T 7.2.1.3 Amplitude Modulation

T 7.2.1.3 

Amplitude 

Modulation 

by Klaus Breidenbach 

New Edition, November 2002 

LEYBOLD DIDACTIC GMBH . Leyboldstrasse 1 . D-50354 Hürth . Phone (02233) 604-0 . Fax (02233) 604-222 . e-mail: info@leybold-didactic.de 

©by Leybold Didactic GmbH 

Printed in the Federal Republic of Germany 

Technical alterations reserved

“The sensitive electronics of the equipment contained in the present experiment literature 

can be impaired due to the discharge of static electricity. Consequently, electrostatic build 

up should be avoided (particularly by utilizing appropriate rooms) or eliminated by discharging 

(e.g. at the panel frames or similar).”

TPS 7.2.1.3 

Contents 

Note on EMC 

European stipulations pertaining to electromagnetic compatibility (EMC) oblige the 

manufacturer of electronic training and educational equipment to draw the operator's 

attention to the following possible sources of interference. The types of interference 

listed below could arise but by no means have to. As the case arises it may prove necessary 

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 electromagnetic 

fields arising from large-scale experiment arrangements. This can occur in 

such a manner that the equipment operates insufficiently, in particular field effects can 

cause digital displays to fail. 

Precautionary and corrective measures: 

Make sure that no RF generating equipment (e.g. cellular phones) which does not belong 

to the experiment set-up is operating in the classroom or in its proximity and that 

connecting 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 damaged 

by the discharge of static electricity. 

Precautionary measures: 

Select work areas where electrostatic energy cannot be built up by the user and/or 

equipment (eliminate carpeting and similar items, ensure equipotential bonding). 

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

bursts 

Switching operations involving large loads can occassionally bring about line-bound 

high-frequency voltage bursts which can lead to the temporary impairment of sensitive 

electronic components which could cause equipment operating failure (e.g. data losses 

or 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 arise 

can be eliminated simply by switching the device off and back on again. 

3


Contents 

Note: 

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

oscilloscope (100 MHz) and further processed with the bench link 

HP 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 principle 

delivers the same results. 

The experiment results given here are just examples. Therefore, the curves 

and results specified in the solutions section should only be taken as guidelines. 

The calculation and representation of the spectra was carried out with EXCEL 

5.0. 

4


Contents 

Contents 

Equipment overview ..............................................................................................................7 

Symbols and abbreviations .................................................................................................... 8 

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

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

Signals9 

Time and spectral domain...................................................................................................... 10 

Modulation ............................................................................................................................ 10 

The communications system according to Shannon.............................................................. 12 

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

2.1 Oscilloscope and spectrum analyzer .......................................................................... 13 

2.2 Equipment descriptions .............................................................................................. 16 

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

726 961 Function generator 200kHz .......................................................................... 17 

726 99 Frequency counter 0..10 MHz ...................................................................... 18 

736 201 CF transmitter 20 kHz .................................................................................. 18 

736 221 CF receiver 20 kHz ...................................................................................... 19 

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

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

The spectrum of amplitude modulation ................................................................................. 24 

Representing amplitude modulation with a vector diagram ................................................... 24 

AM demodulation .................................................................................................................. 25 

Questions ............................................................................................................................... 26 

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

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

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

The DSB SC 

. ............................................................................................................................ 29 

5.1 Investigations on the dynamic characteristic of the DSB .......................................... 30 

5.1.1 DSB ............................................................................................................................ 30 

5.1.2 DSB SC 

................................................................................................................................................................................................................31 

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

5.2.1 DSB ............................................................................................................................ 31 

5.2.2 DSB SC 

................................................................................................................................................................................................................33 

5.2.3 The AM spectrum for modulation with a square-wave signal .................................. 33 

5.3 AM demodulation (synchronous demodulation) ........................................................ 34 

5.3.1 DSB ............................................................................................................................ 34 

5.3.2 Carrier recovery ........................................................................................................ 35 

5.3.3 DSB SC 

Demodulation ................................................................................................. 37 

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

5


Contents 

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

6.1 Investigations on the dynamic characteristic of the SSB ........................................... 42 

6.1.1 SSB RC 

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

6.1.2 SSB SC 

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

6.2 Spectrum of the SSB .................................................................................................. 43 

6.2.1 SSB RC 

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

6.2.2 SSB SC 

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

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

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

7.1 Dynamic response of the ring modulator ................................................................... 49 

7.2 Spectrum at the output of the ring modulator ............................................................ 50 

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

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

6


Contents 

Equipment overview 

Equipment 

TPS 7.2.2.3 Experiments 

2.3 A measurement example 

5.1 Investigations on the dynamic characteristic of the DSB 

5.2 Spectrum and vector representation of the DSB 

5.3 AM demodulation (synchronous demodulation) 

5.4 Beats 

6.1 Investigations on the dynamic characteristic of the SSB 

6.2 Spectrum representation and vector diagram of the SSB 

6.3 SSB demodulation 

7.1 Dynamic response of the ring modulator 

7.2 Spectrum at the output of the ring modulator 

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 2 

Cable pair, black, 100 cm 501 461 2 _ 1 _ 2 _ 1 _ _ 2 

* Optional: 2nd function generator recommended 

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 shifted 

by 4 kHz into the lower frequency range. However, their general structures remain unaffected. 

7


Contents 

Symbols and abbreviations 

A : Amplitude 

∆A C : Amplitude deviation 

A C : Carrier amplitude 

A M : Amplitude of the modulating signal 

A D : Amplitude of the demodulated signal 

A(f) : Transmission factor 

AM : Amplitude modulation 

A R : Square-wave amplitude 

DSB SC : Double sideband AM with suppressed carrier 

BP : Bandpass 

b : Bandwidth 

d : Attenuation 

SSB : Single sideband AM 

f : Frequency 

f M : Frequency of the modulating signal 

m : Modulation index 

USL : Upper sideline 

R : Frequency resolution 

s(t) : Signal function in the time domain, general 

s D (t) : Demodulated signal 

s M (t) : Information signal, modulating signal 

s C (t) : Carrier signal 

S(n) : Amplitude spectrum, general 

S AM (n) : Spectrum of the AM signal 

s AM (t) : Dynamic characteristic of the AM signal 

S R (n) : Spectrum of the square-wave signal 

T : Period duration 

LP : Lowpass filter 

LSL : Lower sideline 

η : Efficiency 

DSB : Double sideband AM 

Bibliography 

E. Stadler Modulationsverfahren 

Vogel Buchverlag, Würzburg 

3rd edition 1983 

Herter, Röcker,Lörcher 

Nachrichtentechnik, Übertragung, Vermittlung, Verarbeitung 

Hanser, München, Wien 


G. Kennedy Electronic Communication Systems, 

McGraw Hill Book Company, Singapore, 


D.G. Fink D. Christiansen 

Electronic Engineer’s Handbook 

McGraw Hill Book Company 

2nd edition 1982 

D. Roddy, J. Coolen Electronic Communications 

Prentice Hall International, Reston Verginia, 


Hewlett Packard Measurement, Computation, Systems, catalog 1986, 

Palo Alto California 

Dipl. Ing. Klaus Breidenbach 

Hürth, February 1997 

8


Introduction 

1 Introduction 

Signals 

In electrical telecommunications engineering, 

messages are usually in the form of time-dependent 

electrical quantities, for example, voltage u(t) 

or current i(t). These kinds of quantities which are 

described by time functions are called signals. In 

order to transmit messages a parameter of the 

electrical signal must be suitably influenced. In 

cases where a signal defined as a time function is 

known and the signal value can be determined 

exactly at any given point in time, then the signal 

is called deterministic. Examples of deterministic 

signals are: 

1. Harmonic oscillation 

u(t) = A · sin (2 π ft + φ) (1.1) 

2. Symmetrical square wave 

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

A t T 

u()= t 

⎧ for 0 < < / 2 

⎨ 

⎩ 0 for T/ 2 < t< T . 

Deterministic telecommunications is useless from 

the point of view of information theory. Only unknown, 

i.e. unpredictable messages are important 

for the message receiver. Nevertheless, when discussing 

modulation methods it is standard procedure 

to work with harmonic signals. The results 

which can be obtained are then clearer and more 

straightforward. If the signal value for any given 

point in time cannot be given because the signal 

curve appears totally erratic, then the signal is 

called stochastic. An example for a stochastic signal 

is noise. Stochastic signals can be described 

using methods of probability mathematics, but 

they will not be taken into consideration here. Signals 

are distinguished according to the characteristic 

curves of their time and signal coordinates. If 

the signal function s(t) produces a signal value at 

any random point in time, the signal function is 

called time-continuous (continuous w.r.t. time). 

In contrast, if the signal values differ from 0 only 

at definite, countable points in time, i.e. its time 

characteristic shows “gaps”, then this is referred 

to as time-discrete (discrete w.r.t. time). What is 

true for the time coordinate, can also be applied to 

the signal coordinates. Accordingly, a signal is 

called level-continuous, if it can assume any 

given value within the system limits. It is called 

value-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 

9


Introduction 

of signal values are permitted. Two important signal 

classes can be defined using these 4 terms: 

Analog signals 

A signal is called analog if it is both time as well 

as value-continuous. 

Digital signals 

A signal is called digital, if it is both time as well 

as value-discrete. 

Fig. 1-1 shows the various kinds of signals. 

Time and spectral domain 

In the technical sciences there exists, in addition 

to the “time domain”, signal representation in the 

“frequency” or “spectral domain”. The equivalence 

of the two types of representation can be 

seen in the depictions in Fig. 1-2. 

If you first consider the harmonic function as 

specified in (1.1), then a display on the oscilloscope 

results in the familiar, dynamic (time) characteristic 

according to Fig. 1-2-A. The sinusoidal 

time function is described by the amplitude A and 

the period duration T. However, a totally equivalent 

representation of this function is reproduced 

when the variables A and f = 1/T are used instead 

of the parameters A and T. If the amplitude is displayed 

on the frequency axis, then this form of 

representation is called the amplitude spectrum. 

Time domain 

Thus, a single line can depict a harmonic function. 

Now, after Fourier, every non-harmonic, periodic 

function can be represented as the superimposition 

of harmonic oscillations with fixed 

amplitudes S(n). As an example Fig. 1-2-B 

presents a symmetrical square-wave signal with 

the amplitude A R and the period of oscillation T R . 

We can see from the corresponding amplitude 

spectrum S R (n) in Fig. 1-2-D that the squarewave 

function is produced from the superposition 

of many (an infinite number of) harmonic oscillations. 

Their frequencies are odd numbered multiples 

of 

f = 1/T R and their amplitudes decrease as a function 

of the ordinal number n, see Table on pg. 11. 

Note: Any precise and comprehensive discussion 

of the spectra not only takes the amplitude 

spectrum S(n) into consideration 

but also the phase spectrum φ(n). However, 

in many practical exercises it suffices 

to determine the amplitude spectrum. 

Modulation 

When speaking of modulation, one generally refers 

to the conversion of a modulation signal s M (t) 

into a time function with altered characteristics 

using a carrier signal. The message signal influences 

a parameter of the carrier in a suitable fash- 

Spectral domain 

(A) 

(C) 

(B) 

(D) 

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 

10


Introduction 

Harmonic Frequency Amplitude 

1 

2 

3 

4 

n 

f R = 1/T R SR(1)= 4 A 

π 

3 f R 

5 f R 

7 f R 

(2 n – 1) f R 

S R (1) 

3 

S R (1) 

5 

S R (1) 

7 

SR (1) 

2n 

−1 

Amplitude spectrum of a symmetrical squarewave 

signal n = 1, 2, 3, 4, ... 

ion. Either harmonic oscillations or pulse trains 

are used as carrier signals. If, for example, a harmonic 

carrier is used with the form: 

s C 

(t) = A C 

cos (2 f C 

t + φ ), (1.3) 

then the message signal s M (t) can have an effect 

either on the amplitude A C , the carrier frequency 

f C or the zero phase angle φ. These effects result in 

the analog modulation methods: 

– Amplitude modulations (AM) 

– Frequency modulation (FM) 

– Phase modulation (PM). 

In the case of analog modulation methods, the 

modulation process means a continuous conversion 

of the modulating signal s M (t) into a higher 

frequency band (frequency conversion). The mod- 

R 

ulating signal is shifted from the baseband (AF 

range, original frequency band), into an RF frequency 

band. It no longer appears in the spectrum 

of the modulated oscillation. A modulation always 

requires that the carrier and the modulation 

signal interact. Both of these signals are fed into a 

modulator. The original signal s M (t) is recovered 

from the modulated signal through demodulation. 

Consequently, modulation and demodulation are 

mutually related, inverse processes. The complexities 

involved in modulation and demodulation are 

considerable. The following reasons explain why 

modulation is worthwhile: 

1. Modulation enables the matching of the 

modulating signal to the characteristics of the 

transmission channel. (radio links e.g. are 

only possible above a certain frequency.) 

2. Existing transmission channels can be multiply 

exploited using modulation, (frequency 

or time division multiplex systems). 

3. Improved signal-to-noise ratios can be obtained 

using modulation. 

The communications system according to Shannon 

Electrical communications engineering is divided 

into three classical subfunctions: 

1. Transmission of the message 

2. Processing of the message 

3. Relaying the message (telephone technology) 

If only a single transmission channel is examined, 

(i.e. no telephone technology), then we can concentrate 

on the remaining functions illustrated by 

the scheme in Fig. 1-3. 

Fig. 1-3: The telecommunications system 

(A) The telecommunications system 

(B) Message transmission 

(C) Message processing 

1 Message source 

(human being, measurment sensor etc.) 

2 Converter (microphone, 

television camera, 

strain gauges, thermo sensor etc.) 

3 Transmitter 

4 Transmission channel (radio link, 

transmission cable, data storage system) 

5 Receiver 

6 Converter 

7 Message recipient 

8 Interference source 

11


Introduction 

The telecommunication system (A) consists of 

equipment used for message transmission (B) and 

message processing (C). The message source (1) 

generates the information, which is to be made 

available to the message recipient (7). The signals 

generated are of the most varied physical nature, 

e.g. sound, light, pressure, temperature, etc. It is 

the function of the converter (2) to convert the 

non-electrical signal of the source into an electrical 

one. The transmitter (3) converts the converter 

signal into one better suited for transmission via 

the channel. Thus the modulation process takes 

place in (3). The transmission channel (4) serves 

either to bridge a spatial distance, or to overcome 

a period of time. The modulated signal, generally 

distorted by the interference source (8), reaches 

the receiver (5), where it is then reconverted into 

its original electrical signal there (demodulation). 

Finally, the converter (6) transforms the electrical 

signal back into the physical signal required by 

the message recipient (7). The message recipient 

can take the form of the human being with eyes 

and ears or a machine in a process control loop. 

12


Measuring instruments 

2 Measuring instruments 

2.1 Oscilloscope and spectrum analyzer 

The oscilloscope 

The oscilloscope is amongst the most important 

measuring instruments used in electrical engineering. 

It is used to graphically display signal 

voltages u(t) in the time domain. It can also be 

regarded as a two dimensional voltmeter. The signal 

is displayed in the form of Cartesian coordinates. 

The abcissa (x-axis) shows the time scale, 

(e.g. ms/Div) and the y-axis shows the voltage 

scale (e.g. V/Div). The oscilloscope provides immediate 

information on the signal shape and is 

therefore superior to moving coil instruments or 

digital voltmeters. The prerequisite for all forms 

of pointer instruments and multimeters is that the 

time characteristic or curve of the electrical signals 

is known. As a rule only DC voltages or harmonic 

AC voltages can be measured using these 

kinds of instruments. The oscilloscope is used for 

the voltage measurement of signals with unknown, 

random time characteristics. Here a distinction 

is drawn between two different cases: 

1. The voltage signal is non-sinusoidal, but periodic 

with “higher” frequency. 

The oscilloscope is operated in repeating real time 

mode. This operating mode is the most frequently 

one used. A sawtooth generator is started each 

time the signal to be measured has exceeded an 

adjustable level (trigger level). This produces a 

time-linear voltage used for the horizontal deflection 

of the cathode ray tube. The sawtooth generator 

is part of the time base. The vertical deflection 

is controlled by the measurement signal itself. The 

result is a standing image of the voltage signal on 

the screen. In real time operation the oscilloscope 

has a slow-motion function. Thus, processes 

which are too fast for the human eye can be made 

visible. 

2. The voltage signal to be measured is non-periodic, 

or has a very long period duration. 

The signal to be measured is digitalized and input 

into a storage system. The contents of the storage 

unit can then be output periodically. Processes 

which are too long can be displayed in the storage 

mode. 

The oscilloscope masks out the amplitude and 

time windows from the signal characteristic, see 

Fig. 2.1-1. 

Fig. 2.1-1:Functioning of the oscilloscope 

(A) Amplitude window 

(T) Time window 

The spectrum analyzer 

Spectrum analyzers are used to display signals in 

the spectral domain. These analyzers operate 

either digitally with the aid of mathematical algorithms 

(Fast Fourier Transformation) or in analog 

mode as a filter bank i.e. according to the principle 

of frequency conversion. The latter principle 

is implemented in the spectrum analyzer 726 94 

training panel. For that reason we shall study this 

in more detail with the aid of Fig. 2.1-2. 

The harmonic signal supplied by the VCO is fed 

into the mixer with the input signal. Depending on 

its spectral quality and the oscillator frequency, an 

AC voltage signal appears at the mixer output 

which lies in the passband of the bandpass filter. 

The IF signal at the output of the bandpass filter is 

produced for the individual spectral components 

of the input signal for correspondingly different 

VCO frequencies. If its frequency is linearly dependent 

on its control voltage, then this can be 

used for the X-deflection of a display unit. Thus 

the X-axis also achieves linear frequency scaling. 

The rectified, amplified output voltage of the IF 

filter is used for Y-deflection. Consequently each 

spectral amplitude of the input signal can be measured 

by adjusting the VCO. The spectrum 

analyzer thus constitutes an application of the superheterodyne 

principle used in radio technology, 

whereby the bandfilter can be regarded as a 

spectral window. The position of this window in 

the frequency domain is determined by the VCO 

13



Fig. 2.1-2: Design of a spectrum analyzer according to the superheterodyne principle 

(A) Signal path 

1Input amplfier/ attenuator V 1 

2Mixer 

3Bandpass (BP) 

4Rectifier 

5Output amplifier V 2 

(B) Oscillator 

6VCO 

7Sawtooth generator 

(C) Display unit 

frequency. The width of the window is determined 

by 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 the 

superhetrodyne principle requires that the time 

law of electrical telecommunications be observed. 

According to this law, the pulse response of a 

lowpass system becomes longer, the smaller its 

bandwidth b is, see Fig. 2.1-4. 

This statement can also be applied to the 

bandpasses present in the spectrum analyzer. The 

time law is similar to the uncertainty relation in 

nuclear physics. It states that it is impossible to 

decrease both the duration T as well as the bandwidth 

b of a signal. When tuning the VCO, the 

slower it takes for the VCO frequency to change, 

the longer the mixer output signal is in the 

passband of the downstream bandpass (BP). The 

frequency change with respect to the time unit 

depends on: 

1. (Periods of the sawtooth generator (SCAN 

TIME) 

2. Absolute frequency domain passed through 

by the VCO (SPAN). 

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

analyzer 

1 Bandpass with bandwidth b 

(spectral window) 

2 Signal spectrum 

14



Fig. 2.1-4:The time law of electrical telecommunications engineering 

(A): Input signals: pulses with equal amplitude A and period T 

(B): Lowpasses with critical frequencies f c1 

and f c2 

; f c1 

< f c2 

(C): Output signals: pulse of varying period and amplitude 

If, for example, a spectrum analysis has to be performed 

over a wide frequency domain, and, in 

addition, a very short sawtooth period is selected, 

then the result of this is a very large change in frequency 

per unit time. The mixer output signal 

passes through the mid-frequencies of the BPF 

with corresponding speed. According to the time 

law the selected bandwidth of the BPF now has to 

be “sufficiently” large if the BPF is to attain the 

input amplitude. However, at greater bandwidth 

of the bandpass filter the analyzer's spectral resolution 

capacity drops. For that reason, work with 

the spectrum analyzer always involves the compromise 

between spectral RESOLUTION and 

fault-free reproduction of the amplitude. For the 

relationship between the SCAN TIME T, bandwidth 

b and frequency window SPAN the following 

approximately applies: 

b = 20 ( f − f ) 

T 

max min (2.1) 

Where: 

f max : maximum frequency 

f min : minimum frequency 

b : bandwidth of the filter 

T : sawtooth period SCAN TIME. 

The difference f max – f min is called frequency 

window = SPAN. 

15



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 V 1 and V 2 as high as 

possible to increase the sensitivity of the signal 

path. However, overdrive - recognizable by the 

lighting 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 generator 

is set with the controllers SCAN TIME and 

SCAN MODE. The selection of the SCAN TIME 

depends on the time law of electrical telecommunications 

engineering (2.1). 

1. Setting the upper limit of the frequency: This 

is carried out in SCAN MODE f max using the 

corresponding controller. 

2. Setting the lower frequency limit: This is carried 

out in SCAN MODE f min using the corresponding 

controller. 

The frequencies can be read off directly at the 

connected COUNTER (TTL). In SCAN MODE 

RUN the VCO runs through the set frequency 

range once (important when using the XY recorder). 

An LED indicates when the upper frequency 

limit is reached. 

Only in the SCAN MODE STOP is the locking 

mechanism of the RESET function disabled. In 

this setting manual operation using a toggle 

switch is possible. The setting “UP” of the toggle 

switch enables the VCO to run in the f max direction, 

while the setting “DOWN” causes a corresponding 

reduction in frequency. 

Attention:For the run through time T = 1/25 s the 

set frequency window is passed through 

in RUN auto-repeat mode. This enables 

us to also use the spectrum 

analyzer as a sweep generator. 

C. Connection of the display unit 

The following external measuring instruments can 

be used as display units: 

– Analog voltmeter 

– Storage oscilloscope 

– XY recorder. 

Fig. 2.2-1:The spectrum analyzer 

Note: 

The analyzer operates in manual mode as 

a frequency-selective voltmeter. This operating 

mode is particularly suitable for 

quantitative evaluations. Due to the beat 

effects in the analyzer the output signal 

can start oscillating particularly when 

working with V 2 = 10. To obtain as accurate 

a reading of the output voltage S(n) as 

possible, a slight frequency adjustment is 

recommended if this should occur. 

16



726 961 Function generator 200kHz 

1. Safety instruction: 

Read the instruction sheet provided with the device! 

The function generator is illustrated in Fig. 2-1. 

Where: 

1 Mains switch 

2 FUNCTION: selection of the output signal 

3 MODE: selection of the signal parameter adjustable 

using the control knob 

4 Control knob for the selected signal parameters 

5 TTL output 

6 Output (50 Ω) 

7 Toggle switch for output attenuator 

8 Multifunction display in LCD technology 

8 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. Actuate 

mains switch 1. When the device is on the mains 

switch lights up. The desired output signal is set 

by actuating the FUNCTION button. By 

repeatedly pressing the FUNCTION button you 

shuttle cyclically through the sequence of output 

signals available, sinussoidal, triangular, squarewave, 

DC. With the MODE pushbutton the 

following signal parameters are selected: 

– Frequency 

– Amplitude (peak-to-peak value) 

– DC offset 

– Duty cycle (only for square-wave) 

You can shuttle cyclically through the program 

menus by pressing the MODE pushbutton repeatedly. 

After the desired signal parameter has been 

set its magnitude can be varied by turning the control 

knob. The maximum output voltage of the device 

lies at approx. ±12 V. 

Fig. 2.2-2: 

DC 

FUNCTION 

MODE 

726 961 

FUNKTIONSGENERATOR 200 kHz 

FUNCTION GENERATOR 200 kHz 

The function generator and the multifunction 

display 

Storing the last setting 

After switch off all of the settings are retained. 

They are at your disposal unchanged after you 

switch the unit back on. 

Calling up the base setting 

If you simultaneously press either the MODE or 

FUNCTION buttons with the device switched on, 

the function generator supplies a sinusoidal signal 

with 1 kHz and 10 V PP , DC = 0 V. The base setting 

for the duty cycle (for square-wave signal) is 

50%. 

kHz 

V 

pp 

= 

% 

ATT 

dB 

0 

20 

40 

OUT 

TTL 

17



726 99 Frequency counter 0..10 MHz 

1 8-digit 7-segment display 

2 TTL inputs (Channel A), f max = 10 MHz. 

3 Analog input (Channel A), f max = 10 MHz. 

4 TTL input (Channel B), f max = 2 MHz. 

5 Toggle switch for switchover between TTL 

and analog input of channel A 

6 Function switch 

FREQ.A 

: Frequency measurement of channel 

A, display in kHz. 

PERIOD A : Period duration channel A, 

display µs. The last respective 

measurement value is stored 

f max = 2 MHz. 

RATIO A/B : Frequency ratio f A /f B . Signal 

B with TTL level! f max = 2 MHz. 

TIME A-B 

: Time interval between a negative 

edge of signal A and the 

next negative edge of the signal 

B, f max = 2 MHz. 

COUNT A : Event counting in channel A 

from 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. Due 

to an unfavorable set up (long connecting leads) 

of the experiment and despite shielding, a display 

might appear even without an input signal, if a signal 

is applied in TTL channel A. This crosstalk 

can be attributed to the high sensitivity of the analog 

input and the spatial proximity of the input 

sockets. For that reason always connect the analog 

input to a signal source using a short connection 

cable after switching to ANALOG. 

736 201 CF transmitter 20 kHz 

The training panel contains the following components: 

1. Input filter 

The input filter sets the upper critical frequency 

limit of the modulating signal to f c = 3.4 kHz. Gain 

in the bandpass: +1. 

2. Modulator M2 

Product modulator with 2 freely accessible inputs: 

– Input for the modulating signal (LF-input) 

0,1s 

0,01s 

GATE 

1s 

10s 

RATIO A/B 

PERIOD A 

FREQ A 

FUNCTION 

TIME A-B 

COUNT A 

CHECK 

TTL - IN(A) 

TTL - IN(A) 

TTL - IN(B) 

ANALOG (A) 

726 99 

FREQUENZZAEHLER 0-10MHz 

FREQUENCY COUNTER 0-10MHz 

Fig. 2.2-3: The frequency counter 

Fig. 2.2-4: The CF transmitter 20 kHz 

18



– Input for the carrier oscillation (RF input) 

In addition, the carrier in the output signal of the 

modulator can be enabled or disabled using a toggle 

switch. (CARRIER, ON-OFF) 

3. Channel filter CH2 

The channel filter is needed for the generation of 

SSB-AM. It suppresses the lower sideband. The 

passband range of approx. 20 kHz...30 kHz extends 

beyond the upper sideband. 

Gain in the passband: +1. 

Both filters (1 and 3) are equipped with freely accessible 

inputs and outputs, which permits the recording 

of amplitude frequency responses. 

4. Output summer 

The output summer (4) has two inputs with the 

gain levels +1. The component is used to linearly 

superimpose signal components of the AM signal. 

At the output of the summing unit you have at 

your disposal the complete AM signal, i.e. 

including any existing pilot tone or, in the case of 

FMUX operation, the multiplex signal for 

transmission via the transmission channel. 

736 221 CF receiver 20 kHz 

The training panel is used for the demodulation of 

amplitude-modulated signals. The auxiliary carrier 

required for synchronous demodulation can 

be forwarded either directly via an external source 

e.g. to the corresponding CF transmitter or 

internally from the subassembly “carrier 

recovery”. 

Design: 

The device contains the following components: 

1. Channel filter CH2 

Bandpass filter for the filtering out of the wanted 

SSB signals. The passband from approx. 

20...30 kHz extends beyond the upper sideband. 

Gain in the passband: +1. For the demodulation of 

single sideband-AM (SSB) a bridging plug is 

needed between the output of the channel filter 

CH2 (1) and the input of the demodulator D2 (2). 

Should the CF receiver demodulate the double 

sideband-AM (DSB), then the SSB-signal has to 

Subassembly for “carrier generation” 

(CARRIER) 

Frequency division f 0 /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 bipolar 

square-wave signal with 4 V PP in the TTL/ 

square-wave converter (6). Conversion into a bipolar 

sine oscillation also with 4 V PP is performed 

in the square-wave/sine converter (7). The adjustable 

phase-shifter (8) φ = 0 0 ...150 0 introduces a 

defined phase-shift between the carrier on the 

modulator side (M2) and the auxiliary carrier on 

the demodulator side. The phase-shifter permits 

the features of coharent demodulation to be examined. 

Furthermore, together with the CF transmitter 

16 kHz (736 211), it is able to generate 

quadrature modulation. 

Subassembly “pilot tone generation” 

(PILOT TONE) 

The quartz oscillator (9) generates the primary 

master clock pulse, symmetrical square-wave, 

TTL with a frequency of 160 kHz. The converter 

(10) and the attenuator (11) connected in series 

form an attenuated unipolar square-wave signal 

of approx. 200 mV pp out of the TTL signal, which 

is transmitted to the CF receiver to recover the 

carrier signal. 

Fig. 2.2-5: The CF receiver 20 kHz 

19



+15V 

(+5V) 

kHz 

V 

pp 

= 

DC 

% 

I > 

FUNCTION 

MODE 

OUT 

U 

ATT 

dB 

0 

U 

20 

40 

I > 

M1 

TTL 

0V 

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

be fed directly into the input of the demodulator 

D2 after the bridging plug has been removed. 

2. Synchronous demodulator D2 

A multiplier IC takes over the function of the synchronous 

demodulator. The AM signal (DSB or 

SSB) and an auxiliary carrier are supplied to the 

demodulator. In addition to the wanted LF signal, 

higher frequency signal components also appear 

in its output signal. 

3. Lowpass filter 

Synchronous demodulation requires a subsequent 

filtering for the suppression of the higher frequency 

signal components. The filter (3) used 

here has an upper critical limit f c = 3.4 kHz and a 

gain of +1. 

Subassembly "carrier recovery" 

Carrier recovery is performed using a PLL circuit 

with subsequent frequency division. The synchronization 

of the PLL circuit is performed by a pilot 

tone of 160 Hz sent by the CF transmitter, which 

is processed in the receiver by a bandpass filter (4) 

and an amplitude limiter (5). The PLL circuit consists 

of the phase comparator (6), the loop filter 

(7) and the VCO (8). In standard operation the 

output of the loop filter is connected directly to 

the input of the VCO using a bridging plug. 

However, the VCO can also be tuned using an 

external DC voltage 0...+5 V. After locking into 

the pilot tone a recovered auxiliary oscillation f 0 = 

160 kHz is available at the output of the PLL. This 

signal is then divided down to the required carrier 

frequency f T = 20 kHz in a frequency divider (9). 


Required equipment and material 

1 Spectrum analyzer 726 94 

1 Frequency counter 0...10 MHz 726 99 

1 Analog multimeter C. A 406 531 16 

Additionally required: 

1 Function generator 0...200 kHz 726 961 

1 DC power supply ±15 V, 3 A 726 86 

1 Digital storage oscilloscope 305 575 292 

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

1 Set of 10 bridging plugs, black 501 511 

2 Cable pairs, black 100 cm 501 461 

Additionally recommended: 

1 XY recorder e.g. 575 663 

Preliminary remark 

The measurement station described here consists 

of a spectrum analyzer, oscilloscope and frequency 

counter. Using this measurement station 

signals can be measured in the time and spectral 

20



domain. This will be used a lot in the following 

experiments. 

Experiment procedure 

Set up the experiment as specified in Fig. 2.3-1. 

Set a square-wave signal with A R = 5 V and 

f R = 2 kHz on the function generator. The TTL input 

A of the frequency counter remains permanently 

connected to the analyzer via bridging 

plugs. In order to test the signal frequency f R plug 

a connecting lead into the analog input and actuate 

the toggle switch. 

Record the spectrum of the square-wave signal in 

the frequency range of approx. 1.5 kHz....20 kHz. 

1. Manual operation with the analog voltmeter. 

Connect an analog voltmeter 10 V DC to the 

analyzer output. 

V 1 : 1 

V 2 : 5, 10 

Analyzer settings 

f r / kHz: 20 b/Hz: 500 

Tabelle 2.3-1: Spectrum square wave signal 

Signal parameter 

A R : V 

τ/T P : 

f R : kHz 

n 

1 

2 

3 

4 

5 

6 

7 

8 

f 

kHz 

Measurements 

S(n) 

V 


V 1 : 

b : Hz 

f r : kHz 

T : s 

S R (n) 

V 2 

V 

Theory 

S 

R 

V 

(n) 

SPAN/kHz: 0.5...20 

T/s: 20 

9 

10 

When V 1 = 2, 5, 10 the input stage is overdriven, 

the OVER LED lights up and the 

measurement results are falsified. 

Now record the spectrum of the square-wave 

signal by starting the VCO in SCAN MODE 

RUN. In the spectral energy range the output 

signal demonstrates a brief increase. Then 

stop the VCO and manually adjust it around 

the frequency of the spectral line using the 

pushbutton up/down. Read off the spectral 

amplitude S(n) on the voltmeter. In this manner 

enter all the amplitudes S(n), the index n 

and the corresponding frequencies f into the 

Table 2.3-1. Also the analyzer settings are to 

be noted down there. Plot the spectrum in a 

graph 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 the 

gain settings V 1 , V 2 remain unchanged. 

Diagram 2.3-1: 

Spectrum of the square-wave signal 

τ 

A R 

= 5 V, = 0.5 

T P 

2.1 Using an XY recorder 

Connect the X+ input of the recorder to the X 

socket of the analyzer. Connect the Y+ input 

of the recorder to the analyzer output; X–, 

Y– to earth. Both recorder axes have to be 

calibrated. The X-axis is set to f max . The Y- 

axis is aligned to the highest spectral amplitude 

(test it out!). The analyzer cycle is 

21



triggered by switching to SCAN MODE 

RUN. 

2.2 Using the storage oscilloscope 

The simplest operation is the recording of 

spectra with the storage oscilloscope in the 

ROLL mode. Then all of the problems involving 

triggering are avoided. The holding 

time base is set so that its period is greater 

than the SCAN TIME set on the analyzer. 

The analyzer output is connected to a Y-input 

of the oscilloscope. By selecting a suitable Y- 

gain setting the screen surface is optimally 

exploited for the spectral display. Once the 

spectrum is completely reproduced on the 

screen, the ROLL modus can be disabled by 

pressing the SINGLE pushbutton. The screen 

contents are then “frozen”. When in SINGLE 

storage mode you have to trigger externally 

on the falling edge of the sawtooth signal 

(socket X). Try out the most effective trigger 

filter. 

Repeat the recording of the spectra one after 

the other for the bandwidths b = 100 Hz, 

b = 50 Hz, b = 10 Hz, b = 5 Hz. What do you 

observe? 

22


Review 

3 Review of amplitude modulation 

In amplitude modulation (AM) the momentary 

value of the message signal s M (t) has an 

immediate effect on the amplitude of the carrier 

oscillation s C (t). This takes place in a modulator, 

see Fig.3-1. 

Here it would be: 

s C 

(t) = A C 

cos (2 π f C 

t) (3-1) 

for the high-frequency carrier and: 

1. s M 

(t) = A M 

cos (2 π f M 

t) (3-2) 

for the low frequency message signal. The combining 

of the carrier and message signal in the 

modulator then provides the following modulation 

product: 

s AM 

(t) = [A C 

+ α s M 

(t)] cos (2 π f C 

t) (3-3) 

= [A C 

+ α A M 

cos (2 π f M 

t)] 

cos (2 π f C 

t). 

Where α stands for the modulator constant, which 

expresses the affect of the message signal s M (t) 

on the amplitude A C of the carrier. Normally (3-3) 

is described in more general terms. For this you 

need the following definitions: 

∆A C 

= α A M 

Amplitude deviation (3-4) 

A 

m = ∆ C 

A 

C 

Modulation index (3-5) 

Amplitude deviation ∆A C describes the maximum 

change away from the original value A C in the carrier 

amplitude. The modulation index m reproduces 

the ratio of the amplitude deviation to the carrier 

Fig. 3-1: Generation of amplitude modulation 

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

follows: 

⎡ ∆A 

⎤ 

C 

sAM 

( t) = A ⎢ 

C 1+ cos( 2π 

fMt) 

⎥cos 

2π 

fCt 

⎢ 

⎣ 

A 

⎥ 

C 

⎦ 

A 1 mcos 

2π 

f t cos 2π 

f t 

C M C 

( ) 

[ ] ( ) 

= + ( ) 

(3-6) 

Fig. 3-2 shows the amplitude modulated signal according 

to (3-6). The modulating signal s M (t) can 

be 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 effect 

m = 1 : full modulation, the envelopes bordering 

the modulating signal just touch at their 

minimum values 

m > 1 : overmodulation, the envelopes permeate 

each other, modulation distortion arises. 

m = 0% 

A C 

s AM 

T C 

Envelope 

∆A C 

∆A C 

m = 100% 

T M 

Envelope 

m > 100% 

Fig. 3-2: The amplitude modulated signal 

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

23


Review 

Special cases are depicted in Fig. 3-3. 

The spectrum of amplitude modulation 

The expression in the brackets of (3-6) describes 

the envelope of amplitude modulation. If you 

multiply the dynamic (time) characteristic of the 

carrier oscillation in this expression, you obtain: 

s AM 

(t) = A C 

[cos (2 π f C 

t) 

+ m cos (2 π f T 

t) cos (2 π f M 

t)] (3-7) 

The application of the addition theorem: 

1 

cos x⋅ cos y= cos( x−y)+ cos x+ 

y 

2 

provides: 

s ( t) A cos 2π 

f t 

AM C C 

[ ( )] 

= ( ) 

m 

+ cos 2π 

( fC 

− fM 

) t 

2 

[ ] 

m 

+ cos 2π 

( fC 

+ fM 

) t 

2 

[ ] 

(3-8) 

From (3-8) you can see the spectral composition of 

amplitude modulation, see Fig. 3-4. 

From the spectrum we can see that besides the 

carrier oscillation with the frequency f C , there are 

also 2 side oscillations with the frequencies f C + f M 

and f C – f M contained in s AM (t). According to (3-8) 

the amplitudes of the equal side oscillations depend 

on the modulation index. The oscillation with the 

lower frequency f C – f M is called the lower sideline, 

the one with the higher frequency is the upper 

sideline f C + f M . The lower sideline (LSL) slips further 

into the range of lower frequencies as the 

signal frequency f M increases. This frequency response 

of the LSL is referred to as inverted position. 

The upper sideline (USL) shifts into the 

higher range of frequencies with increasing signal 

frequency. It lies in the normal position. In Fig. 3- 

5 the terms are in standard representation for the 

transmission of an information band, which extends 

from a lower frequency limit f u up to the 

upper frequency limit f o . 

The representation according to Fig. 3-5 is standard 

particularly in carrier frequency technology. 

The bandwidth requirement of AM equals twice 

the maximum message frequency f Mmax : 

b = 2 f Mmax 

(3-9) 

Representing amplitude modulation with a 

vector diagram 

The vector diagram constitutes an important tool in 

the representation of modulation methods. It frequently 

permits the immediate assessment of interference 

effects or manipulations during modulation. 

For example, asymmetrical attenuation of the 

sideband oscillations in AM can lead to the 

formation of parasitic angular modulation. 

From Fig. 3-6 the following features of amplitude 

modulation can be read off directly: 

An AM signal can be represented by 3 complex 

vectors ( 2 sideband vectors and a vector for the 

carrier). The 3 vectors are displayed in a joint diagram 

for any given point in time, see Fig. 3-6. 

S AM 

S AM 

A C 

m/2 

A C 

m/2 

f M f C 

(f) 

f C – f M 

Fig. 3-4: The spectrum of amplitude modulation 

s M 

f u f o 

s AM 

f C – f o f C f C + f o 

1 

1 

f C 

f C + f M 

(f) 

f 

Fig. 3-5: Normal and inverted position 

f 

24


Review 

t = t 1 

s AM 

USL 

USL 

t = t 2 

LSL 

LSL 

s C 

s C 

s AM 

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

representation 

1. The carrier oscillation is depicted with a constant 

direction (normally perpendicular upwards), 

although in absolute terms it rotates in 

counterclockwise rotation with 2 π f C . 

2. The length of the carrier vector remains constant. 

3. The sideband vectors are symmetrical with 

respect to the carrier. The vector of the USL 

rotates counterclockwise around the tip of the 

carrier vector. The vector of the LSL rotates 

in clockwise rotation. 

4. The vector for the amplitude modulated oscillation 

is obtained through vector addition, i.e. 

construction of the vector parallelogram, 

made up of the vector of the carrier and the 

side oscillations. The resulting vector always 

has the direction of the carrier vector. 

As you can see from Fig. 3-7, the tips of the resulting 

vectors, if you draw them as a function of time, 

again produce the envelope of the amplitude 

modulated oscillation. 

1. A DC voltage component 

2. The original signal with the frequency f M . 

3. Components with higher frequencies f C , 

f C + f M , 2 f C + f M , etc. 

Fourier expansion shows that rectification of the 

AM signal produces many new spectral components 

which are not present at the input of the rectifier. 

A suitable filter is used to suppress these 

unwanted spectral components. Envelope demodulation 

belongs to the so-called incoherent 

demodulation methods, as neither the carrier phase 

nor the carrier frequency are of any importance. 

Fig. 3-9 reproduces the possible circuit configuration 

of an envelope demodulator. 

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 passing 

through the recifier can be subjected to Fourier 

series expansion. It can be shown that a rectified 

AM signal contains the following signal components: 

Fig. 3-8: Envelope curve demodulation 

25


Review 

s AM (t) C 1 R 1 s D (t) 

S AM (t) 

S D (t) 

S H (t) 

Fig. 3-9: The envelope demodulator 

Fig. 3-10: Synchronous demodulation 

Envelope demodulation always requires the carrier. 

After rectification this produces a DC voltage, 

which establishes the working point of the diode. In 

practice envelope demodulation is frequently used 

in AM radio communications due to its simple 

circuitry. 

2. Synchronous demodulation 

In principle synchronous demodulation is simply 

another modulation process. To carry it out, you 

need an auxiliary oscillation in the receiver, which 

in terms of frequency and phase corresponds exactly 

to the carrier oscillation in the modulator. The 

auxiliary carrier s Aux (t) and the modulated signal 

s AM (t) are supplied to a circuit with multiplying capabilities, 

see. Fig. 3-10: 

Three cases can be distinguished DSB, DSB sc and 

SSB: 

1. Demodulation of DSB 

⎧⎪ 

m 

sAM ( t) = AC⎨cos( 2π 

fC t)+ cos 2π( fC − fM 

) t 

⎩⎪ 

2 

m 

+ cos 2π 

( fC 

+ fM 

) t 

2 

s t cos 2π 

f t φ 

( 3 10) 

Aux 

( ) = + 

[ ] ⎫ ⎬ ⎪ ⎭ ⎪ 

Aux 

[ ] 

( ) − 

The amplitude of the auxiliary oscillation is negligible, 

furthermore it is true that f C = f Aux (i.e. frequency 

equality prevails between carrier and 

auxiliary carrier). After lowpass filtering we obtain 

the demodulated signal: 

AC 

m 

sD( t) = ACcosφ+ cos( 2 π fMt) 

cosφ 

(3-11) 

2 

2. Demodulation of DSB sc . 

The constant DC voltage component A C cos φ is 

omitted: 

A m 

s D ( t ) = C 

cos ( 2π f t ) M cosφ (3-12) 

2 

3. Demodulation of SSB SC . 

s D ( t ) 

= AC 

m 

cos( 

2π f ± ) M φ (3-13) 

4 

In the synchronous demodulation of DSB a phase 

error φ reduces the amplitude of the demodulated 

signal by the factor cos φ. In the case of SSB, the 

phase error leads to a shift in the demodulated signal. 

In both cases the phase between the carrier 

and the auxiliary carrier has a noticeable effect on 

the demodulation process. Due to this phase sensitivity 

synchronous demodulation is also called coherent 

demodulation. 

Questions 

3.1 What is meant by modulation? Mixing? 

3.2 Name the reasons for performing modulation! 

3.3 In DSB the carrier's peak values are affected 

by the instantaneous value of the message 

signal, but the spectrum shows that the 

carrier amplitude remains constant! How do 

you explain the apparent contradiction? 

3.4 Which are the characteristic features of a 

beat? 

3.5 Define amplitude deviation and the modulation 

index. 

3.6 Which methods of AM demodulation are 

you familiar with and how do they differ? 

26


Review 

3.7 In radio links the carrier is normally attenuated 

to 5%...10%. What advantages does this 

have 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? 

27


Review 

4 Required equipment and accessories 

1 CF transmitter 20 kHz 736 201 

1 CF receiver 20 kHz 736 211 

Additionally required 

1 Spectrum analyzer 726 94 

1 Function generator 0...200 kHz 726 961 

1 Frequency counter 0-10 MHz 726 99 

1 DC power supply ±15 V, 3 A 726 86 

1 Digital storage oscilloscope 305 575 292 

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

1 Analog multimeter C.A. 406 531 16 

2 Sets of 10 bridging plugs, black 501 511 

1 Cable pair, black, 100 cm 501 461 

Additionally recommended 

1 XY-Yt recorder e.g. 575 663 

Training objectives: 

Distinguish between modulation and linear 

superpositioning. 

The investigation of line spectra in AM. 

The AM as linear modulation (normal position and 

inverted position of sidebands) 

The bandwidth requirement for AM 

Amplitude deviation and modulation index are determined. 

The residual carrier can be measured out. 

Synchronous demodulation is investigated. 

Problems regarding carrier recovery in synchronous 

demodulation are looked at in detail. 

The dynamic characteristic of the output signal at 

the ring modulator is investigated. 

The frequency-periodic structure of the output 

spectra at a ring modulator can be recognized. 

28


Double Sideband AM 

5 Double Sideband AM 

OSL 

s AM 

1 

USL 

m/2 

s C 

f C 

(f) 

Fig. 5-1: Representation of DSB 

f C – f M 

f C + f M 

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

1. 

s DSB 

(t) = [A C 

+ αs M 

(t)] cos (2π f C 

t) (5-1) 

Demodulation methods : Envelope 

demodulation 

: Synchronous 

demodulation 

Bandwidth : b = 2 · f Mmax (5-2) 

Application 

: Radio technology 

The DSB SC 

. 

If in (5-1) the constant component A C inside the 

brackets is suppressed, then we obtain: 

s αs t cos 2π 

f t 

= ( ) ( ) 

DSBSC M C 

= α AM cos( 2π fM t) cos( 2π 

fC 

t ) 

α AM 

= cos[ 2π 

( fC 

− fM 

) t] 

(5-3) 

2 

α AM 

+ cos[ 2π 

( fC 

+ fM 

) t] 

2 

The DSB SC consists of the superimposition of 2 

harmonic oscillations, whose frequencies f C + f M , 

resp. f C – f M are in direct proximity due to the fact 

that f C >> f M . Therefore, the dynamic characteristic 

of the DSB sc is a beat. Here the side oscillations 

arise on account of the frequency conversion 

from f M to f C – f M resp. f C + f M . Since there is no 

carrier, the modulation depth m cannot be defined. 

Overmodulation is not possible. The amplitude of 

the modulation product s DSBSC (t) is directly proportional 

to the instantaneous value of the modulating 

signal s M (t). The upper and lower envelope curves 

have the abcissa as a joint reference line, instead 

of the positive or negative carrier amplitude. The 

features of the DSB SC are summarized in Fig. 5-2. 

Clear to be seen in the dynamic characteristic is 

the abrupt phase change of 180° at the zero 

crossover of the envelope curve. 

The envelope curve contains sinusoidal halfwaves 

of double the signal frequency. 

Demodulation methods 

: Synchronous 

demodulation 

Bandwidth : b = 2 · f Mmax (5-4) 

Application 

: Radio transmission 

USL 

s AM 

1 

LSL 

m/2 

s C 

f C 

(f) 

Fig. 5-2: Representation of the DSB SC 

. 

f C – f M 

f C + f M 

29

% 

0 




Assemble the experiment as specified in Fig. 5-3. 

Switch on the carrier. Connect the output of the 

function generator directly to the modulator input. 

Set the function generator to: sine, A M = 2 V and 

f M = 2 kHz. 

5.1 Investigations on the dynamic 

characteristic of the DSB 

5.1.1 DSB 

Set toggle switch to CARRIER ON setting. Display 

the output signal of the modulator M2 on the 

oscilloscope (this signal is called the modulation 

product) and the modulating signal s M (t) of the 

function generator and sketch them. (Modulation 

product on channel 2, modulating signal on channel 

1 of the oscilloscope). Use Diagram 5.1.1-1. 

GATE 

1s 

10s 

0,1s 

0,01s 

TIME A-B 

COUNT A 

CHECK 

FUNCTION 

RATIO A/B 

PERIOD A 

FREQ A 

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

ANALOG (A) 

TTL - IN(B) 

Diagram 5.1.1-1: Dynamic (time) characteristic of the DSB 

signal 

(1): Modulating signal s M 

(t) 

(2): Modulation product at the output M2 

Shift the AF signal to the upper or lower envelope 

curve of the AM signal. Vary the frequency f M 

and the amplitude A M of the modulating signal. 

What do you observe? 

Settings on the Oscilloscope 

Input attenuator channel 1 


2V/DIV 

2V/DIV 

kHz 

V pp 

= 

MODE 

OUT 

ATT 

dB 

20 

40 

TTL 

Time base 

Trigger 

200 µs/DIV 

s M (t) 

DC 

FUNCTION 

Trigger to the modulating signal s M (t). Reduce the 

A M signal to approx. 1 V. Determine the modulation 

depth m. The following applies for the modulation 

depth m: 

∆ A D d 

m = C − 

= 

(5.1.1-1) 

A D + d 

C 

+15V 

(+5V) 

I > 

U 

U 

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

I > 

M1 

0V 

30



Diagram 5.1.1-2: The modulation trapezoid 

Where: 

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

AM signal 

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

AM signal. 

Use Diagram 5.1.1-1 to determine m. Distortion 

can only be detected with difficulty when determining 

the modulation depth directly from the modulated 

signal. A better approach is to determine m 

from the modulation trapezoid. For this the oscilloscope 

is operated in XY modus and the message 

signal s M (t) is used for horizontal deflection. The 

result obtained on the screen is a trapezoid which 

opens to the left. Sketch the modulation trapezoid 

in Diagram 5.1.1-2. 

Explain how the modulation trapezoid is generated. 

5.1.2 DSB SC 

Set the toggle switch to CARRIER OFF. Set the 

oscilloscope as specified in the Table. 

Settings on the oscilloscope 



Time base 

Trigger / external 

2V/DIV 

2V/DIV 

200 µs/DIV 

mod. signal 

Proceed as described under point 5.1.1. Use Diagram 

5.1.2-1. What is this kind of signal called? 

What characteristics does it have? Display the 

modulation trapezoid im Diagram 5.1.2-2, assess 

the modulation distortion. Repeat the experiment. 

This time feed the modulating signal s M (t) via the 

LP filter in modulator M2. Vary f M . What do you 

observe? 

Diagram 5.1.2-1: Dynamic characteristic of the DSB SC 

signal 



(t) 


5.2 Spectrum of the DSB 

5.2.1 DSB 

Set the toggle switch to the CARRIER ON position. 

Set the spectrum analyzer as shown in the 

Table. 

V 1 :1 

V 2 :10 

SPAN/kHz:1.5 ... 20 


f r /kHz: 50 b/Hz: 100 

T/s:40 

Connect its input to the output of the modulator 

M2. Use a sinusoidal signal with A M = 2 V and 

f M = 2 kHz as the modulating signal s M (t). Feed 

the modulating signal into the input filter of the CF 

transmitter. Measure the AM spectrum in the 

range from approx. 15 kHz up to 25 kHz. Enter the 

measurement values S(n) from the output of the 

analyzer with the corresponding frequencies in 

31



Table 5.2.1-1. The amplitude values of the desired 

spectral components are obtained from: 

S 

AM 

S(n) 

(n) = 

V ⋅ V 

1 2 

Calculate the spectral components S AM (n) with the 

aid of (3-8). Also enter the calculated values for 

S AM (n) into Table 5.2.1-1. Plot the curve of the 

AM spectrum in a graph. Mark the lower and upper 

sidelines appropriately with LSL and USL. 

Repeat the experiment for s M (t): Sinusoidal, A M = 

1 V and f M = 3 kHz. Feed the modulating signal 

s M (t) directly into the modulator M2 (why?). Keep 

the analyzer settings unchanged. Use Table 5.2.1- 

2 and Diagram 5.2.1-2. 

Table 5.2.1-1: DSB spectrum 

Signal parameter Analyzer settings 

A C : V V 1 : 

f C : kHz b : Hz 

f r : kHz 

A M : V T : s 

f M : kHz 



A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

Measurements 

Theory 

Measurements 

Theory 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

Diagram 5.2.1-1: DSB spectrum 


32



Compare the results. How does the USL respond 

as a function of the signal frequency f M ? What 

about the LSL? What is the frequency response of 

the LSL and USL? Determine the transmission 

bandwidth of the AM signal based on the measurements. 

Generalize your results for a randomly taken 

modulating signal. Determine the modulation 

depth m from the various spectra. 

5.2.2 DSB SC 

Set the toggle switch to CARRIER OFF. Use a 

sinusoidal signal with A M = 2 V and f M = 2 kHz as 

a modulating signal. Measure the spectrum as in 

point 5.2.1. Enter all your results in Table 5.2.2-1 

and Diagram 5.2.2-1. 

Table 5.2.2-1: DSB SC Spectrum 



A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

s AM 

f g f C – f g f C f C + f g 

Fig. 5.2-1: 

AM for randomly taken spectrum of the 

modulating signal. 

5.2.3 The AM spectrum for modulation with 

a square-wave signal 

The AM spectrum is linear. For that reason we 

can draw direct conclusions as to the AM spectrum 

based on our knowledge of the spectrum of 

the input signal. Now let us assume that the input 

signal s(t) consists of a frequency mix, whose 

spectrum S(f) is shown in Fig. 5.2-1. What should 

the corresponding AM spectrum look like? 

Repeat the recording of the spectrum for a modulating 

square-wave signal with A M = 2 V and 

f M = 2.0 kHz. Feed the square-wave signal directly 

into the modulator M2. Use Table 5.2.3-1. 

Display the spectrum in Diagram 5.2.3-1. Elucidate 

your findings. 

f 

V 2 

f 

KHz 

Measurements 

S( n) 

Name 

V 

S AM (n) 

V 

Theory 

S AM (n) 

V 

V 1 :2 

V 2 :1 


f r /kHz: 50 b/Hz: 100 

SPAN/kHz: 1 ... 25 

T/s:40 

Diagram 5.2.2-1: DSB SC 

spectrum 

33



A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

V 2 

Table 5.2.3-1: AM spectrum for 

square-wave modulation 


f 

KHz 

Measuerements 

Name 

S( n) 

V 


S AM (n) 

V 

Theory 

S AM (n) 

V 

5.3 AM demodulation (synchronous 

demodulation) 

5.3.1 DSB 




Time base 


1 V/DIV 

1 V/DIV 

200 µs/DIV 

s M (t) 

Start with the settings from point 5.1. Set the phase 

controller on the CF transmitter to far left limit. 

Feed the DSB signal from the output of the 

modulator M2 directly into the demodulator D2 

(do not use channel filter CH2!) Using a connecting 

lead feed the carrier signal (f C = 20 kHz) of the 

CF transmitter into the auxiliary carrier input of the 

demodulator D2. What have you achieved by this? 

Display the modulating signal s M (t) on the oscilloscope 

as well as the demodulated signal s D (t) at the 

output of the LP filter of the CF receiver. Sketch 

the curve of the modulating signal and the demodulated 

signal in Diagram 5.3.1-1. 

Tap the auxiliary carrier for the demodulator D2 in 

front of the phase shifter of the CF transmitter. 

Diagram 5.2.3-1: AM spectrum for square-wave modulation 

Diagram 5.3.1-1: Modulating and demodulated signal for 

the DSB, fixed phase relation 

(1): Modulating signal s M (t) 

(2): Demodulated signal s D 

(t) 

34



Using the oscilloscope set the phase-shifts between 

the carrier of the transmitter and the carrier 

of the receiver as entered in Table 5.3.1-1. Measure 

the amplitude A D of the demodulated signal as 

a function of the phase φ. Complete Table 5.3.1-1. 

Plot the curve of A D /A Dmax in Diagram 5.3.1-1. 

Table 5.3.1-1: Phase response of the DSB 

φ 

degrees 

0 

18 

36 

54 

72 

90 

108 

s M (t): Sine A M = 2 V, f M = 2 kHz 

A D 

V 

A 

A 

D 

Dmax 

cos φ 

5.3.2 Carrier recovery 

Carrier recovery is performed in the CF receiver 

using a PLL circuit. The PLL circuit is a control 

loop 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 circuit. 

Let's assume that the input signal s 1 (t) is supplied 

with the frequency f 1 to the phase detector. You 

can be fairly certain that the VCO is not going to 

be so friendly as to oscillate precisely at the same 

frequency. So its frequency f 2 will initially differ 

from f 1 . At the output of the phase detector an AC 

voltage is generated whose frequency is equal to 

the difference f 2 – f 1 . This AC voltage is now supplied 

to the input of the VCO via the loop filter. 

The VCO will respond to an AC voltage at its input 

with a corresponding change in frequency. In 

turn the VCO's changing frequency is detected by 

the phase detector. With a little luck the PLL locks 

into the frequency of the input signal. The PLL 

corrects the VCO until the input frequency and the 

VCO frequency coincide. A voltage U Φ arises 

behind the PD based on the phase shift. This is 

supplied to the VCO free of interfering AC components 

(U F ) through the loop filter. The following 

relationship prevails between the control voltage 

U F and the frequency f VCO of the VCO: 

f VCO 

= k F 

· U F 

(5.3.2-1) 

Diagram 5.3.1-1: 

Demodulated signal A D 

/A Dmax 

as a function of the phase φ 

Note: 

The synchronous demodulation is performed 

according to Equation (3-11), 

or (3-12) 

The control characteristic of the VCO (CF 

receiver) 

Remove the bridging plug between the loop filter 

and VCO input at the PLL. Feed a variable DC 

voltage U 1 from the function generator into the 

VCO input. Use this variable DC voltage to control 

the frequency of the VCO. Note down your measurement 

results in Table 5.3.2-1. Sketch the results 


Attention: 0 V

< 5 V 

W 

S 1 (t) 

X 

U Φ 

U F 

Fig. 5.3.2-1: 

Design of a PLL 

1 Phase detector PD 

2 Loop filter LF 

3 VCO 

35



Synchronous demodulation with the aid of a 

free-wheeling VCO. 

Table 5.3.2-1: 

Control characteristic of the VCO 

U F 

V 

0.5 

1.0 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

f VCO 

kHz 

Option: This experiment requires a second 

function generator 726 961. 

Feed an AM signal into the input of the CF receiver. 

The modulating signal is harmonic and has 

approximately a frequency of f M = 1000 Hz. Display 

the signal present at the output of the receiver 

on the oscilloscope. Connect the counter in parallel 

to the output. By tuning the controlling DC voltage 

U F of the VCO it is possible to achieve f M = f D ! 

Attention: the tuning has to be carried out with 

care! This is critical! 


PLL-controlled VCO. 

Remove the cable connected to the auxilary carrier 

input of the demodulator D2. For this insert the 

bridging plug between the CARRIER RECOV- 

ERY and auxiliary carrier input of D2. Use now 

for demodulation the recovered auxilary carrier 

from the PLL CARRIER RECOVERY. Sketch 

the pilot tone of the transmitter and the recovered 

signal in the receiver at the output of the PLL circuit 


4.5 

5.0 


The control characteristic of the VCO in the PLL circuit of 

the CF receiver 


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 generated 

out of the pilot tone recovered in the PLL 

circuit by means of frequency division f/8. Depending 

on the initial state of the frequency divider 

this creates a fixed phase shift between the auxiliary 

carrier and carrier oscillation. Consequently, 

the demodulated signal shows an amplitude 

error. (For the sake of testing connect and disconnect 

the bridging plug in the PLL-circuit of the CF 

receiver and observe the amplitude of the demodulated 

signal. 

36



Sketch the 20 kHz square-wave carrier of the 

transmitter at the output of the divider and the corresponding 

recovered signal in the receiver in Diagram 

5.3.2-3. Disconnect and reconnect the 

bridging plug at the receiver between the VCO input 

and the output of the loop filter on the PLL circuit. 


(1): 20 kHz - carrier at the transmitter 

(2): The recovered auxiliary carrier at the receiver 

Discuss the results. 

5.3.3 DSB SC 

Demodulation 

Set the toggle switch to CARRIER OFF. Repeat 

the experiment in accordance with point 5.3.1. 




Time base 

Trigger / AC 

2 V/DIV 

2 V/DIV 

200 µs/DIV 

mod. signal 

Summarize the requirements made on the auxiliary 

carrier in synchronous demodulation. 

5.4 Beats 

Modulation is only produced if the carrier s C (t) and 

modulating signal s M (t) are combined by a non-linear 

element. The following experiment describes 

the linear superimposition of harmonic signals. For 

this the carrier and the message signal are fed to a 

linear quadripole. This is available in the form of an 

summing amplifier on the CF transmitter. Set up 

the experiment as specified in Fig. 5-4. Use the 

connecting lead to feed the sinusoidal carrier of the 

CF transmitter (A 2 = 2 V) into an input of the output 

summer and feed a sine signal from the function 

generator with f 1 = 2.0 kHz, A 1 = 2 V into the 

other input. Display the addition of both signals at 

the output of the summing amplifier (Σ) on the oscilloscope. 




Time base 

Trigger / AC 

2 V/DIV 

_____ 

500 µs/DIV 

Sketch the curve of the modulating signal and the 

demodulated signal in Diagram 5.3.3-1. Discuss 

the results. 


Additive superpositioning of 2 sinusoidal signals with the 

same amplitudes but very different frequencies. 

Sketch the signal curve in Diagram 5.4-1. Record 

the spectrum of the superpositioned signal at the 

output of the summer (summing amplifier). Use 

Table 5.4-1. Depict the spectrum in Diagram 5.4- 

2. 


Modulating and demodulated signal in DSB SC 

(1): Demodulated signal s D (t) 


(t) 

37

% 

0 





2 V/DIV 

GATE 

1s 

10s 

0,1s 

0,01s 

TIME A-B 

COUNT A 

CHECK 

FUNCTION 

RATIO A/B 

PERIOD A 

FREQ A 


ANALOG (A) 

TTL - IN(B) 


Time base 

Trigger / AC 

______ 

500 µs/DIV 

Table 5.4-1: Spectrum of a beat 



A 2 : V V 1 : 

f 2 : kHz b : Hz 

f r : kHz 

A 1 : V T : s 

f 1 : kHz SPAN : kHz 

Measurements 

Theory 

n 

f 

KHz 

Name 

S( n) 

V2 

S AM (n) 

V 

S AM (n) 

V 

kHz 

V pp 

= 

MODE 

OUT 

ATT 

dB 

20 

40 

TTL 

DC 

FUNCTION 

I > 

I > 

U 

U 

+15V 

(+5V) 

0V 

M1 

Fig. 5-4: Experiment set-up for beats 

Diagram 5.4-2: Spectrum of the beat 

38



Repeat the experiment for the message signal of 

f 1 = approx. 20 kHz. Sketch the result in Diagram 

5.4-3. 


Additive superimposing of 2 sinusoidal signals with equal 

amplitudes and approx. equal frequencies 

Depict the spectrum in Diagram 5.4-4. 




A 2 : V V 1 : 

f 2 : kHz b : Hz 

f r : kHz 

A 1 : V T : s 

f 1 : kHz SPAN : kHz 

Measurements 

Theory 

n 

f 

KHz 

Name 

S( n) 

V2 

S(n) 

V 

S(n) 

V 

Diagram 5.4-4: Spectrum of a beat 

39



40


Single Sideband AM 

6 The Single Sideband AM (SSB) 

1 

m/2 

f C 

f C + f M 

(f) 

Fig. 6-1: Representation of SSB 

In DSB each sideband carries all of the information 

contents. The transmission bandwidth could 

thus be reduced by half, if one sideband is suppressed. 

It does not matter which sideband is used 

for transmission and which one is suppressed. The 

upper sideband appears in the normal position, the 

lower one in the inverted position. If, for example, 

we suppress the lower sideband in (3-8) then we 

obtain: 

s ( t) A cos 2π 

f t 

= ( ) 

SSB C C 

m 

+ cos 2π 

( fC 

+ fM 

) t 

2 

[ ] 

(6-1) 

To suppress a sideband, a bandpass filter with 

sharp cutoff is used which only allows the desired 

spectral components to pass. 

The dynamic characteristic of SSB resembles that 

of the DSB SC . However the envelope curve is 

somewhat more distorted. 

Demodulation method : Synchronous demodulation 

Bandwidth requirement : b = f Mmax (6-2) 

Application 

: Line-bound transmission 

of telephone 

signals in frequencydivision 

multiplex 

technology 

The SSB with residual carrier 

If instead of the unattenuated carrier only a defined 

fraction k of the carrier amplitude is transmitted, 

then you obtain the SSB with residual carrier: 

⎡ 

m 

sESB,T ( t)= ⎢ AC kcos( 2π 

fC 

t) + 

⎣⎢ 

2 

cos[ 2π 

( fC 

+ fM 

) t]] 

Demodulation method : Synchronous demodulation 

Bandwidth requirement : b = f Mmax . 

Application 

: SSB radio links 

(6-3) 

The vestigial sideband AM (VSB) 

In message or information signals with very low 

frequency components bandpass filters with very 

sharp cutoffs are required for the filtering out of 

the unwanted sideband. Since this leads to phase 

distortion, part of the unwanted sideband is also 

transmitted. Then the filters used may have cutoffs 

which are less sharp, on the other hand, the slope 

characteristic has to be precisely defined (Nyquist 

slope). 

USL 

1 

m/2 

s C 

f C 

f C + f M 

(f) 

Fig. 6-2: SSB with residual carrier 

41



The overlapping transmission range has to run 

symmetrically with respect to the carrier frequency. 

Demodulation method : Synchronous 

demodulation 

Bandwidth requirement : f Mmax 

Application 

: TV technology 

s 

f C + f M 

f C 

f C + f M 

(f) 


Set up the experiment as specified in Fig. 6-4. 

Connect the output of the function generator directly 

to the AF input of the modulator M2. Set the 

function generator to: sinusoidal, A M = 2 V and f M 

= 2 kHz. 

6.1 Investigations on the dynamic 

characteristic of the SSB 

6.1.1 SSB RC 

Set the toggle switch to CARRIER ON. Display 

the output signal of the channel filter CH2 and the 

modulating signal s M (t) of the function generator 

on the oscilloscope and sketch the signals. (Modulation 

product on channel 2, modulating signal on 

channel 1 of the oscilloscope). Use Diagram 6.1.1- 

1. Shift the AF signal to the upper or lower 

envelope curve of the AM signal. Vary the frequency 

f M and the amplitude A M of the modulating 

signal. What do you observe? 




Time base 

Trigger 

2 V/DIV 

1 V/DIV 

200 µs/DIV 

mod. signal 

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

Trigger to the modulating signal s M (t). Switch the 

modulating signal off. Measure the unattenuated 

carrier amplitude A C at the input of the channel 

filter, as well as the amplitude A RC of the attenuated 

carrier at the output of the channel filter. 

Calculate the ratio k = A RC /A C . Determine the carrier 

suppression t in dB according to (6-4): 

m 

t = 20 log (6-4) 

2 k 

6.1.2 SSB SC 

Set the toggle switch to CARRIER OFF. Set the 

oscilloscope as specified in the Table. 

Proceed as described in point 6.1.1. Use Diagram 

6.1.2-1. What features does the SSB SC signal 

have? 




Time base 


2 V/DIV 

1 V/DIV 

200 µs/DIV 

mod. signal 

Diagram 6.1.1-1: Dynamic characteristic of the SSB RC 

Signals 


(t) 

(2): Modulation product at the output of CH2 

Diagram 6.1.2-1: Dynamic characteristic of the SSB SC 


(t) 


42

% 

0 



6.2 Spectrum of the SSB 

6.2.1 SSB RC 

Set the toggle switch to CARRIER ON. 

GATE 

1s 

10s 

0,1s 

0,01s 

TIME A-B 

COUNT A 

CHECK 

FUNCTION 

RATIO A/B 

PERIOD A 

FREQ A 


ANALOG (A) 

TTL - IN(B) 


V 1 :1 

V 2 :10 

f r /kHz: 50 b/Hz: 100 

SPAN/kHz:1.5 ... 20 

T/s:40 

Set the spectrum analyzer as specified in the Table. 

Connect its input to the output of the modulator 

M2. As the modulating signal use a sinusoidal 

signal with A M = 2 V and f M = 2 kHz. Feed the 

modulating signal into the input filter of the CF 

transmitter. Measure the SSB spectrum in the 

range of approx. 15 kHz up to 25 kHz and enter the 

measured values S(n) from the output of the 

analyzer with their corresponding frequencies in 

Table 6.2.1-1. The amplitude values of the wanted 

spectral components are obtained from: 

S 

AM 

S(n) 

(n) = 

V ⋅ V 

1 2 

Calculate the spectral components S AM (n) with the 

aid of (3-8). Also enter the calculated values for 

S AM (n) in Table 6.2.1-1. Plot the curve of the 

spectrum in Diagram 6.2.1-1. Label the spectral 

lines. 

Determine the transmission bandwidth of the AM 

signal based on the measurements. Generalize the 

results for the case of any modulating signals. 

kHz 

V pp 

= 

DC 

MODE 

FUNCTION 

OUT 

ATT 

dB 

20 

40 

TTL 

6.2.2 SSB SC 

Set the toggle switch to CARRIER OFF. Use a 

sinusoidal signal with A M = 2 V and f M = 2 kHz as 

a modulating signal. Measure the spectrum as described 

in point 6.2.1. Enter your results in Table 

6.2.2-1 and Diagram 6.2.2-1. 

Evaluate your measurement results as shown in 

point 6.2.1. 

I > 

I > 

U 

U 

+15V 

(+5V) 

0V 

M1 

Fig. 6-4: Experiment setup for SSB 

43



Table 6.2.1-1: SSB RC spectrum 


A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

Table 6.2.2-1: SSB SC spectrum 


A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

Measurements 

Theory 

Measurements 

Theory 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

Diagram 6.2.1-1: SSB RC 

spectrum f M 

= 2 kHz 

Diagram 6.2.2-1: SSB SC 

spectrum f M 

= 2 kHz 





Time base 

Trigger 

2 V/DIV 

1 V/DIV 

200 µs/DIV 

mod. signal 

Start with the settings given in point 6.1. With the 

aid of a connecting lead feed the carrier signal 

(f C = 20 kHz) of the CF transmitter directly into 

the RF input of the demodulator D2. What have 

you achieved by this? 

Display the modulating signal s M (t) on the oscilloscope 

as well as the demodulated signal s D (t) at the 

output of the LP filter of the CF receiver. Sketch 

the curve of the modulating signal and the demodulated 

signal in Diagram 6.3-1. Adjust the phase 

between the original carrier of the transmitter and 

the auxiliary carrier of the receiver. What do you 

observe? Remove the connecting lead between 

the CF transmitter and the demodulator. Now for 

demodulation use the recovered auxilary carrier 

from the PLL circuit to recover the carrier. For 

this connect the bridging plug between CARRIER 

44



Diagram 6.3-1: Modulating and demodulated signal in SSB 


(t) 


(t) 

Diagram 6.3-2: Modulating and demodulated signal in 

SSB SC 


(t) 


(t) 

RECOVERY and the auxiliary carrier input of D2. 

Discuss your findings. 

Set the toggle switch to CARRIER OFF. This time 

repeat the experiment for SSB SC . 




Time base 

Trigger 

2 V/DIV 

1 V/DIV 

100 µs/DIV 

mod. signal 

45



46


Ring Modulator 

7 The Ring Modulator 

s M 

s T 

s M 

s M 

+ 

– 

D1 

D3 

D4 

D2 

s C 

s C 

s C 

Fig. 7-1: Ring modulator in diode technology 

s AM 

s AM 

s AM 

Up until now the modulation process has been 

described as a multiplication of a harmonic carrier 

s C (t) with an equally harmonic message signal 

s M (t) using a multiplier IC (e.g. AD632). This is 

how the wanted modulation product is directly 

obtained without any undesired sidelines. However, 

in practice product modulators in the form of 

integrated circuits are of no importance because 

they can only be used at relatively low frequencies. 

Consequently, modulation is performed using discrete 

components with non-linear characteristics 

on account of the high frequencies used in communications 

engineering. A group of modulators important 

in practice is known under the name of 

balanced modulators. These types of balanced 

modulators include the push-pull and ring modulators. 

The response of the ring modulator can also 

be investigated using the training panel 736 201 CF 

transmitter 20 kHz. Ring modulators are generally 

designed with special diode and transistor 

concepts. An example for this is illustrated in Fig. 

7-1. 

The bipolar carrier signal s C (t) is fed into the center 

taps of the two symmetrical differential transformers. 

The diodes are supposed to perform a 

pure switching operation, which is triggered exclusively 

by the carrier amplitude. For this the 

carrier amplitude has to be high enough. During the 

positive half-oscillations of the carrier 2 diodes are 

fully triggered in the forward direction (D1 and 

D2). They function like closed switches while the 

two other diodes are blocked. During this period 

the modulating signal s M (t) fed into the transformer 

on the left flows through to the output 

transformer. In the time in which the carrier's polarity 

is reversed, the previously blocked diodes 

(D3 and D4) perform the job of transmitting the 

modulating signal to the output transformer. However, 

this time the current of the modulating signal 

flows in the reverse direction. 

A symmetrical differential transformer is needed 

for the carrier current to be able to switch the diodes 

without influencing the output signal. Its function 

is explained in Fig. 7-2. 

The total flux Φ C magnetically induced by the carrier 

current is equal to zero when the transformer 

is perfectly symmetrical. Depending on the switching 

state of the diode pairs the current of the modu- 

47



s M 

i 

i 

C 

2 

C 

2 

^↑Φ 

^↓Φ 

T / 2 

T / 2 

⎫ 

⎪ 

⎪ 

⎬ΣΦ 

⎪ 

⎪ 

⎭ 

C 

Φ C Φ 

=+ − 

2 2 

C 

! 0 

0 

f T 

3 f T 

5 f T f 

Fig. 7-2: The principle of the differential transformer 

Fig. 7-3: Dynamic characteristic and spectrum for the ring 

modulator 

lating signal alternates its flow through the output 

transformer. The transformers have to be suitable 

to process radio frequencies (RF). For that reason 

ferrite is used as the core material. Earlier ring 

modulators were manufactured exclusively with 

differential transformers. Today they are being 

overtaken more and more by ICs which operate 

without transformers. Fig. 7-3 shows the dynamic 

characteristic and the spectrum at the output of the 

ring modulator. The AF signal is cancelled out in 

the envelope of the modulated signal. Therefore, 

the line at f = f M is missing in the spectrum 

The following holds true for the spectrum of the 

ring modulator: 

4 

1 

1 

sAM t [cos 2π fCt cos 2π3fCt cos 2π5fCt 

π 

3 

5 

( ) = ( ) − ( ) + ( ) 

−+ ...] A cos( 2π 

f t) 

M 

M 

2 

2 

= AM cos[ 2π 

( fC − fM ) t]+ AM cos 2π 

( fC + fM 

) t 

π 

π 

[ ] 

2 

2 

− AM cos[ 2π 

( 3fC − fM 

) t]− 

AM cos 2π ( 3 fC + fM 

) t 

3π 

3π 

+− 

[ ] 

(7-2) 

If you consider the spectrum of the ring modulator, 

it becomes clear that suitable filters have to be 

used to separate the wanted sidebands from the 

interfering sidebands. 

Questions 

7.1 What features does the ring modulator have? 

7.2 What circuit techniques and measures are 

additionally required, if you want to generate a 

narrow band AM signal with a balanced 

modulator? 

7.3 Which feature is common to all modulating 

components? 

48



+15V 

(+5V) 

kHz 

V 

pp 

= 

DC 

% 

I > 

FUNCTION 

MODE 

ATT 

dB 

OUT 

0,1s 

0,01s 

GATE 

1s 

10s 

U 

0 

20 

40 

U 

FUNCTION 

I > 

RATIO A/B 

PERIOD A 

FREQ A 

TIME A-B 

COUNT A 

CHECK 

M1 

TTL 

TTL - IN(A) 

TTL - IN(A) 

0V 

TTL - IN(B) 

ANALOG (A) 

Fig. 7-4: 

Experiment setup to examine signal characteristics at the ring modulator 


Operating the CF transmitter as a ring 

modulator 

Set up the experiment as specified in Fig. 7-4 auf. 

Set the toggle switch to CARRIER OFF. Use the 

bridging plug to feed the square-wave carrier into 

the RF input of the modulator. Feed a sinusoidal 

signal with f M = 2.0 kHz and A M = 2 V as the 

modulating signal into the AF input of the modulator. 

7.1 Dynamic response of the ring 

modulator 

Display the modulating AF signal and the output 

signal of the modulator on the oscilloscope. Sketch 

the signal in Diagram 7.1-1. 

Diagram 7.1-1: Dynamic characteristic of the modulating 

and modulated signal (CARRIER OFF) 


(2): Modulated signal 




Time base 

Trigger / AC 

1 V/DIV 

1 V/DIV––– 

200 µs/DIV 

mod. signal 

Note: The use of a storage oscilloscope simplifies 

this procedure. If only a real time oscilloscope 

is available, you have to trigger to the 

AF signal and, if necessary, carefully adjust 

its frequency, in order to obtain a standing 

image. 

Repeat the experiment with CARRIER ON. 

Diagram 7.1-2: Dynamic characteristic of the modulating 

signal and modulated signal (CARRIER ON) 


(t) 

(2): Modulated signal 

49




CARRIER OFF! Record the spectrum of the 

modulation product at the output of the modulator 

M2 in the range 0.5 kHz...100 kHz. 


V 1 :2 

V 2 :2 

f r /kHz: 200 b/Hz: 500 

SPAN/kHz: 1 ... 25 T/s:40 

Table 7.2-1: Spectrum of the ring modulator 


A C : V V 1 : 


f r : kHz 

A M : V T : s 

f M : kHz 

Note: 

In the frequency range f r =200 kHz you 

will not come that far under f min = 10 

kHz. Consequently, you will have to 

measure the lower frequency range 

from approx. 0.5 kHz...10 kHz separately 

in the range f r = 20 kHz. For this 

use Table 7.2-1. 

V 2 

f 

KHz 

Measurements 

S( n) 

Name 

V 

S AM (n) 

V 

Theory 

S AM (n) 

V 

Plot the spectrum in a graph in Diagram 7.2-1. 

Sketch the position of the suppressed carrier lines 

with a dashed line. 

Diagram 7.2-1: Spectrum of the ring modulator 

50


Solutions 

Solutions 


1. Manual operation with analog voltmeter 

The amplitude S R (1) of the fundamental harmonic 

is greater than the square-wave amplitude A R by a 

factor 4/π = 1.27. The formation law for the spectrum 

of a symmetrical square-wave signal is: 

S 

R 

4 AR 

( n) 

= 

π ( 2n 

−1) 

n: 1, 2, 3... 


Spectrum of the square-wave signal A R 

= 5 V, τ/T P 

= 0.5 

Table 2.3-1: Spectrum square wave signal 


A R : 5 V 

τ/T P : 5/10 

f R : 2.00 kHz 

n 

f 

kHz 


V 1 : 1 

b : 500 Hz 

f r : 20 kHz 

T : 20 s 

Measurement 

S(n) S R (n) 

V 2 

V 

V 

Theory 

S (n) 

R 

V 

1 2.0 6.6 1 6.6 6.37 

2 4.0 ---- - ---- ---- 

3 6.0 2.1 1 2.1 2.12 

4 8.0 ---- - ---- ---- 

5 10.0 6.6 5 1.32 1.27 

6 12.0 ---- - ---- ---- 

7 14.0 4.7 5 0.94 0.91 

8 16.0 ---- - ---- ---- 

9 18.0 3.6 5 0.72 0.71 

10 20.0 ---- - ---- ---- 

2. Automatic operation with the XY recorder 

or the storage oscilloscope 

The reduction in the bandwidth b narrows the 

spectral window. The manual frequency setting 

thus becomes increasingly difficult, while at the 

same time the spectral lines become clearer. 

Even when using an oscilloscope as a display unit 

which operates (almost) without any inertia, the 

spectrum is no longer reproduced with full amplitude. 

The reason for this lies in the time law of 

electrical communications engineering. The filters 

of the analyzer no longer reach the transient 

recovery state. If mechanical measuring instruments 

subject to inertia are used as display units, 

e.g. a multimeter instrument or an XY recorder, 

then the lowpass response of the entire system is 

further improved. There is practically no pointer 

deflection. The following general statements can 

be made about the spectrum of the symmetrical 

square-wave signal: 

– The spectrum has a line structure. 

– The spectral lines occur at odd numbered multiples 

of the fundamental frequency f R . (3 f R , 

5 f R , 7 f R , ...) 

– The amplitudes S R (n) respond inversely proportional 

to the odd numbered multiples of the 

fundamental frequency.(1/3, 1/5, 1/7, ...). The 

envelope curve has the characteristic 1/f. 

51


Solutions 

3 Review of amplitude modulation 

Answers 

3.1 Modulation means the frequency conversion 

of an information signal from the AF position 

of the baseband into the RF band of the 

carrier. Here, the modulating signal 

influences an appropriate parameter of the 

carrier oscillation, e.g. the amplitude or frequency. 

While f C >> f M always holds true in 

modulation, mixing entails frequency 

conversion being generated between signals 

with comparable frequencies. 

3.2 Modulation offers the following advantages: 

– Matching to the features of the transmission 

channel, i.e. improved efficiency 

during transmission of information signals. 

– Multiple utilization of transmission channels, 

e.g. in frequency multiplexing 

methods. 

– Improved signal-to-noise ratios (modulation 

gain) 

3.3 The DSB is something "new" produced by 

combining the carrier oscillation and the 

modulating signal. While the dynamic characteristic 

of the AM signal can be observed 

as a whole on the oscilloscope the spectrum 

analyzer shows the AM broken down into its 

components. With constant modulation 

signal these components have amplitudes 

contstant with respect to time. 

3.4 In the dynamic characteristic of the beat a 

phase shift of 180° arises in the envelope 

curve. The frequency of the envelope curve 

is approx. half the differential frequency of 

the oscillation components involved. The 

beat frequency corresponds to the arithmetic 

mean value. 

3.5 The amplitude deviation ∆A C indicates the 

maximum change permissible for the carrier 

amplitude A C . It is dependent on the 

modulator constant α and the amplitude A M 

of the modulating signal. The modulation 

index m is the quotient formed out of the 

amplitude deviation and the carrier amplitude. 

The modulation index m can assume 

values between 0 and 1. Overmodulation 

occurs for m > 1. 

3.6 In addition to envelope demodulation, synchronous 

or coherent demodulation are 

common demodulation methods particularly 

in commercial communications systems. In 

contrast to envelope demodulation, it requires 

an auxiliary carrier which is stable in 

terms of frequency, phase and amplitude. 

3.7 The reduction in carrier power means an 

improvement in the transmission efficiency. 

The amount of power and amplifier circuitry 

in the transmitter can be reduced. 

Bandwidth is saved by limiting modulation to 

one sideband. However, coherent demodulation 

becomes problematic when the carrier 

is completely suppressed. For that reason a 

residual carrier is transmitted with which the 

receiver is synchronized. 

3.8 The following applies for the efficiency η: 

useful power 

η = 

total power 

Expressed by the modulation index m the 

following holds true: 

η = 

m 2 

2+ m 2 

For the maximum modulation index 

m = 100% you obtain the best efficiency of 

the DSB when η = 33%! Regarding the 

power needed in DSB at least 2/3 is “squandered” 

in the carrier. Since the carrier contains 

no information it can be suppressed to 

increase the efficiency. 

3.9 Methods of carrier suppression 

– Suppress the carrier using a bandpass filter 

with very sharp cutoffs. 

– Addition of a carrier in phase opposition 

and of equal amplitude to the modulated 

signal. 

– Use of a modulation method which does 

not permit the carrier to reach the modulation 

product, e.g. balanced or ring 

modulator. 

3.10 Here only coherent demodulation still constitutes 

a viable alternative. For this an auxiliary 

oscillation is needed in the receiver, 

which is in agreement with the original carrier 

in terms of frequency and phase and 

whose amplitude remains constant. 

52


Solutions 

5 The Double Sideband AM 

Experiment results 

5.1 Investigating the dynamic characteristic 

of the DSB 

5.1.1 DSB 

modulation signal. At the same time the amplitude 

of the modulated signal drops. Consequently in XY 

display modus a trapezoid is produced which the its 

broad side on the left. 

5.1.2 DSB SC 

Diagram 5.1.1-1: Dynamic characteristic of the DSB signal 


(t) 


The envelope curve of the AM signal nearly coincides 

completely with the modulating signal and 

immediately follows its changes in frequency and 

amplitude. 

Diagram 5.1.2-1: Dynamic characteristic of the DSB SC 

signal 


(2): Modulation product at output M2 

The DSB SC signal has the characteristic of a beat, 

i.e. it is the linear superpositioning of 2 harmonic 

oscillations with very close frequencies. The envelope 

curve of the beat shows zero crossings. There 

the beat signal experiences phase shifts of 180°. 

Also the DSB SC signal follows the frequency 

changes of the AF signal without any visible phase 

delay. There is no overmodulation caused by 

amplitude changes in the modulating signal, as in 

the case of DSB. 

The modulation trapezoid for DSB SC 

. 


m D − d 65 . − 2 

= ≈ ≈ 53% 

D+ 

d 65 . + 2 

The modulation index amounts to approx. 

m = 53%. Observation: the trapezoid chords are 

distorted "cigar-shaped". This is an indication for a 

phase shift between the signals at the X and Y 

input. These kinds of distortions can scarcely be 

seen in Diagrams like 5.1.1-1. 

Generating the modulation trapezoid 

Oscilloscope set to XY mode. Set the coordinate 

origin in the middle of the screen using the X-position 

and Y-position controllers. If the modulating 

AF signal reaches its negative maximum value, 

then the X-deviation is at the far left. From there it 

increases horizontally to the right with a rising 


Observations: 

In the display of the modulation trapezoid in XY 

mode Lissajous figures appear resembling a double 

conic section depending on the modulation frequency 

f M . These figures rotate as a function of 

the frequency f M . The modulation trapezoid is bet- 

53


Solutions 

ter suited for the assessment of moduation distortions 

than direct display of the modulated signal in 

YT modus. Between the modulating and the 

modulated signal there arise, e.g. severe phase 

delay distortions, if the modulation is performed 

using the LP filter connected in series. These visible 

distortions on the oscilloscope are frequencydependent. 

They belong to the group of linear distortions 

and are caused by the phase response of 

the electronic components (especially the LP filter). 

5.2 Spectrum of the DSB 

5.2.1 DSB 



A C : 2.0 V V 1 : 2 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2.0 V T : 40 s 

f M : 2 kHz 



A C : 2.0 V V 1 : 2 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 1 V T : 40 s 

f M : 3 kHz 

Measurements 

Theory 

Measurements 

Theory 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

2 18.00 LSL 4,5 1.1 1 

2 20.01 carrier 8.5 2.1 2 

2 22.01 USL 4.5 1.1 1.00 

2 17.00 LSL 2.1 0.52 0.5 

2 20.01 carrier 8.4 2.2 2.00 

2 23.01 USL 2.2 0.55 0.50 



With f M = 3 kHz the frequency of the modulating 

signal s M (t) already lies in the cutoff range of the 

LP filter. For that reason using a filter can lead to 

the attenuation of the amplitude at the modulator 

input and thus to a reduction in the modulation 

index. 

From the spectra it follows that: 

– With increasing signal frequency f M the 

USLs are shifted away from the carrier in 

the direction of higher frequencies. This frequency 

response of the USL is called the 

normal position, high signal frequencies also 

lie in the modulation spectrum at high 

frequencies. 

– With increasing signal frequency f M the LSLs 

shift further away from the carrier into the 

lower frequencies. The frequency response 

of the LSLs is thus called the inverted position 

54


Solutions 

because high signal frequencies lie in the 

modulation spectrum at low frequencies. 

Basically the following applies: The upper 

sideband is in the normal position, the lower 

sideband is in the inverted position. 

The modulation index m amounts to approx. 60%. 

Calculate the transmission bandwidths in DSB 

based on the spectra. For f M = 2 kHz: 

b = (22 – 18) kHz = 4 kHz = 2 · f M 

. 

For f M = 3 kHz: 

b = (23 – 17) kHz = 6 kHz = 2 · f M 

. 

In general: 

b = 2 f Mmax 

(3-9) 

5.2.3 The AM spectrum for modulation with a 

square-wave signal 

5.2.2 DSB SC 


Table 5.2.2-1: DSB SC spectrum 


A C : 2.0 V V 1 : 2 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2.0 V T : 40 s 

f M : 2 kHz 

V 2 

f 

KHz 

Measurement 

S( n) 

Name 

V 

S AM (n) 

V 

Theory 

S AM (n) 

2 18.00 LSL 4.5 1.1 1.00 

2 ____ ____ ____ ____ _____ 

2 22.01 USL 4.5 1.1 1.00 

V 

V 2 

Table 5.2.3-1: AM spectrum for 

square-wave modulation 

A C : 2 V V 1 : 2 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2 V T : 40 s 

f M : 2 kHz 

f 

KHz 

Measurement 

Name 

S( n) 

5 10 LSL 3 3.2 0.32 

5 14 LSL 2 5,0 0.50 

2 18 LSL 1 5.6 1.40 

2 20 carrier 8.4 2.10 

2 22 USL 1 

5.5 1.38 

5 26 USL 2 

4.6 0.46 

5 30 USL 3 2.7 0.27 

5 34 USL 4 2.0 0.20 

V 

S AM (n) 

V 

Theory 

S AM (n) 

V 

Diagram 5.2.2-1: DSB SC 

spectrum 

Diagram 5.2.3-1: AM spectrum for square-wave modulation 

55


Solutions 

The USL 1 is taken as a reference for the calculation 

of the spectrum. Corresponding to the known 

characteristic curve of the square-wave spectrum 

the LSL and USL have to be located symmetrically 

to the suppressed carrier, where the amplitudes 

decrease inversely to the ordinal number n. The 

deviations between the theory and the measurements 

increase with rising frequency due to the finite 

upper frequency cutoff of the modulator IC. 

Transmission bandwidth based on the spectrum 

b = (22.01 – 18.00) kHz ≈ 4 kHz = 2 f M 

. 

The following is true in the general case of a modulating 

signal with the maximum frequency limit 

f Mmax : 

b = 2 f Mmax 

(3-9) 

5.3 AM demodulation 

(synchronous demodulation) 

5.3.1 DSB 

Table 5.3.1-1: Phase response of the DSB 

s M (t): Sine A M = 2 V, f M = 2 kHz 

φ 

degrees 

A D 

V 

A 

A 

D 

Dmax 

cos φ 

0 2.1 1.00 1.00 

18 1.9 0.91 0.95 

36 1.6 0.79 0.81 

54 1.1 0.55 0.59 

Diagram 5.3.1-1: Modulating and demodulated signal with 

DSB, fixed phase relation 


(t) 


(t) 

72 0.6 0.28 0.31 

90 0.13 0.06 0.00 

108 0.76 0.37 –0.31 

Observation: 

With the exception of a constant amplitude factor 

the modulating signal s M (t) and the demodulated 

signal s D (t) are in agreement. 


Demodulated signal A D /A Dmax as a function of the phase φ 

56


Solutions 

5.3.2 Carrier recovery 

Table 5.3.2-1: 

Control characteristic of the VCO 

U F 

V 

f VCO 

kHz 

0.5 0.0 

corresponds precisely to the frequency difference 

between the carrier and the auxiliary oscillation. 

The frequency shift in the demodulated signal disappears 

completely for f C = f Aux . 


PLL-controlled VCO. 

1.0 0.0 

1.5 0.3 

2.0 14.5 

2.5 41.3 

3.0 69.1 

3.5 96.3 

4.0 121.8 

4.5 148.7 

5.0 167.5 


(1): Pilot tone at the CF transmitter 

(2): Recovered pilot at the output of the PLL (receiver) 

After lock-in of the PLL the original pilot signal 

and the recovered signal have exactly the same 

frequency. A fixed phase-shift occurs between 

the two signals. This leads to a (constant) 

amplitude error during synchronous demodulation. 

Diagram 5.3.2-1: The control characteristic of the VCO in 

the PLL circuit of the receiver 

The synchronous demodulation is performed 

with the aid of a free-wheeling VCO. 

In the demodulated signal a constant frequency 

shift occurs for f C ≈ f Aux . This is maintained during 

variation of the signal frequency f M . It is only dependent 

on the control voltage U F of the VCO, 

which determines the frequency f Aux of the auxiliary 

carrier. The frequency phase-shift between 

the modulating signal and the demodulated signal 


(1): 20 kHz original carrier at the transmitter 

(2): The recovered auxiliary carrier at the receiver 

A fixed phase-shift exists between the two carriers. 

This phase-shift can assume 8 various values 

due to the undefined starting conditions of the frequency 

divider (f/8). These phase-shifts are associated 

with amplitude errors in the demodulated 

signal. 

57


Solutions 

5.3.3 DSB SC 

demodulation 




A 2 : 2 V V 1 : 5 

f 2 : 20.0 kHz b : 500 Hz 

f r : 50 kHz 

A 1 : 2 V T : 20 s 

f 1 : 2 kHz SPAN: 1...25 kHz 

Diagram 5.3.3-1: Modulating and demodulated signal for 

DSB SC 


(t) 


(t) 

The DSB SC shows the same phase-dependency as 

the DSB 

Requirements for the auxiliary carrier in synchronous 

demodulation: 

1. Frequency stability and frequency equality 

with the original carrier frequency. 

2. Constant phase angle < 90°. Ideally φ€= 0°. 

3. Amplitude stability of the auxiliary carrier 

n 

f 

KHz 

Measurement 

Name 

S( n) 

V2 

S AM (n) 

Theory 

1 2 10.5 2.1 2 

1 20 10.5 2.1 2 

V 

S AM (n) 

V 

5.4 Beats 

Diagram 5.4-2: Spectrum of the beat 

Diagram 5.4-1: Additive superpositioning of 2 sinusoidal 

signals with the same amplitudes but very different 

frequencies. 

Linear superpositioning of 2 harmonic signals, here 

with extremely different frequencies f 1 = 2.0 kHz 

and f 2 = 20 kHz, generates a beat. The two 

frequency components are easily distinguishable. 

There is no frequency conversion for beats 

Diagram 5.4-3: Additive superimposing of 2 sinusoidal 

signals with the same amplitudes and almost the same 

frequencies. 

58


Solutions 

If harmonic signals with approximately the same 

frequencies are additively superimposed, then the 

beat takes on a totally different appearance. 

f 1 = 20.01 kHz 

f 2 = 20.03 kHz 




A 2 : 2 V V 1 : 5 

f 2 :20.03 kHz b : 500 Hz 

f r : 50 kHz 

A 1 : 2 V T : 20 s 

f 1 :20.01 kHz SPAN: 1...25 kHz 

Diagram 5.4-4: Spectrum of a beat 

Measurement 

Theory 

n 

f 

KHz 

Name 

S( n) 

V2 

S AM (n) 

V 

S AM (n) 

V 

* 

* 

* Spectral lines cannot be resolved (discriminated) 

because they are packed so closely to 

each other. 

Diagram 5-4-4 shows the spectrum of a beat for 

f 1 ≈ f 2 . The resolution of the analyzer is too low. 

The closely-packed spectral lines of the beat are 

no longer reproduced separately. The amplitude 

display is invalidated. 

Interpretation 

The simple addition of the carrier and information 

signal is not suited for the generation of frequency 

conversion (modulation). Both unmodulated signals 

remain separate. There is no frequency shift 

of the AF signal into the range of higher frequencies, 

as is the standard case for modulation. In 

order to maintain modulation, the carrier and the 

modulating signal have to be supplied to an element 

with non-linear characteristic. 

59


Solutions 

6 The Single Sideband AM (SSB) 


6.1 Investigating the dynamic characteristic 

of the SSB 

6.2 Spectrum of the SSB 

6.2.1 SSB RC 

6.1.1 SSB RT 

Table 6.2.1-1: SSB RC spectrum 


A C : 0.32 V V 1 : 5 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2 V T : 40 s 

f M : 2 kHz 

Diagram 6.1.1-1: Dynamic characteristic of the SSB RC 

signal 


(t) 


The SSB RC signal resembles the DSB signal in 

terms of its dynamic characteristic. 

ARC 

045 . 

k = = = 021 . 

A 21 . 

C 

20log 

m 

t = 

2 k 

(6-4) 

V 2 

f 

KHz 

Measurement 

S( n) 

Name 

V 

S AM (n) 

V 

Theory 

S AM (n) 

10 18 LSL 3.0 0.06 0.00 

2 20 carrier 4.5 0.45 0.00 

2 22 USL 8.0 0.80 1.00 

V 

6.1.2 SSB SC 

Diagram 6.2.1-1: SSB RC 

spectrum f M 

= 2 kHz 

Diagram 6.1.2-1. SSB SC 

time characteristic 


(t) 

(2): Modulated signal s SSBsc (t) 

The modulated SSB SC signal is a pure sinusoidal 

signal when the carrier and the unwanted sideband 

have been completely suppressed. 

60


Solutions 

6.2.2 SSB sc 


Table 6.2.2-1: SSB SC spectrum 


A C : 0.32 V V 1 : 5 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2 V T : 40 s 

f M : 2 kHz 

V 2 

f 

KHz 

Measurement 

S( n) 

Name 

V 

S AM (n) 

V 

Theory 

S AM (n) 

10 18 LSL 3.0 0.06 0.00 

2 22 USL 8.0 0.80 1.00 

V 

Diagram 6.3-1: Modulating and demodulated signal in SSB 


(t) 


(t) 

The synchronous demodulation of a SSB RC signal 

provides a perfectly suitable demodulated signal. 

The phase-shift set by the phase controller of the 

CF transmitter occurs between the modulating signal 

s M (t) and demodulated signal s D (t). Any 

influence on the amplitude of the demodulated 

signal cannot be detected. The following applies 

for the demodulated signal: 

s 

D 

AC 

m 

( t ) = cos 2π fM 

t± 

φ 

4 

( ) 

Diagram 6.2.2-1: SSB SC 

spectrum f M 

= 2 kHz 

Diagram 6.3-2: Modulating and demodulated signal for 

SSB SC 


(t) 

(2): Demodulated signal s D (t) 

Also in the case of SSB signals the carrier has no 

influence on synchronous demodulation. It can be 

switched on and off at will. 

61


Solutions 

7 The ring modulator 

Answers 

7.1 The ring modulator provides an AM signal 

with carrier suppression. The line of the 

modulating signal is missing in the output 

spectrum for f = f M . 

7.2 In balanced modulators frequency-periodic 

modulation spectra are produced. 

Consequentily the wanted bands have to be 

filtered out, i.e. the interfering sidebands 

have to be suppressed for the sake of a narrow 

transmission bandwidth. 

7.3 All of the circuits which have been used for 

modulation have one feature in common: a 

non-linear characteristic. This is true in particular 

for the mixer, multiplier, ring modulators 

etc. A switch can be seen as a very 

extreme case, its characteristic has abrupt 

step changes. 


Diagram 7.1-2: Dynamic characteristic of modulating signal 

and modulated signal (CARRIER ON) 

(1): modulating signal s M 

(t) 

(2): modulated signal 


Table 7.2-1: Spectrum of the ring modulator 



A C : V V 1 : 2 

f C : 20.0 kHz b : 100 Hz 

f r : 50 kHz 

A M : 2 V T : 40 s 

f M : 2 kHz 

Measurement 

Theory 

V 2 

f 

KHz 

Name 

S( n) 

V 

S AM (n) 

V 

S AM (n) 

V 

2 18 LSL2 5.20 1.30 

2 22 LSL1 5.30 1.32 

Diagram 7.1-1: Dynamic characteristic of modulating signal 

and modulated signal (CARRIER OFF) 

(1): modulating signal s M 

(t) 

(2): modulated signal 

2 58 USL1 1.60 0.4 

2 62 USL2 1.70 0.43 

The modulation product has a certain similarity to 

the PAM signal for the special case of a symmetrical 

duty cycle t/T P = 50%. 

Diagram 7.2-1: Spectrum of the ring modulator 

62


Solutions 

Observation: 

Balanced modulators have an extended amplitude 

spectrum. A double line appears for odd number 

multiples of the carrier frequency. When comparing 

theory with the measurement results it is conspicuous 

that the measured spectral amplitudes 

turn out to be smaller as the frequency increases. 

The reason for this lies in the low cutoff frequency 

of the modulator ICs. High frequency spectral 

components are more severely attenuated by the 

modulator than lower frequency components. 

When the carrier is switched on (CARRIER ON) 

additional lines appear for odd numbered multiples 

of the carrier frequency. 

63


Solutions 

64


Keywords 

Keywords 

AM demodulation ............................................................................................................................25 

amplitude deviation ..........................................................................................................................23 

amplitude error .................................................................................................................................57 

amplitude spectrum ..........................................................................................................................10 

auxiliary oscillation ..........................................................................................................................26 

baseband ...........................................................................................................................................11 

beat ............................................................................................................................................ 37, 59 

carrier frequency technology............................................................................................................24 

carrier recovery ................................................................................................................................20 

carrier suppression............................................................................................................... 42, 52, 62 

channel filter .....................................................................................................................................19 

control characteristic ........................................................................................................................35 

phase delay .......................................................................................................................................53 

demodulation, coherent ....................................................................................................................26 

differential transformer ....................................................................................................................47 

double sideband AM ........................................................................................................................29 

efficiency ..........................................................................................................................................52 

envelope curve ........................................................................................................................... 23, 29 

envelop curve modulation ................................................................................................................25 

frequency conversion .......................................................................................................................29 

frequency conversion .......................................................................................................................52 

index .................................................................................................................................................21 

input filter .........................................................................................................................................18 

interfering sideband ..........................................................................................................................48 

inverted position ........................................................................................................................ 24, 54 

line structure .....................................................................................................................................51 

linear distortion ................................................................................................................................54 

Lissajous-figure ................................................................................................................................53 

loop filter ................................................................................................................................... 20, 35 

lowpass filter ....................................................................................................................................20 

message signal ..................................................................................................................................10 

mixing ...............................................................................................................................................52 

modulation ........................................................................................................................................10 

modulation index ....................................................................................................................... 23, 53 

modulation product ..........................................................................................................................23 

modulation trapezoid ................................................................................................................. 31, 53 

modulator..........................................................................................................................................11 

modulator constant ...........................................................................................................................23 

multiplex signal ................................................................................................................................19 

normal position .......................................................................................................................... 24, 54 

Nyquist slope ....................................................................................................................................41 

original frequency band....................................................................................................................11 

oscilloscope ......................................................................................................................................13 

overmodulation .................................................................................................................................52 

phase change.....................................................................................................................................29 

phase detector ...................................................................................................................................35 

phase error ........................................................................................................................................26 

phase shift .........................................................................................................................................57 

phase shifter......................................................................................................................................19 

65


Keywords 

PLL circuit........................................................................................................................................20 

processing of the message ................................................................................................................12 

product modulator ..................................................................................................................... 18, 47 

push-pull modulator .........................................................................................................................47 

relaying the message ........................................................................................................................12 

residual carrier ..................................................................................................................................41 

ring modulator ..................................................................................................................................47 

side oscillation ..................................................................................................................................24 

sideband vector .................................................................................................................................25 

signal, analog ....................................................................................................................................10 

signal, deterministic ...........................................................................................................................9 

signal, digital ....................................................................................................................................10 

signal, stochastic.................................................................................................................................9 

single sideband AM..........................................................................................................................41 

spectral domain ................................................................................................................................10 

spectrum analyzer .............................................................................................................................13 

square-wave signal ...........................................................................................................................10 

superheterodyne ................................................................................................................................13 

switching operation ..........................................................................................................................47 

synchronous demodulation ...............................................................................................................26 

synchronous demodulator ................................................................................................................20 

telecommunication system ...............................................................................................................12 

time continuous ..................................................................................................................................9 

time domain ......................................................................................................................................10 

time function ......................................................................................................................................9 

time law ............................................................................................................................................14 

time law of electrical communications engineering ........................................................................51 

transmission bandwith ............................................................................................................... 43, 56 

transmission channel ........................................................................................................................12 

transmission of the message.............................................................................................................12 

uncertainty relation ...........................................................................................................................14 

VCO ..................................................................................................................................................35 

vector diagram ..................................................................................................................................24 

wanted sideband ...............................................................................................................................48 

66

T 7.2.1.3 Amplitude Modulation

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