Telecommunications
Analog Communications
Courseware Sample
26866-F0
TELECOMMUNICATIONS
ANALOG COMMUNICATIONS
COURSEWARE SAMPLE
by
the Staff
of
Lab-Volt (Quebec) Ltd
Copyright © 1999 Lab-Volt Ltd
All rights reserved. No part of this publication may be reproduced, in any
form or by any means, without the prior written permission of Lab-Volt
Quebec Ltd.
Printed in Canada
September 1999
7DEOH RI &RQWHQWV
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 a
signal.
Sample Exercise from AM / DSB / SSB
Ex. 4-2
Reception and Demodulation of DSB Signals . . . . . . . . . . . . . . . . . . . . 15
Observation and demonstration of DSB reception and demodulation. The
COSTAS loop detector and why it is necessary for DSB demodulation.
Observation and comparison of the demodulated signals obtained using the
envelope 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 deviation
of an FM signal and on the width of the spectrum.
Other samples extracted from FM / PM
Unit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Answers to Procedure Step Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Answers 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-level
training in analog communications. The training system consists of six instrumentation
modules and six training modules. The training modules are divided into two groups: the AM
communications modules and the FM communications modules. The instrumentation modules
are common to both groups.
The training modules have been designed to be as realistic as possible. The operating
frequencies and ranges for AM and FM generators and receivers have been chosen to reflect
standard radio broadcasting usage. The physical design of the system emphasizes
functionality, and the individual modules are stackable. Power is supplied through multi-pin
connectors located on the top and bottom panels of the modules. The Power Supply / Dual
Audio Amplifier module is double-width and forms the physical base for the other system
modules. 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 a
three-volume set of exercise material correlated to the 8080 training system.
Volume 1 provides an introduction to the instrumentation modules and an introductory
coverage of RF communications fundamentals.
Volume 2 deals with the subject of AM (broadcast AM, DSB, SSB), and contains exercises
especially 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 coverage
of fundamental concepts.
V
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INSTRUMENTATION
Unit 1 Basic Concepts and Equipment
Knowledge of the operation of the Dual Function Generator, the True RMS
Voltmeter/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 Audio
Amplifier. 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 measurements. 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, and
determining its bandpass.
Unit 2 Spectral Analysis
Horizontal Calibration and Vertical Scales of the Spectrum Analyzer, their use, and
a 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 to
read the results.
Ex. 2-3 Vertical Scales of the Spectrum Analyzer
Use of the vertical scales of the Spectrum Analyzer to measure the power
and relative voltage level of signal components.
Ex. 2-4 Harmonic Composition of a Signal
Fundamentals of analysis, harmonic decomposition and reconstruction of
a signal.
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INSTRUMENTATION
Ex. 2-5 Spectral Analysis of a Signal
Complete analysis of a signal; measuring harmonic frequencies and
measuring 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
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Appendix G
Appendix H
Appendix I
Appendix J
Radio Wave Propagation
Spectrum Users and Propagation Modes
Noise in Telecommunications
Linking Methods
Guide to Abbreviations
Common Symbols
Answers to Procedure Step Questions
Answers to Review Questions
Module Front Panels
Equipment Utilization chart
Bibliography
Reader’s Comment Form
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AM / DSB / SSB
Introduction
Performing Analog Communications Courseware Using the Lab-Volt Data Acquisition
and Management System (LVDAM-COM)
Parts List
Unit 1 Amplitude Modulation Fundamentals
Basic concepts and terminology used in AM communications. Using the AM
equipment.
Ex. 1-1 An AM Communications System
Definition of basic concepts. Using the AM / DSB / SSB Generator with the
AM / 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 / DSB
Receiver. Time and frequency domain observations of AM signals.
Ex. 1-3 Frequency Conversion of Baseband Signals
Demonstrating frequency conversion of baseband signals. The concepts of
frequency translation and frequency multiplexing.
Unit 2 The Generation of AM Signals
The generation and analysis of AM signals. Observation and measurement of the
parameters associated with AM signals.
Ex. 2-1 An AM Signal
Using the AM / DSB / SSB Generator and test instruments to demonstrate
the 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 the
modulation 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 carrier
and the AM sidebands. Using the Spectrum Analyzer and the True RMS
Voltmeter / Power Meter to determine the power distribution directly.
Transmission efficiency.
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AM / DSB / SSB
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 requirements for the RF filter.
Ex. 3-2 The Mixer and Image Frequency Rejection
The mixer’s role in a superheterodyne receiver. Problems caused by image
frequencies. The image frequency rejection ratio.
Ex. 3-3 The IF Stage Frequency Response
Frequency response characteristics of the IF stage. Bandwidth requirements 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 PLL
detector. 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. Differences
and similarities with AM.
Ex. 4-2 Reception and Demodulation of DSB Signals
Observation and demonstration of DSB reception and demodulation. The
COSTAS loop detector and why it is necessary for DSB demodulation.
Observation and comparison of the demodulated signals obtained using the
envelope and the synchronous detectors.
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AM / DSB / SSB
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 of
generating 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. The
importance of tuning the BFO to the correct frequency. Frequency errors
and sideband reversal.
Unit 6 Troubleshooting AM Communications Systems
Introduction to methods and techniques for troubleshooting AM communications
systems using the AM communications modules. Exercises 6-2 through 6-7 are
designed around the use of schematic diagrams, troubleshooting worksheets and
other provided material. Specific procedure steps are given only where necessary to
allow 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. Presentation
and use of an effective technique for troubleshooting the AM communications modules.
Ex. 6-2 Troubleshooting the AM / DSB section of the AM / DSB/ SSB Generator
Troubleshooting instructor-inserted faults in the AM / DSB section of the
AM / 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
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 communications
system.
Ex. 6-7 Troubleshooting an SSB Communications System
Troubleshooting instructor-inserted faults in an SSB communications
system.
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Answers to Procedure Step Questions
Answers to Review Questions
Module Front Panels
Test Points and Diagrams
Set up and calibration of the 9405 Spectrum Analyzer Module
Equipment Utilization Chart
Bibliography
Reader’s Comment Form
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FM /PM
Introduction
Performing Analog Communications Courseware Using the Lab-Volt Data Acquisition
and 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 an
oscilloscope. Relationship between the level of a modulating signal and the
frequency deviation.
Ex. 1-2 Frequency-Domain Observations
Frequency-domain analysis of frequency modulation. Evaluation of some
parameters of these signals.
Unit 2 Fundamentals of Frequency Modulation
Effect of the modulation index on frequency deviation. Evaluation of the spectral
poser 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 frequency
deviation 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 component 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 PM
modulation and spectral analysis.
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FM /PM
Ex. 3-1 Basic Principles of Narrow Band Angle Modulation
Comparison between bandwidth of NBFM signals and the frequency
deviation. 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 the
PM modulation of the indirect FM / PM Generator.
Ex. 3-3 Spectral Characteristics
Spectral analysis of NBFM and PM signals. Rapid evaluation of the
modulation 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 of
the 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. Principles
of indirect generation and signal analysis. Differences between these two methods
of FM generation.
Ex. 5-1 Direct Method of Generating FM Signals
Direct FM generation and changes in the frequency deviation as a function
of 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
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 type
of receiver.
Ex. 6-1 The Fixed-Frequency Receiver
Different stages in the demodulation process. Evaluation of the selectivity
and sensitivity of a receiver. Effect of the limiter on the RF signal and
plotting 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 and
observation of signals in the intermediate frequency stage. Plotting the Scurve 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. Characteristics
and standards for multiplex frequency modulation.
Unit 8 Noise in Frequency Modulation
Evaluation and improvement of the signal to noise ratio at the detector input and
output. The effect of preemphasis on the S /N ratio.
Ex. 8-1 Improvement of the Signal / Noise Ratio
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FM /PM
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 troubleshooting 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 after
introducing 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
Troubleshooting following the introduction of a fault.
Ex. 9-4 Troubleshooting the FM / PM Receiver
Troubleshooting following the introduction of a fault.
Ex. 9-5 Troubleshooting the WBFM System
Troubleshooting following the introduction of a fault.
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Logarithm Table
Module Front Panels
Test Points and Diagrams
Answers to Procedure Step Questions
Answers to Review Questions
Equipment Utilization Chart
Bibliography
Reader’s Comment Form
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EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to decompose a square wave signal
into its fundamental sinusoidal harmonics using the Spectrum Analyzer.
DISCUSSION
TIME
AMPLITUDE
AMPLITUDE
Signals which repeat, cycle after cycle, are called periodic. The period T is the duration of a
complete cycle. Figure 2-23 shows some common periodic signals.
TIME
T
T
(b) Square wave signal
TIME
AMPLITUDE
AMPLITUDE
(a) Sinusoidal signal
T
TIME
T
(c) Sawtooth signal
(d) Triangular signal
Figure 2-23. Periodic signals.
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Using a combination of periodic signals, it is possible to reconstruct the triangular waveform
of Figure 2-23 (b), or any other periodic signal. Whatever the periodic signal, it can always be
thought of as a superposition of sinusoidal signals which have a certain phase relationship
between them.
Sinusoidal signals which are whole number multiples of the fundamental frequency are
called harmonics. The fundamental frequency corresponds to the frequency of the periodic
signal.
If the fundamental frequency is f0, then the reciprocal gives the period T0:
1
1
or
f0 f0
T0
The 2nd harmonic has a frequency of f2 = 2f0.
T0 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 called
even 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 the
square 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 odd
harmonics, with decreasing amplitude, and therefore power, as the order increases.
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A0
A0
f0
1/3 A
0
3 f0
f0 + 3 f 0
1/5 A 0
5 f0
1/7 A 0
7 f0
f0 + 3 f 0 + 5 f 0 + 7 f 0
Figure 2-24. Reconstruction of a square wave from its harmonics.
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AMPLITUDE
Figure 2-25 shows the lines produced by the Spectrum Analyzer for such a signal.
f0
3 f0
5 f0
7 f0
9 f 0 11 f 0
FREQUENCY
Figure 2-25. Spectral lines of a square wave signal.
AMPLITUDE
If the signal to the analyzer is purely sinusoidal, the analyzer produces the line shown in
Figure 2-26.
f0
FREQUENCY
Figure 2-26. Spectral line of a sine wave with frequency f0.
This spectrum consists of only one line, at the frequency of the signal, and with an amplitude
equal to the rms value of the signal if a linear scale is used. On the logarithmic scale, the line
shows the signal power, expressed in dBm.
When the spectrum contains several lines, the rms voltage An, corresponds to the Nth order
harmonic, calculated using the formulas in Figure 2-27 for (a) square waves, and (b) triangle
waves. Usually, calculations stop at the 5th order, since higher-order components are much
smaller.
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AMPLITUDE
AMPLITUDE
A
2A
An =
f0
TIME
3f 0
4A
n¼ 2
5f 0
FREQUENCY
-A
(a) Square wave signal
AMPLITUDE
AMPLITUDE
A
2A
An =
2A
n¼ 3
f 0 2f 0 3f 0 4f 0 5f 0
TIME
FREQUENCY
-A
(b) Sawtooth wave
Figure 2-27. Harmonic amplitudes.
EQUIPMENT REQUIRED
DESCRIPTION
MODEL
Accessories
Power Supply/Dual Audio Amplifier
Dual Function Generator
True RMS Voltmeter/Power meter
Spectrum Analyzer
Oscilloscope
8948
9401
9402
9404
9405
&
PROCEDURE
*
1. Set up the modules as shown in Figure 2-28. Make sure that all OUTPUT LEVEL and
GAIN controls are turned fully counterclockwise to the MIN position , and power up
the equipment.
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TRUE RMS
VOLTMETER / POWER METER
DUAL FUNCTION
GENERATOR
SPECTRUM
ANALYZER
OSCILLOSCOPE
POWER SUPPLY
DUAL AUDIO AMPLIFIER
Figure 2-28. Suggested Module Arrangement.
Note: The most efficient use of the screen is made if the reference line is
moved completely to the left. To do this, connect the oscilloscope to the
SCOPE OUTPUT of the Spectrum Analyzer, and adjust the oscilloscope as
follows: 1 VOLT/DIV on the 2 channels, X-Y time base, DC coupling. Use
the TUNING knobs to move the reference line over to the left-hand edge of
the screen. The base of the line should be one division from the bottom of
the screen.
*
2. Connect OUTPUT A from the Dual Function Generator to the INPUT of the Spectrum
Analyzer, and to the input of the True RMS Voltmeter/Power Meter, using a
BNC T-connector. Connect the Spectrum Analyzer vertical and horizontal SCOPE
OUTPUTS to the corresponding vertical and horizontal inputs of the oscilloscope.
Set the Spectrum Analyzer controls to the following positions:
INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6
MAXIMUM INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 dBm
FREQUENCY RANGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0-30 MHz
FREQUENCY SPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 kHz/V
OUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CAL
OUTPUT SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOG
MARKERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O
PLOTTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SCOPE (both switches)
MEMORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A
MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIVE
Make the following adjustments on the Function Generator:
OUTPUT FREQUENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 kHz
FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ATTENUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 dB
OUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,4 V (measured with the
True RMS Voltmeter/Power Meter)
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These adjustments produce a frequency spectrum from which you can calculate the
amplitudes 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.
+ 30
POWER [dBm]
+ 20
+ 10
0
- 10
- 20
- 30
f0
3 f0
5 f0
7 f0
FREQUENCY [kHz]
Figure 2-29. Explanation of measurements.
Vertically:
%
Since each vertical division on the oscilloscope represents 10 dB, the six
divisions 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 follows
that, 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 division
represents 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.
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Count the number of horizontal divisions between the 0 Hz reference line and the first
spectral line corresponding to f0. Given that one division represents 10 kHz, what is
the fundamental frequency of the signal?
f0 =
kHz
By counting the number of divisions between each line, find the frequencies of each
harmonic.
*
3f0 =
kHz
5f0 =
kHz
4. If 6 vertical divisions correspond to the maximum dBm at the input, what is the power
of 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 the
power 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 An
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 the
following equation:
An 4 x A
n x
8
%
x
, where n is the number of the harmonic.
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Since
%
3.14, A n 5.6
n x 3.14 x
A3 =
V
A5 =
V
2
Do they agree with the values in Table 2-4?
* Yes
* No
9
+DUPRQLF &RPSRVLWLRQ RI D 6LJQDO
100
10
7
10
1
m
V
1
m
0.1
mW
dB
POWER [mW]
dB
0.1
0.01
0.02
0.01
0.001
0.001
0.0001
-30
-20 -17
-10
0
+10
+20
+30
POWER [dBm]
Figure 2-30. Relationship between power and RMS voltage in 50 6.
10
RMS VOLTAGE INTO 50 æ [V]
100
+DUPRQLF &RPSRVLWLRQ RI D 6LJQDO
*
7. In Figure 2-31, add the vertical amplitudes to get an approximate idea of the
amplitude of a square wave signal.
Values above the horizontal axis are positive, while values below the axis are
negative.
*
8. Turn all OUTPUT LEVEL and GAIN controls to the MIN position. Place all power
switches in the OFF position and disconnect all cables.
0
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 to
performing spectral analysis, and a periodic signal can be indirectly studied by analyzing
sinusoidal components.
This exercise has allowed you to decompose a square wave signal into its principal
harmonics, and to measure their frequency and amplitude using the Spectrum Analyzer. You
11
+DUPRQLF &RPSRVLWLRQ RI D 6LJQDO
have also compared these measurements with theoretical values. Conversely, you have
reconstructed 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 the
square 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 without
going through the Spectrum Analyzer?
5. Can the shape of signals be directly calculated using spectral analysis? Explain.
* Yes
12
* No
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IURP
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EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to explain and demonstrate reception
and 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 through
alternate lobes of the DSB signal waveform. This leads to a problem in demodulation since
a 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 will
be severely distorted. Figure 4-7 shows the audio waveforms for both correct and incorrect
demodulation.
MESSAGE SIGNAL
(b) Correctly Demodulated Audio
(a) DSB Signal
(c) Incorrectly Demodulated Audio
Figure 4-7. Audio waveforms for correct and incorrect demodulation.
As shown in the figure, the waveform of the incorrectly demodulated audio signal corresponds
to a rectified version of the original sine wave, and the frequency is twice that of the original
message signal. This is because the detector being used is not synchronized to detect the
15
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
polarity changes (zero crossover) of the message signal, and is therefore not able to
demodulate the DSB signal.
An ordinary envelope detector will not allow proper demodulation of a DSB signal because it
consists essentially of a rectifier diode which "strips off" the envelope of the RF waveform. The
demodulated audio will be similar to the rectified waveform shown in Figure 4-7 (c). A PLL
synchronous detector will not work properly either, since the phase reversal of the carrier
signal will be taken as a phase error. This will result in an error signal being fed back to the
VCO forcing the VCO output frequency to change in response to the phase change. The end
result 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 in
Figure 4-8, the PLL synchronous detector has been modified to include a COSTAS LOOP
MIXER and a COSTAS LOOP COMPARATOR. The PLL MIXER output, instead of going
directly through the 5-Hz filter to the VCO, now passes through the 11-kHz filter, to be
combined in the COSTAS loop mixer with the output of the COSTAS loop comparator. The
output of the COSTAS loop mixer now becomes the new error signal for the VCO. The
COSTAS loop comparator maintains a constant amplitude signal at one of the COSTAS loop
mixer’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 polarity
when phase reversal of the carrier occurs. Since both signals at the inputs of the COSTAS
loop mixer have now changed sign (polarity), the sign of the mixer output signal remains
constant. (Remember, operation of a mixer in the time domain is mathematically equivalent
to multiplication). In this way the error signal is prevented from indicating a phase error, and
the VCO remains synchronized with the carrier frequency.
EQUIPMENT REQUIRED
16
DESCRIPTION
MODEL
Accessories
Power Supply/Dual Audio Amplifier
Dual Function Generator
Frequency Counter
AM / DSB / SSB Generator
AM / DSB Receiver
Oscilloscope
8948
9401
9402
9403
9410
9411
&
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
IF IN
AUDIO
OUT
TP16
TP15
PLL
MIXER
DETECTOR
MIXER
90° PHASE
SHIFTER
VCO
TP14
35 kHz
5 Hz
TP12
5 kHz
SYNC
TP11
COSTAS LOOP
COMPARATOR
COSTAS
TP13
TP17
11 kHz
COSTAS LOOP
MIXER
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 and
GAIN controls are turned fully counterclockwise to the MIN position, and power up the
equipment.
17
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
AM / DSB/ SSB
GENERATOR
AM / DSB RECEIVER
DUAL FUNCTION
GENERATOR
FREQUENCY COUNTER
OSCILLOSCOPE
POWER SUPPLY
DUAL AUDIO AMPLIFIER
Figure 4-9. Suggested Module Arrangement.
*
*
2. Adjust the channel A controls on the Dual Function Generator to produce a 1.5 kHz
sine wave with the OUTPUT LEVEL control set at ¼ turn cw. Select the 20 dB
ATTENUATOR.
3. Connect the 1.5 kHz signal to both the AUDIO INPUT of the AM / DSB / SSB
Generator and to channel 1 of the oscilloscope. Place the VOLTS / DIV control for
channel 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 / SSB
Generator at TP13, and adjust the RF TUNING control to obtain f c = 1 000 kHz. Place
the RF GAIN (amplifier A2) at ¼ turn clockwise and set the CARRIER LEVEL control
at MIN. Make sure that it is pushed-in to the LINEAR OVERMODULATION position.
5. Connect the AM / DSB RF OUTPUT to the 50
Receiver.
RF INPUT of the AM / DSB
6. The AM receiver must now be tuned to the carrier frequency. At what frequency must
the local oscillator be set to accomplish this?
fLO =
18
6
kHz
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
*
*
*
7. Adjust the RF TUNING on the AM / DSB Receiver to measure 1455 kHz at OSC
OUTPUT so as to tune the receiver to the carrier frequency. Reconnect the
Frequency Counter to TP13 on the AM / DSB / SSB Generator when fLO has been set
to 1455 kHz.
8. Select the COSTAS DETECTOR on the AM / DSB Receiver, and place the AGC
switch in the I (active) position. Connect the AUDIO OUTPUT of the receiver to
channel 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 coupling
for 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 the
COSTAS detector requires that the carrier frequency be within 700 Hz
(approx.) of the frequency to which the receiver is tuned. The fact that the
local oscillator frequency of the receiver is more stable, and drifts much less
with time, will allow you to concentrate only on readjusting the carrier
frequency. As the RF carrier frequency comes within the 1.4 kHz capture
range of the COSTAS loop detector, the "hopping" on the oscilloscope
display will become more rapid, until finally it stops and the signal is lockedin.
*
10. Adjust the position controls so that the original message signal is centered on the
sixth graticule line, and the demodulated signal is centered on the second.
Readjust carefully the RF TUNING on the AM / DSB / SSB Generator until the
oscilloscope 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 the
demodulated audio signal, sketch the waveforms of both signals in Figure 4-10.
19
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
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 to
maintain synchronization between the generator and the receiver. Because of the
very selective nature of the COSTAS loop detector this will probably be required
often.
With the generator and receiver properly synchronized, de-activate and activate the
AGC switch several times before returning it to the I (active) position. What happens?
*
20
14. With the generator and receiver properly synchronized, select the SYNC detector on
the AM / DSB Receiver. Sketch the waveform of the demodulated audio signal in
Figure 4-11.
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
Figure 4-11. Demodulated DSB signal obtained with the SYNC detector.
*
*
15. With the generator and receive properly synchronized, select the ENV detector on the
AM / DSB Receiver. Sketch the waveform of the demodulated audio signal in
Figure 4-12.
16. What are your observations concerning the results obtained with the ENV, SYNC,
and COSTAS detectors?
21
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
Figure 4-12. Demodulated DSB signal obtained with the ENV detector.
*
*
*
*
22
17. Select the COSTAS DETECTOR. Use a BNC T-connector and a BNC cable to
connect the AUDIO OUTPUT of the AM / DSB Receiver to the Dual Audio Amplifier
to 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 the
ENV and SYNC DETECTORS?
20. Disconnect the AM/DSB RF OUTPUT and connect a telescopic antenna to the 50 6
RF INPUT and try to tune-in a local AM station. Use the SYNC DETECTOR and once
a station has been tuned in (if possible), select the COSTAS DETECTOR. What
happens to the sound of the demodulated audio?
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
*
21. Turn all OUTPUT LEVEL and GAIN controls to the MIN position. Place all power
switches in the off (O) position and disconnect all cables.
CONCLUSION
DSB modulation requires the use of a more complex receiver for demodulation and a
COSTAS loop detector is the central element of such a receiver. The COSTAS loop detector
ensures that proper phase and frequency synchronization is maintained between the RF
carrier and the locally generated carrier. The use of a COSTAS loop detector requires that the
RF carrier frequency be highly stable, since the frequency range over which the detector can
maintain proper synchronization is usually small. When a DSB-modulated signal is
demodulated using an envelope detector, or a synchronous detector, the recovered message
signal 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. What
does 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 to
demodulate a DSB signal.
23
5HFHSWLRQ DQG 'HPRGXODWLRQ RI '6% 6LJQDOV
4. Carrier phase reversal and message signal polarity changes occur in synchronization in
a DSB signal. Control signals indicating these changes are combined through the
COSTAS LOOP MIXER. What effect does the mixer output signal have on the VCO
generating the local carrier? Explain.
5. Why does a PLL synchronous detector cause the VCO to change the locally generated
carrier frequency when this type of detector is used to demodulate a DSB signal?
24
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EXERCISE OBJECTIVES
When you have completed this exercise, you will be able to establish the relationship between
variations of the amplitude and frequency of the modulating signal and the sensitivity of the
modulator, and the corresponding variations in the modulation index. You will be able to use
these parameters to change the frequency deviation and the width of the spectrum of an FM
signal.
DISCUSSION
The modulation index is just as important in frequency modulation as it is in amplitude
modulation. 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 deviation
m odulating signal frequency
Therefore, any change in the frequency of the modulating signal will produce an opposite
change 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 frequency
deviation 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 will
decrease to 7.5 (75/10).
If the frequency of the modulating signal remains constant and the frequency deviation is
increased, 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 signal
frequency remains constant at 5 kHz, the modulation index will change from 15 to 10.
27
7KH )0 0RGXODWLRQ ,QGH[
m f (1)
1
m f (2)
2
m f (3)
3
m f (4)
4
(a) Fixed frequency deviation, modulating
signal frequency increases (1 to 4)
(b) Fixed modulating signal frequency,
frequency deviation increases (1 to 4)
Figure 2-1. Spectra of FM signals as a function of the modulation index mf.
The frequency deviation can be varied by changing the amplitude of the modulating signal or
by using the DEVIATION control to vary the sensitivity of the FM modulator. The following
equation shows the relationship between the modulation index, the amplitude and frequency
of the modulating signal, and also the sensitivity of the modulator.
mf kf Am
fm
In this equation kfAm corresponds to the frequency deviation.
You will verify this relationship in the following exercise. The modulation index and the number
of spectral lines will be varied using:
28
7KH )0 0RGXODWLRQ ,QGH[
the frequency and the amplitude of the modulating signal coming from the Dual Function
Generator
the sensitivity of the modulator. This can be varied using the DEVIATION knob on the
Direct FM Multiplex Generator.
EQUIPMENT REQUIRED
DESCRIPTION
MODEL
Accessories
Power Supply/Dual Audio Amplifier
Dual Function Generator
True RMS Voltmeter / Power Meter
Spectrum Analyzer
Direct FM Multiplex Generator
FM / PM Receiver
Oscilloscope
8948
9401
9402
9404
9405
9413
9415
&
PROCEDURE
*
1. Set up the modules as shown in Figure 2-2. Make sure that all OUTPUT LEVEL and
GAIN controls are turned fully counterclockwise to the MIN position, and power up the
equipment.
TRUE RMS
VOLTMETER / POWER METER
DIRECT FM MULTIPLEX
GENERATOR
FM /PM
RECEIVER
DUAL FUNCTION
GENERATOR
SPECTRUM
ANALYZER
OSCILLOSCOPE
POWER SUPPLY
DUAL AUDIO AMPLIFIER
Figure 2-2. Required Module Arrangement.
29
7KH )0 0RGXODWLRQ ,QGH[
*
2. Make the following adjustments
On the Dual Function Generator
Channel A
FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
FREQUENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 kHz
ATTENUATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 dB
OUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MIN
On the True RMS Voltmeter / Power Meter
MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VOLT
On the Direct FM Multiplex Generator
PREEMPHASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O
MULTIPLEX SIGNALS . . . . . . . . . . . . . . . . . . all at O except L + R at I
LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CAL
DEVIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 kHz (knob pushed-in)
RF GAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50% cw
On the Spectrum Analyzer
INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 M6
MAXIMUM INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 dBm
FREQUENCY RANGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85-115 MHz
FREQUENCY SPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 MHz / V
OUTPUT SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOG
OUTPUT LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CAL
*
*
*
30
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 the
WBFM RF INPUTS of the FM / PM Receiver, and to the INPUT of the Spectrum
Analyzer. Adjust the TUNING controls of the Spectrum Analyzer in order to move the
carrier line in the center of the screen. Decrease the FREQUENCY SPAN step by
step 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 power
of about 5 dBm as indicated on the Spectrum Analyzer. (You may have to slightly
readjust the fine TUNING control of the Spectrum Analyzer to keep the carrier line in
the 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.
7KH )0 0RGXODWLRQ ,QGH[
*
*
6. Connect OUTPUT A of the Dual Function Generator to both the INPUT of the True
Rms Voltmeter / Power Meter, and to the LEFT AUDIO INPUT of the Direct Fm
Multiplex Generator.
7. Carefully increase the OUTPUT LEVEL A of the Dual Function Generator until the
second 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.
SECOND SIDEBAND PAIR
f m = 5 kHz,
þf =
kHz,
mf =
Figure 2-3. FM Spectrum. FREQUENCY SPAN = 10 kHz / V.
*
8. On the FM / PM Receiver set the DEVIATION push-button to WBFM. Read the
frequency deviation f indicated by the display.
Frequency deviation f =
kHz
Calculate the modulation index mf using
frequency deviation
f fm
m odulating signal frequency
Record the frequency deviation f and the modulation index mf in Figure 2-3.
mf *
9. Carefully decrease FREQUENCY A of the Dual Function Generator (the modulating
signal 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 shows
the spectrum you should obtain.
31
7KH )0 0RGXODWLRQ ,QGH[
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 Function
Generator.
fm =
kHz
Record the frequency fm in Figure 2-4.
FIRST SIDEBAND PAIR
fm =
kHz,
þf =
kHz,
mf=
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
mf f fm
Record the frequency deviation f and the modulation index mf in Figure 2-4.
32
7KH )0 0RGXODWLRQ ,QGH[
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 the
modulating signal varies?
*
*
*
12. How has decreasing the frequency of the modulating signal affected the modulation
index?
13. Readjust FREQUENCY A of the Dual Function Generator (fm) to obtain the spectrum
of 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 the
modulating signal.
Modulating signal level =
*
mV
15. Carefully increase OUTPUT LEVEL A of the Dual Function Generator (Am) until you
see the first sideband pair pass to a minimum amplitude, then to a maximum
amplitude, and again to a minimum amplitude. Figure 2-5 shows the spectrum you
should obtain.
33
7KH )0 0RGXODWLRQ ,QGH[
FIRST SIDEBAND PAIR
fm =
kHz,
þf =
kHz,
mf=
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 the
spectrum, 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 modulating
signal.
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.
34
7KH )0 0RGXODWLRQ ,QGH[
Explain your observations.
*
17. Calculate the modulation index using
mf f fm
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 have
approximately the same modulation index but they are very different. Explain why.
*
*
18. Readjust OUTPUT LEVEL A of the Dual Function Generator to obtain the spectrum
of Figure 2-3.
19. Turn the DEVIATION knob on the Direct FM Multiplex Generator completely
counterclockwise, and then pull it out. This sets the sensitivity kf of the FM modulator
to its minimum. Observe the spectrum you obtain on the oscilloscope, then compare
it with that of Figure 2-3.
35
7KH )0 0RGXODWLRQ ,QGH[
*
20. Slowly increase the sensitivity of the FM modulator to maximum by turning the
DEVIATION knob on the Direct FM Multiplex Generator clockwise. Observe the
spectrum on the oscilloscope and the frequency deviation indicated by the FM / PM
Receiver. 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 power
switches 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 amplitude
of the modulating signal and the sensitivity of the modulator. The modulation index is a
function of both the frequency deviation and the frequency of the modulating signal. Changing
any 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 its
modulation index if the frequency deviation is 10 kHz?
2. What is the relationship between the modulation index and the amplitude of the
modulating signal?
36
7KH )0 0RGXODWLRQ ,QGH[
3. What parameters can change the frequency deviation?
4. An FM signal has a frequency deviation of 6 kHz when the modulating signal has an
amplitude of 5 V, and a frequency of 1000 Hz. What will be the modulation index if the
frequency of the modulating signal is doubled?
5. When the DEVIATION knob is adjusted, what parameter changes?
37
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8QLW 7HVW
1. Frequency division multiplexing allows transmission of:
a.
b.
c.
d.
several messages, one after the other.
several messages, all at the same time.
one message on several carriers.
several messages on several carriers.
2. In frequency division multiplexing, messages
a.
b.
c.
d.
are shifted in frequency.
are frequency band changed.
are separated in time.
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.
b.
c.
d.
It cannot.
By detecting only the right signal.
By detecting only the (L R) signal.
By detecting only the (L + R) signal.
4. In stereo modulation, the signal which modulates the 38 kHz subcarrier has a frequency
band covering:
a.
b.
c.
d.
0-15 kHz
0-75 kHz
19-34 kHz
25-53 kHz
5. What is seen in the spectrum of an FM stereo signal when there is no audio signal?
a.
b.
c.
d.
Nothing
A carrier with two 19-kHz lines on either side.
Many lines.
One line at 19 kHz.
6. What is the channel separation between the left and right channels of a receiver if the Left
output level is 5 V, including 5 mV from the Right channel?
a.
b.
c.
d.
60 dB
+60 dB
3 dB
1 mV
7. What is WBFM-FM modulation?
41
8QLW 7HVW FRQW·G
a.
b.
c.
d.
Either an WBFM or FM modulation.
A modulation which varies between WBFM and FM.
WBFM modulation of an FM signal.
FM modulation of an WBFM signal.
8. What is the bandwidth of an FM stereo signal without guard bands?
a.
b.
c.
d.
240 kHz
150 kHz
75 kHz
15 kHz
9. How does the bandwidth of an FM signal vary when more and more messages are
multiplexed?
a.
b.
c.
d.
It decreases.
It stays constant.
It increases.
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.
b.
c.
d.
42
75 kHz
33.75 kHz
30 kHz
7.5 kHz
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Note: All measurements, calculations and figures given as Answers to
Procedure Step Questions are approximate, and should be considered only
as a guide. These results may differ considerably from one Analog
Communications Training System to another. The results of calculations
have 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 Channel
B modulates the frequency of the signal from Channel A.
7. The unmodulated sinusoidal signal and the square wave signal.
MODULATING SIGNAL
UNMODULATED CARRIER
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 the
positive and negatives alternances of the square wave.
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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 the
level 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
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Sensitivity kf = 87.5 Hz / V
EXERCISE 1-2
*
6.
Figure 1-8. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, fC = 1 MHz, fm = 5 kHz, small modulating signal.
There is a line on each side of the carrier spectral line.
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*
7.
Figure 1-9. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, fC = 1 MHz, fm = 10 kHz, low level modulating signal.
The two spectral lines, one on each side of the carrier spectral line, move farther
away from the carrier and their amplitude gets smaller.
*
8.
There are more lines; the distance between each line corresponds to the
frequency of the modulating signal (5 kHz).
Figure 1-10. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, fC = 1 MHz, fm = 5 kHz, medium level modulating
signal.
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*
9.
Figure 1-11. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, fC = 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 it
disappears, there is practically no power at this frequency.
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*
11.
Figure 1-12. FM Spectrum. FREQUENCY SPAN = 10 kHz / V, fC = 1 MHz, fm = 1.75 kHz, high level modulating
signal.
When the frequency deviation increases or when the frequency of the modulating
signal is smaller, the number of spectral lines and the width of the spectrum
increases.
EXERCISE 2-1
*
8. Frequency deviation f = 25 kHz
mf *
25
5
5
9. Both spectra have approximately the same width but the spectrum of Figure 2-4
contains many more spectral lines which are closer together.
*
10. fm = 2.5 kHz
*
11.
f = 25 kHz
mf 25
10
2.5
Yes
Because the frequency deviation is a function of both the modulating signal
amplitude, and the sensitivity of the FM modulator: it is not affected by varying the
frequency of the modulating signal.
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*
*
*
*
12. Decreasing the frequency of the modulating signal has caused the modulation index
to increase.
14. Modulating signal level = 165 mV
15. The spectrum of Figure 2-5 is wider and contains more spectral lines than the
spectrum of Figure 2-3. However, the space between the spectral lines is the same
for both spectra.
16. Modulating signal level = 330 mV
f = 50 kHz
Since the frequency deviation is equal to kfAm, increasing the modulating signal level
causes both the frequency deviation and the width of the FM spectrum to increase.
*
17. m f 50
10
5
Since the frequency deviation of Figure 2-5 is approximately two times greater than
that of Figure 2-3, the modulation index of the spectrum of Figure 2-5 is also
approximately 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 modulation
index. However, the frequency deviation and the modulating signal frequency are not
the 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 spectrum
of 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 has
also increased and so has the modulation index.
EXERCISE 2-2
*
6.
MAXIMUM
mf
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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 more
spectral 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
TOTAL
P0 + 2Pn
Pn (mW)
0.01
0.016
0.016
TOTAL
P0 +2Pn
0
0
0
0.1
2Pn (mW)
0.032
0.032
0.074
2Pn (mW)
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mf = 7
Figure 2-10 (b)
mf = 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
TOTAL
P0 + 2Pn
Pn (mW)
0.006
0.001
0.004
0.003
TOTAL
P0 +2Pn
0.002
0.006
0.012
0.026
2Pn (mW)
0.002
0.008
0.006
0.022
2Pn (mW)
Tables 2-3.
*
9. When the modulation index goes from 0 to 10.5, the power at the carrier frequency
decreases (from 0.1 to 0.006 mW) and the power in the first three spectral
components 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, fm = 5 kHz, mf = 0.5.
Bandwidth W (evaluated) = 10 kHz
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*
7.
Figure 2-16. Spectrum of an FM signal. FREQUENCY SPAN = 2 kHz / V, fm = 5 kHz, mf = 2.4.
Bandwidth W (evaluated) = 44 kHz
*
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
Bandwidth W (evaluated) = 70 kHz
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To double the modulation index, the frequency of the modulating signal has been
reduced to half. The number of pairs of spectral lines has almost doubled, while the
frequency gap between each line has been reduced to half. Therefore, the bandwidth
has not changed much.
*
12. Bandwidth W (evaluated) = 64 kHz
EXERCISE 3-1
*
4.
22 dB
Figure 3-4. Spectrum of an NBFM signal. FREQUENCY SPAN = 2 kHz / V, fm = 2 kHz.
W (evaluated) = 4 kHz
W (calculated) = 4 kHz
Difference in power P = 22 dB
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EXERCISE 1-1
EXERCISE 3-1
1.
1.
2.
3.
4.
5.
The size of antennas which must be practical and
reception of only the wanted signal.
Phase modulation and frequency modulation.
The phase.
The frequency.
The sensitivity kf of the modulator, and the amplitude Am
of the modulating signal.
2.
3.
4.
5.
When the modulation index is less than 0.5, the modulation is said to be NBFM.
The other spectral components are small, and can be
ignored.
No. Different AM and NBFM signals can have the same
spectrum.
The carrier.
W = 2fm.
EXERCISE 1-2
EXERCISE 3-2
1.
2.
3.
4.
5.
The frequency fm of the modulating signal.
The sensitivity kf of the modulator, the amplitude Am and
frequency fm of the modulating signal.
2 kHz.
The number of spectral lines increases, and the spectrum becomes wider.
The spectrum of an NBFM signal looks like that of an AM
signal, since there is only one spectral line on either side
of the carrier.
1.
2.
3.
4.
5.
The phase changes by 90(. The amplitude of the signal
becomes inversely proportional to the input frequency.
A signal whose amplitude is inversely proportional to its
frequency must be injected into the phase modulator
input.
The modulation index is reduced by one-half.
It does not change.
Its level increases with its frequency.
EXERCISE 2-1
EXERCISE 3-3
1.
2.
3.
1.
4.
5.
mf = 1
mf = kfAm /fm
The sensitivity kf of the modulator, and the amplitude of
the modulating signal.
mf = 3
The sensitivity kf of the modulator.
EXERCISE 2-2
1.
2.
3.
4.
5.
The order (n) of this spectral component.
Pi = (0.51)² x 100 = 26 W
74 W
The power is divided among mare spectral components.
Since the power is proportional to the square of the n-th
Bessel coefficient Jn(mf), Pn = Jn²(mf) PT.
EXERCISE 2-3
1.
2.
3.
4.
5.
The method using the number of pairs of significant
spectral lines.
The method using the number of spectral lines in the
spectrum that fall within a 20 dB interval.
The modulation index and the frequency of the modulating signal.
To at least 98% of the total power of the FM signal.
Twice the frequency of the modulating signal.
Because the frequency of the modulating signal is much
smaller than the frequency deviation and can be neglected.
2.
3.
4.
5.
The spectrum contains three spectral lines; the central
line corresponds to the carrier; the others are at fc + fm
and fc fm.
J0(mf) w 1
J1(mf) w mf / 2
The power contained in the spectral components decreases.
1.96%
J2(mf) w mf / 2
EXERCISE 4-1
1.
2.
3.
4.
5.
Because frequency multiplication allows the bandwidth
and the frequency modulation of an NBFM signal to be
increased without changing the frequency of the modulating signal.
The multiplication factor.
The multiplication factor.
W = 2f W = 2 x 20 x 50 = 200kHz
lt allows the carrier frequency to be placed within the
allocated frequency band.
EXERCISE 4-2
1.
2.
3.
4.
5.
When its spectrum has a large number of lines.
It also decreases.
15
In the spectral components.
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 of
Volume 1 % Instrumentation. The remainder is used to introduce the fundamental concepts
associated with amplitude modulation, double sideband modulation, and single sideband
modulation.
The basic principles of frequency conversion (translation) and modulation are also defined and
illustrated.
It is in this unit that the student has his first experiences with the RF generators and receivers
used in AM communication. Exercise 1-2, in particular, is designed to allow the student rapid
familiarity 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 the
Spectrum Analyzer is used.
INSTRUCTION PLAN
Ex. 1-1 AN AM COMMUNICATIONS SYSTEM
A.
Illustrate a communications system
1. Unidirectional
2. Bidirectional
B.
Show the transformations necessary to communicate a message.
1. The modulating signal (message)
2. The carrier signal
3. 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 observations
2. Sideband frequencies for a sine wave message signal
3. Sidebands for complex message signals
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B.
Demonstrate operation AM / DSB / SSB Generator controls.
1. Carrier Level
2. RF Gain
3. RF Tuning
C.
Demonstrate operation of AM / DSB Receiver
1.
2.
3.
4.
5.
OSC Output
AGC
SYNC Detector
RF Tuning
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 frequencies
2. 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 transmitted
2. Advantages of frequency translation
B.
Show how a mixer is used for frequency translation.
1.
2.
3.
4.
C.
Mixer symbol
Output frequencies (fc fm and fc + fm)
Sideband frequencies when modulating signal is a sine wave signal.
Sideband frequencies when modulating signal is a more complex voice signal.
Explain frequency multiplexing.
1.
2.
3.
4.
Transmission of several signals having the same baseband
Translating these basebands signals to different frequencies
Spectral analysis of two modulated RF signals
Minimum station separation of 10 kHz
DEMONSTRATIONS
Set up a complete AM transmission system, using the AM / DSB / SSB Generator, the
60
AM / DSB Receiver, telescopic antennas, the Dual Function Generator as an audio
source, and the Dual Audio Amplifier as a monitor. Tune in the AM "station" and listen to
a 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’s
envelope.
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Use the AM / DSB/ SSB Generator to produce an 1100 kHz carrier signal and modulate
the carrier with a 2 kHz sine wave. Observe and explain the effect on the spectrum of the
AM 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 domain
representations with those in the frequency domain.
B. Point out that spectral analysis of communications systems use high-quality, non
distorted sine waves as a message signals. Show the waveforms and spectra of
distorted 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 Spectrum
Analyzer (Z = 1 M6).
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