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TelecommunicationsAnalog Communications

Courseware Sample

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TELECOMMUNICATIONSANALOG COMMUNICATIONS

COURSEWARE SAMPLE

bythe Staff

ofLab-Volt (Quebec) Ltd

Copyright © 1999 Lab-Volt Ltd

All rights reserved. No part of this publication may be reproduced, in anyform or by any means, without the prior written permission of Lab-VoltQuebec Ltd.

Printed in CanadaSeptember 1999

III

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Courseware Outline

Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

AM / DSB / SSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX

FM / PM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII

Sample Exercise from Instrumentation

Ex. 2-4 Harmonic Composition of a Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Fundamentals of analysis, harmonic decomposition and reconstruction of asignal.

Sample Exercise from AM / DSB / SSB

Ex. 4-2 Reception and Demodulation of DSB Signals . . . . . . . . . . . . . . . . . . . . 15

Observation and demonstration of DSB reception and demodulation. TheCOSTAS loop detector and why it is necessary for DSB demodulation.Observation and comparison of the demodulated signals obtained using theenvelope and the synchronous detectors.

Sample Exercise from FM / PM

Ex. 2-1 The FM Modulation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Parameters of the modulation index and their effect on the frequency deviationof an FM signal and on the width of the spectrum.

Other samples extracted from FM / PM

Unit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Answers to Procedure Step Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Answers o Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Instructor's Guide Sample Extract from AM / DSB / SSB

Unit 1 Amplitude Modulation Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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The Lab-Volt® Model 8080 Analog Communications Training System is designed for multi-leveltraining in analog communications. The training system consists of six instrumentationmodules and six training modules. The training modules are divided into two groups: the AMcommunications modules and the FM communications modules. The instrumentation modulesare common to both groups.

The training modules have been designed to be as realistic as possible. The operatingfrequencies and ranges for AM and FM generators and receivers have been chosen to reflectstandard radio broadcasting usage. The physical design of the system emphasizesfunctionality, and the individual modules are stackable. Power is supplied through multi-pinconnectors located on the top and bottom panels of the modules. The Power Supply / DualAudio Amplifier module is double-width and forms the physical base for the other systemmodules. It also ensures efficient overvoltage and short-circuit protection of the system.

In keeping with the hands-on approach to student learning, the courseware consists of athree-volume set of exercise material correlated to the 8080 training system.

Volume 1 provides an introduction to the instrumentation modules and an introductorycoverage of RF communications fundamentals.

Volume 2 deals with the subject of AM (broadcast AM, DSB, SSB), and contains exercisesespecially designed to demonstrate the parameters associated with this type of modulation.

Volume 3 treats the topic of angle modulation (FM and PM) and provides detailed coverageof fundamental concepts.

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INSTRUMENTATION

VII

Unit 1 Basic Concepts and Equipment

Knowledge of the operation of the Dual Function Generator, the True RMSVoltmeter/Power Meter, and the Dual Audio Amplifier.

Ex. 1-1 The Dual Function Generator

Use and knowledge of the operation of the Dual Function Generator.

Ex. 1-2 The True RMS Voltmeter/Power Meter as a Voltmeter

Use of the True RMS Voltmeter/Power Meter as a voltmeter with the AudioAmplifier. Relationship between rms voltage and peak-to-peak voltage.

Ex. 1-3 The True RMS Voltmeter/Power Meter as a Power Meter

Use of the True RMS Voltmeter/Power Meter to make power measure-ments. Relationship and differences between dB, dBm, and dBW.

Ex. 1-4 The Dual Audio Amplifier

Plotting the frequency-response curve of the Dual Audio Amplifier, anddetermining its bandpass.

Unit 2 Spectral Analysis

Horizontal Calibration and Vertical Scales of the Spectrum Analyzer, their use, anda study of a spectral analysis.

Ex. 2-1 Introduction to Spectral Analysis

Observation of signals using the oscilloscope and the Spectrum Analyzer.

Ex. 2-2 Horizontal Calibration of the Spectrum Analyzer

Horizontal calibration of the Spectrum Analyzer, using an oscilloscope toread the results.

Ex. 2-3 Vertical Scales of the Spectrum Analyzer

Use of the vertical scales of the Spectrum Analyzer to measure the powerand relative voltage level of signal components.

Ex. 2-4 Harmonic Composition of a Signal

Fundamentals of analysis, harmonic decomposition and reconstruction ofa signal.

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INSTRUMENTATION

VIII

Ex. 2-5 Spectral Analysis of a Signal

Complete analysis of a signal; measuring harmonic frequencies andmeasuring power. Addition of dBm.

Unit 3 Modulation Fundamentals

Introduction to terminology and waveforms associated with AM and FM.

Ex. 3-1 Amplitude Modulation

Generation and observation of an amplitude-modulated signal.

Ex. 3-2 Frequency Modulation

Generation and observation of a frequency-modulated signal.

Appendix A Radio Wave PropagationAppendix B Spectrum Users and Propagation ModesAppendix C Noise in TelecommunicationsAppendix D Linking MethodsAppendix E Guide to AbbreviationsAppendix F Common SymbolsAppendix G Answers to Procedure Step QuestionsAppendix H Answers to Review QuestionsAppendix I Module Front PanelsAppendix J Equipment Utilization chart

BibliographyReader’s Comment Form

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AM / DSB / SSB

IX

Introduction

Performing Analog Communications Cou rseware Us ing the Lab-Volt Data Acquisitionand Management System (LVDAM-COM)

Parts List

Unit 1 Amplitude Modulation Fundamentals

Basic concepts and terminology used in AM communications. Using the AMequipment.

Ex. 1-1 An AM Communications System

Definition of basic concepts. Using the AM / DSB / SSB Generator with theAM / DSB Receiver to demonstrate an AM communications system.

Ex. 1-2 Familiarization with the AM Equipment

Becoming familiar with the AM / DSB / SSB Generator and the AM / DSBReceiver. Time and frequency domain observations of AM signals.

Ex. 1-3 Frequency Conversion of Baseband Signals

Demonstrating frequency conversion of baseband signals. The concepts offrequency translation and frequency multiplexing.

Unit 2 The Generation of AM Signals

The generation and analysis of AM signals. Observation and measurement of theparameters associated with AM signals.

Ex. 2-1 An AM Signal

Using the AM / DSB / SSB Generator and test instruments to demonstratethe characteristics of an AM signal in the time and frequency domains.

Ex. 2-2 Percentage Modulation

Definition of percentage modulation and methods used to determine themodulation index of an AM signal. Linear and nonlinear overmodulation.

Ex. 2-3 Carrier and Sideband Power

Demonstrating how the total RF power is divided between the RF carrierand the AM sidebands. Using the Spectrum Analyzer and the True RMSVoltmeter / Power Meter to determine the power distribution directly.Transmission efficiency.

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AM / DSB / SSB

X

Unit 3 Reception of AM Signals

The functional operations required of a superheterodyne receiver to select, process,and demodulate AM signals.

Ex. 3-1 The RF Stage Frequency Response

Frequency response characteristics of the RF stage. Bandwidth require-ments for the RF filter.

Ex. 3-2 The Mixer and Image Frequency Rejection

The mixer’s role in a superheterodyne receiver. Problems caused by imagefrequencies. The image frequency rejection ratio.

Ex. 3-3 The IF Stage Frequency Response

Frequency response characteristics of the IF stage. Bandwidth require-ments for the IF stage.

Ex. 3-4 The Envelope Detector

Using an envelope detector to recover the transmitted message signal.Observation and comparison of results obtained using a synchronous PLLdetector. The role of the AGC circuit.

Unit 4 Double Sideband Modulation %% DSB

The concepts associated with DSB modulation. Advantages and disadvantages.Requirements for reception and demodulation.

Ex. 4-1 DSB Signals

Using the AM / DSB / SSB Generator to demonstrate DSB modulation.Observation of DSB signals in the time and frequency domains. Differencesand similarities with AM.

Ex. 4-2 Reception and Demodulation of DSB Signals

Observation and demonstration of DSB reception and demodulation. TheCOSTAS loop detector and why it is necessary for DSB demodulation.Observation and comparison of the demodulated signals obtained using theenvelope and the synchronous detectors.

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AM / DSB / SSB

XI

Unit 5 Single Sideband Modulation (SSB)

The concepts associated with SSB modulation. Advantages and disadvantages.Requirements for reception and demodulation.

Ex. 5-1 Generating SSB Signals by the Filter Method

Using the AM / DSB / SSB Generator to demonstrate the filter method ofgenerating SSB signals. Sideband selection and how it is accomplished.Observation of SSB signals in the time and frequency domains.

Ex. 5-2 Reception and Demodulation of SSB Signals

Observation and demonstration of SSB reception and demodulation. Theimportance of tuning the BFO to the correct frequency. Frequency errorsand sideband reversal.

Unit 6 Troubleshooting AM Communications Systems

Introduction to methods and techniques for troubleshooting AM communicationssystems using the AM communications modules. Exercises 6-2 through 6-7 aredesigned around the use of schematic diagrams, troubleshooting worksheets andother provided material. Specific procedure steps are given only where necessary toallow students to fully synthetise the knowledge gained in Units 1 through 5.

Ex. 6-1 Troubleshooting Techniques

Troubleshooting Fault 11 in the AM / DSB / SSB Generator. Presentationand use of an effective technique for troubleshooting the AM communica-tions modules.

Ex. 6-2 Troubleshooting the AM / DSB sect ion of the AM / DSB/ SSB Gen era-tor

Troubleshooting instructor-inserted faults in the AM / DSB section of theAM / DSB / SSB Generator.

Ex. 6-3 Troubleshooting the SSB section of the AM / DSB/ SSB Generator

Troubleshooting instructor-inserted faults in the SSB section of the AM /DSB / SSB Generator.

Ex. 6-4 Troubleshooting the AM / DSB Receiver

Troubleshooting instructor-inserted faults in the AM / DSB Receiver.

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AM / DSB / SSB

XII

Ex. 6-5 Troubleshooting the SSB Receiver

Troubleshooting instructor-inserted faults in an SSB Receiver.

Ex. 6-6 Troubleshooting an AM / DSB Communications System

Troubleshooting instructor-inserted faults in an AM / DSB communicationssystem.

Ex. 6-7 Troubleshooting an SSB Communications System

Troubleshooting instructor-inserted faults in an SSB communicationssystem.

Appendix A Answers to Procedure Step QuestionsAppendix B Answers to Review QuestionsAppendix C Module Front PanelsAppendix D Test Points and DiagramsAppendix E Set up and calibration of the 9405 Spectrum Analyzer ModuleAppendix F Equipment Utilization Chart


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FM /PM

XIII

Introduction

Performing Analog Communications Cou rseware Us ing the Lab-Volt Data Acquisitionand Management System (LVDAM-COM)

Equipment Required

Unit 1 Frequency Modulation Concepts

Frequency Modulation analyzed in the time and frequency domains.

Ex. 1-1 Time-Domain Observations

Time-domain analysis of phase and frequency-modulated signals, using anoscilloscope. Relationship between the level of a modulating signal and thefrequency deviation.

Ex. 1-2 Frequency-Domain Observations

Frequency-domain analysis of frequency modulation. Evaluation of someparameters of these signals.

Unit 2 Fundamentals of Frequency Modulation

Effect of the modulation index on frequency deviation. Evaluation of the spectralposer distribution and the bandwidth of an FM signal.

Ex. 2-1 The FM Modulation Index

Parameters of the modulation index and their effect on the frequencydeviation of an FM signal and on the width of the spectrum.

Ex. 2-2 Power Distribution

Evaluation of the total power of an Fm signal and of each spectral compo-nent as a function of the modulation index.

Ex. 2-3 Determination of the FM Bandwidth

Evaluation of the bandwidth of an FM signal using the spectrum analyzer.Variation of the bandwidth with the modulation index.

Unit 3 Narrow Band Angle Modulation

Generation of narrow band angle modulation. Relationship between FM and PMmodulation and spectral analysis.

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FM /PM

XIV

Ex. 3-1 Basic Principles of Narrow Band Angle Modulation

Comparison between bandwidth of NBFM signals and the frequencydeviation. Observation of spectral power distribution.

Ex. 3-2 The Relationship between FM and PM

Study of the relationship between NBFM and PM using the integrator in thePM modulation of the indirect FM / PM Generator.

Ex. 3-3 Spectral Characteristics

Spectral analysis of NBFM and PM signals. Rapid evaluation of themodulation index using the frequency spectrum of a signal.

Unit 4 Wide Band Frequency Modulation

The principal characteristics of WBFM; analysis and measurements.

Ex. 4-1 Frequency Multiplication

Principles of frequency multiplication and its effect on the signal.

Ex. 4-2 Spectral Analysis

The principal parameters of wide band frequency modulation. Evaluation ofthe bandwidth for different values of the modulation index.

Unit 5 Generation of FM Signals

Direct generation of FM signals using the Direct FM Multiplex Generator. Principlesof indirect generation and signal analysis. Differences between these two methodsof FM generation.

Ex. 5-1 Direct Method of Generating FM Signals

Direct FM generation and changes in the frequency deviation as a functionof the level of the modulating signal at different modulation sensitives.

Ex. 5-2 Indirect Method of Generating FM Signals

Indirect generation of an FM signal using the Indirect FM / PM Generator.Armstrong modulation. Signal analysis at different stages.

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FM /PM

XV

Unit 6 Reception of FM Signals

Selectivity and sensitivity of fixed-frequency and tunable superheterodyne receivers.Signal observation at various stages. The S-curve of the demodulator for each typeof receiver.

Ex. 6-1 The Fixed-Frequency Receiver

Different stages in the demodulation process. Evaluation of the selectivityand sensitivity of a receiver. Effect of the limiter on the RF signal andplotting the S-curve of the discriminator in the FM / PM Receiver.

Ex. 6-2 The Tunable Receiver

The local oscillator and automatic gain control of a receiver. Operation andobservation of signals in the intermediate frequency stage. Plotting the S-curve of the quadrature detector.

Unit 7 Frequency Division Multiplexing

Principles and applications of multiplexing using the Direct FM Multiplex Generator.

Ex. 7-1 Stereophonic Frequency Modulation

Generation of the baseband and stereophonic modulation.

Ex. 7-2 Stereophonic Reception

Different stages in stereo reception and channel separation.

Ex. 7-3 Multiple Modulation

Use of frequency modulation to transmit an auxiliary signal.

Ex. 7-4 Regulations Concerning FM Broadcasting

Spectral power distribution of baseband multiplex signals. Characteristicsand standards for multiplex frequency modulation.

Unit 8 Noise in Frequency Modulation

Evaluation and improvement of the signal to noise ratio at the detector input andoutput. The effect of preemphasis on the S /N ratio.

Ex. 8-1 Improvement of the Signal / Noise Ratio

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FM /PM

XVI

Evaluation of the signal to noise ratio at the detector input and output.Improvement of the S / N ratio by the detector.

Ex. 8-2 Preemphasis and Deemphasis

Use of preemphasis and deemphasis. Improvement of the S / N ratio.

Unit 9 Troubleshooting FM Communications Systems

Presentation of logical and rational troubleshooting methods. Step by step trouble-shooting of the Direct FM Multiplex Generator as an example.

Ex. 9-1 Techniques of Troubleshooting

Step by step troubleshooting of the Direct FM Multiplex Generator afterintroducing a fault.

Ex. 9-2 Troubleshooting the Direct FM Multiplex Generator

Troubleshooting following the introduction of a fault.

Ex. 9-3 Troubleshooting the Indirect FM / PM Generator


Ex. 9-4 Troubleshooting the FM / PM Receiver


Ex. 9-5 Troubleshooting the WBFM System


Appendix A Logarithm TableAppendix B Module Front PanelsAppendix C Test Points and DiagramsAppendix D Answers to Procedure Step QuestionsAppendix E Answers to Review QuestionsAppendix F Equipment Utilization Chart


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(c) Sawtooth signal

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EXERCISE OBJECTIVE

When you have completed this exercise, you will be able to decompose a square wave signalinto its fundamental sinusoidal harmonics using the Spectrum Analyzer.

DISCUSSION

Signals which repeat, cycle after cycle, are called periodic. The period T is the duration of acomplete cycle. Figure 2-23 shows some common periodic signals.

Figure 2-23. Periodic signals.


2

Using a combination of periodic signals, it is possible to reconstruct the triangular waveformof Figure 2-23 (b), or any other periodic signal. Whatever the periodic signal, it can always bethought of as a superposition of sinusoidal signals which have a certain phase relationshipbetween them.

Sinusoidal signals which are whole number multiples of the fundamental frequency arecalled harmonics. The fundamental frequency corresponds to the frequency of the periodicsignal.

If the fundamental frequency is f0, then the reciprocal gives the period T0:

T0

1f0

or f0

1T0

The 2nd harmonic has a frequency of f2 = 2f0.

The 3rd harmonic has a frequency of f3 = 3f0 etc.

For example, if T0 = 2 ms, then f0 = (1/0.002) = 500 Hz,

and 2f0 = 1 000 Hz, 3 f0 = 1 500 Hz etc.

Harmonics whose frequencies are even multiples of the fundamental frequency are calledeven harmonics, (2 f0, 4 f0, 6 f0 etc.), while the other harmonics are called odd harmonics.

A square wave is an example of signal reconstruction with the superposition of harmonics.Figure 2-24 shows the various stages of reconstruction.

As the third, fifth, and seventh harmonics are added, the signal looks more and more like thesquare wave. However, it is not perfect; only after adding an infinite number of odd harmonics,would the signal be truly square.

Spectral Analysis shows us that a square wave is composed of an infinite number of oddharmonics, with decreasing amplitude, and therefore power, as the order increases.


3

7 f

1/7 A

5 f

1/5 A

3 f

f

f + 3 f + 5 f + 7 f

0A

0A

0

0

01/3 A

0

0

0

0

0 0 0 0

f + 3 f 0 0

Figure 2-24. Reconstruction of a square wave from its harmonics.


4

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FREQUENCY

f 0 3 f 0 5 f 0 7 f 0 9 f 0 11 f 0

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FREQUENCY

f 0

Figure 2-25 shows the lines produced by the Spectrum Analyzer for such a signal.

Figure 2-25. Spectral lines of a square wave signal.

If the signal to the analyzer is purely sinusoidal, the analyzer produces the line shown inFigure 2-26.

Figure 2-26. Spectral line of a sine wave with frequency f 0.

This spectrum consists of only one line, at the frequency of the signal, and with an amplitudeequal to the rms value of the signal if a linear scale is used. On the logarithmic scale, the lineshows the signal power, expressed in dBm.

When the spectrum contains several lines, the rms voltage An, corresponds to the Nth orderharmonic, calculated using the formulas in Figure 2-27 for (a) square waves, and (b) trianglewaves. Usually, calculations stop at the 5th order , since higher-order components are muchsmaller.


5

(a) Square wave signal

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(b) Sawtooth wave

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2 A

2 A

A

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FREQUENCY

f 0 3f 0 5f 0

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FREQUENCY

A =n4 A

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2 An

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Figure 2-27. Harmonic amplitudes.

EQUIPMENT REQUIRED

DESCRIPTION MODEL

Accessories 8948Power Supply/Dual Audio Amplifier 9401Dual Function Generator 9402True RMS Voltmeter/Power meter 9404Spectrum Analyzer 9405Oscilloscope &

PROCEDURE

* 1. Set up the modules as shown in Figure 2-28. Make sure that all OUTPUT LEVEL andGAIN controls are turned fully counterclockwise to the MIN position , and power upthe equipment.


6

POWER SUPPLY DUAL AUDIO AMPLIFIER

OSCILLOSCOPE

SPECTRUMANALYZERGENERATOR

DUAL FUNCTION

VOLTMETER / POWER METERTRUE RMS

Figure 2-28. Suggested Module Arrangement.

Note: The most efficient use of the screen is made if the reference line ismoved completely to the left. To do this, connect the oscilloscope to theSCOPE OUTPUT of the Spectrum Analyzer, and adjust the oscilloscope asfollows: 1 VOLT/DIV on the 2 channels, X-Y time base, DC coupling. Usethe TUNING knobs to move the reference line over to the left-hand edge ofthe screen. The base of the line should be one division from the bottom ofthe screen.

* 2. Connect OUTPUT A from the Dual Function Generator to the INPUT of the SpectrumAnalyzer, and to the input of the True RMS Voltmeter/Power Meter, using aBNC T-connector. Connect the Spectrum Analyzer vertical and horizontal SCOPEOUTPUTS to the corresponding vertical and horizontal inputs of the oscilloscope.

Set the Spectrum Analyzer controls to the following positions:

INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6MAXIMUM INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 dBmFREQUENCY RANGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0-30 MHzFREQUENCY SPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 kHz/VOUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CALOUTPUT SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOGMARKERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OPLOTTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SCOPE (both switches)MEMORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AMODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIVE

Make the following adjustments on the Function Generator:

OUTPUT FREQUENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 kHzFUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ATTENUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 dBOUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,4 V (measured with the

True RMS Voltmeter/Power Meter)


7

FREQUENCY [kHz]

PO

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R [d

Bm

]

f 0 3 f 0 5 f 0 07 f

+ 30

+ 20

+ 10

0

- 10

- 20

- 30

These adjustments produce a frequency spectrum from which you can calculate theamplitudes on the screen. In the LOG position, the vertical scale is graduated in dB.The spectrum in Figure 2-29 is used to show how readings are made.

Figure 2-29. Explanation of measurements.

Vertically:

% Since each vertical division on the oscilloscope represents 10 dB, the sixdivisions show 60 dB in all.

% If the MAXIMUM INPUT is 30 dBm into 50 6, the sixth division represents+30 dBm. Therefore, 0 dBm must be located on the third division. It followsthat, in Figure 2-29, f0 is at +15 dBm and 3 f0 is at 5 dBm.

Horizontally:

% One division represents 1 V and 1 V = 10 kHz, therefore, one divisionrepresents 10 kHz. In Figure 2-29, 3f0 is 20 kHz away from f0.

* 3. Adjust the frequency of the Dual Function Generator at 15 kHz.


8

Count the number of horizontal divisions between the 0 Hz reference line and the firstspectral line corresponding to f0. Given that one division represents 10 kHz, what isthe fundamental frequency of the signal?

f0 = kHz

By counting the number of divisions between each line, find the frequencies of eachharmonic.

3f0 = kHz

5f0 = kHz

* 4. If 6 vertical divisions correspond to the maximum dBm at the input, what is the powerof f0 and of each of the harmonics in dBm.

P(f0) = dBm

P(3f0) = dBm

P(5f0) = dBm

* 5. Given that Power (dBm) = 10 log (P/1 mW), refer to Figure 2-30, and find thepower P, in mW, of the above harmonics, and the corresponding rms voltage An

across a 50 6 load. An illustration of converting �17 dBm to 0.02 mW and 7 V to+30 dBm is shown in the figure.

Complete Table 2-4.

FREQUENCY P RMS VOLTAGE A n

Hz mW V

f0

3f0

5f0

Table 2-4. Harmonic power and rms voltage.

* 6. Given that the amplitude A of the square wave was fixed at 1.4 V during step 2,calculate the theoretical rms voltage (An) of the 3rd and 5th harmonic, using thefollowing equation:

where n is the number of the harmonic.A n

4 x A

n x % x 2,


9

Since % 3.14, A n

5.6

n x 3.14 x 2

A3 = V

A5 = V

Do they agree with the values in Table 2-4?

* Yes * No


10

POWER [dBm]

0 +10 +20 +30-10-20-30 -17

0.0001

0.001

0.01

0.1

1

10

100

7

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S V

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AG

E IN

TO

50

æ [V

]

100

10

1

0.1

0.01

0.001

PO

WE

R [m

W]

mW

dBm

V

d

Bm

0.02

Figure 2-30. Relationship between power and RMS voltage in 50 66.


11

0

* 7. In Figure 2-31, add the vertical amplitudes to get an approximate idea of theamplitude of a square wave signal.

Values above the horizontal axis are positive, while values below the axis arenegative.

* 8. Turn all OUTPUT LEVEL and GAIN controls to the MIN position. Place all powerswitches in the OFF position and disconnect all cables.

Figure 2-31. Near-perfect reconstruction of a signal from its principal harmonics.

CONCLUSION

The ability to decompose a periodic signal into its sinusoidal components is fundamental toperforming spectral analysis, and a periodic signal can be indirectly studied by analyzingsinusoidal components.

This exercise has allowed you to decompose a square wave signal into its principalharmonics, and to measure their frequency and amplitude using the Spectrum Analyzer. You


12

have also compared these measurements with theoretical values. Conversely, you havereconstructed a nearly-perfect square wave from its principal harmonics.

REVIEW QUESTIONS

1. Calculate the frequency of the 3rd and 5th harmonics of a square wave whose period T0

= 5 µs.

2. What is the amplitude of the first two harmonics if the peak-to-peak amplitude of thesquare wave signal is 4 V?

3. What is the Spectrum Analyzer useful for?

4. What does the oscilloscope measure when a signal is applied directly to its leads withoutgoing through the Spectrum Analyzer?

5. Can the shape of signals be directly calculated using spectral analysis? Explain.

* Yes * No

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(c) Incorrectly Demodulated Audio

(b) Correctly Demodulated Audio

(a) DSB Signal

MESSAGE SIGNAL

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EXERCISE OBJECTIVE

When you have completed this exercise, you will be able to explain and demonstrate receptionand demodulation of DSB signals with a COSTAS loop detector.

DISCUSSION

In Exercise 4-1, you saw that the message signal corresponds to the line drawn throughalternate lobes of the DSB signal waveform. This leads to a problem in demodulation sincea way must be found to indicate the polarity change of the message signal. If this is not done,the demodulated audio signal will consist of the external envelope of the DSB signal and willbe severely distorted. Figure 4-7 shows the audio waveforms for both correct and incorrectdemodulation.

Figure 4-7. Audio waveforms for correct and incorrect demodulation.

As shown in the figure, the waveform of the incorrectly demodulated audio signal correspondsto a rectified version of the original sine wave, and the frequency is twice that of the originalmessage signal. This is because the detector being used is not synchronized to detect the


16

polarity changes (zero crossover) of the message signal, and is therefore not able todemodulate the DSB signal.

An ordinary envelope detector will not allow proper demodulation of a DSB signal because itconsists essentially of a rectifier diode which "strips off" the envelope of the RF waveform. Thedemodulated audio will be similar to the rectified waveform shown in Figure 4-7 (c). A PLLsynchronous detector will not work properly either, since the phase reversal of the carriersignal will be taken as a phase error. This will result in an error signal being fed back to theVCO forcing the VCO output frequency to change in response to the phase change. The endresult will be an incorrectly demodulated audio signal as in Figure 4-7 (c).

The COSTAS loop detector will allow proper recovery of the audio signal. As shown inFigure 4-8, the PLL synchronous detector has been modified to include a COSTAS LOOPMIXER and a COSTAS LOOP COMPARATOR. The PLL MIXER output, instead of goingdirectly through the 5-Hz filter to the VCO, now passes through the 11-kHz filter, to becombined in the COSTAS loop mixer with the output of the COSTAS loop comparator. Theoutput of the COSTAS loop mixer now becomes the new error signal for the VCO. TheCOSTAS loop comparator maintains a constant amplitude signal at one of the COSTAS loopmixer’s inputs. This input signal changes polarity in synchronization with the message signal.The other input to the COSTAS loop mixer is the former error signal, and it changes polaritywhen phase reversal of the carrier occurs. Since both signals at the inputs of the COSTASloop mixer have now changed sign (polarity), the sign of the mixer output signal remainsconstant. (Remember, operation of a mixer in the time domain is mathematically equivalentto multiplication). In this way the error signal is prevented from indicating a phase error, andthe VCO remains synchronized with the carrier frequency.

EQUIPMENT REQUIRED

DESCRIPTION MODEL

Accessories 8948Power Supply/Dual Audio Amplifier 9401Dual Function Generator 9402Frequency Counter 9403AM / DSB / SSB Generator 9410AM / DSB Receiver 9411Oscilloscope &


17

SHIFTER90° PHASE

TP13

11 kHz

TP17

5 Hz

TP14

VCO

TP11

PLLMIXER

MIXERCOSTAS LOOP

COSTAS

SYNC

COMPARATORCOSTAS LOOP

TP12

35 kHz

MIXERDETECTOR

5 kHz

TP16TP15

AUDIOOUT

IF IN

Figure 4-8. A COSTAS loop detector.

PROCEDURE

* 1. Set up the modules as shown in Figure 4-9. Make sure that all OUTPUT LEVEL andGAIN controls are turned fully counterclockwise to the MIN position, and power up theequipment.


18


OSCILLOSCOPE

GENERATORDUAL FUNCTION

AM / DSB/ SSBGENERATOR

FREQUENCY COUNTER

AM / DSB RECEIVER

Figure 4-9. Suggested Module Arrangement.

* 2. Adjust the channel A controls on the Dual Function Generator to produce a 1.5 kHzsine wave with the OUTPUT LEVEL control set at ¼ turn cw. Select the 20 dBATTENUATOR.

* 3. Connect the 1.5 kHz signal to both the AUDIO INPUT of the AM / DSB / SSBGenerator and to channel 1 of the oscilloscope. Place the VOLTS / DIV control forchannel 1 at .2 V, and set the TIME / DIV control at .1 ms.

What do you observe on the oscilloscope?

* 4. Use the Frequency Counter to monitor the carrier frequency of the AM / DSB / SSBGenerator at TP13, and adjust the RF TUNING control to obtain fc = 1 000 kHz. Placethe RF GAIN (amplifier A2) at ¼ turn clockwise and set the CARRIER LEVEL controlat MIN. Make sure that it is pushed-in to the LINEAR OVERMODULATION position.

* 5. Connect the AM / DSB RF OUTPUT to the 50 6 RF INPUT of the AM / DSBReceiver.

* 6. The AM receiver must now be tuned to the carrier frequency. At what frequency mustthe local oscillator be set to accomplish this?

fLO = kHz


19

* 7. Adjust the RF TUNING on the AM / DSB Receiver to measure 1455 kHz at OSCOUTPUT so as to tune the receiver to the carrier frequency. Reconnect theFrequency Counter to TP13 on the AM / DSB / SSB Generator when fLO has been setto 1455 kHz.

* 8. Select the COSTAS DETECTOR on the AM / DSB Receiver, and place the AGCswitch in the I (active) position. Connect the AUDIO OUTPUT of the receiver tochannel 2 of the oscilloscope, and set the VOLTS / DIV control at 1 V.

* 9. Set the oscilloscope to trigger on the original audio signal (CH 1). Select dc couplingfor both channels, as well as the ALT position for the display.

What do you observe on the oscilloscope?

Note: It may be very difficult at first to obtain a stable display, because theCOSTAS detector requires that the carrier frequency be within 700 Hz(approx.) of the frequency to which the receiver is tuned. The fact that thelocal oscillator frequency of the receiver is more stable, and drifts much lesswith time, will allow you to concentrate only on readjusting the carrierfrequency. As the RF carrier frequency comes within the 1.4 kHz capturerange of the COSTAS loop detector, the "hopping" on the oscilloscopedisplay will become more rapid, until finally it stops and the signal is locked-in.

* 10. Adjust the position controls so that the original message signal is centered on thesixth graticule line, and the demodulated signal is centered on the second.

Readjust carefully the RF TUNING on the AM / DSB / SSB Generator until theoscilloscope display for channel 2 becomes stable and stops "hopping" up and down.

* 11. When the carrier frequency has been adjusted to provide a stable display for thedemodulated audio signal, sketch the waveforms of both signals in Figure 4-10.


20

Figure 4-10. Original and recovered signals with DSB modulation.

* 12. Compare the original and demodulated message signals.

* 13. Readjust the RF TUNING on the AM / DSB / SSB Generator as necessary tomaintain synchronization between the generator and the receiver. Because of thevery selective nature of the COSTAS loop detector this will probably be requiredoften.

With the generator and receiver properly synchronized, de-activate and activate theAGC switch several times before returning it to the I (active) position. What happens?

* 14. With the generator and receiver properly synchronized, select the SYNC detector onthe AM / DSB Receiver. Sketch the waveform of the demodulated audio signal inFigure 4-11.


21

Figure 4-11. Demodulated DSB signal obtained with the SYNC detector.

* 15. With the generator and receive properly synchronized, select the ENV detector on theAM / DSB Receiver. Sketch the waveform of the demodulated audio signal inFigure 4-12.

* 16. What are your observations concerning the results obtained with the ENV, SYNC,and COSTAS detectors?


22

Figure 4-12. Demodulated DSB signal obtained with the ENV detector.

* 17. Select the COSTAS DETECTOR. Use a BNC T-connector and a BNC cable toconnect the AUDIO OUTPUT of the AM / DSB Receiver to the Dual Audio Amplifierto monitor the demodulated audio signal with the headphones.

* 18. With the generator and receiver properly synchronized, what do you hear?

* 19. What happens to the sound when you try to demodulate the DSB signal using theENV and SYNC DETECTORS?

* 20. Disconnect the AM/DSB RF OUTPUT and connect a telescopic antenna to the 50 6RF INPUT and try to tune-in a local AM station. Use the SYNC DETECTOR and oncea station has been tuned in (if possible), select the COSTAS DETECTOR. Whathappens to the sound of the demodulated audio?


23

* 21. Turn all OUTPUT LEVEL and GAIN controls to the MIN position. Place all powerswitches in the off (O) position and disconnect all cables.

CONCLUSION

DSB modulation requires the use of a more complex receiver for demodulation and aCOSTAS loop detector is the central element of such a receiver. The COSTAS loop detectorensures that proper phase and frequency synchronization is maintained between the RFcarrier and the locally generated carrier. The use of a COSTAS loop detector requires that theRF carrier frequency be highly stable, since the frequency range over which the detector canmaintain proper synchronization is usually small. When a DSB-modulated signal isdemodulated using an envelope detector, or a synchronous detector, the recovered messagesignal is highly distorted.

REVIEW QUESTIONS

1. What type of detector is required to demodulate DSB signals?

2. The envelope of an AM signal corresponds to the waveform of the message signal. Whatdoes the waveform of the message signal correspond to in a DSB signal?

3. Sketch the audio waveform hat will be obtained if an envelope detector is used todemodulate a DSB signal.


24

4. Carrier phase reversal and message signal polarity changes occur in synchronization ina DSB signal. Control signals indicating these changes are combined through theCOSTAS LOOP MIXER. What effect does the mixer output signal have on the VCOgenerating the local carrier? Explain.

5. Why does a PLL synchronous detector cause the VCO to change the locally generatedcarrier frequency when this type of detector is used to demodulate a DSB signal?

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EXERCISE OBJECTIVES

When you have completed this exercise, you will be able to establish the relationship betweenvariations of the amplitude and frequency of the modulating signal and the sensitivity of themodulator, and the corresponding variations in the modulation index. You will be able to usethese parameters to change the frequency deviation and the width of the spectrum of an FMsignal.

DISCUSSION

The modulation index is just as important in frequency modulation as it is in amplitudemodulation. However, it is not calculated in the same way in each case.

Recall that the FM modulation index mf is equal to the ratio:

frequency deviationmodulating signal frequency

Therefore, any change in the frequency of the modulating signal will produce an oppositechange in the modulation index for the same frequency deviation, as shown in Figure 2-1 (a).

If, for example, a carrier is frequency modulated by a 5 kHz signal, and the frequencydeviation is 75 kHz, the modulation index equals 75/5 = 15.

If the frequency of the modulating signal is increased to 10 kHz, the modulation index willdecrease to 7.5 (75/10).

If the frequency of the modulating signal remains constant and the frequency deviation isincreased, the modulation index will increase, as shown in Figure 2-1 (b).

If the frequency deviation is changed from 75 kHz to 50 kHz, while the modulating signalfrequency remains constant at 5 kHz, the modulation index will change from 15 to 10.


28

(b) Fixed modulating signal frequency, frequency deviation increases (1 to 4)

(a) Fixed frequency deviation, modulating signal frequency increases (1 to 4)

m (1)f

m (2)f

m (3)f

m (4)f

1

2

3

4

Figure 2-1. Spectra of FM signals as a function of the modulation index m f.

The frequency deviation can be varied by changing the amplitude of the modulating signal orby using the DEVIATION control to vary the sensitivity of the FM modulator. The followingequation shows the relationship between the modulation index, the amplitude and frequencyof the modulating signal, and also the sensitivity of the modulator.

m f kf A m

fm

In this equation kfAm corresponds to the frequency deviation.

You will verify this relationship in the following exercise. The modulation index and the numberof spectral lines will be varied using:


29


OSCILLOSCOPE

SPECTRUMANALYZERGENERATOR

DUAL FUNCTION

VOLTMETER / POWER METERTRUE RMS

DIRECT FM MULTIPLEXGENERATOR

FM /PMRECEIVER

� the frequency and the amplitude of the modulating signal coming from the Dual FunctionGenerator

� the sensitivity of the modulator. This can be varied using the DEVIATION knob on theDirect FM Multiplex Generator.

EQUIPMENT REQUIRED

DESCRIPTION MODEL

Accessories 8948Power Supply/Dual Audio Amplifier 9401Dual Function Generator 9402True RMS Voltmeter / Power Meter 9404Spectrum Analyzer 9405Direct FM Multiplex Generator 9413FM / PM Receiver 9415Oscilloscope &

PROCEDURE

* 1. Set up the modules as shown in Figure 2-2. Make sure that all OUTPUT LEVEL andGAIN controls are turned fully counterclockwise to the MIN position, and power up theequipment.

Figure 2-2. Required Module Arrangement.


30

* 2. Make the following adjustments

On the Dual Function Generator

Channel A

FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .FREQUENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 kHzATTENUATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 dBOUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MIN

On the True RMS Voltmeter / Power Meter

MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VOLT

On the Direct FM Multiplex Generator

PREEMPHASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OMULTIPLEX SIGNALS . . . . . . . . . . . . . . . . . . all at O except L + R at ILEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CALDEVIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 kHz (knob pushed-in)RF GAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50% cw

On the Spectrum Analyzer

INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M6MAXIMUM INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 dBmFREQUENCY RANGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85-115 MHzFREQUENCY SPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 MHz / VOUTPUT SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOGOUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CAL

* 3. Connect the Spectrum Analyzer to the oscilloscope and calibrate it at 100 MHz.Connect the WBFM RF OUTPUT of the Direct FM Multiplex Generator to one of theWBFM RF INPUTS of the FM / PM Receiver, and to the INPUT of the SpectrumAnalyzer. Adjust the TUNING controls of the Spectrum Analyzer in order to move thecarrier line in the center of the screen. Decrease the FREQUENCY SPAN step bystep to 10 kHz / V, while keeping the carrier line in the center of the screen.

* 4. Adjust the RF GAIN of the Direct FM Multiplex Generator to obtain a carrier powerof about 5 dBm as indicated on the Spectrum Analyzer. (You may have to slightlyreadjust the fine TUNING control of the Spectrum Analyzer to keep the carrier line inthe center of the screen).

* 5. Tune the FM / PM Receiver to the frequency of the Direct FM Multiplex Generator.The green TUNING LED should light when the receiver is properly tuned.


31

f = 5 kHz, þf = kHz, m =m f

SECOND SIDEBAND PAIR

* 6. Connect OUTPUT A of the Dual Function Generator to both the INPUT of the TrueRms Voltmeter / Power Meter, and to the LEFT AUDIO INPUT of the Direct FmMultiplex Generator.

* 7. Carefully increase the OUTPUT LEVEL A of the Dual Function Generator until thesecond sideband pair of the FM spectrum is at a minimum amplitude for the first time.Figure 2-3 shows the spectrum that you should obtain.

Figure 2-3. FM Spectrum. FREQUENCY SPAN = 10 kHz / V.

* 8. On the FM / PM Receiver set the DEVIATION push-button to WBFM. Read thefrequency deviation �f indicated by the display.

Frequency deviation �f = kHz

Calculate the modulation index mf using

m f frequency deviation

modulating signal frequency

�ffm

Record the frequency deviation �f and the modulation index mf in Figure 2-3.

* 9. Carefully decrease FREQUENCY A of the Dual Function Generator (the modulatingsignal frequency fm) until you see the first sideband pair pass to a minimum amplitude,then to a maximum amplitude, and again to a minimum amplitude. Figure 2-4 showsthe spectrum you should obtain.


32

f = kHz, þf = kHz, m =m f

FIRST SIDEBAND PAIR

How does the spectrum of Figure 2-4 compare with that of Figure 2-3?

* 10. Read and note the frequency of the modulating signal fm on the Dual FunctionGenerator.

fm = kHz

Record the frequency fm in Figure 2-4.

Figure 2-4. FM Spectrum. FREQUENCY SPAN - 10 kHz / V.

* 11. Read and note the frequency deviation �f indicated by the FM / PM Receiver.

�f = kHz

Calculate the modulation index using

m f �ffm

Record the frequency deviation �f and the modulation index mf in Figure 2-4.


33

Is the frequency deviation in Figure 2-4 approximately the same as in Figure 2-3?

* Yes * No

Why does the frequency deviation stay the same when the frequency of themodulating signal varies?

* 12. How has decreasing the frequency of the modulating signal affected the modulationindex?

* 13. Readjust FREQUENCY A of the Dual Function Generator (fm) to obtain the spectrumof Figure 2-3. The frequency of the modulating signal should be close to 5 kHz.Record the frequency fm in Figure 2-5.

* 14. Zero the True RMS Voltmeter / Power Meter, then measure the level of themodulating signal.

Modulating signal level = mV

* 15. Carefully increase OUTPUT LEVEL A of the Dual Function Generator (Am) until yousee the first sideband pair pass to a minimum amplitude, then to a maximumamplitude, and again to a minimum amplitude. Figure 2-5 shows the spectrum youshould obtain.


34

f = kHz, þf = kHz, m =m f

FIRST SIDEBAND PAIR

Figure 2-5. FM Spectrum. FREQUENCY SPAN = 10 kHz / V.

Vary the fine TUNING control of the Spectrum Analyzer in order to observe all of thespectrum, then center the carrier line in the center of the screen.

How does the spectrum of Figure 2-5 compare with that of Figure 2-3?

* 16. With the True RMS Voltmeter / Power Meter measure the level of the modulatingsignal.

Modulating signal level = mV

Read and note the frequency deviation �f indicated by the FM / PM Receiver.

�f = kHz

Record the frequency deviation �f in Figure 2-5.


35

Explain your observations.

* 17. Calculate the modulation index using

m f �ffm

Record the modulation index mf in Figure 2-5.

How does this modulation index compare with the modulation index of Figure 2-3?Explain.

Observe the spectra shown in Figures 2-4 and 2-5. These FM spectra haveapproximately the same modulation index but they are very different. Explain why.

* 18. Readjust OUTPUT LEVEL A of the Dual Function Generator to obtain the spectrumof Figure 2-3.

* 19. Turn the DEVIATION knob on the Direct FM Multiplex Generator completelycounterclockwise, and then pull it out. This sets the sensitivity kf of the FM modulatorto its minimum. Observe the spectrum you obtain on the oscilloscope, then compareit with that of Figure 2-3.


36

* 20. Slowly increase the sensitivity of the FM modulator to maximum by turning theDEVIATION knob on the Direct FM Multiplex Generator clockwise. Observe thespectrum on the oscilloscope and the frequency deviation indicated by the FM / PMReceiver. Describe what happens to the spectrum.

What happens to the frequency deviation as the sensitivity is increased?

What happens to the modulation index? Explain.

* 21. Turn all OUTPUT LEVEL and GAIN controls to the MIN position. Place all powerswitches in the off (O) position and disconnect all cables.

CONCLUSION

In this exercise, you have seen that the frequency deviation is a function of both the amplitudeof the modulating signal and the sensitivity of the modulator. The modulation index is afunction of both the frequency deviation and the frequency of the modulating signal. Changingany of these values changes the spectrum of the FM signal.

REVIEW QUESTIONS

1. An FM signal is modulated by a 10 kHz sinusoidal signal. What is the value of itsmodulation index if the frequency deviation is 10 kHz?

2. What is the relationship between the modulation index and the amplitude of themodulating signal?


37

3. What parameters can change the frequency deviation?

4. An FM signal has a frequency deviation of 6 kHz when the modulating signal has anamplitude of 5 V, and a frequency of 1000 Hz. What will be the modulation index if thefrequency of the modulating signal is doubled?

5. When the DEVIATION knob is adjusted, what parameter changes?

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41

8QLW 7HVW

1. Frequency division multiplexing allows transmission of:

a. several messages, one after the other.b. several messages, all at the same time.c. one message on several carriers.d. several messages on several carriers.

2. In frequency division multiplexing, messages

a. are shifted in frequency.b. are frequency band changed.c. are separated in time.d. are all shifted onto the same frequency band.

3. How can a monophonic receiver recover a complete audio signal from a stereo RF signal?

a. It cannot.b. By detecting only the right signal.c. By detecting only the (L � R) signal.d. By detecting only the (L + R) signal.

4. In stereo modulation, the signal which modulates the 38 kHz subcarrier has a frequencyband covering:

a. 0-15 kHzb. 0-75 kHzc. 19-34 kHzd. 25-53 kHz

5. What is seen in the spectrum of an FM stereo signal when there is no audio signal?

a. Nothingb. A carrier with two 19-kHz lines on either side.c. Many lines.d. One line at 19 kHz.

6. What is the channel separation between the left and right channels of a receiver if the Leftoutput level is 5 V, including 5 mV from the Right channel?

a. �60 dBb. +60 dBc. 3 dBd. 1 mV

7. What is WBFM-FM modulation?

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42

a. Either an WBFM or FM modulation.b. A modulation which varies between WBFM and FM.c. WBFM modulation of an FM signal.d. FM modulation of an WBFM signal.

8. What is the bandwidth of an FM stereo signal without guard bands?

a. 240 kHzb. 150 kHzc. 75 kHzd. 15 kHz

9. How does the bandwidth of an FM signal vary when more and more messages aremultiplexed?

a. It decreases.b. It stays constant.c. It increases.d. It becomes unstable.

10. What is the frequency deviation relative to the signal modulating the 38-kHz subcarrier,when there is no SCA signal?

a. 75 kHzb. 33.75 kHzc. 30 kHzd. 7.5 kHz

43

MODULATING SIGNAL

UNMODULATED CARRIER

$QVZHUV WR 3URFHGXUH 6WHS 4XHVWLRQV

Note: All measurements, calculations and figures given as Answers toProcedure Step Questions are approximate, and should be considered onlyas a guide. These results may differ considerably from one AnalogCommunications Training System to another. The results of calculationshave been rounded off to the appropriate number of significant digits.

EXERCISE 1-1

* 4. A sound whose frequency varies continuously up and down. The signal from ChannelB modulates the frequency of the signal from Channel A.

* 7. The unmodulated sinusoidal signal and the square wave signal.

Figure 1-3. Carrier and Modulating signal.

fc = 1 kHz

fm = 100 Hz

* 8. The carrier now has two frequencies, each of which corresponds to one of thepositive and negatives alternances of the square wave.


44

MODULATING SIGNAL

MODULATED CARRIER

Figure 1-4. Modulated carrier and modulating signal.

* 9. The distance between the two frequencies of the modulated carrier increases with thelevel of the modulated signal.

* 10. Tmin = 0.7 ms

Tmax = 1.7 ms

* 11. fC max = 1429 Hz

fC min = 588 Hz

* 12. Frequency deviation (average) = 420 Hz

* 13. Am = 4.0 V peak

Sensitivity kf = 105 Hz / V

* 14. Tmin = 0.7 ms < fmax = 1429 Hz

Tmax = 1.7 ms < fmin = 588 Hz

Frequency deviation (average) = 420 Hz

Am = 4.8 V peak


45

Sensitivity kf = 87.5 Hz / V

EXERCISE 1-2

* 6.

Figure 1-8. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, f C = 1 MHz, fm = 5 kHz, small modulating signal.

There is a line on each side of the carrier spectral line.


46

* 7.

Figure 1-9. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, f C = 1 MHz, fm = 10 kHz, low level modulating signal.

The two spectral lines, one on each side of the carrier spectral line, move fartheraway from the carrier and their amplitude gets smaller.

* 8. There are more lines; the distance between each line corresponds to thefrequency of the modulating signal (5 kHz).

Figure 1-10. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, f C = 1 MHz, fm = 5 kHz, medium level modulatingsignal.


47

* 9.

Figure 1-11. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, f C = 1 MHz, fm = 5 kHz, high level modulating signal.

fm = 5 kHz

* 10. The spectral lines come closer together.

The number of spectral lines increases.

The amplitude of each spectral line changes.

The carrier spectral line gets smaller, disappears, then grows again. When itdisappears, there is practically no power at this frequency.


48

* 11.

Figure 1-12. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, f C = 1 MHz, fm = 1.75 kHz, high level modulatingsignal.

When the frequency deviation increases or when the frequency of the modulatingsignal is smaller, the number of spectral lines and the width of the spectrumincreases.

EXERCISE 2-1

* 8. Frequency deviation �f = 25 kHz

m f 255

5

* 9. Both spectra have approximately the same width but the spectrum of Figure 2-4contains many more spectral lines which are closer together.

* 10. fm = 2.5 kHz

* 11. �f = 25 kHz

m f 252.5

10

Yes

Because the frequency deviation is a function of both the modulating signalamplitude, and the sensitivity of the FM modulator: it is not affected by varying thefrequency of the modulating signal.


49

* 12. Decreasing the frequency of the modulating signal has caused the modulation indexto increase.

* 14. Modulating signal level = 165 mV

* 15. The spectrum of Figure 2-5 is wider and contains more spectral lines than thespectrum of Figure 2-3. However, the space between the spectral lines is the samefor both spectra.

* 16. Modulating signal level = 330 mV

�f = 50 kHz

Since the frequency deviation is equal to kfAm, increasing the modulating signal levelcauses both the frequency deviation and the width of the FM spectrum to increase.

* 17. m f 505

10

Since the frequency deviation of Figure 2-5 is approximately two times greater thanthat of Figure 2-3, the modulation index of the spectrum of Figure 2-5 is alsoapproximately two times greater than that of Figure 2-3.

The ratio �f/fm is the same for both spectra and this leads to the same modulationindex. However, the frequency deviation and the modulating signal frequency are notthe same for these spectra. This is why the two spectra are so different.

* 19. The spectrum is narrower and contains much fewer spectral lines than the spectrumof Figure 2-3.

* 20. Both the width of the spectrum and the number of spectral lines increase.

The frequency deviation increases.

Since the sensitivity of the FM modulator has increased, the frequency deviation hasalso increased and so has the modulation index.

EXERCISE 2-2

* 6.

MAXIMUM mf


50

1 0

2 4

3 7

4 10.5

Table 2-2.

mf (a) = 4 mf(b) = 7 mf(c) = 10.5

* 7. As the modulation index increases, the power is divided among more and morespectral components.

* 8.

mf = 0 mf = 4 Figure 2-10 (a)

n 0 1 2 3 n 0 1 2 3

Pn (dBm) �10 0 0 0 Pn (dBm) �20 �50 �18 �18

Pn (mW) 0.1 0 0 0 TOTALP0 + ��2Pn

Pn (mW) 0.01 0.016 0.016 TOTALP0 +��2Pn

2Pn (mW) 0 0 0 0.1 2Pn (mW) 0.032 0.032 0.074


51

mf = 7 Figure 2-10 (b) m f = 10.5 Figure 2-10 (c)

n 0 1 2 3 n 0 1 2 3

Pn (dBm) �22 �30 �25 �22 Pn (dBm) �22 �30 �24 �25

Pn (mW) 0.006 0.001 0.003 0.006 TOTALP0 + ��2Pn

Pn (mW) 0.006 0.001 0.004 0.003 TOTALP0 +��2Pn

2Pn (mW) 0.002 0.006 0.012 0.026 2Pn (mW) 0.002 0.008 0.006 0.022

Tables 2-3.

* 9. When the modulation index goes from 0 to 10.5, the power at the carrier frequencydecreases (from 0.1 to 0.006 mW) and the power in the first three spectralcomponents also decreases (from 0.064 to 0.016 mW).

EXERCISE 2-3

* 5. fC must be between 88 and 108 MHz.

* 6.

Figure 2-15. Spectrum of an NBFM signal. FREQUENCY SPAN = 2 kHz / V, f m = 5 kHz, mf = 0.5.

Bandwidth W (evaluated) = 10 kHz


52

* 7.

Figure 2-16. Spectrum of an FM signal. FREQUENCY SPAN = 2 kHz / V, f m = 5 kHz, mf = 2.4.


* 8. N = 4

Bandwidth W (calculated ) = 2Nfm = 2 x 4 x 5 = 40 kHz

* 9. Bandwidth W (evaluated)= 50 kHz

N = 7

Bandwidth W = 2 x 7 x 5 = 70 kHz

Bandwidth W = 2 x 5 (4 + 1) = 50 kHz

* 10. Bandwidth W (evaluated) = 70 kHz

* 11. The frequency of the modulating signal must be reduced to half.

Modulating frequency fm = 2.5 kHz



53

22 dB

To double the modulation index, the frequency of the modulating signal has beenreduced to half. The number of pairs of spectral lines has almost doubled, while thefrequency gap between each line has been reduced to half. Therefore, the bandwidthhas not changed much.

* 12. Bandwidth W (evaluated) = 64 kHz

EXERCISE 3-1

* 4.

Figure 3-4. Spectrum of an NBFM signal. FREQUENCY SPAN = 2 kHz / V, f m = 2 kHz.

W (evaluated) = 4 kHz

W (calculated) = 4 kHz

Difference in power �P = 22 dB

55

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EXERCISE 1-1

1. The size of antennas which must be practical andreception of only the wanted signal.

2. Phase modulation and frequency modulation. 3. The phase. 4. The frequency. 5. The sensitivity kf of the modulator, and the amplitude Am

of the modulating signal.

EXERCISE 1-2

1. The frequency fm of the modulating signal.2. The sensitivity kf of the modulator, the amplitude Am and

frequency fm of the modulating signal.3. 2 kHz.4. The number of spectral lines increases, and the spec-

trum becomes wider.5. The spectrum of an NBFM signal looks like that of an AM

signal, since there is only one spectral line on either sideof the carrier.

EXERCISE 2-1

1. mf = 12. mf = kfAm /fm3. The sensitivity kf of the modulator, and the amplitude of

the modulating signal.4. mf = 35. The sensitivity kf of the modulator.

EXERCISE 2-2

1. The order (n) of this spectral component.2. Pi = (0.51)² x 100 = 26 W3. 74 W4. The power is divided among mare spectral components.5. Since the power is proportional to the square of the n-th

Bessel coefficient Jn(mf), Pn = Jn²(mf) PT.

EXERCISE 2-3

1. The method using the number of pairs of significantspectral lines.The method using the number of spectral lines in thespectrum that fall within a 20 dB interval.

2. The modulation index and the frequency of the modulat-ing signal.

3. To at least 98% of the total power of the FM signal.4. Twice the frequency of the modulating signal.5. Because the frequency of the modulating signal is much

smaller than the frequency deviation and can be ne-glected.

EXERCISE 3-1

1. When the modulation index is less than 0.5, the modula-tion is said to be NBFM.

2. The other spectral components are small, and can beignored.

3. No. Different AM and NBFM signals can have the samespectrum.

4. The carrier. 5. W = 2fm.

EXERCISE 3-2

1. The phase changes by 90(. The amplitude of the signalbecomes inversely proportional to the input frequency.

2. A signal whose amplitude is inversely proportional to itsfrequency must be injected into the phase modulatorinput.

3. The modulation index is reduced by one-half. 4. It does not change. 5. Its level increases with its frequency.

EXERCISE 3-3

1. The spectrum contains three spectral lines; the centralline corresponds to the carrier; the others are at fc + fmand fc � fm.

2. J0(mf) w 1J1(mf) w mf / 2

3. The power contained in the spectral components de-creases.

4. 1.96%5. J2(mf) w mf / 2

EXERCISE 4-1

1. Because frequency multiplication allows the bandwidthand the frequency modulation of an NBFM signal to beincreased without changing the frequency of the modu-lating signal.

2. The multiplication factor. 3. The multiplication factor. 4. W = 2�f W = 2 x 20 x 50 = 200kHz 5. lt allows the carrier frequency to be placed within the

allocated frequency band.

EXERCISE 4-2

1. When its spectrum has a large number of lines.2. It also decreases.3. 154. In the spectral components.5. The amplitude Am of the modulating signal, and the

sensitivity kf of the modulator.

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INTRODUCTORY INFORMATION

Part of this unit is used to recall and strengthen concepts seen at the end ofVolume 1 % Instrumentation. The remainder is used to introduce the fundamental conceptsassociated with amplitude modulation, double sideband modulation, and single sidebandmodulation.

The basic principles of frequency conversion (translation) and modulation are also defined andillustrated.

It is in this unit that the student has his first experiences with the RF generators and receiversused in AM communication. Exercise 1-2, in particular, is designed to allow the student rapidfamiliarity with the AM / DSB / SSB Generator and the AM / DSB Receiver.

Many of the spectral observations of RF signals also serve as a concrete revision of how theSpectrum Analyzer is used.

INSTRUCTION PLAN

Ex. 1-1 AN AM COMMUNICATIONS SYSTEM

A. Illustrate a communications system

1. Unidirectional2. Bidirectional

B. Show the transformations necessary to communicate a message.

1. The modulating signal (message)2. The carrier signal3. The demodulated signal (recovered message)

Ex. 1-2 FAMILIARIZATION WITH THE AM EQUIPMENT

Time Domain Observations

A. Show an amplitude-modulated carrier signal.

1. Time domain observations2. Sideband frequencies for a sine wave message signal3. Sidebands for complex message signals


60

B. Demonstrate operation AM / DSB / SSB Generator controls.

1. Carrier Level2. RF Gain3. RF Tuning

C. Demonstrate operation of AM / DSB Receiver

1. OSC Output2. AGC3. SYNC Detector4. RF Tuning5. Local oscillator

Frequency Domain Observations

D. Observe the spectrum of an AM signal, and the effects produced by the AM modules’controls.

1. Evaluate sideband frequencies2. Evaluate frequency range covered by AM / DSB / SSB Generator

Ex. 1-3 FREQUENCY CONVERSION OF BASEBAND SIGNAL

A. Explain necessity of antennas for RF transmission.

1. Antenna height equal to twice the wavelength of signal to be transmitted2. Advantages of frequency translation

B. Show how a mixer is used for frequency translation.

1. Mixer symbol2. Output frequencies (fc � fm and fc + fm)3. Sideband frequencies when modulating signal is a sine wave signal.4. Sideband frequencies when modulating signal is a more complex voice signal.

C. Explain frequency multiplexing.

1. Transmission of several signals having the same baseband2. Translating these basebands signals to different frequencies3. Spectral analysis of two modulated RF signals4. Minimum station separation of 10 kHz

DEMONSTRATIONS

� Set up a complete AM transmission system, using the AM / DSB / SSB Generator, theAM / DSB Receiver, telescopic antennas, the Dual Function Generator as an audiosource, and the Dual Audio Amplifier as a monitor. Tune in the AM "station" and listen toa demodulated 1000 Hz square wave message signal.

� Use an oscilloscope to show the waveforms of the RF signal before and after modulation,and also the original and demodulated message signal.

� Use different waveforms for the message signal and observe the effect on the RF signal’senvelope.


61

� Use the AM / DSB/ SSB Generator to produce an 1100 kHz carrier signal and modulatethe carrier with a 2 kHz sine wave. Observe and explain the effect on the spectrum of theAM signal when the carrier frequency and the message signal frequency are varied.

AIDS TO THE PRESENTATION

A. Recall the various characteristics of a sine wave signal and relate their time domainrepresentations with those in the frequency domain.

B. Point out that spectral analysis of communications systems use high-quality, nondistorted sine waves as a message signals. Show the waveforms and spectra ofdistorted and non-distorted sine waves.

C. Review the operation of the Spectrum Analyzer, its controls and calibration.

D. Try to tune a local AM station and observe the spectrum of the modulated RF signal.To accomplish this install a telescopic antenna at the INPUT of the SpectrumAnalyzer (Z = 1 M6).

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