Analog communication

mixers

cont’d

Learning Objectives• Definition of mixiture• Brief history about the mixer;• Understand operating principles of the mixer• • What makes a good mixer?• modulators• • single/double balance mixers;• Image rejection• Basics of mixer• The circuit of mixer• • Review some mixer design examples

History

• The first mixer with electric motor is thought to be the one invented by American Rufus Eastman in 1885. U.S. Patent 330,829 The Hobart Manufacturing Company was an early manufacturer of large commercial mixers, and they say a new model introduced in 1914 played a key role in the mixer part of their business.

• The Hobart Kitchen Aid and SunbeamMixmaster (first produced 1910) were two very early US brands of electric mixer.

Cont’d

• Domestic electric mixers were rarely used before the 1920s, when they were adopted more widely for home use.

• Older models of mixers originally listed each speed by name of operation (ex: Beat-Whip would be high speed if it is a 3-speed mixer); they are now listed by number.

mixers

• Mixers (sometimes known asfrequency converters), modulators,balanced modulators and other circuitblocks are considered below. Eachworks on the same basic principles.

How a Mixer Works

• A mixer circuit normally has twoinputs - from two separate signalsources. In the diagram below, thesources are two oscillators.

• Each oscillator is a generator producing asine wave output, one at frequency f1 and the other at frequency f2. The mixer multiplies the signals together

• The mixer multiplies the signalstogether. You don't need to know thedetails. Just remember that the outputcomprises a complex mixture of separate sinewaves at many different frequencies. The major output frequencies are shown on the diagram.

Cont’d

Figure 1

oscillator1

mixer

oscillator2

Made up ofSignal f1Signal f2

Signal1(f1+f2)Signal1 (f1-f2)And others

Input signal f2

Input signal f1

Cont’d

• The main point to note is that the output comprises the two separate input frequencies f 1 and f 2 and their sum, (f 1 + f2),

• and their difference, (f 1 - f2).

• In practice, there are other component signals too - but we can ignore those.

• A filter - which can be any one of various sorts - selects the required output from the mixer. In this diagram,

Cont’d

• a simple parallel tuned circuit is shown.

• The output will normally be tuned to the SUM, (f 1 + f2),

or tuned to the DIFFERENCE, (f 1 - f2),

a signal required trigonometrically can illustrate what happens. Note this multiplication:

2 sinA cosB = sin (A + B) + sin (A - B) ]

Cont’d

• Substituting numerical values andusing typical examples for the twoinput frequencies in the diagram canillustrate the effect: Consider Oscillator 1 to generate a 9MHz signal and Oscillator 2 to generate a 5 MHz signal.

Cont’d

• . The output from amixer will contain these two signals, plus their sum, 14 MHz, and the difference, 4 MHz The mixer output tuned circuit could be tuned to 14 MHzif that output was required, or tunedto 4 MHz, should that output berequired

Cont’d

• . The output from a mixer containsmany more combinations offrequencies - generated from theharmonics of the input signals mixingwith the component signals.

• For purposes of this amateur radio examination these can be ignored.

• An alternative name for a mixer isfrequency converter.

What Makes a Mixer?

• Almost any electronic device, diode,transistor, valve, can be used as a mixer.

• A square-law characteristicdevice is preferred - to minimise unwanted outputs. Refer to a radiotext-book for circuits using a single diode, several diodes, transistors – of all kinds -. You need to know the principles.

Cont’d

• The principle is: In a mixer stage, the output contains the SUM and theDIFFERENCE of the input signal frequencies.

Modulators

• A modulator to produce an amplitude modulated signal is generally nothing more than a mixer.In the following example, the radiofrequency carrier signal ( shown as fc ) forms one input, and a band of audiofrequencies ( the incoming speech -shown as fa ), is the other input.

• The audio signal fa does not appear in the output because of the filter action of the modulator output circuits.

RF

Oscillator

Speech amplifier

Modulator

mixer

( fc + fa )

( fc - fa )

fc

Amplitude modulatedAudio signal

microphone

Audio signal fa

Carrier Fc

Cont’d

• So the output from an amplitudemodulator is a band of frequenciesabove and below the carrierfrequency plus the carrier frequency itself. The signal fc is known as the carrierfrequency. The signal at (f c + fa) is the upper side frequency.

• The signal at (f c - fa) is the lower side frequency.

Cont’d

• To get the feel of the modulation principle,

• try this numerical example:

• A signal at 3.60 MHz is amplitude-

modulated with a 1 kHz tone. What are

the output frequencies from this

modulator?

Cont’d

Solution

Given thatFC=3600KHZUSB F ?LSB F ?

USB F= 3600KHZ+1KHZ3061KHZ

LSB F= 3600KHZ- 1KHZ3599KHZ

The Balanced Modulator

Using clever circuitry, it is possible to

arrange a modulator in which one of

the input signals does not appear in

the output. Sometimes both of the

input signals may be balanced out

(suppressed), so that only the products of the

modulation process will appear in the output.

Cont’d

For example, in the modulator

example given above,

we saw that the output comprised

the carrier frequency fc,

the sum, (fc + fa),

and the difference, (fc - fa).

RF

OSCULATOR

Speech

amplifier

Balanced

modulator

(fc +fa)

(fc -fa)

Audio signal fa double sided band output

signalandOutput

al

Carrier fc

microphone

(fc +fa)

(fc -fa)

Cont’d

• With a balanced modulator, only the sum (f c + fa), and the difference (fc - fa), components appear at the output.

• The carrier signal fc has been cleverly cancelled and does not appear at the output. So the output from a balanced modulator comprises two side

• frequencies only - at (f c + fa) and at (f c - fa).

• The carrier at f c has been removed

Cont’d

• This modulator use a ring of diodes

(a ring modulator).

Note the symmetrical form of the circuit.

The oscillator is fed to a centre-tap point across a tuned circuit. The pre-set controls C (a trimmercapacitor), and P (a potentiometer),are used to balance out the carrier (theoscillator signal) appearing at theoutput.

Cont’d

• The output signal is a double-sideband signal - i.e. upper sidebandand lower sideband with no carrier.

• The carrier (oscillator signal) Has been suppressed

Basics of Mixers

figure about mixer

X(t)Y(t)

SLO(t)=Acosω0t

equation

• Y(ω)= [X(ω-ω0)+ X[(ω+ω0)

Up convertedcomponent

component

Down convertedcomponent

Single-ended mixer

RF AMP MIxer

Local

Oscillator

IF AMPLowpass

filter

fRF

fRF

fLO

fIF

=fRF

-fLO

RF input

MIxer

Local

Oscillator

Bandpass

filterfRFf

IF

fLO

fIF

=fRF

+fLO

IF input

RF AMP

Downconverter

Upconverter

The purpose of mixer is to convert either from one frequency to higher frequency or vice versa. The advantages of conversion are (i) to reduce 1/f noise when convert to lower frequency (ii) for easy tuning for a wide band with fixed IF and (iii) frequency off-set between transmitter and receiver by using a single LO as in Radar.

Simplest Single-ended mixer

•Uses nonlinearity of a diode property•The output generated consist of frequencies spectrum dc component, wr,wo,wr-wo, wr+wo.•For IF, we filter out all frequencies except wr-wo. •For upconverter, we filter out all lower frequencies and allow only wr+wo.

bandpass

filterv

icos(w

r-w

o)tMatching

network

Combiner

DC bias

LO

vocosw

ot

vrcosw

rt w

r , w

o ,

wr+ w

o

RFC

RFC

Double Balanced mixer

180o

hybrid

RF input

LO input

IF

output

Zo

Single -ended mixer produces output consisted of all harmonics. The balanced mixer using hybrid suppresses all even harmonics of the LO. Double balanced mixer suppresses all even harmonics both LO and RF.

Image rejection mixer

3dB

power

divider

RF input

Mixer A

Mixer B

90o hybrid

LO

LSB

USB

IF out

90o hybrid

Zo

The RF with frequency wr= wo + wi will also produce the IF (wi) when mixed with LO. The frequency produced will be USB(wr= wo + wi ) and LSB(wr= wo - wi ) . The undesired frequency either USB or LSB is called image frequency. The mixer can produce one single side band is used as modulator.

Advantages of the ring mixer

• Good carrier rejection

• Good Input rejection

Disadvantages of the ring mixer

• High drive current needed on carrier input

• Harmonic distortion (on carrier input)

• Expensive discrete components

• Needs transformers to work properly

Advantages of the double balanced mixer

• Almost linear on each input

• Great carrier and input rejection

• Low drive signals needed.

• Low harmonic distortion on both inputs

• Well suit to IC manufacture

• No transformers

• Cheap (due to IC process)

The ideal mixer

• The ideal mixer represented by figure 1.

• is a device which multplies two input signals .

• If the input are sinusoids. The ideal mixer output is the sum or difference frequencies given by

• vo=[Acos(ω1t)][Acos(ω 2t)=

• AA/2[cos(ω1- ω2)t+cos(ω1+ ω2)t (1)

• Typically either the sum or the difference frequence is removed with afilter.

The inputs to the ideal mixer

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

2000Hz

2200Hz

The output from the ideal mixer

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

200Hz

4200Hz

and

The Product Detector

This device is just another mixer -used for demodulating a signal in areceiver. The term product refers tothe multiplication of the two inputsignals - with sum and differenceoutputs.

Orthogonality

Two things are orthogonal if changing one doesn’t change the other. In geometry this is a right angle.

For example: Latitude, Longitude and Altitude over sea are orthogonal. Over land they are not.

Sine waves of different frequencies are Orthogonal.

Most other waveforms are not orthogonal.

Orthogonality Example

If you feed sine waves at frequencies F and G into a mixer you get sine waves at frequencies F+G and F-G.

If F=G then you get 2F and DC out

So if you take the DC average of the output you will get zero unless F=G. (Only true for orthogonal waveforms such as sine waves)

So if we use an accurate signal generator for G then the DC value is a measure of the harmonic of F at G

The spectrum analyser

If we vary the frequency of our signal generator G into our mixer then we can measure the strength of the signal F at a range of frequencies. (Just like tuning a radio)

If the signal F that we are measuring is not a pure sine wave then as we tune the generator we will only measure the sine wave component of the signal F at the frequency of our generator G.

So by sweeping G we can measure the spectrum of F

The Fourier transform

Previously we said that when you mix F and G and F=G you will get a DC average. This is only true if F and G are in phase. If F and G are antiphase you get a negative DC value.

However if F and G are 90 degrees apart you will get zero. So you can measure the phase of F by measuring at both 0 and 90 degrees (I and Q).

Note that sine and cosine waves at the same frequency are orthogonal.

A square wave to be Fourier transformed

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer input G to measure the fundamental

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for the fundamental

0.0005 0.001 0.0015 0.002

0.2

0.4

0.6

0.8

1

Note the strong positive DC average

Mixer output for the 2nd harmonic

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Note the average is zero (even harmonic)

Mixer output for the 3nd harmonic

Note the 4 positive peaks 2 negative. Average is 2/6. This is 1/3 of the fundamental signal

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for the 4th harmonic

Note the average is zero (even harmonic)

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for 5nd harmonic

Note the 6 positive peaks 4 negative. Average is 2/10. This is 1/5 of the fundamental signal

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for the 6th harmonic

Note the average is zero (even harmonic)

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for 7nd harmonic

Note the 8 positive peaks 6 negative. Average is 2/14. This is 1/7 of the fundamental signal

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

But what about the cosine components?

So far we have only looked at the sine wave (in phase) components. We should check if there are any Cosine (90 degree phase shifted) components.

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Note the Cosine is symmetric about the centre

Mixer output for the Fundamental Cosine

Note the average is zero (anti-symmetric about centre)

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for the 2nd Harmonic Cosine

Note the average is zero (anti-symmetric about centre)

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Mixer output for the 3rd Harmonic Cosine

Note the average is zero (anti-symmetric about centre)

0.0005 0.001 0.0015 0.002

-1

-0.5

0.5

1

Summary of the components of a Square wave

We have seen that you do get the 1/3, 1/5 1/7 ratios (odd harmonics) we used in the signals talk.

The even Sine harmonics have equal numbers of plus and minus (half wave) peaks so are zero

Odd Sine harmonics all have two more positive peaks than negative out of a total of double their harmonic number. Hence the 1/3, 1/5, 1/7 etc. ratios.

Cosine harmonics are all anti-symmetric and thus zero

end

end