t 7.2.1.3 modulación de amplitud

8/3/2019 T 7.2.1.3 Modulacin de amplitud

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T 7.2.1.3

Amplitude

Modulation

by Klaus Breidenbach

New Edition, November 2002

LEYBOLD DIDACTIC GMBH . Leyboldstrasse 1 . D-50354 Hrth . Phone (02233) 604-0 . Fax (02233) 604-222 . e-mail: [email protected]

by Leybold Didactic GmbH Printed in the Federal Republic of GermanyTechnical alterations reserved


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The sensitive electronics of the equipment contained in the present experiment literaturecan be impaired due to the discharge of static electricity. Consequently, electrostatic buildup should be avoided (particularly by utilizing appropriate rooms) or eliminated by dis-charging (e.g. at the panel frames or similar).


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TPS 7.2.1.3 Contents

Note on EMC

European stipulations pertaining to electromagnetic compatibility (EMC) oblige themanufacturer of electronic training and educational equipment to draw the operator'sattention to the following possible sources of interference. The types of interferencelisted below could arise but by no means have to. As the case arises it may prove neces-sary to implement one of the measures recommended for the appropriate case.

Note regarding the interference immunity of the equipment and

experiment set-ups

The sensitive electronics used in the equipment can be interfered with by strong elec-tromagnetic fields arising from large-scale experiment arrangements. This can occur insuch a manner that the equipment operates insufficiently, in particular field effects cancause digital displays to fail.

Precautionary and corrective measures:

Make sure that no RF generating equipment (e.g. cellular phones) which does not be-long to the experiment set-up is operating in the classroom or in its proximity and thatconnecting leads which can act as potential antennas are kept as short as possible.

Note regarding protection against electrostatic discharge (ESD)

The sensitive electronic components in the equipment can be impaired or even dama-ged by the discharge of static electricity.

Precautionary measures:

Select work areas where electrostatic energy cannot be built up by the user and/orequipment (eliminate carpeting and similar items, ensure equipotential bonding).

Note regarding protection from line-bound, high-frequency voltage

burstsSwitching operations involving large loads can occassionally bring about line-boundhigh-frequency voltage bursts which can lead to the temporary impairment of sensitiveelectronic components which could cause equipment operating failure (e.g. data lossesor to changes in the mode of operation).

Corrective measures:

In order to avoid this malfunction, the mains line can be specially filtered. Furthermore,making occasional data back-ups is recommended. Any interference which might arisecan be eliminated simply by switching the device off and back on again.


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Note: The oscillographs in the experiment results were recorded with a HP 54600 A

oscilloscope (100 MHz) and further processed with the bench linkHP 34810 A software.

The oscilloscope recommended in the equipment set is a low-cost version,with limited operation and display comfort (30 MHz display), but in principledelivers the same results.

The experiment results given here are just examples. Therefore, the curvesand results specified in the solutions section should only be taken as guideli-nes.

The calculation and representation of the spectra was carried out with EXCEL5.0.


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Contents

Equipment overview ..............................................................................................................7Symbols and abbreviations ....................................................................................................8

Schrifttum .............................................................................................................................. 8

1 Introduction.........................................................................................................................9

Signals9Time and spectral domain......................................................................................................10Modulation ............................................................................................................................ 10The communications system according to Shannon ..............................................................12

2 Measuring instruments ..................................................................................................... 13

2.1 Oscilloscope and spectrum analyzer ..........................................................................132.2 Equipment descriptions .............................................................................................. 16

726 94 Spectrum analyzer .......................................................................................... 16

726 961 Function generator 200kHz ..........................................................................17726 99 Frequency counter 0..10 MHz ......................................................................18736 201 CF transmitter 20 kHz ..................................................................................18736 221 CF receiver 20 kHz ......................................................................................19

2.3 A measurement example ...........................................................................................20

3 Review of amplitude modulation (AM) .......................................................................... 23

The spectrum of amplitude modulation .................................................................................24Representing amplitude modulation with a vector diagram ...................................................24AM demodulation .................................................................................................................. 25Questions ............................................................................................................................... 26

4 Required equipment and accessories ............................................................................. 28

Training objectives: ................................................................................................................28

5 Double Sideband-AM ........................................................................................................ 29

The DSBSC

. ............................................................................................................................ 295.1 Investigations on the dynamic characteristic of the DSB..........................................305.1.1 DSB ............................................................................................................................ 305.1.2 DSB

SC................................................................................................................................................................................................................ 31

5.2 Spectrum of the DSB.................................................................................................315.2.1 DSB ............................................................................................................................ 31

5.2.2 DSBSC ................................................................................................................................................................................................................ 335.2.3 The AM spectrum for modulation with a square-wave signal .................................. 33

5.3 AM demodulation (synchronous demodulation) ........................................................ 345.3.1 DSB ............................................................................................................................ 345.3.2 Carrier recovery ........................................................................................................355.3.3 DSB

SCDemodulation ................................................................................................. 37

5.4 Beats ..........................................................................................................................37


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6 The Single Sideband AM (SSB) .......................................................................................41

6.1 Investigations on the dynamic characteristic of the SSB ........................................... 426.1.1 SSB

RC......................................................................................................................... 42

6.1.2 SSBSC

.......................................................................................................................... 42

6.2 Spectrum of the SSB..................................................................................................436.2.1 SSB

RC......................................................................................................................... 43

6.2.2 SSBSC

.......................................................................................................................... 43

6.3 SSB demodulation ......................................................................................................44

7 The Ring Modulator .......................................................................................................... 47

7.1 Dynamic response of the ring modulator ................................................................... 497.2 Spectrum at the output of the ring modulator ............................................................50

Solutions................................................................................................................................. 51

Keywords .............................................................................................................................. 65


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Equipment overview

DC power supply 15 V, 3 A 726 86 1 1 1 1 1 1 1 1 1 1

Function generator 0...200 kHz 726 961 1 1 1 1* 1 1 1 1 1 1

Spectrum analyzer 726 94 1 _ 1 _ 1 _ 1 _ _ 1

Frequency counter 0-10 MHz 726 99 1 _ 1 _ 1 _ 1 _ _ 1

CF transmitter 20 kHz 736 201 _ 1 1 1 1 1 1 1 1 1

CF receiver 20 kHz 736 211 _ _ _ 1 _ _ _ 1 _ _

Analog multimeter C.A. 406 531 16 1 _ 1 _ 1 _ 1 _ _ 1

Digital storage oscilloscope 305 575 292 1 1 1 1 1 1 1 1 1 1

Probes 100 MHz, 1:1/10:1 575 231 2 2 2 2 2 2 2 2 2 2

Sets of 10 bridging plugs, black 501 511 1 1 2 2 2 3 3 3 2 2Cable pair, black, 100 cm 501 461 2 _ 1 _ 2 _ 1 _ _ 2

2.3

Ameasurementexample

5.1

InvestigationsonthedynamiccharacteristicoftheDSB

5.2

SpectrumandvectorrepresentationoftheDSB

5.3

AMd

emodulation(synchr

onousdemodulation)

5.4

Beats

6.1

InvestigationsonthedynamiccharacteristicoftheSSB

6.3

SSB

demodulation

6.2

SpectrumrepresentationandvectordiagramoftheSSB

7.1

Dynamicresponseoftheringmodulator

7.2

Spectrumattheoutputoftheringmodulator

Equipment

TPS7.2.2

.3Experiments

Note:

Instead of the 20 kHz CF system you can also use the 16 kHz system (cat. no. 736 211 and 736 231).

This does not have any significant impact on the experiment results. In particular the spectra are shiftedby 4 kHz into the lower frequency range. However, their general structures remain unaffected.

* Optional: 2nd function generator recommended


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Symbols and abbreviationsA : AmplitudeAC : Amplitude deviation

AC : Carrier amplitudeAM : Amplitude of the modulating signalAD : Amplitude of the demodulated signalA(f) : Transmission factorAM : Amplitude modulationAR : Square-wave amplitudeDSBSC : Double sideband AM with suppressed carrierBP : Bandpassb : Bandwidthd : AttenuationSSB : Single sideband AM

f : Frequency

fM : Frequency of the modulating signalm : Modulation indexUSL : Upper sideline

R : Frequency resolutions(t) : Signal function in the time domain, generalsD(t) : Demodulated signalsM(t) : Information signal, modulating signalsC(t) : Carrier signalS(n) : Amplitude spectrum, generalSAM(n) : Spectrum of the AM signalsAM(t) : Dynamic characteristic of the AM signalSR(n) : Spectrum of the square-wave signalT : Period duration

LP : Lowpass filterLSL : Lower sideline : Efficiency

DSB : Double sideband AM

BibliographyE. Stadler Modulationsverfahren

Vogel Buchverlag, Wrzburg3rd edition 1983

Herter, Rcker,Lrcher Nachrichtentechnik, bertragung, Vermittlung, Verarbeitung

Hanser, Mnchen, Wien3rd edition 1984G. Kennedy Electronic Communication Systems,

McGraw Hill Book Company, Singapore,3rd edition 1985

D.G. Fink D. Christiansen Electronic Engineers HandbookMcGraw Hill Book Company2nd edition 1982

D. Roddy, J. Coolen Electronic CommunicationsPrentice Hall International, Reston Verginia,3rd edition 1984

Hewlett Packard Measurement, Computation, Systems, catalog 1986,Palo Alto California

Dipl. Ing. Klaus BreidenbachHrth, February 1997


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TPS 7.2.1.3 Introduction

1 Introduction

Signals

In electrical telecommunications engineering,messages are usually in the form of time-depend-ent electrical quantities, for example, voltage u(t)or current i(t). These kinds of quantities which aredescribed by time functions are called signals. Inorder to transmit messages a parameter of theelectrical signal must be suitably influenced. Incases where a signal defined as a time function isknown and the signal value can be determinedexactly at any given point in time, then the signal

is called deterministic. Examples ofdeterminis-tic signals are:1. Harmonic oscillation

u(t) = A sin (2 ft+ ) (1.1)

2. Symmetrical square wave

u(t) = u(t+ nT) n = 1, 2, 3... (1.2)

u t A t T

T t T( )=

0 < < /2

0 /2 < < .

for

for

Deterministic telecommunications is useless fromthe point of view of information theory. Only un-known, i.e. unpredictable messages are important

for the message receiver. Nevertheless, when dis-cussing modulation methods it is standard proce-dure to work with harmonic signals. The resultswhich can be obtained are then clearer and morestraightforward. If the signal value for any givenpoint in time cannot be given because the signalcurve appears totally erratic, then the signal iscalled stochastic. An example for a stochastic sig-nal is noise. Stochastic signals can be describedusing methods of probability mathematics, butthey will not be taken into consideration here. Sig-

nals are distinguished according to the character-istic curves of their time and signal coordinates. Ifthe signal function s(t) produces a signal value atany random point in time, the signal function iscalled time-continuous (continuous w.r.t. time).In contrast, if the signal values differ from 0 onlyat definite, countable points in time, i.e. its timecharacteristic shows gaps, then this is referredto as time-discrete (discrete w.r.t. time). What istrue for the time coordinate, can also be applied tothe signal coordinates. Accordingly, a signal iscalled level-continuous, if it can assume anygiven value within the system limits. It is calledvalue-discrete or n-level, if only a finite number

Fig 1-1: Classification of signals

(a) time- and level-continuous(b) time-discrete (sampled), level-continuous(c) time-continuous, level-discrete (quantized)(d) time- and level-discrete


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of signal values are permitted. Two important sig-nal classes can be defined using these 4 terms:

Analog signals

A signal is called analog if it is both time as wellas value-continuous.

Digital signals

A signal is called digital, if it is both time as wellas value-discrete.Fig. 1-1 shows the various kinds of signals.

Time and spectral domain

In the technical sciences there exists, in additionto the time domain, signal representation in thefrequency or spectral domain. The equiva-lence of the two types of representation can be

seen in the depictions in Fig. 1-2.If you first consider the harmonic function asspecified in (1.1), then a display on the oscillo-scope results in the familiar, dynamic (time) char-acteristic according to Fig. 1-2-A. The sinusoidaltime function is described by the amplitudeA andthe period duration T. However, a totally equiva-lent representation of this function is reproducedwhen the variablesA andf= 1/Tare used insteadof the parametersA and T. If the amplitude is dis-played on the frequency axis, then this form ofrepresentation is called the amplitude spectrum.

Thus, a single line can depict a harmonic function.Now, after Fourier, every non-harmonic, peri-odicfunction can be represented as the superim-position of harmonic oscillations with fixed

amplitudes S(n). As an example Fig. 1-2-Bpresents a symmetrical square-wave signal withthe amplitudeAR and the period of oscillation TR.We can see from the corresponding amplitudespectrum SR(n) in Fig. 1-2-D that the square-wave function is produced from the superpositionof many (an infinite number of) harmonic oscilla-tions. Their frequencies are odd numbered multi-ples of

f= 1/TR and their amplitudes decrease as a func-tion of the ordinal number n, see Table on pg. 11.

Note: Any precise and comprehensive discus-sion of the spectra not only takes the am-plitude spectrum S(n) into considerationbut also the phase spectrum (n). Howev-er, in many practical exercises it sufficesto determine the amplitude spectrum.

Modulation

When speaking of modulation, one generally re-fers to the conversion of a modulation signal sM(t)into a time function with altered characteristicsusing a carrier signal. The message signal influ-

ences a parameter of the carrier in a suitable fash-

Fig. 1-2: Time and spectral representation

(A) Harmonic function, time representation (C) Harmonic function, spectral representation(B) Symmetrical square-wave oscillation, (D) Symmetrical square-wave oscillation,

time representation spectral representation

Time domain Spectral domain

(A) (C)

(B) (D)


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ulating signal is shifted from the baseband (AFrange, original frequency band), into an RF fre-quency band. It no longer appears in the spectrumof the modulated oscillation. A modulation al-

ways requires that the carrier and the modulationsignal interact. Both of these signals are fed into amodulator. The original signal sM(t) is recoveredfrom the modulated signal through demodulation.Consequently, modulation and demodulation aremutually related, inverse processes. The complex-ities involved in modulation and demodulation areconsiderable. The following reasons explain whymodulation is worthwhile:1. Modulation enables the matching of the

modulating signal to the characteristics of the

transmission channel. (radio links e.g. areonly possible above a certain frequency.)2. Existing transmission channels can be multi-

ply exploited using modulation, (frequencyor time division multiplex systems).

3. Improved signal-to-noise ratios can be ob-tained using modulation.

The communications system according to Shan-

non

Electrical communications engineering is dividedinto three classical subfunctions:

1. Transmission of the message2. Processing of the message3. Relaying the message (telephone technol-

ogy)If only a single transmission channel is examined,(i.e. no telephone technology), then we can con-centrate on the remaining functions illustrated bythe scheme in Fig. 1-3.

Harmonic Frequency Amplitude

1

2

3

4

n

3fR

5fR

7fR

(2 n 1) fR

fR = 1/TR S AR R(1)=4

SR (1)3

SR (1)

5SR (1)

7S

nR (1)

2 1

Fig. 1-3: The telecommunications system(A) The telecommunications system(B) Message transmission(C) Message processing1 Message source

(human being, measurment sensor etc.)2 Converter (microphone,

television camera,strain gauges, thermo sensor etc.)

3 Transmitter4 Transmission channel (radio link,

transmission cable, data storage system)5 Receiver

6 Converter7 Message recipient8 Interference source

Amplitude spectrum of a symmetrical square-wave signal n = 1, 2, 3, 4, ...

ion. Either harmonic oscillations or pulse trainsare used as carrier signals. If, for example, a har-monic carrier is used with the form:

sC(t) =AC cos (2fC t+ ), (1.3)

then the message signal sM(t) can have an effecteither on the amplitudeAC, the carrier frequency

fC or the zero phase angle . These effects result inthe analog modulation methods:

Amplitude modulations (AM) Frequency modulation (FM) Phase modulation (PM).In the case of analog modulation methods, themodulation process means a continuous conver-sion of the modulating signal sM(t) into a higherfrequency band (frequency conversion). The mod-


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The telecommunication system (A) consists ofequipment used for message transmission (B) andmessage processing (C). The message source (1)generates the information, which is to be made

available to the message recipient (7). The signalsgenerated are of the most varied physical nature,e.g. sound, light, pressure, temperature, etc. It isthe function of the converter (2) to convert thenon-electrical signal of the source into an electri-cal one. The transmitter (3) converts the convertersignal into one better suited for transmission viathe channel. Thus the modulation process takes

place in (3). The transmission channel (4) serveseither to bridge a spatial distance, or to overcomea period of time. The modulated signal, generallydistorted by the interference source (8), reaches

the receiver (5), where it is then reconverted intoits original electrical signal there (demodulation).Finally, the converter (6) transforms the electricalsignal back into the physical signal required bythe message recipient (7). The message recipientcan take the form of the human being with eyesand ears or a machine in a process control loop.


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TPS 7.2.1.3 Measuring instruments

2 Measuring instruments

2.1 Oscilloscope and spectrum analyzer

The oscilloscope

The oscilloscope is amongst the most importantmeasuring instruments used in electrical engineer-ing. It is used to graphically display signalvoltages u(t) in the time domain. It can also beregarded as a two dimensional voltmeter. The sig-nal is displayed in the form of Cartesian coordi-nates. The abcissa (x-axis) shows the time scale,(e.g. ms/Div) and the y-axis shows the voltagescale (e.g. V/Div). The oscilloscope provides im-

mediate information on the signal shape and istherefore superior to moving coil instruments ordigital voltmeters. The prerequisite for all formsof pointer instruments and multimeters is that thetime characteristic or curve of the electrical sig-nals is known. As a rule only DC voltages or har-monic AC voltages can be measured using thesekinds of instruments. The oscilloscope is used forthe voltage measurement of signals with un-known, random time characteristics. Here a dis-tinction is drawn between two different cases:

1. The voltage signal is non-sinusoidal, but peri-odic with higher frequency.

The oscilloscope is operated in repeating real timemode. This operating mode is the most frequentlyone used. A sawtooth generator is started eachtime the signal to be measured has exceeded anadjustable level (trigger level). This produces atime-linear voltage used for the horizontal deflec-tion of the cathode ray tube. The sawtooth genera-tor is part of the time base. The vertical deflectionis controlled by the measurement signal itself. Theresult is a standing image of the voltage signal onthe screen. In real time operation the oscilloscopehas a slow-motion function. Thus, processeswhich are too fast for the human eye can be madevisible.

2. The voltage signal to be measured is non-peri-

odic, or has a very long period duration.

The signal to be measured is digitalized and inputinto a storage system. The contents of the storageunit can then be output periodically. Processeswhich are too long can be displayed in the storagemode.

The oscilloscope masks out the amplitude andtime windows from the signal characteristic, seeFig. 2.1-1.

The spectrum analyzer

Spectrum analyzers are used to display signals inthe spectral domain. These analyzers operateeither digitally with the aid of mathematical algo-rithms (Fast Fourier Transformation) or in analog

mode as a filter bank i.e. according to the princi-ple of frequency conversion. The latter principleis implemented in the spectrum analyzer 726 94training panel. For that reason we shall study thisin more detail with the aid of Fig. 2.1-2.The harmonic signal supplied by the VCO is fedinto the mixer with the input signal. Depending onits spectral quality and the oscillator frequency, anAC voltage signal appears at the mixer outputwhich lies in the passband of the bandpass filter.The IF signal at the output of the bandpass filter is

produced for the individual spectral componentsof the input signal for correspondingly differentVCO frequencies. If its frequency is linearly de-pendent on its control voltage, then this can beused for the X-deflection of a display unit. Thusthe X-axis also achieves linear frequency scaling.The rectified, amplified output voltage of the IFfilter is used for Y-deflection. Consequently eachspectral amplitude of the input signal can be meas-ured by adjusting the VCO. The spectrumanalyzer thus constitutes an application of the su-perheterodyne principle used in radio technolo-

gy, whereby the bandfilter can be regarded as aspectral window. The position of this window inthe frequency domain is determined by the VCO

Fig. 2.1-1:Functioning of the oscilloscope(A) Amplitude window(T) Time window


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1. (Periods of the sawtooth generator (SCANTIME)

2. Absolute frequency domain passed throughby the VCO (SPAN).

frequency. The width of the window is determinedby the selected bandwidth of the bandpass filter,see Fig. 2.1-3.

The time law of electrical telecommunications

engineering

The use of analyzers according to thesuperhetrodyne principle requires that the time

law of electrical telecommunications be observed.According to this law, the pulse response of alowpass system becomes longer, the smaller itsbandwidth b is, see Fig. 2.1-4.This statement can also be applied to thebandpasses present in the spectrum analyzer. Thetime law is similar to the uncertainty relation innuclear physics. It states that it is impossible todecrease both the duration Tas well as the band-width b of a signal. When tuning the VCO, theslower it takes for the VCO frequency to change,the longer the mixer output signal is in the

passband of the downstream bandpass (BP). Thefrequency change with respect to the time unitdepends on:

Fig. 2.1-2: Design of a spectrum analyzer according to the superheterodyne principle(A) Signal path

1 Input amplfier/ attenuator V12 Mixer3 Bandpass (BP)4 Rectifier5 Output amplifier V2

(B) Oscillator6 VCO7 Sawtooth generator

(C) Display unit

Fig. 2.1-3:The functioning principle of a spectrum

analyzer1 Bandpass with bandwidth b(spectral window)

2 Signal spectrum


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Fig. 2.1-4:The time law of electrical telecommunications engineering(A): Input signals: pulses with equal amplitudeA and period T(B): Lowpasses with critical frequenciesfc1 andfc2;fc1


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2.2 Equipment descriptions

726 94 Spectrum analyzer

The spectrum analyzer is depicted in Fig. 2.2-1.

A. Setting the signal path

Always set the gain settings V1 and V2 as high aspossible to increase the sensitivity of the signalpath. However, overdrive - recognizable by thelighting up of the OVER-LEDs, must be avoided(overdrive falsifies the measurement results).

B. Setting the oscillator component

Frequency tuning is performed with the aid of a

sawtooth-controlled VCO. The sawtooth genera-tor is set with the controllers SCAN TIME andSCAN MODE. The selection of the SCAN TIMEdepends on the time law of electrical telecommu-nications engineering (2.1).1. Setting the upper limit of the frequency: This

is carried out in SCAN MODE fmax using thecorresponding controller.

2. Setting the lower frequency limit: This is car-ried out in SCAN MODEfmin using the corre-sponding controller.

The frequencies can be read off directly at the

connected COUNTER (TTL). In SCAN MODERUN the VCO runs through the set frequencyrange once (important when using the XY re-corder). An LED indicates when the upper fre-quency limit is reached.Only in the SCAN MODE STOP is the lockingmechanism of the RESET function disabled. Inthis setting manual operation using a toggleswitch is possible. The setting UP of the toggleswitch enables the VCO to run in the fmax direc-tion, while the setting DOWN causes a corre-

sponding reduction in frequency.Attention:For the run through time T= 1/25 s the

set frequency window is passed throughin RUN auto-repeat mode. This ena-bles us to also use the spectrumanalyzer as a sweep generator.

C. Connection of the display unit

The following external measuring instruments canbe used as display units: Analog voltmeter Storage oscilloscope

XY recorder.

Note: The analyzer operates in manual mode asa frequency-selective voltmeter. This op-

erating mode is particularly suitable forquantitative evaluations. Due to the beateffects in the analyzer the output signalcan start oscillating particularly whenworking with V2 = 10. To obtain as accu-rate a reading of the output voltage S(n) aspossible, a slight frequency adjustment isrecommended if this should occur.

Fig. 2.2-1:The spectrum analyzer


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726 961 Function generator 200kHz

1. Safety instruction:

Read the instruction sheet provided with the de-

vice!The function generator is illustrated in Fig. 2-1.Where:1 Mains switch2 FUNCTION: selection of the output signal3 MODE: selection of the signal parameter ad-

justable using the control knob4 Control knob for the selected signal param-

eters5 TTL output6 Output (50 )7 Toggle switch for output attenuator

8 Multifunction display in LCD technology8 Power bus lines and ground

Multifunction display in LCD technology with:

- Function symbols and signs- Numerical display with decimal points- Signal parameter

Putting the system into operation

Connect the mains plug into the socket. Actuatemains switch 1 . When the device is on the mainsswitch lights up. The desired output signal is setby actuating the FUNCTION button. Byrepeatedly pressing the FUNCTION button youshuttle cyclically through the sequence of outputsignals available, sinussoidal, triangular, square-wave, DC. With the MODE pushbutton thefollowing signal parameters are selected: Frequency Amplitude (peak-to-peak value) DC offset Duty cycle (only for square-wave)You can shuttle cyclically through the programmenus by pressing the MODE pushbutton repeat-

edly. After the desired signal parameter has beenset its magnitude can be varied by turning the con-trol knob. The maximum output voltage of the de-vice lies at approx. 12 V.

Fig. 2.2-2: The function generator and the multifunctiondisplay

726 961FUNKTIONSGENERATOR 200 kHz

FUNCTION GENERATOR 200 kHz

OUT

0

20

40

TTL

FUNCTIONMODE

ATTdB

%

=ppVkHz

DC

Storing the last setting

After switch off all of the settings are retained.They are at your disposal unchanged after youswitch the unit back on.

Calling up the base setting

If you simultaneously press either the MODE orFUNCTION buttons with the device switched on,

the function generator supplies a sinusoidal signalwith 1 kHz and 10 VPP, DC = 0 V. The base set-ting for the duty cycle (for square-wave signal) is50%.


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726 99 Frequency counter 0..10 MHz

1 8-digit 7-segment display2 TTL inputs (Channel A),fmax = 10 MHz.3 Analog input (Channel A),fmax = 10 MHz.

4 TTL input (Channel B),fmax = 2 MHz.5 Toggle switch for switchover between TTL

and analog input of channel A6 Function switchFREQ.A : Frequency measurement of chan-

nel A, display in kHz.PERIOD A : Period duration channel A,

display s. The last respectivemeasurement value is stored

fmax = 2 MHz.RATIO A/B : Frequency ratio fA/fB. Signal

B with TTL level!fmax = 2 MHz.TIME A-B : Time interval between a nega-tive edge of signal A and thenext negative edge of the sig-nal B,fmax = 2 MHz.

COUNT A : Event counting in channel Afrom 0 - 10.000.000.

7 Gate : Gate time (meas. duration)0.01s/0.10s/1.00s/10.0s

Note:

The analog input is coupled with AC power. Dueto an unfavorable set up (long connecting leads)of the experiment and despite shielding, a display

might appear even without an input signal, if a sig-nal is applied in TTL channel A. This crosstalkcan be attributed to the high sensitivity of the ana-log input and the spatial proximity of the inputsockets. For that reason always connect the ana-log input to a signal source using a short connec-tion cable after switching to ANALOG.

736 201 CF transmitter 20 kHz

The training panel contains the following compo-nents:

1. Input filterThe input filter sets the upper critical frequencylimit of the modulating signal tofc= 3.4 kHz. Gainin the bandpass: +1.

2. Modulator M2

Product modulator with 2 freely accessible inputs: Input for the modulating signal (LF-input)

Fig. 2.2-3: The frequency counter Fig. 2.2-4: The CF transmitter 20 kHz

TTL - IN(B)

TTL - IN(A) TTL - IN(A)

ANALOG (A)

RATIO A/B

PERIOD AFREQ A

FUNCTION

GATE

0,1s

0,01s

TIME A-B

COUNT ACHECK

1s

10s

726 99FREQUENZZAEHLER 0-10MHz

FREQUENCY COUNTER 0-10MHz


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Input for the carrier oscillation (RF input)In addition, the carrier in the output signal of themodulator can be enabled or disabled using a tog-gle switch. (CARRIER, ON-OFF)

3. Channel filter CH2

The channel filter is needed for the generation ofSSB-AM. It suppresses the lower sideband. Thepassband range of approx. 20 kHz...30 kHz ex-tends beyond the upper sideband.Gain in the passband: +1.Both filters (1 and 3) are equipped with freely ac-cessible inputs and outputs, which permits the re-cording of amplitude frequency responses.

4. Output summer

The output summer (4) has two inputs with thegain levels +1. The component is used to linearlysuperimpose signal components of the AM signal.At the output of the summing unit you have atyour disposal the complete AM signal, i.e.including any existing pilot tone or, in the case ofFMUX operation, the multiplex signal fortransmission via the transmission channel.

Subassembly for carrier generation

(CARRIER)

Frequency divisionf0/8 (5) is used to generate the

carrier frequency of 20 kHz out of the pilot tone.The unipolar TTL signal is converted into a bipo-lar square-wave signal with 4 VPP in the TTL/square-wave converter (6). Conversion into a bi-polar sine oscillation also with 4 VPP is performedin the square-wave/sine converter (7). The adjust-able phase-shifter (8)= 00...1500 introduces adefined phase-shift between the carrier on themodulator side (M2) and the auxiliary carrier onthe demodulator side. The phase-shifter permitsthe features of coharent demodulation to be exam-ined. Furthermore, together with the CF transmit-

ter 16 kHz (736 211), it is able to generatequadrature modulation.

Subassembly pilot tone generation

(PILOT TONE)

The quartz oscillator (9) generates the primarymaster clock pulse, symmetrical square-wave,TTL with a frequency of 160 kHz. The converter(10) and the attenuator (11) connected in seriesform an attenuated unipolar square-wave signalof approx. 200 mVpp out of the TTL signal, whichis transmitted to the CF receiver to recover the

carrier signal.

736 221 CF receiver 20 kHz

The training panel is used for the demodulation ofamplitude-modulated signals. The auxiliary car-rier required for synchronous demodulation can

be forwarded either directly via an external sourcee.g. to the corresponding CF transmitter orinternally from the subassembly carrierrecovery.

Design:

The device contains the following components:

1. Channel filter CH2

Bandpass filter for the filtering out of the wantedSSB signals. The passband from approx.20...30 kHz extends beyond the upper sideband.Gain in the passband: +1. For the demodulation ofsingle sideband-AM (SSB) a bridging plug isneeded between the output of the channel filterCH2 (1) and the input of the demodulator D2 (2).Should the CF receiver demodulate the doublesideband-AM (DSB), then the SSB-signal has to

Fig. 2.2-5: The CF receiver 20 kHz


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2 0


Fig. 2.3-1: Experiment setup for learning to handle the spectrum analyzer

be fed directly into the input of the demodulatorD2 after the bridging plug has been removed.

2. Synchronous demodulator D2

A multiplier IC takes over the function of the syn-chronous demodulator. The AM signal (DSB orSSB) and an auxiliary carrier are supplied to thedemodulator. In addition to the wanted LF signal,higher frequency signal components also appearin its output signal.

3. Lowpass filter

Synchronous demodulation requires a subsequentfiltering for the suppression of the higher fre-quency signal components. The filter (3) usedhere has an upper critical limitfc = 3.4 kHz and a

gain of +1.

Subassembly "carrier recovery"

Carrier recovery is performed using a PLL circuitwith subsequent frequency division. The synchro-nization of the PLL circuit is performed by a pilottone of 160 Hz sent by the CF transmitter, whichis processed in the receiver by a bandpass filter (4)and an amplitude limiter (5). The PLL circuit con-sists of the phase comparator (6), the loop filter(7) and the VCO (8). In standard operation theoutput of the loop filter is connected directly tothe input of the VCO using a bridging plug.

However, the VCO can also be tuned using anexternal DC voltage 0...+5 V. After locking intothe pilot tone a recovered auxiliary oscillation f0=

160 kHz is available at the output of the PLL. Thissignal is then divided down to the required carrierfrequencyfT= 20 kHz in a frequency divider (9).

2.3 A measurement example

Required equipment and material

1 Spectrum analyzer 726 941 Frequency counter 0...10 MHz 726 991 Analog multimeter C. A 406 531 16

Additionally required:

1 Function generator 0...200 kHz 726 9611 DC power supply 15 V, 3 A 726 861 Digital storage oscilloscope 305 575 2922 Probes 100 MHz, 1:1/10:1 575 2311 Set of 10 bridging plugs, black 501 5112 Cable pairs, black 100 cm 501 461

Additionally recommended:

1 XY recorder e.g. 575 663

Preliminary remark

The measurement station described here consistsof a spectrum analyzer, oscilloscope and fre-

quency counter. Using this measurement stationsignals can be measured in the time and spectral

OUT

0

20

40

TTL

FUNCTIONMODE

ATTdB

%

=ppVkHz

DC

+15V

0V

(+5V)

M1

U

U

I >

I >


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2 1


domain. This will be used a lot in the followingexperiments.

Experiment procedureSet up the experiment as specified in Fig. 2.3-1.Set a square-wave signal with AR = 5 V and

fR = 2 kHz on the function generator. The TTL in-put A of the frequency counter remains perma-nently connected to the analyzer via bridgingplugs. In order to test the signal frequencyfR pluga connecting lead into the analog input and actu-ate the toggle switch.Record the spectrum of the square-wave signal inthe frequency range of approx. 1.5 kHz....20 kHz.1. Manual operation with the analog voltmeter.

Connect an analog voltmeter 10 V DC to theanalyzer output.

Analyzer settings

SPAN/kHz: 0.5...20

When V1 = 2, 5, 10 the input stage is over-driven, the OVER LED lights up and themeasurement results are falsified.Now record the spectrum of the square-wavesignal by starting the VCO in SCAN MODERUN. In the spectral energy range the outputsignal demonstrates a brief increase. Thenstop the VCO and manually adjust it aroundthe frequency of the spectral line using thepushbutton up/down. Read off the spectral

amplitude S(n) on the voltmeter. In this man-ner enter all the amplitudes S(n), the index nand the corresponding frequencies finto theTable 2.3-1. Also the analyzer settings are tobe noted down there. Plot the spectrum in agraph in Diagram 2.3-1.Discuss your results.

2. Automatic operation with the XY recorder

or the storage oscilloscope.

In automatic operation the scanning process

is performed without interruption. Also thegain settings V1, V2 remain unchanged.

Tabelle 2.3-1: Spectrum square wave signal

Signal parameter Analyzer settings

Measurements Theory

n

1

2

3

4

5

6

7

8

9

10

V1 :b : Hz

fr : kHzT : s

AR : V/TP :

fR : kHz

f

kHzV2

S (n)R

V

S (n)R

V

S(n)

V

Diagram 2.3-1: Spectrum of the square-wave signal

AR = 5 V,

TP= 0.5

T/s: 20

fr/kHz: 20 b/Hz: 500

V1: 1V2: 5, 10

2.1 Using an XY recorder

Connect the X+ input of the recorder to the Xsocket of the analyzer. Connect the Y+ inputof the recorder to the analyzer output; X,Y to earth. Both recorder axes have to be

calibrated. The X-axis is set to fmax. The Y-axis is aligned to the highest spectral ampli-tude (test it out!). The analyzer cycle is


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triggered by switching to SCAN MODERUN.

2.2 Using the storage oscilloscope

The simplest operation is the recording ofspectra with the storage oscilloscope in theROLL mode. Then all of the problems in-volving triggering are avoided. The holdingtime base is set so that its period is greaterthan the SCAN TIME set on the analyzer.The analyzer output is connected to a Y-inputof the oscilloscope. By selecting a suitable Y-gain setting the screen surface is optimally

exploited for the spectral display. Once thespectrum is completely reproduced on thescreen, the ROLL modus can be disabled bypressing the SINGLE pushbutton. The screen

contents are then frozen. When in SINGLEstorage mode you have to trigger externallyon the falling edge of the sawtooth signal(socket X). Try out the most effective triggerfilter.Repeat the recording of the spectra one afterthe other for the bandwidths b = 100 Hz,b = 50 Hz, b = 10 Hz, b = 5 Hz. What do youobserve?


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TPS 7.2.1.3 Review

3 Review of amplitude modulation

In amplitude modulation (AM) the momentaryvalue of the message signal sM(t) has animmediate effect on the amplitude of the carrieroscillation sC(t). This takes place in a modulator,see Fig.3-1.Here it would be:

sC(t) =AC cos (2 fCt) (3-1)

for the high-frequency carrier and:

1. sM(t) =AM cos (2 fM t) (3-2)

for the low frequency message signal. The com-

bining of the carrier and message signal in themodulator then provides the following modulationproduct:

sAM(t) = [AC + sM(t)] cos (2 fC t) (3-3)

= [AC + AM cos (2 fMt)]

cos (2 fC t).

Where stands for the modulator constant, which

expresses the affect of the message signal sM(t)on the amplitudeAC of the carrier. Normally (3-3)

is described in more general terms. For this youneed the following definitions:

AC = AM Amplitude deviation (3-4)

mA

A= C

CModulation index (3-5)

Amplitude deviation AC describes the maximumchange away from the original valueAC in the car-rier amplitude. The modulation index m reproducesthe ratio of the amplitude deviation to the carrier

Fig. 3-1: Generation of amplitude modulation

Fig. 3-2: The amplitude modulated signal

AC

sAM

TC

Envelope

EnvelopeTM

AC

AC

Fig. 3-3: Limiting cases for the modulation factor

m = 100%

m > 100%

m = 0%

amplitude. Thus it is possible to convert (3-3) asfollows:

s t AA

A f t f t

A m f t f t

AM CC

C

M C

C M C

( ) cos cos

cos cos

= + ( )

( )

= + ( )[ ] ( )

1 2 2

1 2 2

(3-6)

Fig. 3-2 shows the amplitude modulated signal ac-cording to (3-6). The modulating signal sM(t) canbe recognized in the envelope curve.Normally the following holds true: 0 < m < 1.The following limiting cases for m are interesting:m = 0 : no modulation effectm = 1 : full modulation, the envelopes bordering

the modulating signal just touch at theirminimum values

m > 1 : overmodulation, the envelopes permeateeach other, modulation distortion arises.


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TPS 7.2.1.3 Review

Special cases are depicted in Fig. 3-3.

The spectrum of amplitude modulation

The expression in the brackets of (3-6) describesthe envelope of amplitude modulation. If youmultiply the dynamic (time) characteristic of thecarrier oscillation in this expression, you obtain:

sAM(t) =AC [cos (2 fC t)

+ m cos (2 fT t) cos (2 fM t)] (3-7)

The application of the addition theorem:

cos cos cos cos x y x y x y = ( ) + +( )[ ]1

2

provides:

s t A f t

m f f t

m f f t

AM C C

C M

C M

( ) cos

cos

cos

= ( )

+ ( )[ ]

+ +( )[ ]

2

22

22

(3-8)

From (3-8) you can see the spectral composition ofamplitude modulation, see Fig. 3-4.

From the spectrum we can see that besides thecarrier oscillation with the frequencyfC, there arealso 2 side oscillations with the frequencies fC +fMandfC fM contained in sAM(t). According to (3-8)the amplitudes of the equal side oscillations dependon the modulation index. The oscillation with thelower frequencyfC fM is called the lower sideline,

the one with the higher frequency is the uppersidelinefC + fM. The lower sideline (LSL) slips fur-ther into the range of lower frequencies as thesignal frequency fM increases. This frequency re-

sponse of theLSL is referred to as inverted posi-tion. The upper sideline (USL) shifts into thehigher range of frequencies with increasing signalfrequency. It lies in the normal position. In Fig. 3-5 the terms are in standard representation for thetransmission of an information band, which ex-tends from a lower frequency limit fu up to theupper frequency limitfo.The representation according to Fig. 3-5 is stand-ard particularly in carrier frequency technology.The bandwidth requirement of AM equals twice

the maximum message frequencyfMmax:b = 2fMmax (3-9)

Representing amplitude modulation with a

vector diagram

The vector diagram constitutes an important tool inthe representation of modulation methods. It fre-quently permits the immediate assessment of inter-ference effects or manipulations during modula-tion. For example, asymmetrical attenuation of thesideband oscillations in AM can lead to theformation of parasitic angular modulation.

From Fig. 3-6 the following features of amplitudemodulation can be read off directly:An AM signal can be represented by 3 complexvectors ( 2 sideband vectors and a vector for thecarrier). The 3 vectors are displayed in a joint dia-gram for any given point in time, see Fig. 3-6.

Fig. 3-4: The spectrum of amplitude modulation Fig. 3-5: Normal and inverted position

sM

fu fo

sAM

fC fo fC fC + fof f

1

SAM

AC

m/2

fM fC (f)

1

SAM

AC

m/2

fC + fMfC fM

(f)fC


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TPS 7.2.1.3 Review

1. The carrier oscillation is depicted with a con-stant direction (normally perpendicular up-wards), although in absolute terms it rotates incounterclockwise rotation with 2 fC.

2. The length of the carrier vector remains con-stant.

3. The sideband vectors are symmetrical withrespect to the carrier. The vector of the USLrotates counterclockwise around the tip of the

carrier vector. The vector of the LSL rotatesin clockwise rotation.

4. The vector for the amplitude modulated oscil-lation is obtained through vector addition, i.e.construction of the vector parallelogram,made up of the vector of the carrier and theside oscillations. The resulting vector alwayshas the direction of the carrier vector.

As you can see from Fig. 3-7, the tips of the result-ing vectors, if you draw them as a function of time,again produce the envelope of the amplitude

modulated oscillation.AM demodulation

Envelopes and synchronous demodulation

1st envelope demodulation

First the AM signal is rectified, see Fig. 3-8.The dynamic characteristic of the current passingthrough the recifier can be subjected to Fourierseries expansion. It can be shown that a rectifiedAM signal contains the following signal compo-nents:

1. A DC voltage component2. The original signal with the frequencyfM.3. Components with higher frequencies fC,

fC +fM, 2 fC +fM, etc.

Fourier expansion shows that rectification of theAM signal produces many new spectral compo-nents which are not present at the input of the rec-tifier. A suitable filter is used to suppress these

unwanted spectral components. Envelope de-modulation belongs to the so-called incoherentdemodulation methods, as neither the carrier phasenor the carrier frequency are of any importance.Fig. 3-9 reproduces the possible circuit configura-tion of an envelope demodulator.

USL

t= t1

sAM

sC

Fig. 3-6: Amplitude modulation in a vector diagram Fig. 3-7: Relationship between envelope and vectorrepresentation

LSL

t= t2USL

sC

sAM

LSL

Fig. 3-8: Envelope curve demodulation


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TPS 7.2.1.3 Review

Envelope demodulation always requires the car-rier. After rectification this produces a DC voltage,which establishes the working point of the diode. Inpractice envelope demodulation is frequently usedin AM radio communications due to its simplecircuitry.

2. Synchronous demodulation

In principle synchronous demodulation is simplyanother modulation process. To carry it out, youneed an auxiliary oscillation in the receiver, whichin terms of frequency and phase corresponds ex-actly to the carrier oscillation in the modulator. Theauxiliary carrier sAux(t) and the modulated signalsAM(t) are supplied to a circuit with multiplying ca-pabilities, see. Fig. 3-10:

Three cases can be distinguishedDSB,DSBsc andSSB:1. Demodulation of DSB

s t A f t m

f f t

m f f t

s t f t

AM C C C M

C M

Aux Aux

( ) cos cos

cos

cos ( )

= ( )+ ( )[ ]

+ +( )[ ]

( ) = +( )

22

2

22

2 3 10

The amplitude of the auxiliary oscillation is negligi-ble, furthermore it is true that fC = fAux (i.e. fre-quency equality prevails between carrier andauxiliary carrier). After lowpass filtering we obtainthe demodulated signal:

s t AA m

f tD CC

M( ) cos cos cos= + ( ) 2

2 (3-11)

sAM(t) C1 R1 sD(t)

Fig. 3-9: The envelope demodulator Fig. 3-10: Synchronous demodulation

2. Demodulation ofDSBsc.The constant DC voltage componentAC cos isomitted:

s t A m f tD ( ) cos cos= ( )C

M

22 (3-12)

3. Demodulation ofSSBSC.

s tA m

fD ( ) cos= ( )C

M

42 (3-13)

In the synchronous demodulation ofDSB a phaseerror reduces the amplitude of the demodulatedsignal by the factor cos . In the case ofSSB, thephase error leads to a shift in the demodulated sig-nal. In both cases the phase between the carrierand the auxiliary carrier has a noticeable effect onthe demodulation process. Due to this phase sensi-tivity synchronous demodulation is also called co-herent demodulation.

Questions3.1 What is meant by modulation? Mixing?3.2 Name the reasons for performing modula-

tion!3.3 InDSB the carrier's peak values are affect-

ed by the instantaneous value of the mes-

sage signal, but the spectrum shows that thecarrier amplitude remains constant! How doyou explain the apparent contradiction?

3.4 Which are the characteristic features of abeat?

3.5 Define amplitude deviation and the modula-tion index.

3.6 Which methods of AM demodulation areyou familiar with and how do they differ?

SAM(t) SD(t)

SH(t)


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TPS 7.2.1.3 Review

3.7 In radio links the carrier is normally attenuat-ed to 5%...10%. What advantages does thishave compared to transmission with 100%carrier amplitude? Why isn't the carrier

completely suppressed?3.8 How high is the maximum efficiency in

DSB? How can the efficiency be increased?3.9 Which methods of carrier suppression are

there?3.10 Which demodulation method is used for AM

with supressed carrier?


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TPS 7.2.1.3 Review

4 Required equipment and accessories

1 CF transmitter 20 kHz 736 2011 CF receiver 20 kHz 736 211

Additionally required

1 Spectrum analyzer 726 941 Function generator 0...200 kHz 726 9611 Frequency counter 0-10 MHz 726 991 DC power supply 15 V, 3 A 726 861 Digital storage oscilloscope 305 575 2922 Probes 100 MHz, 1:1/10:1 575 2311 Analog multimeter C.A. 406 531 16

2 Sets of 10 bridging plugs, black 501 5111 Cable pair, black, 100 cm 501 461

Additionally recommended

1 XY-Yt recorder e.g. 575 663

Training objectives:

Distinguish between modulation and linearsuperpositioning.The investigation of line spectra in AM.The AM as linear modulation (normal position andinverted position of sidebands)The bandwidth requirement for AMAmplitude deviation and modulation index are de-termined.The residual carrier can be measured out.Synchronous demodulation is investigated.

Problems regarding carrier recovery in synchro-nous demodulation are looked at in detail.The dynamic characteristic of the output signal atthe ring modulator is investigated.The frequency-periodic structure of the outputspectra at a ring modulator can be recognized.


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2 9

TPS 7.2.1.3 Double Sideband AM

5 Double Sideband AM

OSL USL

sAM

sC

1

m/2

fC

fC + fMfC fM

(f)

Fig. 5-1: Representation of DSB

The DSBSC consists of the superimposition of 2harmonic oscillations, whose frequenciesfC +fM,resp.fC fM are in direct proximity due to the factthatfC >> fM. Therefore, the dynamic characteris-tic of theDSBsc is a beat. Here the side oscillationsarise on account of the frequency conversionfromfM tofC fM resp.fC +fM. Since there is nocarrier, the modulation depth m cannot be defined.Overmodulation is not possible. The amplitude ofthe modulation product sDSBSC(t) is directly propor-tional to the instantaneous value of the modulating

signal sM(t). The upper and lower envelope curveshave the abcissa as a joint reference line, insteadof the positive or negative carrier amplitude. Thefeatures of theDSBSC are summarized in Fig. 5-2.Clear to be seen in the dynamic characteristic isthe abrupt phase change of 180 at the zerocrossover of the envelope curve.The envelope curve contains sinusoidal halfwavesof double the signal frequency.Demodulation methods : Synchronous

demodulationBandwidth : b = 2 f

Mmax(5-4)

Application : Radio transmission

The features of the DSB are summarized in Fig. 5-1.

sDSB(t) = [AC + sM(t)] cos (2fCt) (5-1)

Demodulation methods : Envelopedemodulation

: Synchronousdemodulation

Bandwidth : b = 2 fMmax (5-2)Application : Radio technology

TheDSBSC.If in (5-1) the constant componentAC inside thebrackets is suppressed, then we obtain:

s s t f t

A f t f t

A f f t

A f f t

DSBSC M C

M M C

M

C M

M

C M

= ( ) ( )

= ( ) ( )

= ( )[ ]

+ +( )[ ]

cos

cos cos

cos

cos

2

2 2

2

2

2

2

(5-3)

USL LSL

sAM

sC

1

m/2

fC

fC + fMfC fM

(f)

Fig. 5-2: Representation of the DSBSC.


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Experiment procedureAssemble the experiment as specified in Fig. 5-3.Switch on the carrier. Connect the output of thefunction generator directly to the modulator input.

Set the function generator to: sine,AM = 2 V andfM = 2 kHz.

5.1 Investigations on the dynamic

characteristic of the DSB5.1.1 DSB

Set toggle switch to CARRIER ON setting. Dis-play the output signal of the modulator M2 on theoscilloscope (this signal is called the modulationproduct) and the modulating signal sM(t) of thefunction generator and sketch them. (Modulation

product on channel 2, modulating signal on channel1 of the oscilloscope). Use Diagram 5.1.1-1.

Diagram 5.1.1-1: Dynamic (time) characteristic of theDSBsignal(1): Modulating signal sM(t)(2): Modulation product at the output M2

Shift the AF signal to the upper or lower envelopecurve of the AM signal. Vary the frequency fMand the amplitude AM of the modulating signal.What do you observe?

Settings on the Oscilloscope

Input attenuator channel 1 2V/DIV


Time base 200 s/DIV

Trigger

Trigger to the modulating signal sM(t). Reduce theAM signal to approx. 1 V. Determine the modula-tion depth m. The following applies for the modula-tion depth m:

mA

A

D d

D d

= =

+

C

C

(5.1.1-1)

OUT

020

40

FUNCTION

MODE

ATT

dB

+15

V

0V

(+

5V)

M1

U UII

TTL-IN(B)

TTL-IN(A)

TTL-IN(A)

AN

ALOG

(A)

RATIO

A/B

PERIOD

A

FREQ

A

FUNCTION

GATE

0,1s

0,01s

TIMEA-B

COUNTA

CHECK

1s10s

% = p

p

V k H

z

D C

Fig. 5-3: Experiment set-up for DSB

sM(t)


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3 1


Where:D: Peak-to-peak value of the maximum of the

AMsignald: Peak-to-peak value of the minimum of the

AMsignal.

Use Diagram 5.1.1-1 to determine m. Distortioncan only be detected with difficulty when deter-mining the modulation depth directly from the mod-ulated signal. A better approach is to determine mfrom the modulation trapezoid. For this the oscillo-scope is operated in XY modus and the messagesignal sM(t) is used for horizontal deflection. Theresult obtained on the screen is a trapezoid whichopens to the left. Sketch the modulation trapezoidin Diagram 5.1.1-2.

Explain how the modulation trapezoid is generated.

5.1.2 DSBSCSet the toggle switch to CARRIER OFF. Set theoscilloscope as specified in the Table.

Settings on the oscilloscope



Time base 200 s/DIV

Trigger / external mod. signal

Proceed as described under point 5.1.1. Use Dia-gram 5.1.2-1. What is this kind of signal called?What characteristics does it have? Display themodulation trapezoid im Diagram 5.1.2-2, assessthe modulation distortion. Repeat the experiment.This time feed the modulating signal sM(t) via theLP filter in modulator M2. Vary fM. What do youobserve?

Diagram 5.1.1-2: The modulation trapezoid Diagram 5.1.2-1: Dynamic characteristic of theDSBSCsignal

5.2 Spectrum of the DSB

5.2.1 DSB

Set the toggle switch to the CARRIER ON posi-tion. Set the spectrum analyzer as shown in theTable.

Analyzer settings

SPAN/kHz:1.5 ... 20

Connect its input to the output of the modulatorM2. Use a sinusoidal signal with AM = 2 V and

fM = 2 kHz as the modulating signal sM(t). Feedthe modulating signal into the input filter of the CFtransmitter. Measure the AM spectrum in therange from approx. 15 kHz up to 25 kHz. Enter the

measurement values S(n) from the output of theanalyzer with the corresponding frequencies in

Diagram 5.1.2-2: The modulation trapezoid(1): Modulating signal sM(t)(2): Modulation product at the output M2

V1:1

V2:10


T/s:40


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Table 5.2.1-1. The amplitude values of the desiredspectral components are obtained from:

S (n)S(n)

V VAM

1 2

==

Calculate the spectral components SAM(n)with theaid of (3-8). Also enter the calculated values forSAM(n) into Table 5.2.1-1. Plot the curve of theAM spectrum in a graph. Mark the lower and up-per sidelines appropriately withLSL and USL.

Table 5.2.1-1:DSB spectrum

AC : V V1 :fC : kHz b : Hz

fr : kHzAM : V T : sfM : kHz


Measurements Theory

Namef

KHzV2

S n( )

V

SAM(n)

V

SAM(n)

V

Diagram 5.2.1-1:DSB spectrum

Repeat the experiment for sM(t): Sinusoidal,AM =1 V andfM = 3 kHz. Feed the modulating signalsM(t) directly into the modulator M2 (why?). Keepthe analyzer settings unchanged. Use Table 5.2.1-

2 and Diagram 5.2.1-2.

Table 5.2.1-2:DSB spectrum




Measurements Theory

Namef

KHzV2

S n( )

V

SAM(n)

V

SAM(n)

V

Diagram 5.2.1-2:DSB spectrum


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Compare the results. How does the USL respondas a function of the signal frequency fM? Whatabout theLSL? What is the frequency response ofthe LSL and USL? Determine the transmission

bandwidth of theAMsignal based on the measure-ments. Generalize your results for a randomly tak-en modulating signal. Determine the modulationdepth m from the various spectra.

5.2.2 DSBSCSet the toggle switch to CARRIER OFF. Use asinusoidal signal withAM = 2 V andfM = 2 kHz asa modulating signal. Measure the spectrum as inpoint 5.2.1. Enter all your results in Table 5.2.2-1and Diagram 5.2.2-1.

5.2.3 The AM spectrum for modulation with

a square-wave signal

The AM spectrum is linear. For that reason wecan draw direct conclusions as to the AM spec-trum based on our knowledge of the spectrum of

the input signal. Now let us assume that the inputsignal s(t) consists of a frequency mix, whosespectrum S(f) is shown in Fig. 5.2-1. What shouldthe corresponding AM spectrum look like?Repeat the recording of the spectrum for a modu-lating square-wave signal with AM = 2 V and

fM = 2.0 kHz. Feed the square-wave signal di-rectly into the modulator M2. Use Table 5.2.3-1.Display the spectrum in Diagram 5.2.3-1. Eluci-date your findings.

Analyzer settings

SPAN/kHz: 1 ... 25

Table 5.2.2-1:DSBSC Spectrum



f

KHzV2

S n( )

V

SAM(n)

V

SAM(n)

V

Diagram 5.2.2-1:DSBSC spectrum

sAM

fg fC fg fC + fgfC f

Fig. 5.2-1: AM for randomly taken spectrum of themodulating signal.


Measurements Theory

NameV1:2

V2:1


T/s:40


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5.3 AM demodulation (synchronous

demodulation)

5.3.1 DSB


Input attenuator channel 1 1 V/DIV


Time base 200 s/DIV

Trigger / external

Start with the settings from point 5.1. Set the phasecontroller on the CF transmitter to far left limit.

Feed the DSB signal from the output of themodulator M2 directly into the demodulator D2(do not use channel filter CH2!) Using a connect-ing lead feed the carrier signal (fC = 20 kHz) of theCF transmitter into the auxiliary carrier input of thedemodulator D2. What have you achieved by this?Display the modulating signal sM(t) on the oscillo-scope as well as the demodulated signal sD(t) at theoutput of the LP filter of the CF receiver. Sketchthe curve of the modulating signal and the demod-ulated signal in Diagram 5.3.1-1.

Tap the auxiliary carrier for the demodulator D2 infront of the phase shifter of the CF transmitter.



V2f

KHz

S n( )

V

SAM(n)

V

SAM(n)

V


Measuerements Theory

Name

Table 5.2.3-1: AM spectrum forsquare-wave modulation

sM(t)

Diagram 5.2.3-1: AM spectrum for square-wave modula-tion

Diagram 5.3.1-1: Modulating and demodulated signal fortheDSB, fixed phase relation(1): Modulating signal sM(t)(2): Demodulated signal sD(t)


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Using the oscilloscope set the phase-shifts be-tween the carrier of the transmitter and the carrierof the receiver as entered in Table 5.3.1-1. Meas-ure the amplitudeAD of the demodulated signal as

a function of the phase . Complete Table 5.3.1-1.Plot the curve ofAD/ADmax in Diagram 5.3.1-1.

5.3.2 Carrier recovery

Carrier recovery is performed in the CF receiverusing a PLL circuit. The PLL circuit is a controlloop whose function is to match the frequency and

phase of an oscillator to the reference oscillation.Fig. 5.3.2-1 illustrates the structure of a PLL cir-cuit.Let's assume that the input signal s1(t) is suppliedwith the frequency f1 to the phase detector. Youcan be fairly certain that the VCO is not going tobe so friendly as to oscillate precisely at the samefrequency. So its frequency f2 will initially differfromf1. At the output of the phase detector an ACvoltage is generated whose frequency is equal tothe differencef2 f1. This AC voltage is now sup-

plied to the input of the VCO via the loop filter.The VCO will respond to an AC voltage at its in-put with a corresponding change in frequency. Inturn the VCO's changing frequency is detected bythe phase detector. With a little luck the PLL locksinto the frequency of the input signal. The PLLcorrects the VCO until the input frequency and theVCO frequency coincide. A voltage U

arises

behind the PD based on the phase shift. This issupplied to the VCO free of interfering AC com-ponents (UF) through the loop filter. The followingrelationship prevails between the control voltage

UF and the frequencyfVCO of the VCO:

fVCO = kF UF (5.3.2-1)

The control characteristic of the VCO (CF

receiver)

Remove the bridging plug between the loop filterand VCO input at the PLL. Feed a variable DCvoltage U1 from the function generator into theVCO input. Use this variable DC voltage to controlthe frequency of the VCO. Note down your meas-

urement results in Table 5.3.2-1. Sketch the resultsin Diagram 5.3.2-1.

Attention: 0 V< UF < 5 V

W

S1(t)

X

U

UF

Fig. 5.3.2-1: Design of a PLL1 Phase detector PD2 Loop filter LF3 VCO

0

18

36

54

72

90

108

Table 5.3.1-1: Phase response of the DSB

degrees

AD

V

A

A

D

Dmax

cos

sM(t): SineAM = 2 V,fM = 2 kHz

Diagram 5.3.1-1:Demodulated signalAD/ADmax as a function of the phase

Note: The synchronous demodulation is per-formed according to Equation (3-11),or (3-12)


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Synchronous demodulation with the aid of a

free-wheeling VCO.

Table 5.3.2-1:Control characteristic of the VCO

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

UF

V

fVCO

kHz

Diagram 5.3.2-1:

The control characteristic of the VCO in the PLL circuit ofthe CF receiver

Option: This experiment requires a second

function generator 726 961.

Feed an AM signal into the input of the CF re-ceiver. The modulating signal is harmonic and has

approximately a frequency offM = 1000 Hz. Dis-play the signal present at the output of the receiveron the oscilloscope. Connect the counter in parallelto the output. By tuning the controlling DC voltageUF of the VCO it is possible to achieve fM =fD!Attention: the tuning has to be carried out withcare! This is critical!

Synchronous demodulation with the aid of a

PLL-controlled VCO.

Remove the cable connected to the auxilary car-rier input of the demodulator D2. For this insert the

bridging plug between the CARRIER RECOV-ERY and auxiliary carrier input of D2. Use nowfor demodulation the recovered auxilary carrierfrom the PLL CARRIER RECOVERY. Sketchthe pilot tone of the transmitter and the recoveredsignal in the receiver at the output of the PLL cir-cuit in Diagram 5.3.2-2.

Diagram 5.3.2-2:

Pilot tone and recovered signal of the receiver(1): Pilot tone at the CF transmitter(2). Recovered pilot at the output of the PLL (receiver)

Hint:

The required auxiliary carrier oscillation is gene-rated out of the pilot tone recovered in the PLLcircuit by means of frequency divisionf/8. De-pending on the initial state of the frequency divid-er this creates a fixed phase shift between the aux-iliary carrier and carrier oscillation. Consequent-ly, the demodulated signal shows an amplitudeerror. (For the sake of testing connect and discon-nect the bridging plug in the PLL-circuit of the CFreceiver and observe the amplitude of the demod-ulated signal.


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Sketch the 20 kHz square-wave carrier of thetransmitter at the output of the divider and the cor-responding recovered signal in the receiver in Dia-gram 5.3.2-3. Disconnect and reconnect the

bridging plug at the receiver between the VCO in-put and the output of the loop filter on the PLL cir-cuit.

Diagram 5.3.2-3:(1): 20 kHz - carrier at the transmitter(2): The recovered auxiliary carrier at the receiver

Discuss the results.

5.3.3 DSBSC Demodulation

Set the toggle switch to CARRIER OFF. Repeatthe experiment in accordance with point 5.3.1.




Time base 200 s/DIV

Trigger / AC mod. signal

Sketch the curve of the modulating signal and thedemodulated signal in Diagram 5.3.3-1. Discussthe results.

Diagram 5.3.3-1:

Modulating and demodulated signal inDSBSC(1): Demodulated signal sD(t)(2): Modulating signal sM(t)

Summarize the requirements made on the auxiliarycarrier in synchronous demodulation.

5.4 BeatsModulation is only produced if the carrier sC(t) andmodulating signal sM(t) are combined by a non-lin-ear element. The following experiment describesthe linear superimposition of harmonic signals. Forthis the carrier and the message signal are fed to alinear quadripole. This is available in the form of ansumming amplifier on the CF transmitter. Set upthe experiment as specified in Fig. 5-4. Use theconnecting lead to feed the sinusoidal carrier of theCF transmitter (A2 = 2 V) into an input of the out-put summer and feed a sine signal from the func-

tion generator withf1 = 2.0 kHz,A1 = 2 V into theother input. Display the addition of both signals atthe output of the summing amplifier () on the os-cilloscope.



Input attenuator channel 2 _____

Time base 500 s/DIV

Trigger / AC

Diagram 5.4-1:Additive superpositioning of 2 sinusoidal signals with thesame amplitudes but very different frequencies.

Sketch the signal curve in Diagram 5.4-1. Recordthe spectrum of the superpositioned signal at theoutput of the summer (summing amplifier). UseTable 5.4-1. Depict the spectrum in Diagram 5.4-2.


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Input attenuator channel 2 ______Time base 500 s/DIV

Trigger / AC

Table 5.4-1: Spectrum of a beat


Measurements Theory

Name

A2 : V V1 :f2 : kHz b : Hz

fr : kHzA1 : V T : sf1 : kHz SPAN : kHz

nf

KHz

SAM(n)

V

SAM(n)

V

S n( )

V2

O U T

0 2 0

4 0

F U N C T I O N

M O D E

A T T

d B

+15

V

0V

(+

5V)

M1

U UII

TTL-IN(B)

TTL-IN(A)

TTL

-IN(A)

ANAL

OG

(A)

RATIO

A/B

PERIOD

A

FREQ

A

FUNCTION

GATE

0,1s

0,01s

TIMEA-B

COUNTA

CHECK

1s10s

% = p

p

V k H

z

D C

Fig. 5-4: Experiment set-up for beats Diagram 5.4-2: Spectrum of the beat


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Repeat the experiment for the message signal off1 = approx. 20 kHz. Sketch the result in Diagram5.4-3.

Diagram 5.4-3:Additive superimposing of 2 sinusoidal signals with equalamplitudes and approx. equal frequencies

Depict the spectrum in Diagram 5.4-4.

Table 5.4-2: Spectrum of a beat


Measurements Theory

Name

A2 : V V1 :f2 : kHz b : Hz

fr : kHzA1 : V T : sf1 : kHz SPAN : kHz

nf

KHz

S(n)

V

S(n)

V

S n( )

V2

Diagram 5.4-4: Spectrum of a beat


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TPS 7.2.1.3 Single Sideband AM

6 The Single Sideband AM (SSB)

In DSB each sideband carries all of the informa-tion contents. The transmission bandwidth couldthus be reduced by half, if one sideband is sup-pressed. It does not matter which sideband is usedfor transmission and which one is suppressed. Theupper sideband appears in the normal position, thelower one in the inverted position. If, for example,we suppress the lower sideband in (3-8) then weobtain:

s t A f t

m f f t

SSB C C

C M

( ) cos

cos

= ( )

+ +( )[ ]

2

22

(6-1)

To suppress a sideband, a bandpass filter withsharp cutoff is used which only allows the desiredspectral components to pass.The dynamic characteristic ofSSB resembles thatof the DSBSC. However the envelope curve issomewhat more distorted.Demodulation method : Synchronous de-

modulationBandwidth requirement : b = fMmax (6-2)Application : Line-bound transmis-

sion of telephone

signals in frequency-division multiplextechnology

The SSB with residual carrier

If instead of the unattenuated carrier only a definedfraction kof the carrier amplitude is transmitted,then you obtain the SSB with residual carrier:

s t A k f t m

f f t

ESB,T C C

C M

( ) = ( ) +

+( )[ ]]

cos

cos

22

2

(6-3)

Demodulation method : Synchronous de-

modulationBandwidth requirement : b =fMmax.Application : SSB radio links

The vestigial sideband AM (VSB)

In message or information signals with very lowfrequency components bandpass filters with verysharp cutoffs are required for the filtering out ofthe unwanted sideband. Since this leads to phasedistortion, part of the unwanted sideband is alsotransmitted. Then the filters used may have cutoffswhich are less sharp, on the other hand, the slope

characteristic has to be precisely defined (Nyquistslope).

fC + fM

fC (f)

m/2

1

Fig. 6-2: SSB with residual carrier

fC + fM

fC

(f)

m/2

1

Fig. 6-1: Representation of SSB

USL

sC


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The overlapping transmission range has to runsymmetrically with respect to the carrier fre-quency.Demodulation method : Synchronous

demodulationBandwidth requirement : fMmax< b < 2 fMmaxApplication : TV technology

Experiment procedureSet up the experiment as specified in Fig. 6-4.Connect the output of the function generator di-rectly to the AF input of the modulator M2. Set thefunction generator to: sinusoidal,AM = 2 V andfM= 2 kHz.

6.1 Investigations on the dynamic

characteristic of the SSB

6.1.1 SSBRCSet the toggle switch to CARRIER ON. Displaythe output signal of the channel filter CH2 and themodulating signal sM(t) of the function generatoron the oscilloscope and sketch the signals. (Modu-lation product on channel 2, modulating signal onchannel 1 of the oscilloscope). Use Diagram 6.1.1-

1. Shift the AF signal to the upper or lowerenvelope curve of the AM signal. Vary the fre-quencyfM and the amplitudeAM of the modulatingsignal. What do you observe?




Time base 200 s/DIV

Trigger mod. signal

Trigger to the modulating signal sM(t). Switch themodulating signal off. Measure the unattenuatedcarrier amplitude AC at the input of the channel

filter, as well as the amplitude ARC of the attenu-ated carrier at the output of the channel filter.Calculate the ratio k=ARC/AC. Determine the car-rier suppression tin dB according to (6-4):

tm

k= 20

2log (6-4)

6.1.2 SSBSCSet the toggle switch to CARRIER OFF. Set theoscilloscope as specified in the Table.

Proceed as described in point 6.1.1. Use Diagram6.1.2-1. What features does the SSBSC signalhave?




Time base 200 s/DIV

Trigger / external mod. signal

fC + fMfC + fM(f)fC

s

Fig. 6-3: Filter characteristic with Nyquist slope for VSB

Diagram 6.1.1-1: Dynamic characteristic of the SSBRCSignals(1): Modulating signal sM(t)(2): Modulation product at the output of CH2

Diagram 6.1.2-1: Dynamic characteristic of the SSBSC(1): Modulating signal sM(t)(2): Modulation product at the output of CH2


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6.2 Spectrum of the SSB

6.2.1 SSBRCSet the toggle switch to CARRIER ON.

Analyzer settings

SPAN/kHz:1.5 ... 20

Set the spectrum analyzer as specified in the Ta-ble. Connect its input to the output of the modulator

M2. As the modulating signal use a sinusoidalsignal with AM = 2 V and fM = 2 kHz. Feed themodulating signal into the input filter of the CFtransmitter. Measure the SSB spectrum in therange of approx. 15 kHz up to 25 kHz and enter themeasured values S(n) from the output of theanalyzer with their corresponding frequencies inTable 6.2.1-1. The amplitude values of the wantedspectral components are obtained from:

S (n)S(n)

V V

AM

1 2

==

Calculate the spectral components SAM(n) with theaid of (3-8). Also enter the calculated values forSAM(n) in Table 6.2.1-1. Plot the curve of thespectrum in Diagram 6.2.1-1. Label the spectrallines.Determine the transmission bandwidth of the AMsignal based on the measurements. Generalize theresults for the case of any modulating signals.

6.2.2 SSBSCSet the toggle switch to CARRIER OFF. Use a

sinusoidal signal withAM = 2 V andfM = 2 kHz asa modulating signal. Measure the spectrum as de-scribed in point 6.2.1. Enter your results in Table6.2.2-1 and Diagram 6.2.2-1.Evaluate your measurement results as shown inpoint 6.2.1.

OUT

020

40

FUNCTION

MODE

ATT

dB

+15

V

0V

(+5

V)

M1

U UII

TTL-IN(B)

TTL-IN(A)

TTL-IN(A)

ANALOG

(A)

RATIO

A/B

PERIODA

FREQ

A

FUNCTION

GATE

0,1s

0,01s

TIMEA-B

COUNTA

CHECK

1s10s

% = p

p

V k H

z

D C

Fig. 6-4: Experiment setup for SSB

V1:1

V2:10


T/s:40


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Table 6.2.1-1: SSBRC spectrum




Measurements Theory

Namef

KHzV2

S n( )

V

SAM(n)

V

SAM(n)

V

Table 6.2.2-1: SSBSC spectrum




Measurements Theory

Namef

KHzV2

S n( )

V

SAM(n)

V

SAM(n)

V

Diagram 6.2.1-1: SSBRC spectrum fM = 2 kHz Diagram 6.2.2-1: SSBSC spectrum fM = 2 kHz

6.3 SSB demodulation




Time base 200 s/DIV

Trigger mod. signal

Start with the settings given in point 6.1. With theaid of a connecting lead feed the carrier signal(fC = 20 kHz) of the CF transmitter directly into

the RF input of the demodulator D2. What haveyou achieved by this?Display the modulating signal sM(t) on the oscillo-scope as well as the demodulated signal sD(t) at the

output of the LP filter of the CF receiver. Sketchthe curve of the modulating signal and the demod-ulated signal in Diagram 6.3-1. Adjust the phasebetween the original carrier of the transmitter andthe auxiliary carrier of the receiver. What do youobserve? Remove the connecting lead betweenthe CF transmitter and the demodulator. Now fordemodulation use the recovered auxilary carrierfrom the PLL circuit to recover the carrier. Forthis connect the bridging plug between CARRIER


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Diagram 6.3-1: Modulating and demodulated signal in SSB(1): Modulating signal sM(t)(2): Demodulated signal sD(t)

Diagram 6.3-2: Modulating and demodulated signal inSSBSC(1): Modulating signal sM(t)(2): Demodulated signal sD(t)

RECOVERY and the auxiliary carrier input of D2.Discuss your findings.Set the toggle switch to CARRIER OFF. This timerepeat the experiment for SSBSC.




Time base 100 s/DIV

Trigger mod. signal


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TPS 7.2.1.3 Ring Modulator

7 The Ring Modulator

Up until now the modulation process has beendescribed as a multiplication of a harmonic carriersC(t) with an equally harmonic message signalsM(t) using a multiplier IC (e.g. AD632). This ishow the wanted modulation product is directlyobtained without any undesired sidelines. How-ever, in practice product modulators in the form ofintegrated circuits are of no importance becausethey can only be used at relatively low frequencies.Consequently, modulation is performed using dis-crete components with non-linear characteristics

on account of the high frequencies used in commu-nications engineering. A group of modulators im-portant in practice is known under the name ofbalanced modulators. These types of balancedmodulators include the push-pull and ring modula-tors. The response of the ring modulator can alsobe investigated using the training panel 736 201 CFtransmitter 20 kHz. Ring modulators are generallydesigned with special diode and transistorconcepts. An example for this is illustrated in Fig.7-1.The bipolar carrier signal sC(t) is fed into the cent-er taps of the two symmetrical differential trans-formers. The diodes are supposed to perform apure switching operation, which is triggered ex-clusively by the carrier amplitude. For this thecarrier amplitude has to be high enough. During thepositive half-oscillations of the carrier 2 diodes arefully triggered in the forward direction (D1 andD2). They function like closed switches while thetwo other diodes are blocked. During this periodthe modulating signal sM(t) fed into the transform-er on the left flows

t 7.2.1.3 modulación de amplitud

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