Com1_Lab4

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Communications I

Laboratory #4

By: Prof. Rubn Flores Flores and Prof. Caroline Gonzlez Rivera Rev. 06/02/08

1

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OBJECTIVES

The purpose of this experiment is to show how the frequency-modulated signalsare generated and the importance of it. Also, in this experiment you will be able to see

the modulated signal in the oscilloscope and its power spectrum.

EQUIPMENT LIST

1. Spectrum Analyzer2. Arbitrary waveform generator3. Oscilloscope4. Audio Input Module and Microphone5. 47 resistor6. ANACOM 2 Trainer7. Power supply8. N to BNC connector adapter9. Cables10.Two oscilloscope probes11.HP-VEE

DISCUSSION

Modulation is a process that causes a shift of the range of frequencies in a signal.

It is used to facilitate transmission over a given channel. Baseband signals produced byvarious information sources are not always suitable for direct transmission over a given

channel. These signals are usually further modified to facilitate transmission. Thisconversion process is known as modulation. In this process the baseband signal is used

to modify some parameter of a high frequency carrier signal.

A carrier is a sinusoid of high frequency, and one of the parameters such as

amplitude, frequency or phase is varied in proportion to the baseband signal m(t). In FMmodulation the frequency of the carrier is modify in proportion to the baseband signal. A

baseband signal is used to designate the band of frequencies of the signal delivered bythe source.

Another advantages of modulation are the ease of radiation of electromagneticenergy allowing antenna sizes to be reasonable and simultaneous transmission of several

signals over the same channel.

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Frequency Modulation

Another means of encoding a wave of information is by producing a complex

wave whose frequency is varied in proportion to the instantaneous amplitude of the

information wave. Such an encoding is frequency modulation. The result of thisencoding or modulation process is a complex modulated wave whose instantaneous

frequency is a function of the amplitude of the modulating wave and differs from thefrequency of the carrier from instant to instant as the amplitude of the modulating wave

varies.

The following equation provides the equivalent formula for FM:

))sin(sin()( tMtAtv ifc +=

where

v(t) is the instantaneous voltageA is the peak value of the carrier

c is the carrier angular velocityMfis the modulation index

i is the modulating signal angular velocity

The FM formula is really complex. In figure 1 is the waveform of a FM signal. To solve

for the frequency components of an FM wave requires the use of the Bessel functions.They show that frequency-modulating carrier with a pure sine actually generates an

infinite number of sidebands spaced at multiples of the intelligence frequency, fm, above

and below the carrier. Fortunately, the amplitude of these sidebands approaches a

negligible level the farther away they are from the carrier, which allow FM transmissionwithin finite bandwidths.

Figure 1: FM Signal Representation

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The Bessel functions solution to the FM equation is

[ ]

[ ]

[ ] ....))3cos(())3cos(()(

))2cos(())2cos(()(

))cos(())cos(()()cos()()(

4

3

3

2

2

1

1

0

++

++

+=

44444444 844444444 76

44444444 844444444 76

44444444 844444444 7644 844 76

ttMJ

ttMJ

ttMJtMJtf

icicf

icicf

icicfcfc

where

1 = carrier component2 = component at fiaround the carrier

3 = component at 2fiaround the carrier

4 = component at 3fiaround the carrier

To solve for the amplitude of any side-frequency component,Jn is equal to

+

+

+

+

+

= ...

)!3(!3

)2(

)!2(!2

)2(

)!1(!1

)2(

!

1

2)(

642

n

M

n

M

n

M

n

MnMJ

ffff

fN

In figure 2 is an example of a FM spectrum

Figure 2: FM Spectrum

Center Frequency

The center frequency is that frequency assigned to the carrier, but duringmodulation the carrier is not always present in the complex modulated wave and the

instantaneous frequency of the complex modulated wave varies above and below the

frequency assigned to the carrier. This assigned frequency, then, is the center aboutwhich the instantaneous frequencies of the modulated wave vary.

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Frequency Deviation

In FM the shift in frequency is proportional to the amplitude of the modulating

wave. A weak modulating wave will have a small peak amplitude, which will produce a

small peak frequency variation. A strong modulating wave whose peak amplitude is themaximum that the modulating system is designed to handle will produce the maximum

peak frequency variation. Any of these peak variations from the center frequency iscalled the frequency deviation (fd).

=

min

maxmax

ff

fff

c

c

d

The maximum value of the frequency deviation (fD) is a system constant, and

when it is intended that the modulated wave be radiated, its magnitude is established by

law.

Frequency Swing

The overall extreme of the excursion of instantaneous frequencies from maximumnegative to maximum positive is called the frequency swing. Frequency swing,

therefore, is equal to twice the maximum design frequency deviation. In FM thefrequency swing is a system constant and is usually expressed in terms of the maximumfrequency deviation as fD.

Deviation Ratio

Any modulating system is intended to accommodate some specific band of

modulating frequencies. Therefore the lower limit and especially the upper limit of this

band are of importance in the design of the equipment. The upper frequency is the mostimportant because it determines the maximum bandwidth requirements. In FM, the

highest modulating frequency (fM) is a system constant. The ratio of the maximum

frequency deviation (fD) to the highest modulating frequency (fM) is called the deviationratio (D).

M

D

f

fD =

The deviation ratio is strictly an equipment characteristic and is a quantity used to set the

circuit bandwidth of a modulating system.

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Modulation Index

There is a very important signal characteristic that resembles the deviation ratio

and under certain circumstances is equal to it. It is the ratio,

m

df

ffM =

Notice, however, that fd is any frequency deviation, not necessarily maximum and fm is

any modulating frequency, not necessarily the highest. There are system restrictions that

apply; for example fd cannot exceed fD and fm cannot be greater than fM.

Bandwidth Calculations

Since the sidebands are separated by multiples of the modulating frequency, thefrequency of the highest important sidebands is given by

)1( +fm Mf

The overall bandwidth from the highest to the lowest side frequency whose amplitude is15 % (or greater) of the unmodulated carrier is twice this value. In figure 3 is the

commercial FM bandwidth allocation for two adjacent stations

)(2

12

)1(2

md

m

d

m

m

d

f

fm

ffBW

f

f

fBW

f

fM

MfBW

+=

+=

=

+=

Figure 3: Commercial FM bandwidth allocation for two adjacent stations

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FM Generation Circuit (Reactance Modulator)

The reactance modulator is a very popular means of FM generation and is shown

in figure 4. The reactance modulator is an amplifier designed so that its input impedance

has a reactance that varies as a function of the amplitude of the applied input voltage-

modulating signal).

Figure 4: FM Reactance Modulator

PROCEDURE

1. Connect the power supply to the trainer with all equipment turned off. Follow thefollowing diagram.

2. Select the following conditions in the trainera. Mixer/Amplifier Amplitude dial : Maximum clockwise directionb. VCO switch (PLL detector block): OFF positionc. Modulation switch : Reactance

3. Turn on the power supply. Connect the oscilloscope to test point 1. Turn AudioOscillator amplitude dial to the maximum position. Using the oscilloscope adjust

+12 V

0V

-12 V

+12 V

0V

-12 V

Power Supply ANACOM 2

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the Audio Oscillator frequency to 2 kHz (fm = 2 kHz). This signal is themodulating signal.

4. Using a cable jumper, connect the Audio Oscillator output to the ModulatorCircuits audio input.

5. The output of the Reactance modulator can be measured in test point 13, but toavoid the capacitive effect of the probe, connect the oscilloscopes probe to testpoint 34. The input impedance of the mixer/amplifier block is high enough to get

a good measurement.

6. Turn the REACTANCE MODULATOR CARRIER FREQUENCY dial to themiddle position.

7. Turn the Audio Oscillator amplitude dial to the minimum position.8.

Connect the oscilloscope to test point 34 and measure the frequency, peak to peakvoltage and average voltage of the carrier. Record in table 1.

9. Disconnect the oscilloscope and connect the universal (frequency) counter to testpoint 34 to measure the carrier frequency. Start changing the modulating signalamplitude and determine the maximum and minimum frequency measured in the

frequency counter. Whats the frequency deviation (fd)? Did you see a significant

change in the carrier frequency? Whats the signal bandwidth? Record in table 2.

10. Disconnect the frequency counter and connect the spectrum analyzer to test point34. Set the spectrum analyzer center frequency with the frequency determined in

step 8 and span of 20 kHz. Start changing the modulating signal amplitude andsee what happen with the FM spectrum. Print out the frequency spectrum with a)

Audio Oscillator amplitude dial in the minimum position, b) middle position and

c) maximum position. What happen with the frequency spectrum?

11. Turn the power off and disconnect the Audio Oscillator from the modulator, thenconnect the microphone Audio Input Modules output to the Audio Input socket inthe Modulator Circuits block. Turn the power on and connect the oscilloscope to

test point 34 and start talking into the microphone. See how your frequency

modulated voice looks like, then connect the spectrum analyzer at the same point.

Examine the signal spectrum.

12. Connect the waveform generator to the 50 as illustrated in the diagram.

Output

Waveform

Generator

Circuit

Board

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13. Run HP-VEE program in the computer and call up the function generator control

panel from the I/O instruments menu. Set the following parameters in the

instrument using HP-VEE.

Main Panel:

Function: SinusoidFreq: 15 kHz

Amplitude: 5 Vp-p

Load: 50 Modulation Pan:

Frequency Panel

Function: SinusoidFreq: 1 Hz

Deviation: 5 kHz

FM State: ON

14.

Connect the oscilloscope probe in parallel with the resistance. Measure themaximum and minimum frequency, deviation factor and modulation index.Whats the signal bandwidth? Record in table 3.

15. Disconnect the oscilloscope and connect the spectrum analyzer. Set centerfrequency to 15 kHz and span of 20 kHz. Whats the signal bandwidth? What didyou see?

________________=BW

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RESULTS

Table 1: Carrier Frequency

Carrier Signal

fc

Vp-p

Vavg

Table 2: Modulated Signal (Part 1)

Modulated Signal

fmax

fmin

fdMf

BW

Table 3: Modulated Signal (Part 2)

Modulated Signal

fmax

fmin

fd

MfBW

QUESTIONS

1. Which of the two cases require a greater bandwidth? Why?2. Which system provides a greater voice quality at the receiver end? Why?3. Explain how the frequency-modulated signals are generated.4. Which system the AM or FM provides better noise immunity? Why?5. Explain the relationship between bandwidth and voice quality.

Com1_Lab4

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