Feedback Communications Systems boards Student Manual

8/11/2019 Feedback Communications Systems boards Student Manual

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T

eknikitAnalogu

eCommunication-Student'sW

orkbook

5

3-001S


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Teknikit

Analogue Communications

Students Workbook

53-001S

Feedback

Feedback Instruments Ltd, Park Road, Crowborough, E. Sussex, TN6 2QR, UK.Telephone: +44 (0) 1892 653322, Fax: +44 (0) 1892 663719.

email: [email protected] website: http://www.fbk.com

Manual: 53-001S Ed03 072003 Printed in England by Fl Ltd, CrowboroughFeedback Part No. 116053001S


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Notes


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ANALOGUE COMMUNICATIONS -STUDENTS WORKBOOK Preface

53-001S i

THE HEALTH AND SAFETY AT WORK ACT 1974

We are required under the Health and Safety at Work Act 1974, to make available to users of this equipment certain informationregarding its safe use.+

The equipment, when used in normal or prescribed applications within the parameters set for its mechanical and electrical performance,should not cause any danger or hazard to health or safety if normal engineering practices are observed and they are used inaccordance with the instructions supplied.

If, in specific cases, circumstances exist in which a potential hazard may be brought about by careless or improper use, these will bepointed out and the necessary precautions emphasised.

While we provide the fullest possible user information relating to the proper use of this equipment, if there is any doubt whatsoeverabout any aspect, the user should contact the Product Safety Officer at Feedback Instruments Limited, Crowborough.

This equipment should not be used by inexperienced users unless they are under supervision.

We are required by European Directives to indicate on our equipment panels certain areas and warnings that require attention by theuser. These have been indicated in the specified way by yellow labels with black printing, the meaning of any labels that may be fixed tothe instrument are shown below:

CAUTION -RISK OFDANGER

CAUTION -RISK OF

ELECTRIC SHOCK

CAUTION -ELECTROSTATIC

SENSITIVE DEVICE

Refer to accompanying documents

PRODUCT IMPROVEMENTS

We maintain a policy of continuous product improvement by incorporating the latest developments and components into our equipment,even up to the time of dispatch.

All major changes are incorporated into up-dated editions of our manuals and this manual was believed to be correct at the time ofprinting. However, some product changes which do not affect the instructional capability of the equipment, may not be included until it isnecessary to incorporate other significant changes.

COMPONENT REPLACEMENT

Where components are of a Safety Critical nature, i.e. all components involved with the supply or carrying of voltages at supplypotential or higher, these must be replaced with components of equal international safety approval in order to maintain full equipmentsafety.

In order to maintain compliance with international directives, all replacement components should be identical to those originallysupplied.

Any component may be ordered direct from Feedback or its agents by quoting the following information:

1. Equipment type

3. Component reference

2. Component value

4. Equipment serial number

Components can often be replaced by alternatives available locally, however we cannot therefore guarantee continued performance

either to published specification or compliance with international standards.


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ANALOGUE COMMUNICATIONS -STUDENTS WORKBOOK Preface

ii 53-001S

DECLARATION CONCERNING ELECTROMAGNETIC COMPATIBILITY

Should this equipment be used outside the classroom, laboratory study area or similar such place for which it is designed and sold thenFeedback Instruments Ltd hereby states that conformity with the protection requirements of the European Community ElectromagneticCompatibility Directive (89/336/EEC) may be invalidated and could lead to prosecution.

This equipment, when operated in accordance with the supplied documentation, does not cause electromagnetic disturbance outside itsimmediate electromagnetic environment.

COPYRIGHT NOTICE

Feedback Instruments Limited

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by anymeans, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Feedback Instruments Limited.

ACKNOWLEDGEMENTS

Feedback Instruments Ltd acknowledge all trademarks.

IBM, IBM - PC are registered trademarks of International Business Machines.

MICROSOFT, WINDOWS 2000, WINDOWS 98, WINDOWS 95, WINDOWS 3.1 are registered trademarks of Microsoft Corporation.


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ANALOGUE COMMUNICATIONS -STUDENTS WORKBOOK Contents

53-001S TOC-1

TABLE OF CONTENTS

1 Introduction 1-1

2 Assignments using the Amplitude Modulation Workboard 2-1

2.1 Amplitude Modulation with Full Carrier Assignment 2-1

2.1.1 Objectives 2-1

2.1.2 Practicals 2-1

2.1.3 Workboard Required 2-1

2.1.4 Theory 2-2

2.1.5 Practical 1: A Simple Amplitude Modulator 2-5

2.1.6 Practical 2: Envelope Detectors 2-9

2.1.7 Practical 3: Product Detection 2-12

2.2 Amplitude Modulation with No Carrier Assignment 2-15




2.2.4 Theory 2-16

2.2.5 Practical 1: Double Sideband Suppressed Carrier 2-19

2.2.6 Practical 2: Generation of Single Sideband Suppressed Carrier (SSB) 2-22

2.2.7 Practical 3: Demodulation of SSB 2-25

3 Assignments using the Frequency Modulation Workboard 3-1

3.1 Generation of Frequency Modulation Assignment 3-1




3.1.4 Theory 3-2

3.1.5 Practical 1: Concepts Of Frequency Modulation 3-5


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TOC-2 53-001S

3.1.6 Practical 2: Generation of FM with a VCO 3-9

3.1.7 Practical 3: Spectrum of an FM signal with a large Modulation Index 3-11

3.2 Demodulation of Frequency Modulated Signals Assignment 3-13




3.2.4 Theory 3-14

3.2.5 Practical 1: Quadrature Detector 3-16

3.2.6 Practical 2: Phase lock loop detector (PLL) 3-20

3.3 Limiters and the Effect of Noise on FM Demodulation Assignment 3-25




3.3.4 Theory 3-26

3.3.5 Practical 1: A Quadrature Detector with Limiter 3-29

3.3.6 Practical 2: The Effect of Noise on a Quadrature Detector 3-32

3.3.7 Practical 3: PLL Detector with a Limiter 3-35

3.3.8 Practical 4: The Effect of Noise on a PLL Detector 3-37

4 Assignments using the Signal Sources Workboard 4-1

4.1 Wien Bridge Oscillator Assignment 4-1




4.1.4 Theory 4-2

4.1.5 Practical 1: Basic Wien Bridge Oscillator 4-5

4.1.6 Practical 2: Amplitude Stabilisation 4-8

4.1.7 Practical 3: Changes from Standard 4-11

4.2 L-C Oscillator Assignment 4-134.2.1 Objectives 4-13


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53-001S TOC-3



4.2.4 Theory 4-14

4.2.5 Practical 1: Tuned-Collector Oscillator 4-17

4.2.6 Practical 2: Effect of Supply Variations 4-20

4.3 Crystal Oscillator Assignment 4-22




4.3.4 Theory 4-23

4.3.5 Practical 1: Fundamental and Overtone Modes 4-27

4.4 Multivibrator Assignment 4-30



4.4.3 Workboard Required 4-304.4.4 Theory 4-31

4.4.5 Practical 1: Basic Circuit 4-35

4.4.6 Questions 4-38

4.4.7 Practical 2: Effect of Variable Supply 4-39

4.4.8 Practical 3: Mark/space Ratio Control 4-41

5 Assignments using the Tuned Circuits and Filters Workboard 5-1

5.1 Audio Low-Pass Filters Assignment 5-1




5.1.4 Theory 5-2

5.1.5 Practical 1: Passive Low-Pass Filter 5-9

5.1.6 Practical 2: Passive Low-Pass Filter, Swept Frequency 5-12

5.1.7 Practical 3: Active Low-Pass Filter 5-14

5.1.8 Practical 4: Active Low-Pass Filter, Swept Frequency 5-17


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TOC-4 53-001S

5.2 RF Selectivity Assignment 5-19




5.2.4 Theory 5-20

5.2.5 Practical 1: L/C Tuned Circuit 5-24

5.2.6 Practical 2: L/C Tuned Circuit, Swept Frequency 5-26

5.2.7 Practical 3: L/C Tuned Circuit, Transient Response 5-28

5.2.8 Practical 4: Crystal Filter 5-31

5.2.9 Practical 5: Crystal Filter, Swept Frequency 5-33

5.3 RF Band-Pass Filters Assignment 5-35




5.3.4 Theory 5-36

5.3.5 Practical 1: Coupled L/C Circuits 5-42

5.3.6 Practical 2: Coupled L/C Circuits, Swept Frequency 5-45

5.3.7 Practical 3: Ceramic Filter 5-48

5.3.8 Practical 4: Ceramic Filter, Swept Frequency 5-50

5.4 Tuned Amplifier with Gain Control Assignment 5-52




5.4.4 Theory 5-53

5.4.5 Practical 1: Gain Control 5-55

5.4.6 Practical 2: Automatic Gain Control 5-58

5.4.7 Practical 3: Frequency Response with Automatic Gain Control 5-61

5.4.8 Practical 4: Decibel Gain 5-63


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Chapter 1ANALOGUE COMMUNICATIONS -STUDENTS WORKBOOK Introduction

53-001S 1-1

1 Introduction

This manual provides computer-based assignments which make use of AnalogueWorkboards, theDiscovery IIenvironment and Analogue Telecommunications 53-921software package to provide an understanding of the fundamental principles on whichcomplex analogue communication systems are based.

Assignments are divided into practicals whose objectives are clearly defined. Every

practical is designed to contain as much circuit investigation, measurement andobservation as possible. Explanatory text, diagrams and instrumentation are fullyintegrated.

Details of hardware and software installation are given in manual 53-001-3 together withDiscovery IIenvironment and product operating instructions.


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Chapter 1ANALOGUE COMMUNICATIONS -STUDENTS WORKBOOK Introduction

1-2 53-001S

Notes


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Chapter 2ANALOGUE COMMUNICATIONS - Assignments using theSTUDENTS WORKBOOK Amplitude Modulation Workboard

53-001S 2-1

2 Assignments using the Amplitude Modulation Workboard

2.1 Amplitude Modulation with Full Carrier Assignment

2.1.1 Objectives

On completion of this assignment you will be familiar with:

Basic amplitude modulation and demodulation,

AM characteristics in the time domain,

AM characteristics in the frequency domain,

Envelope detectors,

Product detectors.

2.1.2 Practicals

Practical exercises are provided as follows:

Practical 1: A simple amplitude modulator

Practical 2: Envelope detectors

Practical 3: Product detection

2.1.3 Workboard Required

Amplitude Modulation Workboard 53-130 which comprises the following blocks:

Signal Generation

Modulation

Filters

Demodulation


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2-2 53-001S

2.1.4 Theory

2.1.4.1 Modulation

The equation of a sinusoidal voltage waveform is given by:

v = Vmax.sin(t+)

where:

v is the instantaneous voltage

Vmaxis the maximum voltage amplitude

is the angular frequency

is the phase

A steady voltage corresponding to the above equation conveys little information.

To convey information the waveform must be made to vary so that the variationsrepresent the information. This process is called modulation.

Any of these may be varied to convey information.

2.1.4.2 Amplitude Modulation

Amplitude modulation uses variations in amplitude (Vmax) to convey information. The wavewhose amplitude is being varied is called the carrier wave. The signal doing the variationis called the modulating signal.

For simplicity, suppose both carrier wave and modulating signal are sinusoidal; ie,

vc= Vcsin ct (cdenotes carrier)

and

vm= Vmsin mt (mdenotes modulation)

We want the modulating signal to vary the carrier amplitude, Vc, so that:

vc= (Vc+ Vmsin mt).sin ct

where (Vc+ Vmsin mt) is the new, varying carrier amplitude.


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53-001S 2-3

Expanding this equation gives:

vc= Vcsin ct + Vmsin ct. sin mt

which may be rewritten as:

vc= Vc[sin ct + m sin ct. sin mt]

where m = Vm/Vcand is called themodulation index.

Now:

sin ct.sin mt = (1/2) [cos(c - m) t - cos(c+ m) t]

so, from the previous equation:

vc = Vc[sin ct + m sin ct. sin mt]

we can express vcas:

vc= Vc sin ct + (mVc/2) [cos(c- m)t] - (mVc/2) [cos(c + m)t]

This expression for vchas three terms:

1. The original carrier waveform, at frequency c, containing no variations and thuscarrying no information.

2. A component at frequency (c- m)whose amplitude is proportional to themodulation index. This is called the Lower Side Frequency.

3. A component at frequency (c+ m)whose amplitude is proportional to themodulation index. This is called the Upper Side Frequency.

It is the upper and lower side frequencies which carry the information. This is shown bythe fact that only their terms include the modulation index m. Because of this, theamplitudes of the side frequencies vary in proportion to that of the modulation signal.

2.1.4.3 Sidebands

If the modulating signal is a more complex waveform, for instance an audio voltage from aspeech amplifier, there will be many side frequencies present in the total waveform.

This gives rise to components 2 and 3 in the last equation being bands of frequencies,known as sidebands.

Hence we have the upper sideband and the lower sideband, together with the carrier.


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2-4 53-001S

2.1.4.4 Experimental Determination of the Modulation Index

This is most easily done by measuring the maximum and minimum values which theinstantaneous amplitude of the carrier reaches. Let us call these xand y.

Taking our previous equation:

vc= Vc[sin ct + m sin ct. sin mt]

and re-arranging it yet again, we can express vcas:

vc= Vcsin ct [1 + m sin mt]

so that the instantaneous amplitude of the carrier is:

Vc[1 + m sin mt]

Since sin wmt can vary between +1 and -1,

x = Vc(1 + m) and y = Vc(1 - m)

To get the value of modulation index m from x and y, we eliminate V cbetween theseequations by division, giving:

y /x = (1 - m)/(1 + m).

Solving for mgives:

m = (x - y)/(x + y)


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53-001S 2-5

2.1.5 Practical 1: A Simple Amplitude Modulator

This practical introduces the concept of Amplitude Modulation.

You will meet the terms Carrier, Modulation and Modulated Signal and how they arerelated in both the time domain and frequency domain.

A simple form of information transfer is Morse code, where the signal at the frequencyselected for transmission is switched off and on in dots and dashes. The transmissionfrequency is selected by consideration of the transmission medium and, within reason,

has nothing to do with the information it has to carry. For this reason it is called the carrierfrequency.

In order to carry any information some characteristic of the carrier must be changed, ormodulated with that information; hence the term modulating signal. In the Morse codeexample where the carrier is switched off and on, it is the amplitude of the carrier that iscarrying the information.

This is a very crude form of Amplitude Modulation(or AM) because there are only twostates: zero amplitude and full amplitude. In order to carry more complex information suchas speech or television, the amplitude is varied linearly so that the instantaneous carrier

amplitude is proportional to the amplitude of the modulation signal.

Clearly, for a given carrier amplitude there are limits for the size of the modulating signal;the minimum must give zero carrier, the maximum gives twice the unmodulated carrieramplitude. If these limits are exceeded, the modulated signal cannot be recovered withoutdistortion and the carrier is said to be overmodulated.

When the modulating signal is varying the carrier from zero to twice its amplitude, thecarrier is said to be fully, or 100%, modulated. Modulation depth is calculated from theformula:

(x -y) / (x + y)

where xis the maximum instantaneous carrier amplitude and y the minimum. Theresulting fraction is often expressed as a percentage. If the fraction exceeds 1(modulation depth greater than 100%), then the carrier is said to be over-modulated.

2.1.5.1 Amplitude Modulation in the Time Domain

One of the easiest methods of examining a signal is by using the oscilloscope. This is inthe time domain.

The amplitude variation of the carrier in time with the modulation can be seen easily andthe operation of a system analysed.


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2-6 53-001S

In the practicals we use a sine wave as the modulation source as this makes theoscilloscope pattern clearest, in a practical system the modulating signal could be verycomplex. Also, to make the principles clearer, the modulating frequency is one ninth of thecarrier so that individual carrier cycles show.

Again, in a practical system, the modulating frequency would probably be lower. In orderfor the oscilloscope trace to be stable it must be triggered from the modulation source.

2.1.5.2 Amplitude Modulation in the Frequency Domain

The use of a spectrum analyser for examining signals in the frequency domain is a verypowerful tool. However, this facility is not always available, as a spectrum analyser costsmuch more than an oscilloscope. As an aid to understanding modulation principles it isinvaluable.

The spectrum analyser shows the modulated signal to have three components:

1. The Carrier, at the same frequency as the carrier source.

2. A lower side frequency at the carrier minus the modulation frequency.

3. An upper side frequency at the carrier plus the modulation frequency.

The amplitude of the carrier is independent of the modulation, while the amplitudeof the side frequencies depends entirely on modulation depth.

In the practical the modulation source is a sine wave, containing only one frequency, andtherefore is represented by a narrow line in the frequency spectrum.

In practice, where the modulating signal is more complex, there would be a range, orband, of side frequencies above the carrier frequency and a band below it, the upper andlower sidebands. They extend either side of the carrier to an extent equal to the maximummodulating frequency.


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53-001S 2-7

2.1.5.3 Procedure

In this practical the hardware is configured as shown. You have available an oscilloscopeand a spectrum analyser. Set the carrier levelto maximum. Set modulation leveltozero. Note the signals at all monitoring points. Now increase the modulation levelandobserve at monitor point 6.

Increase the modulation leveluntil the carrier amplitude just reaches zero on negativemodulation peaks. This is 100% modulation. Observe the signals at all the monitoringpoints both with the oscilloscope and the spectrum analyser at various modulation levels.

Also, with a fixed modulation level try adjusting the carrier level.

You will need to return to the practical and make some measurements in order to answerthe questions.


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2-8 53-001S

2.1.5.4 Questions

1. The 'envelope' of the modulated carrier wave is a curve joining its peaks. The positiveenvelope, joining the positive peaks, should follow the shape of the modulating signalin one polarity and the negative envelope, joining the negative peaks, in the oppositepolarity. What happens to the positive and negative envelopes when over-modulationoccurs?

2. How would you recognise over-modulation on the spectrum analyser display?

3. What is the amplitude of the two sidebands relative to the carrier expressed in dB for50 percent modulation with a sine wave? (HINT: Use the oscilloscope to set themodulation level and the spectrum analyser to measure the sidebands)

4. See if you can use the theory mathematics to calculate the value in question three and

compare it with the practical measurement.


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53-001S 2-9

2.1.6 Practical 2: Envelope Detectors

In this practical you will investigate the demodulation of an AM signal with an envelopedetector.

The purpose of any detector or demodulator is to recover the original modulating signalwith the minimum of distortion and interference. The simplest way of dealing with an AMsignal is to use a simple half- wave rectifier circuit. If the signal were simply passedthrough a diode to a resistive load, the output would be a series of half-cycle pulses atcarrier frequency. So the diode is followed by a filter, typically a capacitor and resistor inparallel.

The capacitor is charged by the diode almost to the peak value of the carrier cycles andthe output therefore follows the envelope of the amplitude modulation. Hence the termenvelope detector.

The time constant of the RC network is very important because if it is too short the outputwill contain a large component at carrier frequency. However, if it is too long it will filter outa significant amount of the required demodulated output.

In this practical the output of the AM generator that you used in the Simple Amplitude

Modulator practical is fed to an envelope detector.

You can monitor the output and compare it with the original modulation source. The timeconstant of the filter following the detector can be adjusted. This filter is often called apost-detection filter. It also introduces a phase shift between the original signal and theoutput.


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2-10 53-001S

2.1.6.1 Procedure

Here the signal from the amplitude modulator from the previous practical is demodulatedusing an envelope detector. Confirm that the modulated signal is the same.

Use the oscilloscope to monitor the detector output 16and adjust the time constant.Note that a large carrier component is present if the time constant is too short.

Increase the time constantand note that the amplitude of the detected output decreasesand becomes distorted as the filter cannot discharge in time to follow the required output.Use the spectrum analyser to observe the carrier component amplitude.

Compare the original modulating signal with the detector output in both shape and phaseat various time constants using the oscilloscope.


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53-001S 2-11

2.1.6.2 Questions

1. Is the phase shift caused by the post detection filter a lead or lag?

2. Why do you think that the filter causes a phase shift?

3. How does the ratio of modulating frequency to carrier frequency affect the design of

the detector and the post detection filter?

4. What problems could be caused if the range of modulating frequencies was quitelarge?


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2-12 53-001S

2.1.7 Practical 3: Product Detection

In this practical you will investigate an alternative demodulator called a product detector. Ithas certain advantages over the simple envelope detector but at the expense of somecomplexity.

It is not often used for AM but is the only type of detector that will demodulate thesuppressed carrier amplitude modulations that are investigated in the next assignment.

It is important to appreciate that a product detector will demodulate all forms ofAM.

2.1.7.1 What is a Product Detector?

If the AM signal is mixed with (ie, modulated by) a frequency equal to that of its carrier,the two sidebands are mixed down to the original modulating frequency and the carrierappears as a dc level.

The mathematics of the process show that this will only happen if the mixing frequency isequal not only in frequency to that of the carrier, but also in phase; ie, the two signals aresynchronous. This is why a product detector when used for AM is sometimes called asynchronous detector. For AM the effect is very similar to a full-wave rectifier rather thanthe half-wave of the envelope detector.

The output still needs a post-detection filter to remove the residual ripple, but this time theripple is at twice the carrier frequency and is therefore further away from the modulationand hence easier to remove. In general terms the product detector gives less distortion,partly because it uses both positive and negative peaks of the carrier.

2.1.7.2 Generating the Mixing Frequency

This is produced by an oscillator which is usually referred to as a Beat Frequency

Oscillator or BFO. This is because if it is not at the same frequency as the carrier theoutput of the product detector is a frequency equal to the difference between the twowhich is called a beat frequency. (You will be able to see this when you adjust the BFO forsynchronism).

As previously described, it is vital that the BFO be synchronised to the carrier. In practicethis is achieved with a special recovery circuit but here for simplicity a sample of thecarrier is fed directly to the BFO and when the free running frequency of the BFO is nearto that of the carrier it locks into synchronism.


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53-001S 2-13

2.1.7.3 Procedure

Here is a product detector demodulating AM. The oscilloscope shows its input at monitorpoint 6,which is the output of the same modulator as before.

Now monitor the BFO output with the oscilloscope and use the BFO frequencycontrol tolock it to the carrier. This will be indicated by a stationary trace.

Use the oscilloscope to look at the output of the detector before the filter and note thefrequency of the ripple compared with the carrier. Use the spectrum analyser to confirmthis. Examine the output of the filter and compare it with the modulation source.

Monitor the detector output before the filter with the oscilloscope, then unlock the BFOwith the BFO frequencycontrol and observe the result. Repeat whilst observing thefiltered output.


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2-14 53-001S

2.1.7.4 Questions

1. Are the design considerations for a post-detection filter different from those for theenvelope detector?

2. Examine the filtered output, using the spectrum analyser at large size, with the BFOsynchronised. The trace should show three points where the level is above thebackground ripple. What do they represent?

3. Again examine the filtered output, using the spectrum analyser at large size. Decreasethe amplitude of the modulation signal as far as possible without the instrument triggerfailing. Then vary the BFO control. How wide is the available range of beat frequency?


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53-001S 2-15

2.2 Amplitude Modulation with No Carrier Assignment

2.2.1 Objectives


Amplitude modulation with suppressed carrier,

Double sideband suppressed carrier (DSB) modulation,

Single sideband suppressed carrier (SSB) modulation, Balanced modulators,

Generating SSB with filters,

Demodulation methods.

2.2.2 Practicals

Practical exercises are provided:

Practical1: Double sideband suppressed carrier

Practical 2: Generation of single sideband carrier (SSB)

Practical 3: Demodulation of SSB


Amplitude Modulation Workboard 53-130 which comprises the following blocks:

Signal Generation

Modulation

Filters

Demodulation


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2-16 53-001S

2.2.4 Theory

2.2.4.1 Double Sideband Suppressed Carrier

In the theory for the Amplitude Modulation with Full Carrier assignment, Practical 1, it wasestablished that if:

vc= Vcsin ct

describes a carrier signal and,

vm= Vmsin mt

describes a modulating signal, then the normal AM signal is:

vc= (Vc+ Vmsin mt) .sin ct

which may be rewritten as:

vc= Vcsin ct + Vmsin ct . sin mt

In DSB suppressed carrier modulation, the carrier term Vcsin ct is suppressed, leavingjust:

Vmsin mt.sin ct

= (Vm/2) [cos(c- m) t - cos(c+ m) t]

as the modulated signal.

The two cosine terms represent the lower and upper sidebands respectively.

In the case of SSB suppressed carrier modulation, one of these sidebands will also be

suppressed.

2.2.4.2 Demodulating the DSB Signal

In order to change the sideband frequencies back to the original modulating frequency, alocally-generated carrier frequency (from the BFO) is used to modulate the DSB signal.(Remember that modulation for the purpose of frequency changing is traditionally calledmixing).

Suppose that the BFO signal is:

vo= Vosin(o+ )


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53-001S 2-17

The modulation process will produce a signal proportional to:

[Vosin(o+ )] (Vc/2) [cos(c- m) t - cos(c+ m) t]

or to:

2 sin(o+ ) [cos(c- m) t - cos(c+ m) t]

This can be divided into two terms:

2 sin(o+ ) cos(c- m) t... (1)

and:

- 2 sin(o+ ) cos(c+ m) t... (2)

but as

2 sin A cos B = sin(A + B) + sin (A - B)

the first term, (1), becomes:

sin(o+ + c- m) t + sin(o+ - c+ m) t

Since ois supposed to be equal to c, (o+ c- m) will be a frequency roughly twicethat of the carrier.

This does not contribute to the desired signal. The rest of the expression, which doescontribute, is:

sin(wo+ - c+ m) t

If o= c, then sin(o+ - c+ m) t becomes simply

sin( + m) t,

which is the original modulating frequency. Similarly the other term, (2), makes acontribution:

- sin(o+ - c- m) t

which, for o= c, becomes:

sin(- + m) t


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2-18 53-001S

We now have two terms, or components of the output signal, each of the originalmodulating frequency. However, there is a problem when we combine them.

The two terms are:

sin( + m) t

and

sin(- + m) t

If the phase is zero, the two terms become identical, so they combine to produce thesignal:

2 sin mt

i.e a signal at the original modulating frequency.

Now suppose that the phase now changes through /2 radians (90 degrees).

The two sinusoids would now be radians (180 degrees) apart in phase and wouldcancel each other out.

We have assumed that o= c. If this were not true, the effect would be the same as if were continually changing, making the two terms alternately reinforce and cancel eachother.

This may be shown mathematically thus:

sin( + m) t + sin(- + m) t = 2 sin mt cos

Since cos 0 = 1, the strongest output is obtained for = 0.

With = /2, cos = 0, so no output is obtained.


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53-001S 2-19

2.2.5 Practical 1: Double Sideband Suppressed Carrier

This practical introduces the idea of AM with suppressed carrier. After it you willunderstand the following ideas:

Balanced modulators and carrier suppression

The BFO as a carrier insertion oscillator

In the assignment on basic amplitude modulation we saw that the modulated signal

comprises a carrier and two sidebands.

The carrier is of constant amplitude and only the sidebands vary in frequency andamplitude with the modulation. It is therefore clear that only the sidebands carry themodulating informationwhile the carrier does nothing except, as we will see, help in thedemodulation process.

The transmission of the carrier takes a large proportion of the total transmitted power, soif the carrier were removed all the power could be used to transmit the sidebands which,after all, contain the information.

If the modulation process is carried out by a balanced modulator, the output signal doesnot contain the carrier component because it is cancelled out by the balanced nature ofthe modulator.

This signal is described as double sideband, suppressed carrieror DSB.

2.2.5.1 Carrier Unbalance

If the modulator were perfectly balanced there would be no carrier in the output.

In practice, due to circuit imperfections, some carrier is always present.

The ratio of the actual carrier to that which would be there in a simple AM system is calledthe carrier suppression ratioand is an important parameter in such systems. Normallythe ratio is expressed in dB to make the numbers manageable; 30 dB would be a typicalfigure.

To calculate the carrier suppression ratio, you need to know what amplitude of carrierwould have been present, if not suppressed. This is the carrier which would give 100%modulation by the maximum signal level for which the system is designed.

Since 100% modulation produces side frequencies of half the carrier amplitude, the

unsuppressed carrier amplitude may be taken as twice the allowable amplitude of eithersideband.


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2-20 53-001S

In this practical, a carrier and modulation source are connected to a balanced modulatorto provide a DSB signal which can be examined with the oscilloscope and spectrumanalyser.

2.2.5.2 Procedure

Use the oscilloscope and spectrum analyser to examine the signals at monitor point 4 andmonitor point 5.

Set the carrier balanceto mid-scale. Note that they are the same as for simple AM. Now

examine at monitor point 6and note the waveshape.

Use the spectrum analyser to observe that there are two sidebands but no carrier.

Adjust the carrier balance; note the effect on carrier amplitude. Adjust modulation leveland carrier leveland note the effects.

Note that the output from the envelope detector is not the same as the modulating signal.

Monitor at monitor point 13 and adjust the BFO frequencyfor a stable trace, so that theBFO is in phase with the original carrier. Observe that the product detector output is thesame as the modulating signal. Unlock the BFO and observe the result.


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53-001S 2-21

2.2.5.3 Questions

1. Why does AM have a low efficiency when the full carrier is transmitted?

2. How can you tell whether the modulator is balanced when using the oscilloscope?, andwhen using the spectrum analyser?

3. Measure the carrier suppression ratio for the system in Practical 1 when set formaximum modulation and minimum carrier amplitude.

4. Does the term overmodulation have any meaning in a DSB system?


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2-22 53-001S

2.2.6 Practical 2: Generation of Single Sideband Suppressed Carrier (SSB)

This practical introduces the concept of single sideband suppressed carrieror SSBoperation.

In the double sideband suppressed carrier practical it was demonstrated that it waspossible to recover the modulating signal without the presence of a transmitted carrier.

This is achieved by inserting a local carrier at the demodulator. That practical used DSB;ie, both sidebands were transmitted.

It is obvious that as both sidebands are generated from the same carrier and modulation,they must contain the same information, and therefore the modulating frequency could berecovered from only one sideband. This saves further transmitter power.

Another very important advantage is that the bandwidth is half that of simple AM or DSB.

2.2.6.1 Generating SSB

The generator in the practical is a balanced modulator, producing DSB, followed by abandpass filter for the required sideband.

There are other methods but this filter methodis the simplest to understand and is invery common usage in communication systems. It may be necessary for the bandpassfilter to have a very good shape factor because, at normal carrier and audio frequencies,the upper and lower sidebands are quite close in frequency.

Another consideration is that the sideband filter should offer significant attenuation to thecarrier, so that the balanced modulator need not be so accurately balanced. In practicethe balanced modulator might provide 30 db of carrier suppression and the filter a further10db. The other sideband would normally be about 30 to 40 db down on the wanted one.

In order to achieve this, the SSB filter has several poles and is, in most cases a ceramic

filter or crystal filter. Various filters are commercially available with differentspecifications depending on the application.

In the practical we use a high modulating frequency so you can see clearly therelationship between the various frequency components. This means that the filterspecification can be relaxed and here a single tuned circuit is used. Separate filters areprovided for upper and lower sidebands and the means is provided to monitor the outputof both.

You might be surprised that the output from the SSB filters is simply a sinusoidal signalbut, since we use sinusoidal carrier and modulating frequencies, the sum or difference of

the two must be a single frequency.


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53-001S 2-23

When the modulation is a band of frequencies, the SSB output will also be a bandof frequencies.

2.2.6.2 Upper or Lower Sideband?

An obvious question is which sideband should be transmitted? The answer owes more toconvention than theory!

There is no reason why one sideband gives better results than the other, but generalpractice seems to favour the upper sideband.

One convention is that with carrier frequencies below 10 MHz the lower sideband shouldbe used, but this is not always the case. The result of this is that many pieces ofcommunication equipment have to be able to deal with both.

To begin the practical, please turn to the next page.

2.2.6.3 Procedure

Use the spectrum analyser and oscilloscope to observe at monitor point 6. Note that thesignal is DSB. Adjust the carrier balanceas before.

Monitor at monitor point 8, and at monitor point 9, and note that only one sideband ispresent. Note that the carrier suppression is less dependent on the carrier balance thanbefore the filter.

Use the oscilloscope to observe that the SSB output is a sinusoidal signal. Use thespectrum analyser to note that the upper sideband frequency is the sum of the carrier andmodulation frequencies and the lower sideband is the difference.


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2-24 53-001S

2.2.6.4 Questions

1. Why is the balance of the modulator less important in a filter method SSB generatorthan for a DSB generator?

2. How is the width of the SSB filter related to the maximum and minimum modulatingfrequencies?


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2.2.7 Practical 3: Demodulation of SSB

This practical is about the demodulation of SSB.

In the double sideband suppressed carrier practical we saw how DSB is demodulatedusing the BFO to reinsert the carrier. In the case of DSB the BFO must be in phase withthe original carrier or the process will not work correctly.

Since SSB is transmitted without a carrier it is not surprising that a similar method isemployed.

The main difference is that, for SSB, the BFO need not be in phase with the carrier . Itdoes need to be at the same frequency but even a small error in the frequency resultsonly in a small error in the frequency of the demodulated output.

This means that in non-critical applications, such as speech, a small overall frequencyerror does not make the system useless. The effect on speech is to raise or lower thetone of the voice, which within limits does not reduce intelligibility.

The fact that the BFO need not be locked, greatly simplifies the design of the receiver,and makes SSB one of the most powerful techniques for transmitting audio frequencies

over radio links with its narrow bandwidth and efficient useof available transmitterpower.

In the practical you can use both upper and lower sidebands and see that with the BFOset correctly, near to the original carrier frequency, even though the two sidebands are atdifferent frequencies the demodulated output is the same. You can also see that changingthe BFO frequency causes the demodulated output to change in frequency by a similaramount.


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2-26 53-001S

2.2.7.1 Procedure

Monitor at monitor point 6, and observe the DSB signal. Move to monitor point 10andnote the upper sideband signal.

Use the spectrum analyser to confirm that the frequency is that of the upper sideband.Change to lower sideband (by pressing the button) and repeat.

Now monitor at monitor point 14and compare the output with the modulation input. Useeither the oscilloscope or analyser to set the BFO frequencyto that of the carrier, bymonitoring at monitor point 13.

Note that both sidebands give the same output frequency.

Move the BFO frequencyand observe the effect on the output using first one and thenthe other sideband.


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2.2.7.2 Questions

1. Why is SSB more efficient than either simple AM or DSB?

2. If the BFO frequency rises, what happens to the frequency: a) of the upper sideband?b) of the lower sideband?

3. Calculate the bandwidth of the transmitted signal when the modulation frequency bandextends from 500 Hz to 50 kHz for simple AM, DSB and SSB.

4. If a SSB channel has no modulating signal, what is the modulated signal like?


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2-28 53-001S

Notes


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Chapter 3ANALOGUE COMMUNICATIONS - Assignments using theSTUDENTS WORKBOOK Frequency Modulation Workboard

53-001S 3-1

3 Assignments using the Frequency Modulation Workboard

3.1 Generation of Frequency Modulation Assignment

3.1.1 Objectives


Frequency modulators,

Modulation index,

Bandwidth,

FM signals in the time domain,

FM signals in the frequency domain.

3.1.2 Practicals


Practical 1: Concepts of Modulation

Practical 2: Generation of FM with a VCO

Practical 3: Spectrum of an FM signal with a large Modulation Index


Frequency Modulation Workboard 53-140 which comprises the following blocks:

Signal Generation, Modulator,

Limiter,

Quadrative Demodulator,

VCO,

Phase Comparator.


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3-2 53-001S

3.1.4 Theory

3.1.4.1 Modulation


v = Vmax.sin(t+)

where:

v is the instantaneous voltage, Vmaxis the maximum voltage amplitude,

is the angular frequency,

is the phase.

A steady voltage corresponding to the above equation conveys little information.

To convey information the waveform must be made to vary so that the variationsrepresent the information. This process is called modulation.


3.1.4.2 Frequency Modulation

Frequency modulation uses variations in frequencyto convey information.

We shall think in terms of the angular frequency . The wave whose frequency is beingvaried is called the carrier wave. The signal doing the variation is called the modulatingsignal.

For simplicity, suppose both carrier wave and modulating signal are sinusoidal; ie:.

vc= Vcsin ct

(cdenotes carrier) and

vm= Vmcos mt

(mdenotes modulation)


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3.1.4.3 What is Frequency?

If the frequency is varying, how do we define it?

We can no longer count the number of cycles over a longish interval to count the cyclesper second. Instead we define frequency as the rate of change of phase .

This is consistent with the simple definition, because at a constant (angular) frequency radians/second the phase is changing at radians per second, which is /2cycles persecond.

Since we can only define what the instantaneous frequency is by reference to the phase,we must look at the phase in order to arrive at an expression for the frequency-modulatedsignal.

3.1.4.4 Phase of the FM Signal

For the unmodulated carrier vc= Vcsin ct, the phase is:

s = ct

We want the modulating signal to vary the carrier frequency, c, so that its frequencytakes the form:

= c+ D cos mt

(where Ddenotes the peak value of the deviation)

It is related to the amplitude of the modulating signal vmby the 'frequency slope' of thefrequency modulator (VCO) say k radians/s per V. The peak value of vmproducesdeviation D, so:

D = k Vm

The total phase change undergone at time t is found by integrating the angular frequency.It is

s = !(c+ D cos mt) dt

= ct + (D/m) sin mt.

(If you are not familiar with integration you will have to take this result on trust).

So the FM signal can be expressed as:

Vcsin [ct + (D/m) sin mt]


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3-4 53-001S

3.1.4.5 Modulation Index

In the expression for the FM signal:


the coefficient (D/m) turns out to be quite important and is given the name modulationindex.

It is often represented by the Greek letter beta, .

So we may write the FM signal as:

vc= Vcsin (ct + sin m) t

where is the modulation index (D/m).

In this expression, the factor sin (ct + sin m) t (let us call it F) is of the form sin (a + b)which can be expanded to sin a cos b + cos a sin b.

Applying this expansion to F, we get:

F = sin ct cos(sin m) t + cos ct sin (sin m) t

3.1.4.6 FM Sidebands

These complicated functions can be expanded, using mathematics too elaborate toexplain here, into a series of terms like this:

F = J0() sin ct+ J1() [ sin (c+ m)t - sin (c- m)t ]

+ J2() [ sin (c+ 2m)t - sin (c- 2m)t ]

+ J3() [ sin (c+ 3m)t - sin (c- 3m)t ]

+ J4() [ sin (c+ 4m)t - sin (c- 4m)t ]

+ ...

where J0(), J1(), J2() etc are constants whose values depend only on . They arecalled Bessel Functions.

There is an infinite series of these functions, and so an infinite number of FMsidebands. But in practice the values of the Bessel functions become very small as the

series goes on. For example, when = 2

J0(2) = 0.224J1(2) = 0.577

J2(2) = 0.353

J3(2) = 0.129


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53-001S 3-5

J4(2) = 0.034

J5(2) = 0.007

3.1.4.7 A Practical Approximate Rule

Because the higher-order sidebands become very small, in practice the bandwidth of theFM signal may be restricted to a finite bandwidth.

The practical rule that is used, often called Carsons Rule, is to take the bandwidthrequired as:

B = 2 ( Fd+ Fm)

where Bis the bandwidth, Fdthe deviation and Fmis the bandwidth of the modulation, allin the same units.

3.1.5 Practical 1: Concepts Of Frequency Modulation

This practical introduces the idea of frequency modulation. Before you start it is necessaryto appreciate some fundamental concepts.

As in amplitude modulation, a carrier frequency is modulated by the information that isbeing sent. In AM it is the amplitude of the carrier that is varied in time with themodulation, in FM it is the frequency that is varied. The amplitude is constant as we willsee.

When no modulation is being applied the carrier is at its nominal frequency i.e the carrierfrequency. The modulating signal causes the frequency to deviate, i.e. to move aboveand below its nominal value. With the greatest possible deviation, the minimum frequencycould be near zero and, assuming the modulating signal to have no d.c component, themaximum frequency would then be about twice the carrier frequency.

However, this would take a very large amount of frequency spectrum and the bandwidthwould have no relationship to the modulating signal bandwidth. A set limit is normallymade on the amount that the carrier can deviate from its nominal frequency and this iscalled the maximum deviation.

Different systems use different values of maximum deviation, depending on a number offactors some of which are very complex


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3-6 53-001S

3.1.5.1 Bandwidth of an FM Signal

It is important that we can understand and estimate the bandwidth of the transmittedsignal so that the transmission parameters can be chosen to fit into the availablespectrum.

Clearly the bandwidth must be at least equal to twicethe deviation, as the carrier actuallymoves above and below its nominal frequency by that amount. But it also depends onhow fast the frequency is being changed; ie, on the bandwidth of the modulating signal.

The mathematical analysis of FM is quite involved and it shows that an FM signal has

sidebands far above and below the maximum deviation.

However the power in these sidebands decreases quickly as they become further awayfrom the carrier and it can be shown that, for practical purposes, a good approximation tothe bandwidth is given by:

B = 2 ( Fd+ Fm)

(where Bis the bandwidth, Fdthe deviation and Fmis the bandwidth of the modulation.)

This is sometimes called Carsons Rule, and the bandwidth Bcan be viewed as

containing the majority of the transmitted power, certainly sufficient for successfuldemodulation.

3.1.5.2 Modulation Index

As we have seen, the bandwidth of an FM signal depends on both the deviation and themodulation bandwidth.

It might be thought that, in order to keep the bandwidth as narrow as possible, all FMsystems should be operated with a very small deviation.

However, there are significant advantages to operating with a wide deviation. The mainone is an apparent improvement in noise performance.

So as you can see, a specific bandwidth can be the result of wide deviation with a lowmodulation bandwidth or a narrow deviation with a large modulation bandwidth.

The ratio of deviation to modulation bandwidth is called the modulation indexand is animportant parameter in describing a FM system.

Modulation index is given by:

MI = Fd/ Fm

where MIis the modulation index.


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53-001S 3-7

Modulation index is sometimes represented by the Greek letter beta ().

In the practical a frequency modulator is formed from a voltage controlled oscillator. Avoltage is applied to it from a control on the hardware board and the oscillator output canbe examined on the oscilloscope and spectrum analyser.

Using this configuration the fundamental concept of an oscillator frequency beingchanged by an external signal can be understood.

3.1.5.3 Procedure

In this practical the hardware is configured as shown.

You have available an oscilloscope and a spectrum analyser. Using this configuration youcan see how the oscillator frequency can be controlled by an external signal.

Set Carrier levelto about half scale.

Use the oscilloscope to observe that when the manual frequencycontrol is moved thefrequency changes. Monitor at monitor point 16to see the voltage applied to the oscillatorand monitor point 4to see the output.

Monitoring monitor point 4use the large oscilloscope calibration to measure the totalfrequency range of the oscillator.

Use the spectrum analyser to confirm the frequency range measured on the oscilloscope.


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3.1.5.4 Questions

1. Is it easier to measure the frequency range on the oscilloscope or on the spectrumanalyser?

2. Choose two voltages levels at the control input to the oscillator and measure thecorresponding output frequencies. Hence calculate the 'frequency slope' of theoscillator in kilohertz per volt.

3. Can you see any amplitude variation over the frequency range? Should there be any?


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53-001S 3-9

3.1.6 Practical 2: Generation of FM with a VCO

In this practical a sine wave signal is used to frequency-modulate a carrier so that you caninvestigate the appearance of such signals in both the time and frequency domains.

You can adjust the amount of deviation and hence change the modulation index. Noticethat the appearance of an FM signal on the spectrum analyser is similar to that of an AMsignal when the modulation index is small.

Try to reconcile the explanation of the bandwidth of an FM signal given in the previousbackground pages with the observations you make in this practical.

Move to the next page to start the practical.

3.1.6.1 Procedure

In this practical the variable voltage used to control the VCO frequency has been replacedby a sine wave oscillator. This sine wave now frequency-modulates the carrier.

Set Carrier levelto about half scale. Look at the signal at monitor point 4with theoscilloscope.

Turn the modulation levelup and down and observe the effect.

Notice that the frequency is changing. Note where the output at monitor point 4has ahigher frequency. Change to monitor point 3and observe how the instantaneousfrequency depends on the instantaneous value of the modulating signal.

Use the spectrum analyser to examine the sidebands of the signal. Adjust themodulation leveland observe that, at low deviation, only the sidebands at Fc- Fmand Fc+ Fmare present.

At higher deviation, ie, a larger modulation index, higher-order sidebands appear.


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3-10 53-001S

3.1.6.2 Questions

1. By looking at the spectrum of the modulated signal, can you estimate the frequency ofthe modulating signal? (Explain carefully how).

2. Would it be equally easy to estimate the bandwidth of the modulating signal from thespectrum if the modulating signal were complex, having many frequencies?

3. As the modulation level varies, how constant are: (a) the carrier-frequency componentof the modulated signal? (b) the amplitude of the modulated signal?


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53-001S 3-11

3.1.7 Practical 3: Spectrum of an FM signal with a large Modulation Index

This is a simple practical where the frequency modulator is connected to the spectrumanalyser. The carrier frequency has been reduced to about 5 kHz so, since the maximumdeviation is the same as in the other practicals of this Assignment, the modulation index ismuch greater.

As we saw, the bandwidth is:

B = 2 ( Fd+Fm)

where B is the bandwidth, Fdthe deviation and Fmis the bandwidth of the modulation.

So if Fmis small compared with Fd, ie, the modulation index is large, then:

B = 2 Fd

On the analyser the spectrum appears to be continuous but in reality it is made up of alarge number of sidebands spaced at 5 kHz intervals from the carrier up to Fd.

This practical simply shows how when the modulation index is large the bandwidth is

determined almost exclusively by the deviation.

3.1.7.1 Procedure

In this practical the modulation frequency has been set to 5 kHz. This means that themodulation index can be very high. This enables you to see that under these conditionsthe bandwidth of an FM signal is almost equal to twice the deviation.

Set Carrier levelto about half scale. Turn the 5 kHz levelup and down and observe thebandwidth changing. Note that the bandwidth is almost proportional to the deviation.


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3-12 53-001S

3.1.7.2 Questions

1. If the modulating frequency is 5 kHz and the deviation is 50 kHz, calculate themodulation index.

2. Calculate the signal bandwidth using Carson's rule.

3. If a bandpass filter were to be added at the input of an FM detector what factorsdetermine the bandwidth required?


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53-001S 3-13

3.2 Demodulation of Frequency Modulated Signals Assignment

3.2.1 Objectives


Quadrature detectors,

PLL detectors,

Noise.

3.2.2 Practicals


Practical 1: A Quadrature Detector with Limiter

Practical 2: The Effect of Noise on a Quadrature Detector

Practical 3: PLL Detector with a Limiter

Practical 4: The Effect of Noise on a PLL Detector



Signal Generation,

Modulator,

Limiter,


VCO,

Phase Comparator.


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3-14 53-001S

3.2.4 Theory

3.2.4.1 Quadrature Detector

The quadrature detector splits the incoming FM signal into two paths. One path isconnected directly to one input of a phase detector. The other path contains a simplenetwork which shifts the phase of the signal in proportion to its frequency deviation.

Let us consider the nature of a typical phase shifter ...

Regard this as a simple potential divider, with input at point 1, output at point 2. The upperarm has impedance

jL + R

and the lower arm

1/(jC)

where w is the angular frequency.

The circuit's transmission factor is

e2/e1= [1/jwC] / [R + jL + (1/jwC)]

e2/e1= 1 / [ 1 - 2LC + jCR ]


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53-001S 3-15

It is convenient to express the transmission factor in terms of o, the resonant frequency,at which:

oL = 1/(oC) , or o2LC = 1 ,

and the quality factor Q, given by:

Q = oL/R = 1/(oCR)

Using these definitions, we can substitute 1/o2for LC and 1/Q ofor CR. So the

transmission factor:

e2/e1= 1 / [ 1 - 2LC + jCR ]

becomes:

e2/e1= 1 / [ 1 - 2/o

2+ j/oQ ]

The phase of this expression is:

= - arctan [/oQ ] / [1 - (/o)2]

which, if we define y = /ocan be written as:

= arctan [ y / Q (y2- 1) ]

= arctan [ Q (y2- 1) / y ]

= (/2) - arctan [ Q (y2- 1) / y ]

= (/2) + arctan Q [ y - (1/y)]

Replacing y by /oonce more, this can be written as:

= (/2) + arctan [Q (2- o2)/ o]

= (/2) + arctan [Q (- o) (+ o)/ o]

= (/2) + arctan [Q d( 2o+ d) ]/[ (o+ d)

o]

where dis defined as - o.

Neglecting din comparison with oin:


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3-16 53-001S

= (/2) + arctan [Q d( 2o+ d) ]/[ (o+ d) o]

we get:

= (/2) + arctan [Q d( 2o) ]/[(o)

o]

= (/2) + arctan [ 2 Q d/ o]

If dw is sufficiently small, the argument of the arctan is small, and therefore close to thearctan value in radians. So, still to a good approximation:

= (/2) + [ 2 Q d/ o]

It must be noted however, that if Q has a high value, these approximations may become

invalid, for quite moderate values of deviation (d).

This indicates that for low distortion, the value of Q must be kept low. For good sensitivity,Q should be high. So here is an instance where a degree of compromise in the design isneeded.

Summing up, if the carrier is at its nominal frequency (d= 0), the phase is just

(/2). The change in phase from (/2) is proportional to the deviation (d), provided

that 2 Q d/ois small.

3.2.5 Practical 1: Quadrature Detector

The purpose of an FM demodulator is to return the modulating signal to baseband. Since,in FM, the instantaneous frequency is proportional to the modulating signal, all that isneeded is a circuit block which produces a voltage proportional to the input frequency.This is not quite as simple as it sounds.

A very crude way of achieving this is to feed the signal through a filter with its cut-off nearto the carrier frequency. The signal is then attenuated by an amount depending on itsfrequency. The filter output is now AM and can be demodulated by any AM detector. Thistype of detector uses the slope of the filter characteristic and therefore is called a SlopeDetector.

Slope detectors are not satisfactory in most applications as they are not very linear anddo not reject noise well.


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53-001S 3-17

3.2.5.1 Quadrature Detectors

Another way is to turn the FM to phase modulation and then use a phase detector. This isa very common technique and is the basis of the Quadrature Detector.

In this practical you will see how a quadrature detector works. The incoming FM signal issplit into two paths. One path is connected directly to one input of a phase detector. Theother path contains a simple network which shifts the phase of the signal in proportion toits frequency deviation.

The output of the phase shift network is connected to the other input of the phasedetector. As the frequency varies, both detector inputs vary together in frequency, but onealso shifts in phase relative to the other. It is this varying phase shift that produces theoutput from the detector.

A minor complication is that most phase detectors produce their mean output for 90degrees phase difference between the input signals. This is the required condition whenthe FM signal is at its centre frequency, so an additional constant 90 degree phase shift isadded to one of the paths. When unmodulated, the two inputs to the phase detector areat 90 degrees apart, or in quadrature; hence the name of the detector.

This constant phase shift is usually added by means of a simple inductor. The output ofthe phase detector still contains a large component at twice the carrier frequency and thedetector is usually followed by a filter that passes the baseband but not the carrier.

Quadrature detectors are used extensively in domestic FM radios and in a lot ofcommunications equipment.

In this practical, the same modulator is used as in the Generation of FrequencyModulation assignment. The modulation is a sine wave so that the signal can be followedthrough the circuit.


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3-18 53-001S

3.2.5.2 Procedure

This practical shows a quadrature detector working. Monitor at 9 and observe the FMsignal at different settings of modulation level. Note the two signals at the inputs of thephase detector 9and 11. Set the modulation levelto about half scale.

Observe the signal at the phase detector output 12and then after the post-detection filterat 14.


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53-001S 3-19

3.2.5.3 Questions

1. Use the large oscilloscope to try and measure the phase shift between the two phasedetector inputs when there is no modulation.

2. What frequencies must the output filter:(a) pass?(b) reject?

3. Would your answer to question 2(b) be altered if the phase comparator were imperfectin some way?


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3-20 53-001S

3.2.6 Practical 2: Phase lock loop detector (PLL)

This practical introduces the phase locked loop (or PLL) demodulator. This type ofdetector offers some advantages over the quadrature detector when the signal to noiseratio is poor.

Before trying to understand how a PLL can demodulate an FM signal it is necessary tounderstand what a PLL is. The concept is of an oscillator synchronised in phase to anexternal signal source using a feedback loop.

As frequency is the same thing as rate of change of phase, once the phase of the local

oscillator is synchronised to the external signal, the frequencies are automatically madeidentical.

A phase locked loop consists of three main blocks:

1. An oscillator, the frequency of which is controlled by an external voltage or currentsource. A voltage controlled oscillator or VCO is used in this assignment.

2. A phase detector, which compares the phase of the oscillator with that of theexternal signal.

3. A filter, which smoothes the output from the detector to provide the control signalto the VCO, adjusting its frequency so as to reduce the phase difference.


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53-001S 3-21

3.2.6.1 Operation of a PLL

Imagine an incoming signal at a constant frequency within the range of the VCO.

Its phase is compared with that of the VCO and a voltage produced that alters the VCOfrequency. The phase of the VCO therefore starts changing relative to the incomingsignal, until eventually the phases match. Once they are equal, the control signal goes tozero and the system settles into equilibrium. Any drift of the VCO will be corrected by the

control voltage which again appears. The two signals are said to be phase locked.

A filter is used in the control loop to keep the system stable and limit the maximum rate ofchange of oscillator frequency.

This whole description is a very simplified view, and the parameters that set the filtercharacteristics are very complex. An important factor in the design is the time before thetwo signals become locked.

Phase locked loops are used extensively in communications systemswhere it isnecessary to produce a reference oscillator in phase with an incoming signal; also in

special signal sources called frequency synthesizers.


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3-22 53-001S

3.2.6.2 The PLL as an FM Detector

Now that you have appreciated the concept of a PLL, how can it be applied to demodulateFM?

Suppose that there was a PLL locked onto an incoming carrier which was unmodulated.The VCO would be at the same frequency as the carrier and the VCO control voltagewould be constant.

If the carrier were to change in frequency the VCO would follow the change by means of achange in control voltage. So the VCO control voltage varies with the carrier

frequency, and if the carrier were frequency modulated the modulation would appearsuperimposed on the VCO control voltage.

When a post-detection filter is added to the simple PLL to remove all the frequencycomponents above the maximum modulating frequency we now have a PLL FM detector.

In this practical you will see a PLL detector demodulating the same FM signal as before.

The PLL is used when the ability to demodulate in the presence of noise is important. The

distortion produced by this type of detector is determined mainly by the linearity of theVCO but this is often less important in noisy applications.

FM detection under noisy conditions is investigated in the next assignment.


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3.2.6.3 Procedure

This practical shows a phase lock loop detector working. Monitor at 9and observe the FMsignal at different settings of modulation level. Examine the two signals at the input ofthe phase detector at 9and the tracking VCO at 11 . Set carrier levelto maximum.

Observe the signal at the phase detector output 12and then after the post detection filterat 14.


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3-24 53-001S

3.2.6.4 Questions

1. What happens to the demodulated output when you reduce the control from maximumto half amplitude? Explain your answer in a sentence or two.

2. What happens to the demodulated output when you reduce the control to lowerlevels?

3. What is the special problem which occurs for very low signal levels?

4. Why do you think it happens and what do you think could be done about it?


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53-001S 3-25

3.3 Limiters and the Effect of Noise on FM Demodulation Assignment

3.3.1 Objectives


Limiters,

Predetection noise,

Postdetection noise.

3.3.2 Practicals


Practical 1: A Quadrature Detector with Limiter

Practical 2: The Effect of Noise on a Quadrature Detector

Practical 3: PLL Detector with a Limiter

Practical 4: The Effect of Noise on a PLL Detector



Signal Generation,

Modulator,

Limiter,


VCO,

Phase Comparator.


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3.3.4 Theory

3.3.4.1 Frequency Modulation


v = Vmax.sin(t+)

where v is the instantaneous voltage

Vmaxis the maximum voltage amplitude

is the angular frequency

is the phase

A steady voltage corresponding to the above equation conveys little information. Toconvey information the waveform must be made to vary so that the variations representthe information. This process is called modulation.

From the above equation, the basic parameters of such a waveform are:

its amplitude, Vmax

its frequency, (or f)

its phase,


Frequency modulation uses variations in frequencyto convey information. We shallthink in terms of the angular frequency w. The wave whose frequency is being varied iscalled the carrier wave. The signal doing the variation is called the modulating signal.

For simplicity, suppose both carrier wave and modulating signal are sinusoidal; ie,

vc= Vcsin ct

(c denotes carrier) and

vm= Vmcos mt

(m denotes modulation)


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3.3.4.2 What is Frequency?

If the frequency is varying, how do we define it? We can no longer count the number ofcycles over a longish interval to count the cycles per second. Instead we definefrequency as the rate of change of phase. This is consistent with the simple definition,

because at a constant (angular) frequency w radians/second the phase is changing at

radians per second, which is /2cycles per second.

Since we can only define what the instantaneous frequency is by reference to the phase,we must look at the phase in order to arrive at an expression for the frequency-modulatedsignal.

3.3.4.3 Phase of the FM Signal

For the unmodulated carrier vc= Vcsin ct, the phase is

s = ct

We want the modulating signal to vary the carrier frequency, c, so that its frequencytakes the form

= c+ D cos mt

(where D denotes the peak value of the deviation)

It is related to the amplitude of the modulating signal vmby the 'frequency slope' of thefrequency modulator (VCO) say k radians/s per V. The peak value of vmproducesdeviation D, so

D = k Vm

The total phase change undergone at time t is found by integrating the angular frequency.It is

s = (c+ D cos mt) dt

= ct + (D/m) sin mt.(If you are not familiar with integration you will have to take this result on trust).

So the FM signal can be expressed as:

Vcsin [ct + (D/m) sin mt],


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3.3.4.4 The Modulation Index

In that expression for the FM signal:


the coefficient (D/m) turns out to be quite important and is given the name 'modulationindex'. It is often represented by the Greek letter beta, .

So we may write the FM signal as:

vc= Vcsin (ct + sin m) t

where is the modulation index (D/m)

In this expression, the factor sin (ct + sin m) t (let us call it F) is of the form sin (a + b)which can be expanded to sin a cos b + cos a sin b.

Applying this expansion to F, we get

F = sin ct cos( sin m) t + cos ct sin ( sin m) t

3.3.4.5 FM Sidebands

These complicated functions can be expanded, using mathematics too elaborate toexplain here, into a series of terms like this:

F = J0( ) sin ct+ J1( ) [ sin (c+ m)t - sin (c- m)t ]

+ J2( ) [ sin (c+ 2m)t - sin (c- 2m)t ]

+ J3( ) [ sin (c+ 3m)t - sin (c- 3m)t ]+ J4( ) [ sin (c+ 4m)t - sin (c- 4m)t ]+ ...

where J0( ), J1( ), J2( ) etc are constants whose values depend only on . They are calledBessel Functions.

There is an infinite series of these functions, and so an infinite number of FMsidebands. But in practice the values of the Bessel functions become very small as theseries goes on. For example, when = 2

J0(2) = 0.224J1(2) = 0.577J2(2) = 0.353J3(2) = 0.129

J4(2) = 0.034J5(2) = 0.007


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3.3.4.6 A Practical Approximation Rule

Because the higher-order sidebands become very small, in practice the bandwidth ofthe FM signal may be restricted to a finite bandwidth .

The practical rule that is used, often called Carson's Rule, is to take the bandwidthrequired as:

B = 2 ( Fd+ Fm)

where B is the bandwidth, Fdthe deviation and Fmis the bandwidth of the modulation, all

in the same units.

3.3.5 Practical 1: A Quadrature Detector with Limiter

In this practical you will see how a limiter works.

In an FM system the information is carried by variations in carrier frequency. Since thevariations in amplitude carry no information,they can be removed before the signalarrives at the detector. This is the function performed by a limiter.

A limiter is simply a high gain amplifier that turns the usually sine-wave carrier of varyingamplitude into a square wave of constant amplitude. The square wave still contains thefrequency variations that contain the modulation.

The addition of a limiter means that the FM detector has a constant amplitudesignal to deal with which means that its output is only dependent on phasechanges and not changes in amplitude.

This can be shown in the practical by varying the carrier amplitude with no limiter inoperation and finding that the output signal also varies in amplitude. When the limiter isplaced in circuit the output no longer varies in this way.

Of course, the limiter cannot produce a signal from nothing so as the input carrieramplitude to the limiter falls the noise content increases. Ultimately the signal becomesunrecognisable because of noise.

The effect of noise on the detector performance is investigated in more detail in the nextPractical.


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3.3.5.1 Procedure

This practical shows the effect of a limiter on a quadrature detector. Start with the limiterout of circuit. Set modulation levelto maximum. Observe the signal at the detectoroutput 14 while varying the carrier level.

Use the Limiter Buttonto switch the limiter into circuit. Repeat your observations.


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3.3.5.2 Questions

1. In the absence of a limiter, does the demodulated output depend on the carrieramplitude?

2. Should it, ideally?

3. With the limiter in use, how does the demodulated output vary with carrier amplitude?

4. How does the waveform of the input to the phase comparator (point 9) differ with andwithout the limiter?


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3.3.6 Practical 2: The Effect of Noise on a Quadrature Detector

In the first Practical of this Assignment we saw how a limiter forces the input to thedetector to be of constant amplitude. This has an important effect on how the detectorbehaves when the signal is noisy.

3.3.6.1 What is Noise?

Noise is simply an unwanted signal which is mixed up with the required signal. In manycases it is not a specific frequency but is made up of random combinations of manyfrequencies.

Such unwanted noise may be generated internally by circuit elements like amplifiers orcome from the transmission medium such as cables or antennas. A very importantcharacteristic of a communication system is how well it works in the presence ofnoise.

FM systems offer some advantage over AM systems in their noise performance. Thetheory behind this is quite complex and will not be dealt with here.

3.3.6.2 Signal/Noise Ratios

One measure of the quality of the received signal applied to the detector is its Signal toNoise Ratio (SNR). This is simply the ratio of signal power to noise power, usuallyexpressed in decibels for convenience. A high SNR means that there is much more signalthan noise.

After passing through the detector the demodulated output also has noise on it, andtherefore has a signal to noise ratio. These two ratios are often called predetection SNR(SNRi) and post detection SNR (SNRo).

In an AM system these two values are approximately equal, but in an FM system the

SNRocan be greater than SNRi. How much greater depends on many things, butespecially on the modulation index.

Another contrast between AM and FM is that in an AM channel, SNR iis proportional toSNRobut in FM it is not; instead, as SNRiis reduced below a certain level, called thethreshold, SNRodrops very quickly.

This means that FM systems tend to degenerate very quickly at low SNR. In general, thegreater the modulation index (and therefore the bandwidth)

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