FM DEVIATION FM DEVIATION FM DEVIATION

MULTIPLICATIONMULTIPLICATIONMULTIPLICATIONMULTIPLICATION

PREPARATION................................................................................ 2

the angle modulated signal ........................................................ 2

FM or PM ?........................................................................................... 3

the need for frequency multipliers.............................................. 3

wideband FM with Armstrong`s modulator ............................... 4

FM UTILITIES ........................................................................ 4

EXPERIMENT.................................................................................. 5

the Armstrong modulator....................................................................... 5

the frequency multiplier times-9 ............................................................ 5

the WAVE ANALYSER........................................................................ 5

choosing the message frequency................................................ 6

BPF bandwidth measurement ................................................................ 6

assembling the models ............................................................... 7

preparation ............................................................................................ 7

Armstrong`s carrier ............................................................................... 7

modelling the frequency multiplier ........................................................ 7

Armstrong`s modulator.......................................................................... 8

measuring the FM spectrum ...................................................... 9

special cases.............................................................................. 9



FM DEVIATION FM DEVIATION FM DEVIATION FM DEVIATION

MULTIPLICATIONMULTIPLICATIONMULTIPLICATIONMULTIPLICATION

ACHIEVEMENTS: introduction to the frequency multiplier; wide-band FM

spectrum from Armstrong`s modulator; wide-band spectrum

measurement.

PREREQUISITES: familiarity with the theory outlined in the Chapter entitled

Analysis of the FM spectrum and completion of the experiment

entitled Armstrong`s phase modulator, both in this Volume. For

Tables of Bessel Coefficients see the Appendix to this Volume.

EXTRA MODULES: 100 kHz CHANNEL FILTERS (V.2); FM UTILITIES;

SPECTRUM UTILITIES.


the angle modulated signalthe angle modulated signalthe angle modulated signalthe angle modulated signal

This experiment is about generating a wideband angle modulated signal, based on

an Armstrong modulator, and examining its spectrum.

An angle modulated signal is one defined as:

y(t) = E.cos(ωt + β.cosµt) ........ 1

where the parameter β is the one which varies with the message in accordance with

the definition given in the Chapter entitled Analysis of the FM spectrum.

Two examples of an angle modulated signal are those of phase modulation (PM)

and frequency modulation (FM).

You will need an understanding of the theory if you are going to relate your

measurements to expectations. This is especially so if the measurements are not in

complete agreement, since you should be able to explain the discrepancy !

In a following experiment, entitled FM and Bessel zeros, some more insights into

the behaviour of the spectrum with changing depths of modulation - deviation - will

be examined.

FM deviation multiplication


FM or PMFM or PMFM or PMFM or PM ????

If either a PM or an FM transmitter is modulated by a single tone message, of fixed

amplitude and frequency, there is no way an observer, by examining the spectrum,

can distinguish which transmitter is being used.

They are both described by eqn.(1) above.

The degree of modulation (the ‘deviation’) is determined by the magnitude of β.

An expansion of eqn. (1) shows that the number of sidebands, and their amplitudes,

are governed completely by the magnitude of β. Their frequency spacing is

determined by the message frequency of µ rad/s.

• the magnitude of β is directly proportional to the message amplitude.

• for a PM signal β is equal to the peak phase deviation ∆φ.

• for an FM signal β is equal to ∆φ / µ

The difference between the two signals shows itself when the message frequency is

changed. Suppose there is an increase of message frequency:

• for a PM transmitter β remains fixed. The amplitude of each spectral

component remains the same, but their spacing increases. The bandwidth

therefor increases in proportion to the message frequency change.

• for an FM transmitter the magnitude of β reduces, since it is inversely

proportional to the message frequency. The spacing of spectral components

increases. Some spectral component amplitudes will increase, some reduce, but

the sum of the squares of their amplitudes remains fixed. The bandwidth will

not increase in proportion to the message frequency change, since a smaller βrequires less components. To a rough approximation, the bandwidth remains

much the same.

In the experiment to follow you will be using a fixed message frequency, so it is

immaterial whether it is called an FM or a PM signal. In principle it is going to be

a PM transmitter, since there will not be an integrator (1 / µ characteristic)

associated with the message source.

the need for frequency multipliersthe need for frequency multipliersthe need for frequency multipliersthe need for frequency multipliers

To achieve the signal-to-noise ratio advantages of which FM is capable it is

necessary to use a deviation large enough to ensure that the signal has at least two

or more pairs of ‘significant sidebands’.

A frequency multiplier is a device for increasing the deviation. It would have been

better to have called it a deviation multiplier. It does indeed multiply the

frequency, but this is of secondary importance in this application.

Frequency multipliers are used following PM and FM modulators which are

themselves unable, usually because of linearity considerations, to provide sufficient

deviation.

They are essential for most applications of Armstrong`s modulator, which was

examined in the experiment entitled Armstrong`s phase modulator (this Volume).

This modulator is restricted to phase deviations of less than one radian before the

generated distortion becomes unacceptable.


Frequency multipliers consist of an amplitude limiter followed by a bandpass filter.

They are discussed in the Chapter entitled Analysis of the FM spectrum. These

devices are also called harmonic multipliers.

wideband FM with Armstrong`s wideband FM with Armstrong`s wideband FM with Armstrong`s wideband FM with Armstrong`s

modulatormodulatormodulatormodulator

The experiment will examine the operation of a FREQUENCY MULTIPLIER (in

fact, two such operations in cascade) on the output of an ARMSTRONG

MODULATOR. The spectral components will be identified with a WAVE

ANALYSER. This instrumentation was introduced in the experiment entitled

Spectrum analysis - the WAVE ANALYSER in this Volume.

The aim of this experiment is to generate a signal at 100 kHz with sufficient

frequency deviation to enable several significant sidebands to be found in the

spectrum. This requires a phase deviation of a radian or more. Since the

Armstrong modulator is only capable of a deviation of a fraction of a radian, if

distortion at the demodulator is to be kept low, then a FREQUENCY

MULTIPLIER is required.

FM UTILITIESFM UTILITIESFM UTILITIESFM UTILITIES

The FM UTILITIES module contains two amplitude LIMITER sub-systems, a

33.333 kHz BPF, and a source of sinusoidal carrier at 11.111 kHz. These sub-

systems will be combined as shown in Figure 1 below.

tripler tripler

33.333 kHz 100 kHz

IN

Armstrong`ssignal at

11.111 kHz

wideband

at 100 kHz

anglemodulation

Figure 1: deviation multiplication times-9

The Armstrong modulator (not shown) uses the 11.111 kHz sinusoidal carrier.

The 100 kHz BPF is available in the 100 kHz CHANNEL FILTERS module.




The modelling arrangement of the block diagram of Figure 1 is illustrated in

Figure 2. This has been sub-divided into three distinct parts, as in Figure 1, and

each is described below.

Frequency MultiplierArmstrong`s Generator WAVE ANALYSER

11.111 kHz

variable DC

100 kHz

Figure 2: the models

the Armstrong mthe Armstrong mthe Armstrong mthe Armstrong modulatorodulatorodulatorodulator

For an FM signal at 100 kHz the Armstrong modulator must operate at a frequency

several multiples below this. The frequency of 11.111 kHz has been chosen,

providing a deviation multiplication, and an inevitable frequency multiplication, of

times-9.

The 11.111 kHz sinusoidal carrier is obtained from the FM UTILITIES module.

This contains a sub-system which produces a sinusoidal carrier at 11.111 kHz from

a sinusoidal input at 100 kHz.

the frequency multiplier timesthe frequency multiplier timesthe frequency multiplier timesthe frequency multiplier times----9999

The FM UTILITIES module can model the two triplers of Figure 1. It has two

LIMITER sub-systems, and a 33.3 kHz BPF. The 100 kHz BPF is obtained from a

100 kHz CHANNEL FILTERS module (channel #3). The patching is shown in

Figure 2.


The spectrum of the FM signal is examined with a WAVE ANALYSER, modelled as

shown in Figure 2. Of particular importance is the method of fine tuning the VCO,

using a combination of the controls of the VARIABLE DC and the GAIN of the

VCO.

The fine tuning technique was described in the experiment entitled Spectrum

analysis - the WAVE ANALYSER.


choosing the message frequencychoosing the message frequencychoosing the message frequencychoosing the message frequency

The design of the BPF in a frequency multiplier chain is a compromise between

allowing sufficient bandwidth for the desired sidebands, while still attenuating the

adjacent harmonics of the non-linear action of the preceding LIMITER.

This is generally not a problem in a commercial system for speech, since the

frequency ratios (speech bandwidth, and so the modulated bandwidth, to the carrier

frequency) are significantly lower. But in the modelling environment of TIMS,

where carrier frequencies are relatively low, some design difficulties do arise.

You have been presented with existing 33.333 kHz and 100 kHz bandpass filters,

so have no control over their bandwidths. They will set an upper limit to your

message frequency. This you will need to determine.

First see Tutorial Questions Q2 and Q3.

Bandwidth measurement is best performed before patching up the complete system,

since, using the suggested method for the 33 kHz BPF, it is necessary to have easy

access to the VCO board for tuning purposes (see below).

Alternatively you might prefer to devise your own method of providing a 33 kHz

variable frequency sinewave, without the need to use the VCO in FSK mode. See

Tutorial Question Q4.

BPF bandwidth measurementBPF bandwidth measurementBPF bandwidth measurementBPF bandwidth measurement

33333333 kHz BPFkHz BPFkHz BPFkHz BPF

T1 set the on-board switch SW2 of the VCO to ‘FSK’. Plug in the FM

UTILITIES module and the VCO, leaving plenty of room for hand-

access to the on-board control RV8 (FSK2) of the VCO. Connect a

TTL HI to the DATA input of the VCO (this switches the output of the

VCO to the FSK2 frequency). Select the HI frequency mode of the

VCO with the front panel toggle switch.

T2 connect the VCO output to the input of the 33 kHz BPF of the FM UTILITIES

module, and the output to the oscilloscope. Sweep the VCO frequency

through the filter, and measure the frequency response.

100100100100 kHz BPFkHz BPFkHz BPFkHz BPF

T3 using the VCO in ‘VCO’ mode make a sweep of the 100 kHz BPF of the

100 kHz CHANNEL FILTERS module, and measure its bandwidth.

message frequencymessage frequencymessage frequencymessage frequency

T4 from the two bandwidth measurements determine an upper limit for the

message frequency. See Tutorial Question Q3.

You will now realize that extending the message frequency to 3 kHz is not possible,

considering the bandwidths involved. Something below 1 kHz would be preferable.



assembling the modelsassembling the modelsassembling the modelsassembling the models

The system to be patched up is illustrated in Figure 2.

preparationpreparationpreparationpreparation

T5 before plugging in the PHASE SHIFTER (of the Armstrong modulator) set the

on-board switch to ‘HI’. Set the on-board switch of the VCO (of the

WAVE ANALYSER) to ‘VCO’, and the front toggle switch to ‘HI’.

T6 plug in the modules. Put the ARMSTRONG MODULATOR to the left, the

FREQUENCY MULTIPLIER in the centre, and the WAVE

ANALYSER to the right. Do not yet do any patching. This will be

done in easy stages, detailed below.

Armstrong`s carrierArmstrong`s carrierArmstrong`s carrierArmstrong`s carrier

To test the frequency multiplier, first use only the 11.111 kHz unmodulated carrier

from the Armstrong modulator.

The 11.111 kHz sinusoidal carrier is provided by the FM UTILITIES module,

derived from a 100 kHz sinusoidal input. This carrier is 1/9 of the final output

carrier frequency of 100 kHz.

T7 patch the 11.111 kHz sine wave from the FM UTILITIES module via the

phase shifter to the ‘G’ input of the ADDER. Adjust the ADDER

output to the TIMS ANALOG REFERENCE LEVEL. Leave the ‘g’

input of the ADDER empty.

The carrier is now ready for testing the FREQUENCY MULTIPLIER.

modelling the frequency multipliermodelling the frequency multipliermodelling the frequency multipliermodelling the frequency multiplier

the first triplerthe first triplerthe first triplerthe first tripler

The first tripler is modelled with a LIMITER and 33.333 kHz BPF in the FM

UTILITIES module.

T8 patch the output of the Armstrong modulator (the unmodulated 11.111 kHz

carrier) to the first tripler. Confirm that the output is a 33.333 kHz

sinusoid at or about the TIMS ANALOG REFERENCE LEVEL. Its

amplitude may be adjusted with an on-board trimmer. Precise level

adjustment is not necessary.


the second triplerthe second triplerthe second triplerthe second tripler

The second tripler is modelled with a LIMITER from the FM UTILITIES module,

and a 100 kHz BPF from the 100 kHz CHANNEL FILTERS module.

T9 patch the output of the 33.333 kHz BPF to the unused LIMITER of the FM

UTILITIES module. Connect its output to the 100 kHz CHANNEL

FILTERS module, switched to the 100 kHz BPF.

T10 confirm that the output of the second tripler is a 100 kHz sinewave. It

should be at or about the TIMS ANALOG REFERENCE LEVEL. Its

amplitude may be adjusted with an on-board trimmer. Precise level

adjustment is not necessary.

You have now modelled the FREQUENCY MULTIPLIER, although with an

unmodulated carrier.

Armstrong`s modulatorArmstrong`s modulatorArmstrong`s modulatorArmstrong`s modulator

It is now time to complete the model of Armstrong`s modulator by adding the

DSBSC to the carrier in the ADDER.

We want the Armstrong modulator to have as large a deviation as possible, so as to

have several significant sidebands on the 100 kHz carrier, yet not so large as to

generate too much distortion (which would upset the predictable amplitude ratios of

the sidebands).

After adjusting the quadrature phase of the DSBSC and carrier, a suggestion is to

set the DSBSC to carrier amplitude ratio to a about 1:3.

T11 complete the modelling of the ARMSTRONG MODULATOR. Set the

AUDIO OSCILLATOR to, say, 500 Hz 1. There is no DC involved, so

switch the MULTIPLIER to AC coupling. Remember it is easier to set

the phase 2, while watching the envelope, with the ratio of DSBSC to

CARRIER approximately unity. The detailed procedure was described

in the experiment entitled Armstrong`s phase modulator.

T12 having adjusted the phase, reduce the phase deviation to 0.33 radians, in

preparation for the next part of the experiment. Remember to keep

signal levels, where possible, at or near the TIMS ANALOG

REFERENCE LEVEL.

1 do you agree that this is acceptable ? If not, or in any case, you are free to choose your own frequency.

2 the on-board switch SW1 is probably best set to ‘HI’.



measuring the FM spectrummeasuring the FM spectrummeasuring the FM spectrummeasuring the FM spectrum

The ARMSTRONG MODULATOR now has a phase deviation of 0.33 radians.

The FREQUENCY MULTIPLIER output will be a phase modulated signal with a

peak phase deviation of nine times this, or 3.0 radians.

T13 examine the output of the FREQUENCY MULTIPLIER with the

oscilloscope. As seen in the time domain (the oscilloscope being

triggered by the signal itself) it will have the appearance of a

compressed and expanded spring. It should be at about the TIMS

ANALOG REFERENCE LEVEL. Notice that the envelope is flat.

Now use the WAVE ANALYSER to check the 100 kHz spectrum.

it is essential that you are familiar with

the method of fine tuning the VCO

T14 patch up the WAVE ANALYSER. Set the VCO to the ‘HI’ frequency range

with the front panel switch.

T15 examine the output of the FREQUENCY MULTIPLIER with the WAVE

ANALYSER. Record the frequency and amplitude of each spectral

component of significance 3.

T16 use the Tables of Bessel Coefficients in Appendix C to this text to draw the

amplitude spectrum of an angle modulated signal with β = 3.0.

Compare with your measurements.

sssspecial casespecial casespecial casespecial cases

It is always interesting to investigate special cases. The obvious cases are those of

the Bessel zeros. With these special values of β the amplitude of particular

components falls to zero. These and other cases are examined in the experiment

entitled FM and Bessel zeros.

3 that is, significantly above the noise level.



Q1 see first the tutorial questions in the Chapter entitled Analysis of the FM

spectrum.

Q2 suppose a message frequency range of 300 to 3000 Hz was desired. Knowing

the maximum phase deviation allowed by the limitations of the

Armstrong modulator, specify the characteristics of the two BPF of

the system. Remember they must pass the wanted sidebands, but stop

the unwanted components from the preceding LIMITER.

Q3 from your measurements of the bandpass filter bandwidths, and knowing the

limits upon the phase deviation set by the Armstrong modulator, how

would you specify the upper message frequency ?

Q4 you may have found it inconvenient to use the suggested method of tuning the

VCO around 33 kHz for the BPF measurement. Devise another

method, which does not involve adjustment of the on-board control of

the VCO; that is, all frequency changes are made using front panel

controls of existing TIMS modules. hint: there is a 130 kHz sinusoid

at TRUNKS.


FM AND BESSEL ZEROSFM AND BESSEL ZEROSFM AND BESSEL ZEROSFM AND BESSEL ZEROS

PREPARATION................................................................................ 2

introduction .............................................................................. 2

EXPERIMENT.................................................................................. 3

spectral components.................................................................. 4

locate the ‘carrier’..................................................................... 4

the method of Bessel zeros........................................................ 6

looking for a Bessel zero ........................................................... 6

using the WAVE ANALYSER .............................................................. 6

without a WAVE ANALYSER.............................................................. 7



FM AND BESSEL ZEROSFM AND BESSEL ZEROSFM AND BESSEL ZEROSFM AND BESSEL ZEROS

ACHIEVEMENTS: calibration of the frequency deviation of an FM transmitter

using the method of Bessel Zeros.

PREREQUISITES: completion of the experiments entitled Armstrong`s phase

modulator, and FM deviation multiplication in this Volume; a

knowledge of the relationships between the phase deviation and the

spectrum of a PM signal. See Appendix C to this text for Tables of

Bessel Coefficients.

EXTRA MODULES: 100 kHz CHANNEL FILTERS (version 2); FM UTILITIES,

SPECTRUM UTILITIES.


introductionintroductionintroductionintroduction

This experiment investigates methods of deviation calibration of a PM transmitter

by observation of the spectrum. It includes the method of ‘Bessel zeros’.

The outcome of the experiment could be a calibration curve, showing the position

of the modulator deviation control versus β, the deviation of the modulator 1.

This curve could already have been obtained in the experiment entitled Armstrong`s

phase modulator, by measuring the ratio of the DSBSC to carrier amplitudes out of

the ADDER. From this ratio the magnitude of the spectral components could have

been deduced by calculation. But in this experiment you will be examining the

spectrum itself, and from this working backwards to determine the phase deviation.

Make sure you appreciate the difference between the two methods.

The model required to generate a PM signal is that used in the experiment entitled

FM deviation multiplication. Refer to that experiment for setting up details.

1 the principle of the method is what will be learned. You cannot actually plot the curve, since TIMS knobs

are not graduated

FM and Bessel zeros


Figure 1 shows the arrangement in simplified block diagram form, and Figure 2

shows patching details.

FREQUENCYMULTIPLIER

X9

SPECTRUMANALYSER

ββββ1

ββββ9

GeneratorArmstrong`s

adjust ββββ(by amplitude ratio)

Figure 1: the measurement set-up


The block diagram of Figure 1 is shown modelled in Figure 2 below. This model

was examined in the experiment entitled FM deviation multiplication, so the

setting up details here will be brief.

T1 set up the model illustrated in Figure 2. Choose a suitable message frequency

(this will be below 1 kHz ?). Adjust the phasing in the Armstrong

modulator, using the envelope as a guide (see the experiment entitled

Armstrong`s phase modulator).

Frequency MultiplierArmstrong`s Generator WAVE ANALYSER

11.111 kHz

variable DC

100 kHz

TTL

Figure 2: patching details

To ensure the modulator does not introduce spectral distortion, ensure at all times

that the phase deviation at the ARMSTRONG MODULATOR is kept well below


1.0 radian. This means that the ratio of DSBSC to carrier, at the ADDER output,

must remain less than unity.

Note that the phase deviation at the FREQUENCY MULTIPLIER output will be

the Armstrong phase deviation multiplied by a factor of 9.

Let us denote the phase deviation at the ARMSTRONG MODULATOR as β1 and

the phase deviation at the FREQUENCY MULTIPLIER output as β9, as in

Figure 1.

spectral componentsspectral componentsspectral componentsspectral components

You will be using the WAVE ANALYSER to measure the amplitude and frequency of

the spectral components of various signals. For this experiment the absolute

amplitudes of the spectral components are of secondary importance. What will

interest you is their relative amplitudes. Thus it is not necessary to calibrate the

amplitude sensitivity of the WAVE ANALYSER.

locate the ‘carrier’locate the ‘carrier’locate the ‘carrier’locate the ‘carrier’

T2 with β1 set to zero, locate the unmodulated carrier with the WAVE ANALYSER.

It should be at about the TIMS ANALOGUE REFERENCE LEVEL.

Spectral amplitudes are typically quoted with respect to the amplitude of the

unmodulated carrier. Thus it is convenient to set this component to full scale on

the measuring equipment. This can be done by tuning to the carrier and manually

setting the on-board adjuster RV1, labelled ‘SCALING’, for this condition.

T3 adjust the reference signal to full scale deflection on the meter of the

SPECTRUM UTILITY module.

T4 check that there are no other components of significance within 10 kHz of the

carrier.

T5 set β1 to about 0.16 and search for components of significance within 10 kHz

of the carrier. Record the frequency and amplitude of all components

found.

The component at the carrier frequency ω, and the components at

(ω ± µ), should have been of about equal magnitude.

This fact can be checked by reference to the curves of Figure 3 below. For:

β1 = 0.16

FM and Bessel zeros


then

β9 = 1.44

0J ββββ( )

J ββββ( )1 J ββββ( )

2

1.0

0

0.4-

β

0 1.0 2.0 3.0 4.0

Figure 3: Bessel function plots

You will note that J0(β) is approximately equal to J1(β) when β9 is about 1.4. In

fact they approach equality for β =1.435.

But the amplitude of the carrier is proportional to J0(β), and that of the first pair of

sidebands is proportional to J1(β).

So here is a way of calibrating the ARMSTRONG MODULATOR phase deviation

control. Adjust the DSBSC amplitude, at the output of the ADDER in the

ARMSTRONG GENERATOR, until these two components are equal.

You have now set

β9 = 1.435

Note that the method did not involve the measurement of an absolute amplitude,

but rather the matching of two amplitudes to equality. So the amplitude sensitivity

of the WAVE ANALYSER need not be calibrated.

This amplitude matching method can be applied to determine other values of β9.

From the curves of Figure 3 one could suggest the following pairs:

components ββββ9 ββββ1

carrier and second 1.85 0.21

first and second 2.6 0.29

carrier and second 3.8 0.42

Table 1: equal amplitude sidefrequency pairs

T6 check some or all of the pairs of sidefrequencies listed in Table 1. These will

give other points on the curve of β versus the modulator phase

deviation control.


the method of Bessel zerosthe method of Bessel zerosthe method of Bessel zerosthe method of Bessel zeros

So far the calibration points have been obtained by equating the amplitudes of two

spectral components.

There is an even more precise method of obtaining points on the calibration curve.

Not only is an absolute amplitude reading not required, but there is only a single

measurement to make - and this is a null measurement. There is no need for a

calibrated instrument.

This is the method of Bessel zeros.

Note from Figure 3 that the Bessel functions are oscillatory (but not, incidentally,

periodic). In fact they are damped oscillatory, which means that successive

maxima are monotonically decreasing. But for the moment the important property

is that they are oscillatory about zero amplitude, which means that there are values

of their argument for which they become zero.

There are precise, and multiple values, of β, for which the

amplitude of a particular spectral component of an angle

modulated signal falls to zero.

If you can find when the amplitude of a particular spectral component falls to zero,

you have a precise measure of β9, and another point on the calibration curve. It is

easier to find a single zero, by trimming of the ARMSTRONG MODULATOR

phase deviation control 2, than it is to adjust the amplitudes of two components to

equality.

looking for a Bessel zerolooking for a Bessel zerolooking for a Bessel zerolooking for a Bessel zero

One would normally think of using a WAVE ANALYSER when looking for Bessel

zeros. So in the first instance this will be done.

using thusing thusing thusing the e e e WAVE ANALYSERWAVE ANALYSERWAVE ANALYSERWAVE ANALYSER

Table 2 below shows some particular Bessel zeros which you can use

experimentally. These can be checked by reference to the curves of Figure 3.

Bessel

coefficient

side

frequency

first

zero

second

zero

Table 2 J0(β) central carrier 2.41 5.52

J1(β) first pair 3.83 7.02

J2(β) second pair 5.13 8.4

2 the ADDER gain control g which adjusts the DSBSC amplitude

FM and Bessel zeros


Each Bessel zero will give a point on the calibration curve.

For a multiplication factor of 9, as you are using, and the Armstrong modulator as

the source of the phase deviations, β9 is restricted to the range 0 to about 3

radians 3. So only the first carrier zero, and the first sidefrequency pair zero, are

available to you. But these are quite sufficient to demonstrate the method.

Note that it is necessary to keep track of which zero one is seeking. This is

relatively simple when finding the first or second, but care is needed with the

higher zeros. The problem will not arise in this experiment.

T7 whilst monitoring the amplitude of the component at carrier frequency,

increase the phase deviation control on the ARMSTRONG

MODULATOR from zero until the amplitude is reduced to zero.

Measure the amplitude ratio of the DSBSC and carrier at the ADDER

output. This should be about (2.4/9.0) = 0.27. Check this expected

value against your tables. Explain any disagreement between

measured and expected values.

T8 with β9 as for the previous Task, locate either of the first pair of

sidefrequencies (100 kHz ± message frequency). Increase the phase

deviation control on the ARMSTRONG MODULATOR until the

amplitude of the chosen component is reduced to zero. Measure the

amplitude ratio of the DSBSC and carrier at the ADDER output. This

should be about (3.8/9.0) = 0.42. Explain any disagreement between

measured and expected values.

without a without a without a without a WAVE ANALYSERWAVE ANALYSERWAVE ANALYSERWAVE ANALYSER

In practical engineering one is often (always ?) looking for ways and means of

simplifying procedures, and avoiding the use of expensive equipment, especially

when in the field.

The Bessel zero method of frequency deviation calibration is extremely precise, but

appears to need an expensive SPECTRUM ANALYSER for its execution. But this

need not be so, especially if one is content to use only the zeros of the carrier

component.

All that is needed is an oscillator close to the carrier frequency, a multiplier, and a

pair of headphones.

The principle is that the unmodulated FM signal and the local oscillator are

multiplied together, and the difference component of the product monitored with

the headphones. The local oscillator is adjusted to give a convenient difference

frequency - say about 1 kHz.

Now, while concentrating on this tone, the transmitter frequency deviation is

increased from zero. The message should be a single tone. The amplitude of the

1 kHz tone will decrease, until it falls to zero when β is at the first zero of Jo(β) -

approximately β = 2.4.

It is true that under this condition there will be other tones present in the

headphones. But by ‘suitable’ choice of message frequency these will lie above the

3 distortion is discussed in the experiment entitled Armstrong`s frequency modulator.


1 kHz tone that is being monitored, and one can, with experience, ignore them.

The key to the method lies in choosing a ‘suitable’ message frequency.

Suffice to say, the method is used with success in practice.

There is no need for a true MULTIPLIER; almost any non-linear device will do,

typically an overloaded transistor amplifier which will generate intermodulation

products, including the wanted 1 kHz difference component.

T9 demonstrate the method of setting a Bessel zero, using only a listening device

and a non-linear element (there is a rectifier in the UTILITIES

module), as described above.


There are suitable tutorial questions in the Chapter entitled Analysis of the FM

spectrum.


FM DEMODULATION WITHFM DEMODULATION WITHFM DEMODULATION WITHFM DEMODULATION WITH

THE PLLTHE PLLTHE PLLTHE PLL

PREPARATION................................................................................ 2

the phase locked loop - PLL...................................................... 2

EXPERIMENT.................................................................................. 4

FM demodulation...................................................................... 4

more measurements................................................................... 5



FM DEMODULATION WITHFM DEMODULATION WITHFM DEMODULATION WITHFM DEMODULATION WITH

THE PLLTHE PLLTHE PLLTHE PLL

ACHIEVEMENTS: introduction to the PLL as an FM demodulator

PREREQUISITES: an understanding of the contents of the Chapter entitled

Analysis of the FM spectrum (this Volume) is desirable, but not

essential. A familiarity with the analysis of a PLL will allow some

quantitative measurements to be made and interpreted.


the phase locked loop the phase locked loop the phase locked loop the phase locked loop ---- PLL. PLL. PLL. PLL.

The phase locked loop is a non-linear feedback loop. To analyse its performance to

any degree of accuracy is a non-trivial exercise. To illustrate it in simplified block

diagram form is a simple matter. See Figure 1.

VCO

LPF

inFM

outmessage

Figure 1: the basic PLL

This arrangement has been used in an earlier experiment (this Volume), namely

that entitled Carrier acquisition and the PLL, where an output was taken from the

VCO. As an FM demodulator, the output is taken from the LPF, as shown.

It is a simple matter to describe the principle of operation of the PLL as a

demodulator, but another matter to carry out a detailed analysis of its performance.

FM demodulation with the PLL


It is complicated by the fact that its performance is described by non-linear

equations, the solution to which is generally a matter of approximation and

compromise.

The principle of operation is simple - or so it would appear. Consider the

arrangement of Figure 1 in open loop form. That is, the connection between the

filter output and VCO control voltage input is broken.

Suppose there is an unmodulated carrier at the input.

The arrangement is reminiscent of a product, or multiplier-type, demodulator. If

the VCO was tuned precisely to the frequency of the incoming carrier, ω0 say, then

the output would be a DC voltage, of magnitude depending on the phase difference

between itself and the incoming carrier.

For two angles within the 3600 range the output would be precisely zero volts DC.

Now suppose the VCO started to drift slowly off in frequency. Depending upon

which way it drifted, the output voltage would be a slowly varying AC, which if

slow enough looks like a varying amplitude DC. The sign of this DC voltage would

depend upon the direction of drift.

Suppose now that the loop of Figure 1 is closed. If the sign of the slowly varying

DC voltage, now a VCO control voltage, is so arranged that it is in the direction to

urge the VCO back to the incoming carrier frequency ω0, then the VCO would be

encouraged to ‘lock on’ to the incoming carrier.

This is the principle of carrier acquisition. This was examined in the experiment

entitled Carrier acquisition and the PLL, where this same description was used.

Next suppose that the incoming carrier is frequency modulated. For a low

frequency message, and small deviation, you can imagine that the VCO will

endeavour to follow the incoming carrier frequency. What about wideband FM ?

With ‘appropriate design’ of the lowpass filter and VCO circuitry the VCO will

follow the incoming carrier for this too.

The control voltage to the VCO will endeavour to keep the

VCO frequency locked to the incoming carrier, and thus

will be an exact copy of the original message.

Rather than attempt to analyse the operation of the arrangement of Figure 1 as a

demodulator, you will make a model of it, and demonstrate that it is able to recover

the message from an FM signal.



FM demodulationFM demodulationFM demodulationFM demodulation

There is an FM signal at TRUNKS. It is based on a nominal 100 kHz carrier. You

will model the PLL, and recover the message from the FM signal.

T1 make a model of the PLL of Figure 1. Use the RC-LPF in the UTILITIES

module. Remember to set up the VCO module in 100 kHz VCO mode.

In the first instance set the front panel GAIN control to its mid-range

position.

T2 examine, with your oscilloscope, the FM signal at TRUNKS. Identify those

features which suggest it could indeed be an FM signal.

T3 connect the FM signal at TRUNKS to the PLL.

The PLL may or may not at once lock on to the incoming FM signal. This will

depend upon several factors, including:

• the frequency to which the PLL is tuned

• the capture range of the PLL

• the PLL loop gain - the setting of the front panel GAIN control of the VCO

You will also need to know what method you will use to verify that lock has taken

place.

When you have satisfied yourself that you understand the significance of these

considerations then you should proceed.

T4 make any necessary adjustments to the PLL to obtain lock, and record how

this was done. Measure the amplitude and frequency of the recovered

message (if periodic), or otherwise describe it (speech or music ?).

Are any of these measurements dependent upon the setting of the VCO

GAIN control ?

If you are familiar with the analysis of the PLL you should complete the next task.

FM demodulation with the PLL


T5 measure the properties of each element of the PLL, and then predict some of

its properties as a demodulator. If the message was a single tone,

from its amplitude can you estimate the frequency deviation of the FM

signal ?

more measurementsmore measurementsmore measurementsmore measurements

If you have two VCO modules you can make your own FM signal. You will then

have access to both the original message and the demodulator output. This will

allow further measurements.

T6 set up an FM signal, using a VCO, as described in the experiment entitled

Introduction to FM using a VCO. Use any suitable message

frequency, and a frequency deviation of say 5 kHz.

T7 compare the waveform and frequency of the message at the transmitter, and

the message from the demodulator.

T8 check the relationship between the message amplitude at the transmitter, and

the message amplitude from the demodulator.

T9 as a further confidence check, use the more demanding two-tone signal as a

test message. The two tones can come from an AUDIO OSCILLATOR

and the 2.033 kHz message from the MASTER SIGNALS module,

combined in an ADDER.



Even if you are unable to complete any of the following questions in detail, you

should read them, and a text book on the subject, so as to obtain some appreciation

of the behaviour of the PLL, especially as an FM demodulator.

Q1 define capture range, lock range, demodulation sensitivity of the PLL as an

FM demodulator. What other parameters are important ?

Q2 how does the sensitivity of the VCO, to the external modulating signal,

determine the performance of the demodulator ?

Q3 what is the significance of the bandwidth of the LPF in the phase locked

loop ?


THE COSTAS LOOPTHE COSTAS LOOPTHE COSTAS LOOPTHE COSTAS LOOP

PREPARATION................................................................................ 2

the basic loop............................................................................ 2

phase ambiguity..................................................................................... 3

experiment philosophy............................................................... 3

measurements ........................................................................... 3

EXPERIMENT.................................................................................. 4

setting up the Costas loop ......................................................... 4

measurements ........................................................................... 6

VCO simulation .................................................................................... 6


APPENDIX A ................................................................................... 8

a simplified analysis ................................................................... 8

message output ...................................................................................... 9


THE COSTAS LOOPTHE COSTAS LOOPTHE COSTAS LOOPTHE COSTAS LOOP

ACHIEVEMENTS: using the Costas loop for carrier acquisition from, and

demodulation of, a DSBSC signal.

PREREQUISITES: familiarity with the quadrature modulator (as, for example, in

the experiment entitled Phase division multiplex, in this Volume,

would be an advantage.

ADVANCED MODULES: BIT CLOCK REGEN and SPECTRUM UTILITIES are

both optional.

EXTRA MODULES: a total of three MULTIPLIER, two PHASE SHIFTER, and

two TUNEABLE LPF modules.


the basic loopthe basic loopthe basic loopthe basic loop

Read about the Costas loop in your text book.

This loop, and its variations, is much-used as a method of carrier acquisition (and

simultaneous message demodulation) in communication systems, both analog and

digital.

It has the property of being able to derive a carrier from the received signal, even

when there is no component at carrier frequency present in that signal (eg,

DSBSC). The requirement is that the amplitude spectrum of the received signal be

symmetrical about this frequency.

The basic Costas loop is illustrated in Figure 1.

in

cosω t

VCO

Q

ππππ2

carrier out

message

I

loop filter

DSBSC

Figure 1: the Costas loop

The Costas loop


The Costas loop1 is based on a pair of quadrature modulators - two multipliers fed

with carriers in phase-quadrature. These multipliers are in the in-phase (I) and

quadrature phase (Q) arms of the arrangement.

Each of these multipliers is part of separate synchronous demodulators. The

outputs of the modulators, after filtering, are multiplied together in a third

multiplier, and the lowpass components in this product are used to adjust the phase

of the local carrier source - a VCO - with respect to the received signal.

The operation is such as to maximise the output of the I arm, and minimize that

from the Q arm. The output of the I arm happens to be the message, and so the

Costas loop not only acquires the carrier, but is a (synchronous) demodulator as

well.

A complete analysis of this loop is non-trivial. It would include the determination

of conditions for stability, and parameters such as lock range, capture range, and so

on. A simplified analysis is given in Appendix 1 to this experiment.

phase ambiguityphase ambiguityphase ambiguityphase ambiguity

Although the Costas loop can provide a signal at carrier frequency, there remains a

1800 phase uncertainty.

A phase ambiguity of 1800 in many (typically analog) situations is of no

consequence - for example, where the message is speech. In digital

communications it will give rise to data inversion, and this may not be acceptable -

but there are methods to overcome the problem.


experiment philosophyexperiment philosophyexperiment philosophyexperiment philosophy

In most of the experiments involved with demodulation a stolen carrier is used.

This allows full attention to be paid to the performance of the demodulator.

Considerations of how to acquire a carrier from the received signal are ignored.

In this experiment, following a similar principle, attention will be paid to the

means of acquiring a carrier from a DSBSC signal, without paying attention to the

subsequent performance of the device for which the carrier is required (eg, a

demodulator).

However, you could combine the two if you like.

measurementsmeasurementsmeasurementsmeasurements

The experiment to follow is described in outline only. It will take you only to the

point at which the carrier is acquired.

Thus, before the experiment, you should prepare a list of those performance

attributes with which you may be interested, with some suggestions as to how these

might be measured.

1 Costas, J.P. ‘Synchronous Communications’. Proc.IRE, 44, pp1713-1718, Dec.1956



setting up the Costas loopsetting up the Costas loopsetting up the Costas loopsetting up the Costas loop

T1 obtain a DSBSC signal. There should be one or more at TRUNKS, each

based on a carrier at or near 100 kHz. Alternatively, if you have a

fourth MULTIPLIER module, you could generate your own.

For the Costas loop:

1. use TUNEABLE LPF modules for the filters in the I and Q arms. Set them both

to their WIDE range, and TUNE them to their widest bandwidth.

2. use the RC LPF in the UTILITIES module to filter the control signal to the

VCO (although you might find the LOOP FILTER in a BIT CLOCK REGEN

module to be preferable).

3. before patching in the PHASE SHIFTER set the on-board toggle switch to the

HI range. Then set it to approximately 900 using a 100 kHz sine wave.

4. before inserting the VCO set the on-board FSK/VCO switch to VCO. Select the

HI frequency range with the front panel toggle switch.

5. if making your own DSBSC use an AUDIO OSCILLATOR for the message.

You will find the loop will lock using any frequency within the tuning range,

but for measurement purposes something well above the cut-off of the RC filter

may be found more convenient.

T2 model the Costas loop of Figure 1. A suitable model is shown in Figure 2.

DSBSC

in

I & Q

outputs

Figure 2: model of the Costas loop of Figure 1

T3 look for a DSBSC signal at TRUNKS. If there is more than one, select one

based on a 100 kHz carrier (hint: examine it with one arm of the

Costas loop, with a stolen 100 kHz carrier from the TIMS MASTER

SIGNALS module).

The Costas loop


T4 check the amplitudes at all module interfaces. Check the gain of the

TUNEABLE LPF modules in the I and Q arms so that the third

MULTIPLIER is not overloaded (will the input amplitudes to this

module change between the lock and not-locked condition ?).

It is now time to lock the loop to the carrier of the incoming signal. There are

various techniques to be adopted in the laboratory (where a reference carrier is

available) while performing the alignment technique described in the next Task.

Two of these are:

1. watch the reference carrier and the VCO on two channels of the scope.

2. watch the outputs of the filters in the I and Q arms.

Make your choice. Then:

T5 synchronise the oscilloscope to either the reference carrier, or the output of

the I channel, according to whichever of the above options you have

chosen.

T6 disable the feedback loop by turning the GAIN of the VCO fully anti-clockwise.

T7 tune the VCO to within a few hundred Hertz (preferably less !) of 100 kHz,

using the FREQUENCY COUNTER.

T8 slowly increase the VCO GAIN until the VCO locks to the DSBSC carrier, as

indicated by the oscilloscope traces becoming stationary with respect

to each other or by observing that the FREQUENCY COUNTER now

reads 100.000 kHz.

T9 observe the demodulated output from the filter of the I arm. If lock has been

achieved, but the demodulated waveform (the message) is other than

sinusoidal, fine tune the VCO while still locked. The frequency won`t

change (it is locked to the carrier) but this will result in a ‘cleaner’

and smaller control signal to the VCO, and a maximum amplitude

minimum-distortion demodulated output.

You will notice that lock is achieved when the VCO GAIN setting is above a certain

minimum value. If the gain is increased ‘too far’, the lock will eventually be lost.

From the behaviour of the VCO output signal (or otherwise) during this procedure,

can you explain the meaning of ‘too far’ ?


T10 open and close the connection from the DSBSC signal to the input of the

Costas loop, and show that carrier acquisition is lost and regained.

Although lock may appear to happen ‘instantaneously’ it will in fact

take a finite number of carrier cycles after the connection is made.

Note that the phase difference between the reference and recovered

carrier takes one of two values, 1800 apart. This phase ambiguity of

the acquired carrier is associated with many carrier acquisition

schemes.

T11 examine the other DSBSC at TRUNKS (if any). If they are not based on a

100 kHz carrier you will have to plan a different approach than the

one suggested above. How will you know when lock has been

achieved ?

measurementsmeasurementsmeasurementsmeasurements

There are many measurements and observations that could now be made. This will

depend upon the level of your course work.

Of practical interest would be a knowledge of the loop acquisition time under

different conditions, lock range, holding range, conditions for stability, and so on.

These dynamic measurements require more sophisticated instrumentation than you

probably have.

Thus it is suggested that you confine your observations to checking that the loop

actually works (already done), and some less sophisticated measurements.

VCO simulationVCO simulationVCO simulationVCO simulation

A technique of interest is to replace the VCO signal with a ‘stolen’ carrier

connected, via a PHASE SHIFTER, into the loop. This simulates the locked

VCO 2, and allows static observations of all points of the loop for various values of

the phase angle α.

Appendix A to this experiment gives an exact

analysis of this condition.

In particular, the control signal to the VCO can be monitored.

You are looking for the condition where the magnitude of the control signal is a

minimum. This must be the condition when final lock is achieved, since any other

value would tend to move the VCO until it was met.

It is best to use a message frequency as high as possible so as not to confuse the

measurement of the DC control signal with the unavoidable unwanted terms.

2 you may not agree with this !

The Costas loop


The analysis shows that every time a signal is processed by a multiplier followed by

a filter there is an amplitude reduction of the signal under observation of one half

due to the analytic process, and a further half due to the ‘k factor’ of each TIMS

MULTIPLIER module. Squaring the message introduces another reduction of one

half.

Remember, then, that you will be looking for quite small signals, especially the DC

control to the VCO.

This can be measured very conveniently with the SPECTRUM UTILITIES module.

This is a meter which responds to DC or slowly-varying AC. Refer to the

Advanced Modules User Manual for more details.

Your measurements under these conditions will confirm the predictions of the

analysis. You could show that:

1. the message appears at the output of both the I and Q lowpass filters.

2. the AC term, at the output of the third multiplier, before removal by filtering, is

at twice the message frequency

3. by adjusting the phase α until the DC from the filter at the output of the ‘third’

multiplier is reduced to zero,

a) the I-filter output is maximized

b) the Q-filter output is minimized (see Tutorial Question Q8)



Q1 a Costas loop can acquire a carrier from a received signal which itself

contains no term at carrier frequency. Describe another scheme

which can do this.

Q2 what are the required properties of the lowpass filter from which the VCO

control signal is output ?

Q3 what properties of the Costas loop differentiate it from the phase locked

loop ?

Q4 do any of the multipliers in a Costas loop need to be DC coupled ?

Q5 if you have achieved lock, it will be regained if:

a) the inputs to the I and Q filters are swapped

b) the outputs from the I and Q arms are swapped

What will happen to the I and Q outputs in each case ?

Q6 what would happen if the polarity of the control signal to the VCO is

reversed ?

Q7 would you anticipate any differences in performance if the sinusoidal

message was replaced with speech ?

Q8 if you used a filter from the 100 kHz CHANNEL FILTERS module to simulate

a channel (for added realism) you may have had difficulty in

achieving a deep null from the output of the Q-filter. How could this

be ?

Q9 in a digital communications system the phase ambiguity introduced by a

Costas loop for carrier acquisition need not necessarily be

unacceptable. For example,

a) some line codes would not be affected.

b) a training sequence may be used.

Explain.

Q10 in the block diagram of Figure 1 there is a phase shifter of 900 (π/2). How

would the performance of the loop be affected if this was set to 800 ?

APPENDIX AAPPENDIX AAPPENDIX AAPPENDIX A

a simplified analysisa simplified analysisa simplified analysisa simplified analysis

A simplified analysis of the Costas loop (Figure 1) starts by assuming that a stable

lock has already been achieved.

The Costas loop


This in turn assumes that the VCO is operating at the correct frequency, but that its

relative phase is unknown. Call the angle α the phase difference between the

received carrier and the VCO.

Let the received DSBSC be derived from the message m(t), and based on a carrier

frequency of ω rad/s. This then is also the frequency of the VCO when locked.

The ‘k (= ½) factor’ of the TIMS MULTIPLIER modules has been included.

Define the signals into the multipliers of the I and Q arms as I and Q. Then:

I = m(t).k.cosωt.cos(ωt + α) ........ A-1

Q = m(t).k.cosωt.sin(ωt + α) ........ A-2

Equations (A-1) and (A-2) may be expanded, and only the low frequency terms

retained, to obtain the signals from the lowpass filters. These go into the ‘third’

multiplier. Let these be named ILF: and QLF. Then:

ILF = ½.m(t).k.cosα........ A-3

QLF = ½.m(t).k.sinα........ A-4

After these are multiplied together, the output of the ‘third’ multiplier is:

‘third’ mult out = ½.¼.m2(t).k2.sin2α........ A-5

No matter what the message m(t), the square of it will be positive, and contain a

DC component, which can be filtered off.

If the message is a sine wave, and the DSBSC amplitude is unity, then:

filter output = 1

1622

k sin α ......... A-6

The DC from the filter has a magnitude which is a function of the phase error α.

This DC is the control signal to the VCO. It can change sign, according to the

magnitude of α. Providing the loop is stable the tendency will be to shift the phase

of the VCO until α is reduced to zero, since only then will the VCO come to rest.

message outputmessage outputmessage outputmessage output

The message appears at the output of each of the I and Q filters. But under lock

condition the phase error α will be zero, and eqns. A-3 and A-4 tell us that the

message amplitude at the output of the I filter will be maximized, and minimized at

the output of the Q filter.

Vol A2, appendix, rev 1.1

Appendix A

to Volume A2

Tables of Bessel coefficients


A-2 Tables of Bessel coefficients


Tables of Bessel coefficients A-3

Tables of Bessel coefficients

arg =>

order 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0 0.9975 0.9900 0.9776 0.9604 0.9385 0.9120 0.8812 0.8463 0.8075 0.7652

1 0.0499 0.0995 0.1483 0.1960 0.2423 0.2867 0.3290 0.3688 0.4059 0.4401

2 0.0012 0.0050 0.0112 0.0197 0.0306 0.0437 0.0588 0.0758 0.0946 0.1149

3 0.0000 0.0002 0.0006 0.0013 0.0026 0.0044 0.0069 0.0102 0.0144 0.0196

4 0.0000 0.0000 0.0000 0.0001 0.0002 0.0003 0.0006 0.0010 0.0016 0.0025

5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0002

6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

arg =>

order 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

0 0.7196 0.6711 0.6201 0.5669 0.5118 0.4554 0.3980 0.3400 0.2818 0.2239

1 0.4709 0.4983 0.5220 0.5419 0.5579 0.5699 0.5778 0.5815 0.5812 0.5767

2 0.1366 0.1593 0.1830 0.2074 0.2321 0.2570 0.2817 0.3061 0.3299 0.3528

3 0.0257 0.0329 0.0411 0.0505 0.0610 0.0725 0.0851 0.0988 0.1134 0.1289

4 0.0036 0.0050 0.0068 0.0091 0.0118 0.0150 0.0188 0.0232 0.0283 0.0340

5 0.0004 0.0006 0.0009 0.0013 0.0018 0.0025 0.0033 0.0043 0.0055 0.0070

6 0.0000 0.0001 0.0001 0.0002 0.0002 0.0003 0.0005 0.0007 0.0009 0.0012

7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002

8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

arg =>

order 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00

0 0.1666 0.1104 0.0555 0.0025 -0.0484 -0.0968 -0.1424 -0.1850 -0.2243 -0.2601

1 0.5683 0.5560 0.5399 0.5202 0.4971 0.4708 0.4416 0.4097 0.3754 0.3391

2 0.3746 0.3951 0.4139 0.4310 0.4461 0.4590 0.4696 0.4777 0.4832 0.4861

3 0.1453 0.1623 0.1800 0.1981 0.2166 0.2353 0.2540 0.2727 0.2911 0.3091

4 0.0405 0.0476 0.0556 0.0643 0.0738 0.0840 0.0950 0.1067 0.1190 0.1320

5 0.0088 0.0109 0.0134 0.0162 0.0195 0.0232 0.0274 0.0321 0.0373 0.0430

6 0.0016 0.0021 0.0027 0.0034 0.0042 0.0052 0.0065 0.0079 0.0095 0.0114

7 0.0002 0.0003 0.0004 0.0006 0.0008 0.0010 0.0013 0.0016 0.0020 0.0025

8 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0005

9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001

10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000



arg =>

order 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00

0 -0.2921 -0.3202 -0.3443 -0.3643 -0.3801 -0.3918 -0.3992 -0.4026 -0.4018 -0.3971

1 0.3009 0.2613 0.2207 0.1792 0.1374 0.0955 0.0538 0.0128 -0.0272 -0.0660

2 0.4862 0.4835 0.4780 0.4697 0.4586 0.4448 0.4283 0.4093 0.3879 0.3641

3 0.3264 0.3431 0.3588 0.3734 0.3868 0.3988 0.4092 0.4180 0.4250 0.4302

4 0.1456 0.1597 0.1743 0.1892 0.2044 0.2198 0.2353 0.2507 0.2661 0.2811

5 0.0493 0.0562 0.0637 0.0718 0.0804 0.0897 0.0995 0.1098 0.1207 0.1321

6 0.0136 0.0160 0.0188 0.0219 0.0254 0.0293 0.0336 0.0383 0.0435 0.0491

7 0.0031 0.0038 0.0047 0.0056 0.0067 0.0080 0.0095 0.0112 0.0130 0.0152

8 0.0006 0.0008 0.0010 0.0012 0.0015 0.0019 0.0023 0.0028 0.0034 0.0040

9 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0005 0.0006 0.0008 0.0009

10 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002

11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

arg =>

order 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00

0 -0.3887 -0.3766 -0.3610 -0.3423 -0.3205 -0.2961 -0.2693 -0.2404 -0.2097 -0.1776

1 -0.1033 -0.1386 -0.1719 -0.2028 -0.2311 -0.2566 -0.2791 -0.2985 -0.3147 -0.3276

2 0.3383 0.3105 0.2811 0.2501 0.2178 0.1846 0.1506 0.1161 0.0813 0.0466

3 0.4333 0.4344 0.4333 0.4301 0.4247 0.4171 0.4072 0.3952 0.3811 0.3648

4 0.2958 0.3100 0.3236 0.3365 0.3484 0.3594 0.3693 0.3780 0.3853 0.3912

5 0.1439 0.1561 0.1687 0.1816 0.1947 0.2080 0.2214 0.2347 0.2480 0.2611

6 0.0552 0.0617 0.0688 0.0763 0.0843 0.0927 0.1017 0.1111 0.1209 0.1310

7 0.0176 0.0202 0.0232 0.0264 0.0300 0.0340 0.0382 0.0429 0.0479 0.0534

8 0.0048 0.0057 0.0067 0.0078 0.0091 0.0106 0.0122 0.0141 0.0161 0.0184

9 0.0011 0.0014 0.0017 0.0020 0.0024 0.0029 0.0034 0.0040 0.0047 0.0055

10 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0010 0.0012 0.0015

11 0.0000 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0003 0.0004

12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001

13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000


Tables of Bessel coefficients A-5

arg =>

order 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00

0 -0.1443 -0.1103 -0.0758 -0.0412 -0.0068 0.0270 0.0599 0.0917 0.1220 0.1506

1 -0.3371 -0.3432 -0.3460 -0.3453 -0.3414 -0.3343 -0.3241 -0.3110 -0.2951 -0.2767

2 0.0121 -0.0217 -0.0547 -0.0867 -0.1173 -0.1464 -0.1737 -0.1990 -0.2221 -0.2429

3 0.3466 0.3265 0.3046 0.2811 0.2561 0.2298 0.2023 0.1738 0.1446 0.1148

4 0.3956 0.3985 0.3996 0.3991 0.3967 0.3926 0.3866 0.3788 0.3691 0.3576

5 0.2740 0.2865 0.2986 0.3101 0.3209 0.3310 0.3403 0.3486 0.3559 0.3621

6 0.1416 0.1525 0.1637 0.1751 0.1868 0.1986 0.2104 0.2223 0.2341 0.2458

7 0.0592 0.0654 0.0721 0.0791 0.0866 0.0945 0.1027 0.1113 0.1203 0.1296

8 0.0209 0.0237 0.0267 0.0300 0.0337 0.0376 0.0418 0.0464 0.0513 0.0565

9 0.0064 0.0074 0.0086 0.0099 0.0113 0.0129 0.0147 0.0166 0.0188 0.0212

10 0.0017 0.0021 0.0024 0.0029 0.0034 0.0039 0.0045 0.0053 0.0061 0.0070

11 0.0004 0.0005 0.0006 0.0007 0.0009 0.0011 0.0013 0.0015 0.0017 0.0020

12 0.0001 0.0001 0.0001 0.0002 0.0002 0.0003 0.0003 0.0004 0.0005 0.0005

13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001

14 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

arg =>

order 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00

0 0.1773 0.2017 0.2238 0.2433 0.2601 0.2740 0.2851 0.2931 0.2981 0.3001

1 -0.2559 -0.2329 -0.2081 -0.1816 -0.1538 -0.1250 -0.0953 -0.0652 -0.0349 -0.0047

2 -0.2612 -0.2769 -0.2899 -0.3001 -0.3074 -0.3119 -0.3135 -0.3123 -0.3082 -0.3014

3 0.0846 0.0543 0.0240 -0.0059 -0.0353 -0.0641 -0.0918 -0.1185 -0.1438 -0.1676

4 0.3444 0.3294 0.3128 0.2945 0.2748 0.2537 0.2313 0.2077 0.1832 0.1578

5 0.3671 0.3708 0.3731 0.3741 0.3736 0.3716 0.3680 0.3629 0.3562 0.3479

6 0.2574 0.2686 0.2795 0.2900 0.2999 0.3093 0.3180 0.3259 0.3330 0.3392

7 0.1392 0.1491 0.1592 0.1696 0.1801 0.1908 0.2015 0.2122 0.2230 0.2336

8 0.0621 0.0681 0.0744 0.0810 0.0880 0.0954 0.1031 0.1111 0.1194 0.1280

9 0.0238 0.0266 0.0297 0.0330 0.0366 0.0405 0.0446 0.0491 0.0539 0.0589

10 0.0080 0.0091 0.0104 0.0118 0.0133 0.0150 0.0168 0.0189 0.0211 0.0235

11 0.0024 0.0028 0.0032 0.0037 0.0043 0.0049 0.0057 0.0065 0.0073 0.0083

12 0.0006 0.0008 0.0009 0.0011 0.0013 0.0015 0.0017 0.0020 0.0023 0.0027

13 0.0002 0.0002 0.0002 0.0003 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008

14 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002

15 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001




with

Volume D1 Fundamental Digital

Experiments

Tim Hooper


Volume D1 - Fundamental Digital Experiments. Author: Tim Hooper

Issue Number: 4.9

Published by:






EXPERIMENT AIMSEXPERIMENT AIMSEXPERIMENT AIMSEXPERIMENT AIMS


The experiments have been written with the idea that each model examined could eventually become part of a larger telecommunications system, the aim of this large system being to transmit a message from input to output. The origin of this message, for the analog experiments in Volumes A1 and A2, would ultimately be speech. But for test and measurement purposes a sine wave, or perhaps two sinewaves (as in the two-tone test signal) are generally substituted. For the digital experiments (Volumes D1, D2 and D3) the typical message is a pseudo random binary sequence.











PRBS generation.........................................................................D1-01

Eye patterns ................................................................................D1-02

The noisy channel model .............................................................D1-03

Detection with the DECISION MAKER .....................................D1-04

Line coding .................................................................................D1-05

ASK - amplitude shift keying.......................................................D1-06

FSK - frequency shift keying .......................................................D1-07

BPSK - binary phase shift keying.................................................D1-08

Signal constellations....................................................................D1-09

Sampling with SAMPLE & HOLD..............................................D1-10

PCM encoding ............................................................................D1-11

PCM decoding ............................................................................D1-12

Delta modulation.........................................................................D1-13

Delta demodulation .....................................................................D1-14

Adaptive delta modulation...........................................................D1-15

Delta-sigma modulation...............................................................D1-16

Copyright © 2005 Emona Instruments Pty Ltd D1-01-rev 2.0 - 1

PRBS GENERATIONPRBS GENERATIONPRBS GENERATIONPRBS GENERATION

PREPARATION ................................................................................2

digital messages.........................................................................2

random binary sequences ...........................................................2

viewing.................................................................................................. 3

applications ...............................................................................4

bit clock acquisition ............................................................................... 4

EXPERIMENT ..................................................................................4

the ‘snapshot’ display ................................................................4

band limiting..............................................................................6

two generator alignment ............................................................7

two sequence alignment.............................................................9

the sliding window correlator................................................................. 9

the model............................................................................................. 10

TUTORIAL QUESTIONS...............................................................11

APPENDIX......................................................................................12

PRBS generator - sequence length...........................................12

error counting utilities - X-OR ..................................................12

D1-01 - 2 Copyright © 2005 Emona Instruments Pty Ltd

PRBS GENERATIONPRBS GENERATIONPRBS GENERATIONPRBS GENERATION

ACHIEVEMENTS: introduction to the pseudo random binary sequence (PRBS)

generator; time domain viewing: snap shot and eye patterns; two

generator synchronization and alignment with the ‘sliding window

correlator’

PREREQUISITES: none

EXTRA MODULES: a second SEQUENCE GENERATOR, ERROR

COUNTING UTILITIES.

PREPARATIPREPARATIPREPARATIPREPARATIONONONON

digital messagesdigital messagesdigital messagesdigital messages

In analog work the standard test message is the sine wave, followed by the two-

tone signal 1 for more rigorous tests. The property being optimized is generally

signal-to-noise ratio (SNR). Speech is interesting, but does not lend itself easily

to mathematical analysis, or measurement.

In digital work a binary sequence, with a known pattern of ‘1’ and ‘0’, is

common. It is more common to measure bit error rates (BER) than SNR, and

this is simplified by the fact that known binary sequences are easy to generate

and reproduce.

A common sequence is the pseudo random binary sequence.

random binary sequencesrandom binary sequencesrandom binary sequencesrandom binary sequences

The output from a pseudo random binary sequence generator is a bit stream of

binary pulses; ie., a sequence of 1`s (HI) or 0`s (LO), of a known and

reproducible pattern.

The bit rate, or number of bits per second, is determined by the frequency of an

external clock, which is used to drive the generator. For each clock period a

1 see the experiment entitled Amplifier overload in Volume A2.

PRBS generation

Copyright © 2005 Emona Instruments Pty Ltd D1-01 - 3

single bit is emitted from the generator; either at the ‘1’ or ‘0’ level, and of a

width equal to the clock period. For this reason the external clock is referred to

as a bit clock.

For a long sequence the 1`s and 0`s are distributed in a (pseudo) random manner.

The sequence pattern repeats after a defined number of clock periods. In a

typical generator the length of the sequence may be set to 2n clock periods, where

n is an integer. In the TIMS SEQUENCE GENERATOR (which provides two,

independent sequences, X and Y) the value of n may be switched to one of three

values, namely 2, 5, or 11. There are two switch positions for the case n = 5,

giving different patterns. The SYNCH output provides a reference pulse generated

once per sequence repetition period.

This is the start-of-sequence pulse. It is invaluable as a trigger source for an

oscilloscope.

viewingviewingviewingviewing

There are two important methods of viewing a sequence in the time domain.

the snapshotthe snapshotthe snapshotthe snapshot

A short section, about 16 clock periods of a TTL sequence, is illustrated in

Figure 1 below.

bit clock

+5 volt

0 volt sequenceTTL

time

Figure 1: a sequence of length 16 bits

Suppose the output of the generator which produced the TTL sequence, of which

this is a part, was viewed with an oscilloscope, with the horizontal sweep

triggered by the display itself.

The display will not be that of Figure 1 above ! Of course not, for how would the

oscilloscope know which section of the display was wanted ?

Consider just what the oscilloscope might show !

Specific sections of a sequence can be displayed on a general purpose

oscilloscope, but the sequence generator needs to provide some help to do this.

As stated above, it gives a start-of-sequence pulse at the beginning of the

sequence. This can be used to start (trigger) the oscilloscope sweep. At the end

of the sweep the oscilloscope will wait until the next start-of-sequence is received

before being triggered to give the next sweep.

Thus the beginning ‘n’ bits of the sequence are displayed, where ‘n’ is

determined by the sweep speed.


For a sequence length of many-times-n bits, there would be a long delay between

sweeps. The persistence of the screen of a general purpose oscilloscope would be

too short to show a steady display, so it will blink. You will see the effect during

the experiment.

the eye patternthe eye patternthe eye patternthe eye pattern

A long sequence is useful for examining ‘eye patterns’. These are defined and

examined in the experiment entitled Eye patterns in this Volume.

applicationsapplicationsapplicationsapplications

One important application of the PRBS is for supplying a known binary

sequence. This is used as a test signal (message) when making bit error rate

(BER) measurements.

For this purpose a perfect copy of the transmitted sequence is required at the

receiver, for direct comparison with the received sequence. This perfect copy is

obtained from a second, identical, PRBS generator.

The second generator requires:

1. bit clock information, so that it runs at the same rate as the first

2. a method of aligning its output sequence with the received sequence. Due to

transmission through a bandlimited channel, it will be delayed in time with

respect to the sequence at the transmitter.

bit clock acquisitionbit clock acquisitionbit clock acquisitionbit clock acquisition

In a laboratory environment it is a simple matter to use a ‘stolen carrier’ for bit

clock synchronization purposes, and this will be done in most TIMS

experiments. In commercial practice this bit clock must be regenerated from the

received signal. Methods of bit clock recovery are investigated in a later

experiment.


the ‘snapshot’ display the ‘snapshot’ display the ‘snapshot’ display the ‘snapshot’ display

Examine a SEQUENCE GENERATOR module, and read about it in the TIMS

User Manual.

A suitable arrangement for the examination of a SEQUENCE GENERATOR is


Notice that the length of the sequence is controlled by the settings of a DIP

switch, SW2, located on the circuit board. See the Appendix to this experiment

for details.

PRBS generation


start-of-sequence signal to oscilloscope `ext. trig`

CH1-A

CH2-A

TTL sequence

`ANALOG` sequence

bit clock

CH2-B

Figure 2: examination of a SEQUENCE GENERATOR

T1 before inserting the SEQUENCE GENERATOR set the on-board DIP

switch SW2 to generate a short sequence. Then patch up the model

of Figure 2 above. Set the AUDIO OSCILLATOR, acting as the bit

clock, to about 2 kHz. Set the oscilloscope sweep speed to suit; say

about 1 ms/cm.

T2 observe the TTL sequence on CH1-A. Try triggering the oscilloscope to the

sequence itself (CH1-A). Notice that you may be able to obtain a

stable picture, but it may change when the re-set button is pressed

(this re-starts the sequence each time from the same point, referred

to as the ‘start of sequence’).

T3 try triggering off the bit clock. Notice that it is difficult (impossible ?) to

obtain a stable display of the sequence.

T4 change the mode of oscilloscope triggering. Instead of using the signal

itself, use the start-of-sequence SYNC signal from the SEQUENCE

GENERATOR, connected to ‘ext. trig’ of the oscilloscope.

Reproduce the type of display of Figure 1 (CH1-A ).

T5 increase the sequence length by re-setting the on-board switch SW2. Re-

establish synchronization using the start-of-sequence SYNC signal

connected to the ‘ext. trig’ of the oscilloscope. Notice the effect

upon the display. See Tutorial Question Q8.

T6 have a look with your oscilloscope at a yellow analog output from the

SEQUENCE GENERATOR. The DC offset has been removed, and

the amplitude is now suitable for processing by analog modules (eg.,

by a filter representing an analog channel - see the experiment

entitled The noisy channel model in this Volume). Observe also

that the polarity has been reversed with respect to the TTL version.

This is just a consequence of the internal circuitry; if not noticed it

can cause misunderstandings !


band limitingband limitingband limitingband limiting

The displays you have seen on the oscilloscope are probably as you would have

expected them to be ! That is, either ‘HI’ or ‘LO’ with sharp, almost invisible,

transitions between them. This implies that there was no band limiting between

the signal and the viewing instrument.

If transmitted via a lowpass filter, which could represent a bandlimited

(baseband) channel, then there will be some modification of the shape, as viewed

in the time domain.

For this part of the experiment you will use a TUNEABLE LPF to limit, and

vary, the bandwidth. Because the sequence will be going to an analog module it

will be necessary to select an ‘analog’ output from the SEQUENCE

GENERATOR.

T7 select a short sequence from the SEQUENCE GENERATOR.

T8 connect an analog version of the sequence (YELLOW) to the input of a

TUNEABLE LPF.

T9 on the front panel of the TUNEABLE LPF set the toggle switch to the WIDE

position. Obtain the widest bandwidth by rotating the TUNE control

fully clockwise.

T10 with the oscilloscope still triggered by the ‘start-of-sequence’ SYNC signal,

observe both the filter input and output on separate oscilloscope

channels. Adjust the gain control on the TUNEABLE LPF so the

amplitudes are approximately equal.

T11 monitor the filter corner frequency, by measuring the CLK signal from the

TUNEABLE LPF with the FREQUENCY COUNTER 2. Slowly

reduce the bandwidth, and compare the difference between the two

displays. Notice that, with reducing bandwidth:

a) identification of individual bits becomes more difficult

b) there is an increasing delay between input and output

Remember that the characteristics of the filter will influence the results of the last

Task.

2 divide by 880 (normal) or 360 (wide). For detail see the TIMS User Manual.

PRBS generation


two generator alignmenttwo generator alignmenttwo generator alignmenttwo generator alignment

In an experiment entitled BER measurement in the noisy channel (within Volume

D2 - Further & Advanced Digital Experiments) you will find out why it is

important to be able to align two sequences. In this experiment you will find out

how to do it.

Two SEQUENCE GENERATOR modules may be coupled so that they deliver

two identical, aligned, sequences.

• that they should deliver the same sequence it is sufficient that the

generator circuitry be identical

• that they be at the same rate it is necessary that they share a common bit

clock

• that they be aligned requires that they start at the same time.

TIMS SEQUENCE GENERATOR modules (and those available commercially)

have inbuilt facilities to simplify the alignment operation. One method will be

examined with the scheme illustrated in block diagram form in Figure 3 below.

BIT

CLOCK

common (̀ stolen`) clock

#1 #2

OUT 2OUT 1

Figure 3: aligning two identical generators

The scheme of Figure 3 is shown modelled with TIMS in Figure 4 below.

GENERATOR #1 CH1-A

GENERATOR #2 CH2-A

ext. trig OSCILLOSCOPE

common (or `stolen`) clock

Figure 4: TIMS model of the block diagram of Figure 3.


You will now investigate the scheme. Selecting short sequences will greatly

assist during the setting-up procedures, by making the viewing of sequences on

the oscilloscope much easier.

T12 before plugging in the SEQUENCE GENERATOR modules, set them both

to the same short sequence.

T13 patch together as above, but omit the link from the ‘GENERATOR #1’

SYNC to ‘GENERATOR #2’ RESET. Do not forget to connect the

‘start-of-sequence’ SYNC signal of the GENERATOR #1 to the

‘ext. trig’ of the oscilloscope.

T14 press the ‘GENERATOR #2’ RESET push button several times. Observe on

the oscilloscope that the two output sequences are synchronised in

time but the data bits do not line-up correctly. Try to synchronise

the sequences manually by repeating this exercise many times. It is

a hit-and-miss operation, and is likely to be successful only

irregularly.

T15 connect the SYNC of the ‘GENERATOR #1’ to the RESET of the

‘GENERATOR #2’. Observe on the oscilloscope that the two output

sequences are now synchronised in time and their data are aligned.

T16 break the synchronizing path between the two generators. What happens

to the alignment ?

Once the two generators are aligned, they will remain

aligned, even after the alignment link between them is

broken. The bit clock will keep them in step.

The above scheme has demonstrated a method of aligning two generators, and

was seen to perform satisfactorily. But it was in a somewhat over simplified

environment.

What if the two generators had been separated some distance, with the result that

there was a delay between sending the SYNC pulse from GENERATOR #1 and its

reception at GENERATOR #2 ?

The sequences would be offset by the time delay

In other words, the sequences would not be aligned.

PRBS generation


two sequence alignmenttwo sequence alignmenttwo sequence alignmenttwo sequence alignment In the previous section two PRBS generators were synchronized in what might be

called a ‘local’ situation. There were two signal paths between them:

1. one connection for the bit clock

2. another connection for the start-of-sequence command

Consider a transmitter and a receiver separated by a transmission medium.

Then:

1. there would be an inevitable transmission time delay

2. the two signal paths are not conveniently available

It may be difficult (impossible ?) to align the two generators, at remote sites. But

it is possible, and frequently required, that a local generator can be aligned with

a received sequence (from a similar generator).

The sliding window correlator is an example of an arrangement which can

achieve this end.

the sliding window correlatorthe sliding window correlatorthe sliding window correlatorthe sliding window correlator

Consider the arrangement shown in block diagram form in Figure 5 below.

CHANNEL

STOLEN CLOCK

DETECTOR

clocked X-OR

BIT CLOCK

Figure 5 - the sliding window correlator

The detector is present to re-generate TTL pulses from the bandlimited received

signal. We will assume this regeneration is successful.

The regenerated received sequence (which matches, but is a delayed version of

the transmitted sequence) is connected to one input of a clocked X-OR logic gate.

The receiver PRBS generator (using a stolen bit clock in the example) is set to

generate the same sequence as its counterpart at the transmitter. Its output is

connected to the other input of the clocked X-OR gate. The clock ensures that

the comparison is made at an appropriate instant within a bit clock period.

At each bit clock period there is an output from the X-OR gate only if the bits

differ. In this case the receiver generator will be RESET to the beginning of the

sequence.

This resetting will take place repeatedly until there are no errors. Thus every bit

must be aligned. There will then be no further output from the X-OR gate.


Once alignment has been achieved, it will be maintained

even when the RESET signal to the receiver generator is

broken.

It is the common bit clock which maintains the alignment. Because of the nature

of this X-OR comparison technique the arrangement is called a sliding window

correlator.


You will now model the block diagram of Figure 5. In later experiments you will

meet the channel and the detector, but in this experiment we will omit them both.

Thus there will in fact be no delay, but that does not in any way influence the

operation of the sliding window correlator.

The patching arrangement to model Figure 5 is shown in Figure 6 below.

This model will regenerate, at the receiver, an identical sequence to that sent

from the transmitter. To avoid additional complications a stolen carrier is used.

TRANSMITTER GENERATOR

STOLEN CLOCK

CHA

NN

EL

GENERATOR RECEIVER

BITCLOCK

CH1-A

CH2-A

ext. trig CH1-B

Figure 6: modelling the sliding window correlator

T17 before patching up select the shortest length sequence on each

SEQUENCE GENERATOR.

T18 patch together as above. Do not close the link from the X-OR output of

the ERROR COUNTING UTILITIES 3 module to the RESET of the

RECEIVER GENERATOR.

T19 view CH1-A and CH2-A simultaneously. The two output sequences are

synchronised in time but the data bits are probably not aligned.

Press the RESET push button of the RECEIVER GENERATOR

repeatedly. Notice that once in a while it is possible to achieve

alignment. With a longer sequence this would be a rare event

indeed.

3 see the Appendix to this experiment for some information about the ERROR COUNTING UTILITIES

module.

PRBS generation


T20 switch to CH1-B; observe the error sequence produced by the X-OR

operation on the two data sequences.

T21 now close the alignment link by connecting the error signal at the X-OR

output to the RESET input of the RECEIVER GENERATOR.

T22 confirm that the error sequence is now zero. Confirm that, if the RESET

push button of the RECEIVER GENERATOR is repeatedly pressed,

the error signal appears for a short time and then disappears.

T23 repeat the previous Task with a long sequence. Note that the system takes

a longer time to acquire alignment.

T24 having achieved alignment, disconnect the error signal from the RESET

input of the RECEIVER GENERATOR, and observe that the two

sequences remain in alignment.

Future experiments will assume familiarity with the operation of the

SEQUENCE GENERATOR, and the alignment of two sequences using the

sliding window correlator. So, before you finish this experiment, make sure you

have looked at as many aspects of this arrangement as you have time for.


Q1 you have seen the first ‘n’ bits of a sequence, using the start-of-sequence

signal to initiate the oscilloscope sweep. How could you show the

next ‘n’ bits of the same sequence ? Can you demonstrate your

method with TIMS ?

Q2 estimate the bandwidth of the sequence as a function of bit rate clock

frequency. Describe a method for estimating the maximum rate at

which a binary sequence can be transmitted through a lowpass

filter. Relate its predictions with your observations.

Q3 explain what is meant when two sequences are ‘synchronized’ and

‘aligned’.

Q4 was there any obvious misalignment between the TTL sequence input to,

and the bandlimited sequence output from, the TUNEABLE LPF ?

Explain.

Q5 in the last model examined, explain why the sequence alignment takes

longer when the sequence length is increased.

Q6 suppose the TIMS SEQUENCE GENERATOR is driven by an 8.333 kHz

TTL clock. What would the TIMS FREQUENCY COUNTER read if

connected to the output sequence ? Explain.

Q7 what should an rms meter read if connected to a TTL pseudo random

binary sequence ?


Q8 with a 2.083 kHz clock what is the delay, for a 2048 bit sequence, between

consecutive displays ?


PRBS generator PRBS generator PRBS generator PRBS generator ---- sequence lengthsequence lengthsequence lengthsequence length

The length of the sequences from the SEQUENCE GENERATOR can be set

with the DIP switch SW2 located on the circuit board.

See Table A-1 below.

LH toggle RH toggle n sequence length

UP UP 5 32

UP DOWN 8 256

DOWN UP 8 256

DOWN DOWN 11 2048

Table A-1: on-board switch SW2 settings

There are two sequences of length 256 bits. These sequences are different.

error counting utilities error counting utilities error counting utilities error counting utilities ---- XXXX----OROROROR

This is the first time the ERROR COUNTING UTILITIES module has been

used. It contains two independent sub-systems, only one of which (X-OR) is

required in this experiment.

A complete description of its characteristics and behaviour can be obtained from

the TIMS Advanced Modules User Manual.

A condensed description of the X-OR function, suitable for this experiment, is

given in the experiment entitled Digital utility sub-systems (within Volume D2 -

Further & Advanced Digital Experiments), under the heading Exclusive-OR.


EYE PATTERNSEYE PATTERNSEYE PATTERNSEYE PATTERNS

PREPARATION................................................................................ 2

pulse transmission ..................................................................... 2

maximum transmission rate assessment...................................... 3

EXPERIMENT.................................................................................. 4

snap-shot assessment................................................................. 5

eye pattern assessment .............................................................. 5

your conclusions ....................................................................... 7



EYE PATTERNSEYE PATTERNSEYE PATTERNSEYE PATTERNS

ACHIEVEMENTS: understanding the Nyquist I criterion; transmission rates via

bandlimited channels; comparison of the ‘snap shot’ display with the

‘eye patterns’.

PREREQUISITES: some acquaintance with basic notions of digital transmission

ADVANCED MODULES: BASEBAND CHANNEL FILTERS


pulse transmissionpulse transmissionpulse transmissionpulse transmission

It is well known that, when a signal passes via a bandlimited channel it will suffer

waveform distortion. As an example, refer to Figure 1. As the data rate increases

the waveform distortion increases, until transmission becomes impossible.

time

BANDLIMITED

SEQUENCEOUTPUT

(showing delay)

SEQUENCE

BIT CLOCK

0+

-BIPOLAR INPUT

Figure 1: waveforms before and after moderate bandlimiting

In this experiment you will be introduced to some important aspects of pulse

transmission which are relevant to digital and data communication applications.

Issues of interest include:

• In the 1920s Harry Nyquist proposed a clever method now known as

Nyquist`s first criterion, that makes possible the transmission of telegraphic

signals over channels with limited bandwidth without degrading signal

Eye patterns


quality. This idea has withstood the test of time. It is very useful for digital

and data communications.

The method relies on the exploitation of

pulses that look like sin(x)/x - see the

Figure opposite. The trick is that zero

crossings always fall at equally spaced

points. Pulses of this type are known as

‘Nyquist I’ (there is also Nyquist II and

III).

• In practical communication channels distortion causes the dislocation of the

zero crossings of Nyquist pulses, and results in intersymbol interference

(ISI) 1. Eye patterns provide a practical and very convenient method of

assessing the extent of ISI degradation. A major advantage of eye patterns is

that they can be used ‘on-line’ in real-time. There is no need to interrupt

normal system operation.

• The effect of ISI becomes apparent at the receiver when the incoming signal

has to be ‘read’ and decoded; ie., a detector decides whether the value at a

certain time instant is, say, ‘HI’ or ‘LO’ (in a binary decision situation). A

decision error may occur as a result of noise. Even though ISI may not itself

cause an error in the absence of noise, it is nevertheless undesirable because

it decreases the margin relative to the decision threshold, ie., a given level of

noise, that may be harmless in the absence if ISI, may lead to a high error

rate when ISI is present.

• Another issue of importance in the decision process is timing jitter. Even if

there is no ISI at the nominal decision instant, timing jitter in the

reconstituted bit clock results in decisions being made too early or too late

relative to the ideal point. As you will discover in this experiment, channels

that are highly bandwidth efficient are more sensitive to timing jitter.

maximum transmission rate maximum transmission rate maximum transmission rate maximum transmission rate

assessmentassessmentassessmentassessment

This is what is going to be done:

1. first, set up a pseudorandom sequence. To start you will use the shortest

available sequence, so that you can easily observe it with an oscilloscope. Very

long sequences are not easy to observe because the time elapsed between trigger

pulses is too long. The oscilloscope will be triggered to the start of sequence

signal. The display has been defined as a ‘snap shot’ 2.

2. next you will pass this sequence through a selection of filters. Three are

available in the BASEBAND CHANNEL FILTERS module, and a fourth will

be the TUNEABLE LPF module. You will observe the effect of the filters on

the shape of the sequence, at various pulse rates.

3. then the above observations will be repeated, but this time the oscilloscope will

be triggered by the bit clock, giving what is defined as an eye pattern.

1 ie., ‘inter-pulse’ interference.

2 see the experiment entitled PRBS generation.


4. finally you will compare the performance of the various cases in terms of

achievable transmission rate and ‘eye opening’.


T1 set up the model of Figure 2. The AUDIO OSCILLATOR serves as the bit

clock for the SEQUENCE GENERATOR. A convenient rate to start

with is 2 kHz. Select CHANNEL #1. Select a short sequence (both

toggles of the on-board switch SW2 UP)

CH1-A

CH2-A

SNAP-SHOText. trig

EYE PATTERN

ext. trig

Figure 2: viewing snap shots and eye patterns

T2 synchronize the oscilloscope to the ‘start-of-sequence’ synchronizing signal

from the SEQUENCE GENERATOR. Set the sweep speed to display

between 10 and 20 sequence pulses (say 1 ms/cm). This is the ‘snap

shot’ mode. Both traces should be displaying the same picture, since

CHANNEL #1 is a ‘straight through’ connection.

The remaining three channels (#2, #3, and #4) in the BASEBAND CHANNEL

FILTERS module represent channels having the same slot bandwidth 3 (40 dB

stopband attenuation at 4 kHz), but otherwise different transmission characteristics,

and, in particular, different 3 dB frequencies. Graphs of these characteristics are

shown in Appendix A.

You should also prepare a TUNEABLE LPF to use as a fourth channel, giving it a

40 dB attenuation at 4 kHz. To do this:

T3 using a sinusoidal output from an AUDIO OSCILLATOR as a test input:

a) set the TUNE and GAIN controls of the TUNEABLE LPF fully

clockwise. Select the NORM bandwidth mode.

3 see Appendix A to Volume A1 for a definition of slotband.

Eye patterns


b) set the AUDIO OSCILLATOR to a frequency of, say, 1 kHz. This

is well within the current filter passband.

c) note the output amplitude on the oscilloscope.

d) increase the frequency of the AUDIO OSCILLATOR to 4 kHz.

e) reduce the bandwidth of the TUNEABLE LPF (rotate the TUNE

control anti-clockwise) until the output amplitude falls 100 times.

This is a 40 dB reduction relative to the passband gain.

snapsnapsnapsnap----shot assessmentshot assessmentshot assessmentshot assessment

Now it is your task to make an assessment of the maximum rate, controlled by the

frequency of the AUDIO OSCILLATOR, at which a sequence of pulses can be

transmitted through each filter before they suffer unacceptable distortion. The

criterion for judging the maximum possible pulse rate will be your opinion that you

can recognise the output sequence as being similar to that at the input.

It is important to remember that the four filters have the same slot bandwidth (ie.,

4 kHz, where the attenuation is 40 dB) but different 3 dB bandwidths.

To relate the situation to a practical communication system you should consider the

filters to represent the total of all the filtering effects at various stages of the

transmission chain, ie., transmitter, channel, and the receiver right up to the input

of the decision device.

T4 record your assessment of the maximum practical data rate through each of

the four channels.

At the very least your report will be a record of the four maximum transmission

rates. But it is also interesting to compare these rates with the characteristics of the

filters. Perhaps you might expect the filter with the widest passband to provide the

highest acceptable transmission rate ?

eye pattern assessmenteye pattern assessmenteye pattern assessmenteye pattern assessment

Now you will repeat the previous exercise, but, instead of observing the sequence as

a single trace, you will use eye patterns. The set-up will remain the same except

for the oscilloscope usage and sequence length.

So far you have used a short sequence, since this was convenient for the snapshot

display. But for eye pattern displays a longer sequence is preferable, since this

generates a greater number of patterns. Try it.

T5 change the oscilloscope synchronizing signal from the start-of-sequence SYNC

output of the SEQUENCE GENERATOR to the sequence bit clock.

Increase the sequence length (both toggles of the on-board switch

SW2 DOWN). Make sure the oscilloscope is set to pass DC. Why ?

Try AC coupling, and see if you notice any difference.


T6 select CHANNEL #2. Use a data rate of about 2 kHz. You should have a

display on CH2-A similar to that of Figure 3 below.

Figure 3: a ‘good’ eye pattern

T7 increase the data rate until the eye starts to close. Figure 4 shows an eye not

nearly as clearly defined as that of Figure 3.

Figure 4: compare with Figure 3; a faster data rate

T8 take some time to examine the display, and consider what it is you are looking

at ! There is one ‘eye’ per bit period. Those shown in Figure 3 are

considered to be ‘wide open’. But as the data rate increases the eye

begins to close.

The actual shape of an eye is determined (in a linear system) primarily by the filter

(channel) amplitude and phase characteristics (for a given input waveform).

Timing jitter will have an influence too. See the experiment entitled Bit clock

regeneration (within Volume D2 - Further & Advanced Digital Experiments).

The detector must make a decision, at an appropriate moment in the bit period, as

to whether or not the signal is above or below a certain voltage level. If above it

decides the current bit is a HI, otherwise a LO. By studying the eye you can make

that decision. Should it not be made at the point where the eye is wide open, clear

of any trace ? The moment when the vertical opening is largest ?

You can judge, by the thickness of the bunch of traces at the top and bottom of the

eye, compared with the vertical opening, the degree-of-difficulty in making this

decision.

Eye patterns


T9 determine the highest data rate for which you consider you would always be

able to make the correct decision (HI or LO). Note that the actual

moment to make the decision will be the same for all bits, and

relatively easy to distinguish. Record this rate for each of the four

filters.

You have now seen two different displays, the snapshot and the eye pattern.

It is generally accepted that the eye pattern gives a better

indication of the appropriate instant the HI or LO

decision should be made, and its probable success, than

does the snapshot display. Do you agree ?

Noise and other impairments will produce the occasional transition which will

produce a trace within the apparently trace-free eye. This may not be visible on the

oscilloscope, but will none-the-less cause an error. Turning up the oscilloscope

brilliance may reveal some of these transitions.

Such a trace is present in the eye pattern of Figure 4.

An oscilloscope, with storage and other features (including in-built signal

analysis !), will reveal even more information.

It does not follow that the degradation of the eye worsens as the clock rate is

increased. Filters can be designed for optimum performance at a specific clock

rate, and performance can degrade if the clock rate is increased or reduced.

The present experiment was aimed at giving you a ‘feel’ and appreciation of the

technique in a non-quantitative manner.

In later experiments you will make quantitative measurements of error rates, as

data is transmitted through these filters, with added noise.

your conclusionsyour conclusionsyour conclusionsyour conclusions

Theory predicts a maximum transmission rate of 2 pulses per Hz of baseband

bandwidth available. On the basis of your results, what do you think ?



Q1 explain why it is important to have the oscilloscope switched to ‘DC’ when

viewing eye patterns. Explain the meaning, and possible causes of,

‘baseline wander’.

Q2 why have the filters in the BASEBAND CHANNEL FILTERS module got

common slotband widths (instead, for example, of having common

passband widths) ?

Q3 why would a storage oscilloscope provide a more reliable eye pattern

display ?

Q4 why is a long sequence preferable for eye pattern displays ?

Q5 how would timing jitter show up in an eye pattern ?


THE NOISY CHANNEL THE NOISY CHANNEL THE NOISY CHANNEL THE NOISY CHANNEL

MODELMODELMODELMODEL

PREPARATION................................................................................ 2

lowpass (or baseband) channels ................................................. 2

bandpass channels ..................................................................... 2

over simplification..................................................................... 3

noise ......................................................................................... 3

the noisy channel model ............................................................ 3

diagrammatic representation...................................................... 4

channel gain .......................................................................................... 5

noise level ............................................................................................. 5

revision ..................................................................................... 6

EXPERIMENT.................................................................................. 6

filter amplitude response............................................................ 6

signal to noise ratio ................................................................... 8

speech-plus-noise .................................................................... 10

group delay............................................................................. 11



THE NOISY CHANNEL THE NOISY CHANNEL THE NOISY CHANNEL THE NOISY CHANNEL

MODELMODELMODELMODEL

ACHIEVEMENTS: definition of the macro CHANNEL MODEL module. Ability to

set up a noisy bandlimited channel for subsequent experiments;

measurement of filter characteristics; measurement of signal-to-noise

ratio with the WIDEBAND TRUE RMS METER. Observation of

different levels of signal-to-noise ratio with speech.

PREREQUISITES: none

EXTRA MODULES: WIDEBAND TRUE RMS METER, NOISE GENERATOR,

BASEBAND CHANNEL FILTERS module; 100 kHz CHANNEL

FILTERS module optional.


Since TIMS is about modelling communication systems it is not surprising that it

can model a communications channel.

Two types of channels are frequently required, namely lowpass and bandpass.

lowpass (or baseband) channelslowpass (or baseband) channelslowpass (or baseband) channelslowpass (or baseband) channels

A lowpass channel by definition should have a bandwidth extending from DC to

some upper frequency limit. Thus it would have the characteristics of a lowpass

filter.

A speech channel is often referred to as a lowpass channel, although it does not

necessarily extend down to DC. More commonly it is called a baseband channel.

bandpass channelsbandpass channelsbandpass channelsbandpass channels

A bandpass channel by definition should have a bandwidth covering a range of

frequencies not including DC. Thus it would have the characteristics of a bandpass

filter.

Typically its bandwidth is often much less than an octave, but this restriction is not

mandatory. Such a channel has been called narrow band.

The noisy channel model


Strictly an analog voice channel is a bandpass channel, rather than lowpass, as

suggested above, since it does not extend down to DC. So the distinction between

baseband and bandpass channels can be blurred on occasion.

Designers of active circuits often prefer bandpass channels, since there is no need to

be concerned with the minimization of DC offsets.

For more information refer to the chapter entitled Introduction to modelling with

TIMS, within Volume A1 - Fundamental Analog Experiments, in the section

entitled ‘bandwidths and spectra’.

oooover simplificationver simplificationver simplificationver simplification

The above description is an oversimplification of a practical system. It has

concentrated all the bandlimiting in the channel, and introduced no intentional

pulse shaping. In practice the bandlimiting, and pulse shaping, is distributed

between filters in the transmitter and the receiver, and the channel itself. The

transmitter and receiver filters are designed, knowing the characteristics of the

channel. The signal reaches the detector having the desired characteristics.

noisenoisenoisenoise

Whole books have been written about the analysis, measurement, and optimization

of signal-to-noise ratio (SNR).

SNR is usually quoted as a power ratio, expressed in decibels. But remember the

measuring instrument in this experiment is an rms voltmeter, not a power meter.


Although, in a measurement situation, it is the magnitude of the ratio S/N which is

commonly sought, it is more often the ( )S N

N

+

which is available. In other words,

in a non-laboratory environment, if the signal is present then so is the noise; the

signal is not available alone.

In this, and most other laboratory environments, the noise is under our control, and

can be removed if necessary. So that N

S, rather than

( )S N

N

+

, can be measured

directly.

For high SNRs there is little difference between the two measures.

the noisy channel modelthe noisy channel modelthe noisy channel modelthe noisy channel model

A representative noisy, bandlimited channel model is shown in block diagram form

in Figure 1 of the following page.

Band limitation is implemented by any appropriate filter.

The noise is added before the filter so that it becomes bandlimited by the same filter

that band limits the signal. If this is not acceptable then the adder can be moved to

the output of the filter, or perhaps the noise can have its own bandlimiting filter.


input

noisesource

anysuitable

filteroutput

calibrated attenuator

Figure 1: channel model block diagram

Controllable amounts of random noise, from the noise source, can be inserted into

the channel model, using the calibrated attenuator. This is non signal-dependent

noise.

For lowpass channels lowpass filters are used.

For bandpass channels bandpass filters are used.

Signal dependent noise is typically introduced by channel non-linearities, and

includes intermodulation noise between different signals sharing the channel (cross

talk). Unless expressly stated otherwise, in TIMS experiments signal dependent

noise is considered negligible. That is, the systems must be operated under linear

conditions. An exception is examined in the experiment entitled Amplifier

overload (within Volume A2 - Further & Advanced Analog Experiments).

diagrammatic representationdiagrammatic representationdiagrammatic representationdiagrammatic representation

In patching diagrams, if it is necessary to save space, the noisy channel will be

represented by the block illustrated in Figure 2 below.

IN OUT

Figure 2: the macro CHANNEL MODEL module

Note it is illustrated as a channel model module. Please do not look for a physical

TIMS module when patching up a system with this macro module included. This

macro module is modelled with five real TIMS modules, namely:

1. an INPUT ADDER module.

2. a NOISE GENERATOR module.

3. a bandlimiting module. For example, it could be:

a. any single filter module; such as a TUNEABLE LPF (for a baseband

channel).



b. a BASEBAND CHANNEL FILTERS module, in which case it contains

three filters, as well as a direct through connection. Any of these four

paths may be selected by a front panel switch. Each path has a gain of

unity. This module can be used in a baseband channel. The filters all

have the same slot bandwidth (40 dB at 4 kHz), but differing passband

widths and phase characteristics.

c. a 100 kHz CHANNEL FILTERS module, in which case it contains two

filters, as well as a direct through connection. Any of these three paths

may be selected by a front panel switch. Each path has a gain of unity.

This module can be used in a bandpass channel.

Definition of filter terms, and details of each filter module characteristic,

are described in Appendix A to this text.

4. an OUTPUT ADDER module, not shown in Figure 1, to compensate for any

accumulated DC offsets, or to match the DECISION MAKER module

threshold.

5. a source of DC, from the VARIABLE DC module. This is a fixed module,

so does not require a slot in the system frame.

Thus the CHANNEL MODEL is built according to the patching diagram illustrated

in Figure 3 below, and (noting item 5 above) requires four slots in a system unit.

INPUT andnoise level

adjust

ANYFILTERMODULE

IN

OUTIN

OUTPUT and

adjustDC threshold

Figure 3: details of the macro CHANNEL MODEL module

channel gainchannel gainchannel gainchannel gain

Typically, in a TIMS model, the gain through the channel would be set to unity.

This requires that the upper gain control, ‘G’, of both ADDER modules, be set to

unity. Both the BASEBAND CHANNEL FILTER module and the 100 kHz

CHANNEL FILTER module have fixed gains of unity. If the TUNEABLE LPF is

used, then its adjustable gain must also be set to about unity.

However, in particular instances, these gains may be set otherwise.

noise levelnoise levelnoise levelnoise level

The noise level is adjusted by both the lower gain control ‘g’ of the INPUT ADDER,

and the front panel calibrated attenuator of the NOISE GENERATOR module.

Typically the gain would be set to zero [g fully anti-clockwise] until noise is

required. Then the general noise level is set by g, and changes of precise

magnitude introduced by the calibrated attenuator.


Theory often suggests to us the means of making small improvements to SNR in a

particular system. Although small, they can be of value, especially when combined

with other small improvements implemented elsewhere. An improvement of 6 dB

in received SNR can mean a doubling of the range for reception from a satellite, for

example.

revisionrevisionrevisionrevision

You should look now at the Tutorial Questions, as important preparation for the

experiment.


filter filter filter filter amplitude responseamplitude responseamplitude responseamplitude response

These days even the most modest laboratory is equipped with computer controlled

apparatus which makes the measurement of a filter response in a few seconds, and

provides the output result in great detail. At the very least this is in the form of

amplitude, phase, and group delay responses in both soft and hard copy.

It is instructive, however, to make at least one such measurement using what might

be called ‘first principles’. In this experiment you will make a measurement of the

amplitude-versus-frequency response of one of the BASEBAND CHANNEL

FILTERS.

A typical measurement arrangement is illustrated in Figure 4 below.

Figure 4: measurement of filter amplitude response

In the arrangement of Figure 4:

• the audio oscillator provides the input to the filter, at the TIMS ANALOG

REFERENCE LEVEL, and over a frequency range suitable for the filter being

measured.

• the BUFFER allows fine adjustment of the signal amplitude into the filter. It is

always convenient to make the measurement with a constant amplitude signal



at the input to the device being measured. The TIMS AUDIO OSCILLATOR

output amplitude is reasonably constant as the frequency changes, but should

be monitored in this sort of measurement situation.

• the filter can be selected from the three in the module by the front panel switch

(positions #2, #3, and #4). Each has a gain in the passband of around unity.

Remember there is a ‘straight through’ path - switch position #1.

• the WIDEBAND TRUE RMS METER will measure the amplitude of the

output voltage

• the FREQUENCY COUNTER will indicate the frequency of measurement

• the OSCILLOSCOPE will monitor the output waveform. With TIMS there is

unlikely to be any overloading of the filter if analog signals remain below the

TIMS ANALOG REFERENCE LEVEL; but it is always a good idea in a less

controlled situation to keep a constant check that the analog system is

operating in a linear manner - not to big and not too small an input signal.

This is not immediately obvious by looking at the WIDEBAND TRUE RMS

METER reading alone (see Tutorial Q2). Note that the oscilloscope is

externally triggered from the constant amplitude source of the input signal.

The measuring procedure is:

T1 decide upon a frequency range, and the approximate frequency increments to

be made over this range. A preliminary sweep is useful. It could

locate the corner frequency, and the frequency increments you choose

near the corner (where the amplitude-frequency change is fastest)

could be closer together.

T2 set the AUDIO OSCILLATOR frequency to the low end of the sweep range.

Set the filter input voltage to a convenient value using the BUFFER

AMPLIFIER. A round figure is often chosen to make subsequent

calculations easier - say 1 volt rms. Note that the input voltage can

be read, without the need to change patching leads, by switching the

front panel switch on the BASEBAND CHANNEL FILTERS module to

the straight-through condition - position #1. Record the chosen input

voltage amplitude.

T3 switch back to the chosen filter, and record the output voltage amplitude and

the frequency

T4 tune to the next frequency. Check that the input amplitude has remained

constant; adjust, if necessary, with the BUFFER AMPLIFIER.

Record the output voltage amplitude and the measurement frequency.

T5 repeat the previous Task until the full frequency range has been covered.

The measurements have been recorded. The next step is usually to display them

graphically. This you might like to do using your favourite software graphics

package. But it is also instructive - at least once in your career - to make a plot by

hand, since, instead of some software deciding upon the axis ranges, you will need

to make this decision yourself !


Conventional engineering practice is to plot amplitude in decibels on a linear scale,

and to use a logarithmic frequency scale. Why ? See Tutorial Question Q1.

A decibel amplitude scale requires that a reference voltage be chosen. This will be

your recorded input voltage. Since the response curve is shown as a ratio, there is

no way of telling what this voltage was from most response plots, so it is good

practice to note it somewhere on the graph.

T6 make a graph of your results. Choose your scales wisely. Compare with the

theoretical response (in Appendix A).

signal to noise ratiosignal to noise ratiosignal to noise ratiosignal to noise ratio

This next part of the experiment will introduce you to some of the problems and

techniques of signal-to-noise ratio measurements.

The maximum output amplitude available from the NOISE GENERATOR is about

the TIMS ANALOG REFERENCE LEVEL when measured over a wide bandwidth

- that is, wide in the TIMS environment, or say about 1 MHz. This means that, as

soon as the noise is bandlimited, as it will be in this experiment, the rms value will

drop significantly 1.

You will measure both N

S, (ie, SNR) and

( )S N

N

+

, and compare calculations of

one from a measurement of the other.

The uncalibrated gain control of the ADDER is used for the adjustment of noise

level to give a specific SNR. The TIMS NOISE GENERATOR module has a

calibrated attenuator which allows the noise level to be changed in small calibrated

steps.

Within the test set up you will use the macro CHANNEL MODEL module already

defined. It is shown embedded in the test setup in Figure 5 below.

ext. trig.

Figure 5: measurement of signal-to-noise ratio

As in the filter response measurement, the oscilloscope is not essential, but

certainly good practice, in an analog environment. It is used to monitor

waveforms, as a check that overload is not occurring.

The oscilloscope display will also give you an appreciation of what signals look like

with random noise added.

1 to overcome the problem the noise could first be bandlimited, then amplified



T7 set up the arrangement of Figure 5 above. Use the channel model of

Figure 3. In this experiment use a BASEBAND CHANNEL FILTERS

module (select, say, filter #3).

You are now going to set up independent levels of signal and noise, as recorded by

the WIDEBAND TRUE RMS METER., and then predict the meter reading when

they are present together. After bandlimiting there will be only a small rms noise

voltage available, so this will be set up first.

T8 reduce to zero the amplitude of the sinusoidal signal into the channel, using

the ‘G’ gain control of the INPUT ADDER.

T9 set the front panel attenuator of the NOISE GENERATOR to maximum

output.

T10 adjust the gain control ‘g’ of the INPUT ADDER to maximum. Adjust the ‘G’

control of the OUTPUT ADDER for about 1 volt rms. Record the

reading. The level of signal into the BASEBAND CHANNEL

FILTERS module may exceed the TIMS ANALOG REFERENCE

LEVEL, and be close to overloading it - but we need as much noise

out as possible. If you suspect overloading, then reduce the noise

2 dB with the attenuator, and check that the expected change is

reflected by the rms meter reading. If not, use the INPUT ADDER to

reduce the level a little, and check again.

Before commencing the experiment proper have a look at the noise alone; first

wideband, then filtered.

T11 switch the BASEBAND CHANNEL FILTERS module to the straight-through

connection - switch position #1. Look at the noise on the oscilloscope.

T12 switch the BASEBAND CHANNEL FILTERS module to any or all of the

lowpass characteristics. Look at the noise on the oscilloscope.

Probably you saw what you expected when the channel was not bandlimiting the

noise - an approximation to wideband white noise.

But when the noise was severely bandlimited there is quite a large change. For

example:

a. the amplitude dropped significantly. Knowing the filter bandwidth you could

make an estimate of the noise bandwidth before bandlimiting ?

b. the appearance of the noise in the time domain changed quite significantly.

You might like to repeat the last two tasks, using different sweep speeds, and

having a closer look at the noise under these two different conditions.

Record your observations. When satisfied:


T13 reduce to zero the amplitude of the noise into the channel by removing its

patch cord from the INPUT ADDER, thus not disturbing the ADDER

adjustment.

T14 set the AUDIO OSCILLATOR to any convenient frequency within the

passband of the channel. Adjust the gain ‘G’ of the INPUT ADDER

until the WIDEBAND TRUE RMS METER reads the same value as it

did earlier for the noise level.

T15 turn to your note book, and calculate what the WIDEBAND TRUE RMS

METER will read when the noise is reconnected.

T16 replace the noise patch cord into the INPUT ADDER. Record what the meter

reads.

T17 calculate and record the signal-to-noise ratio in dB.

T18 measure the signal-plus-noise, then the noise alone, and calculate the SNR

in dB. Compare with the result of the previous Task.

T19 increase the signal level, thus changing the SNR. Measure both N

S , and

( )S N

N

+

, and predict each from the measurement of the other. Repeat

for different SNR.

speechspeechspeechspeech----plusplusplusplus----noisenoisenoisenoise

It is interesting to listen to speech corrupted by noise. You will be able to obtain a

qualitative idea of various levels of signal-to-noise ratios.

T20 obtain speech either from TRUNKS or a SPEECH MODULE. Listen to it

using the HEADPHONE AMPLIFIER alone. Switch the in-built LPF

in and out and observe any change of the speech quality. Comment.

The filter has a cut-off of 3 kHz - confirm this by measurement.

T21 pass the speech through the macro CHANNEL MODEL module, using the

BASEBAND CHANNEL FILTERS module as the band limiter. Add

noise and observe, qualitatively, the sound of different levels of

signal-to-noise ratio.

T22 what can you say about the intelligibility of the speech when corrupted by

noise ? If you are using bandlimited speech, but wideband noise, you

can make observations about the effect upon intelligibility of

restricting the noise to the same bandwidth as the speech. Do this,

and report your conclusions.

Emona tims-analog-communication-part1 2

Technology

Transcript of Emona tims-analog-communication-part1 2