T 7.2.1.3 Amplitude Modulation
T 7.2.1.3 Amplitude Modulation
T 7.2.1.3 Amplitude Modulation
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T <strong>7.2.1.3</strong><br />
<strong>Amplitude</strong><br />
<strong>Modulation</strong><br />
by Klaus Breidenbach<br />
New Edition, November 2002<br />
LEYBOLD DIDACTIC GMBH . Leyboldstrasse 1 . D-50354 Hürth . Phone (02233) 604-0 . Fax (02233) 604-222 . e-mail: info@leybold-didactic.de<br />
©by Leybold Didactic GmbH<br />
Printed in the Federal Republic of Germany<br />
Technical alterations reserved
“The sensitive electronics of the equipment contained in the present experiment literature<br />
can be impaired due to the discharge of static electricity. Consequently, electrostatic build<br />
up should be avoided (particularly by utilizing appropriate rooms) or eliminated by discharging<br />
(e.g. at the panel frames or similar).”
TPS <strong>7.2.1.3</strong><br />
Contents<br />
Note on EMC<br />
European stipulations pertaining to electromagnetic compatibility (EMC) oblige the<br />
manufacturer of electronic training and educational equipment to draw the operator's<br />
attention to the following possible sources of interference. The types of interference<br />
listed below could arise but by no means have to. As the case arises it may prove necessary<br />
to implement one of the measures recommended for the appropriate case.<br />
Note regarding the interference immunity of the equipment and<br />
experiment set-ups<br />
The sensitive electronics used in the equipment can be interfered with by strong electromagnetic<br />
fields arising from large-scale experiment arrangements. This can occur in<br />
such a manner that the equipment operates insufficiently, in particular field effects can<br />
cause digital displays to fail.<br />
Precautionary and corrective measures:<br />
Make sure that no RF generating equipment (e.g. cellular phones) which does not belong<br />
to the experiment set-up is operating in the classroom or in its proximity and that<br />
connecting leads which can act as potential antennas are kept as short as possible.<br />
Note regarding protection against electrostatic discharge (ESD)<br />
The sensitive electronic components in the equipment can be impaired or even damaged<br />
by the discharge of static electricity.<br />
Precautionary measures:<br />
Select work areas where electrostatic energy cannot be built up by the user and/or<br />
equipment (eliminate carpeting and similar items, ensure equipotential bonding).<br />
Note regarding protection from line-bound, high-frequency voltage<br />
bursts<br />
Switching operations involving large loads can occassionally bring about line-bound<br />
high-frequency voltage bursts which can lead to the temporary impairment of sensitive<br />
electronic components which could cause equipment operating failure (e.g. data losses<br />
or to changes in the mode of operation).<br />
Corrective measures:<br />
In order to avoid this malfunction, the mains line can be specially filtered. Furthermore,<br />
making occasional data back-ups is recommended. Any interference which might arise<br />
can be eliminated simply by switching the device off and back on again.<br />
3
TPS <strong>7.2.1.3</strong><br />
Contents<br />
Note:<br />
The oscillographs in the experiment results were recorded with a HP 54600 A<br />
oscilloscope (100 MHz) and further processed with the bench link<br />
HP 34810 A software.<br />
The oscilloscope recommended in the equipment set is a low-cost version,<br />
with limited operation and display comfort (30 MHz display), but in principle<br />
delivers the same results.<br />
The experiment results given here are just examples. Therefore, the curves<br />
and results specified in the solutions section should only be taken as guidelines.<br />
The calculation and representation of the spectra was carried out with EXCEL<br />
5.0.<br />
4
TPS <strong>7.2.1.3</strong><br />
Contents<br />
Contents<br />
Equipment overview ..............................................................................................................7<br />
Symbols and abbreviations .................................................................................................... 8<br />
Schrifttum .............................................................................................................................. 8<br />
1 Introduction ......................................................................................................................... 9<br />
Signals9<br />
Time and spectral domain...................................................................................................... 10<br />
<strong>Modulation</strong> ............................................................................................................................ 10<br />
The communications system according to Shannon.............................................................. 12<br />
2 Measuring instruments ..................................................................................................... 13<br />
2.1 Oscilloscope and spectrum analyzer .......................................................................... 13<br />
2.2 Equipment descriptions .............................................................................................. 16<br />
726 94 Spectrum analyzer .......................................................................................... 16<br />
726 961 Function generator 200kHz .......................................................................... 17<br />
726 99 Frequency counter 0..10 MHz ...................................................................... 18<br />
736 201 CF transmitter 20 kHz .................................................................................. 18<br />
736 221 CF receiver 20 kHz ...................................................................................... 19<br />
2.3 A measurement example ........................................................................................... 20<br />
3 Review of amplitude modulation (AM) .......................................................................... 23<br />
The spectrum of amplitude modulation ................................................................................. 24<br />
Representing amplitude modulation with a vector diagram ................................................... 24<br />
AM demodulation .................................................................................................................. 25<br />
Questions ............................................................................................................................... 26<br />
4 Required equipment and accessories ............................................................................. 28<br />
Training objectives: ................................................................................................................ 28<br />
5 Double Sideband-AM ........................................................................................................ 29<br />
The DSB SC<br />
. ............................................................................................................................ 29<br />
5.1 Investigations on the dynamic characteristic of the DSB .......................................... 30<br />
5.1.1 DSB ............................................................................................................................ 30<br />
5.1.2 DSB SC<br />
................................................................................................................................................................................................................31<br />
5.2 Spectrum of the DSB................................................................................................. 31<br />
5.2.1 DSB ............................................................................................................................ 31<br />
5.2.2 DSB SC<br />
................................................................................................................................................................................................................33<br />
5.2.3 The AM spectrum for modulation with a square-wave signal .................................. 33<br />
5.3 AM demodulation (synchronous demodulation) ........................................................ 34<br />
5.3.1 DSB ............................................................................................................................ 34<br />
5.3.2 Carrier recovery ........................................................................................................ 35<br />
5.3.3 DSB SC<br />
Demodulation ................................................................................................. 37<br />
5.4 Beats .......................................................................................................................... 37<br />
5
TPS <strong>7.2.1.3</strong><br />
Contents<br />
6 The Single Sideband AM (SSB) ....................................................................................... 41<br />
6.1 Investigations on the dynamic characteristic of the SSB ........................................... 42<br />
6.1.1 SSB RC<br />
......................................................................................................................... 42<br />
6.1.2 SSB SC<br />
.......................................................................................................................... 42<br />
6.2 Spectrum of the SSB .................................................................................................. 43<br />
6.2.1 SSB RC<br />
......................................................................................................................... 43<br />
6.2.2 SSB SC<br />
.......................................................................................................................... 43<br />
6.3 SSB demodulation ...................................................................................................... 44<br />
7 The Ring Modulator .......................................................................................................... 47<br />
7.1 Dynamic response of the ring modulator ................................................................... 49<br />
7.2 Spectrum at the output of the ring modulator ............................................................ 50<br />
Solutions ................................................................................................................................. 51<br />
Keywords .............................................................................................................................. 65<br />
6
TPS <strong>7.2.1.3</strong><br />
Contents<br />
Equipment overview<br />
Equipment<br />
TPS 7.2.2.3 Experiments<br />
2.3 A measurement example<br />
5.1 Investigations on the dynamic characteristic of the DSB<br />
5.2 Spectrum and vector representation of the DSB<br />
5.3 AM demodulation (synchronous demodulation)<br />
5.4 Beats<br />
6.1 Investigations on the dynamic characteristic of the SSB<br />
6.2 Spectrum representation and vector diagram of the SSB<br />
6.3 SSB demodulation<br />
7.1 Dynamic response of the ring modulator<br />
7.2 Spectrum at the output of the ring modulator<br />
DC power supply ±15 V, 3 A 726 86 1 1 1 1 1 1 1 1 1 1<br />
Function generator 0...200 kHz 726 961 1 1 1 1* 1 1 1 1 1 1<br />
Spectrum analyzer 726 94 1 _ 1 _ 1 _ 1 _ _ 1<br />
Frequency counter 0-10 MHz 726 99 1 _ 1 _ 1 _ 1 _ _ 1<br />
CF transmitter 20 kHz 736 201 _ 1 1 1 1 1 1 1 1 1<br />
CF receiver 20 kHz 736 211 _ _ _ 1 _ _ _ 1 _ _<br />
Analog multimeter C.A. 406 531 16 1 _ 1 _ 1 _ 1 _ _ 1<br />
Digital storage oscilloscope 305 575 292 1 1 1 1 1 1 1 1 1 1<br />
Probes 100 MHz, 1:1/10:1 575 231 2 2 2 2 2 2 2 2 2 2<br />
Sets of 10 bridging plugs, black 501 511 1 1 2 2 2 3 3 3 2 2<br />
Cable pair, black, 100 cm 501 461 2 _ 1 _ 2 _ 1 _ _ 2<br />
* Optional: 2nd function generator recommended<br />
Note:<br />
Instead of the 20 kHz CF system you can also use the 16 kHz system (cat. no. 736 211 and 736 231).<br />
This does not have any significant impact on the experiment results. In particular the spectra are shifted<br />
by 4 kHz into the lower frequency range. However, their general structures remain unaffected.<br />
7
TPS <strong>7.2.1.3</strong><br />
Contents<br />
Symbols and abbreviations<br />
A : <strong>Amplitude</strong><br />
∆A C : <strong>Amplitude</strong> deviation<br />
A C : Carrier amplitude<br />
A M : <strong>Amplitude</strong> of the modulating signal<br />
A D : <strong>Amplitude</strong> of the demodulated signal<br />
A(f) : Transmission factor<br />
AM : <strong>Amplitude</strong> modulation<br />
A R : Square-wave amplitude<br />
DSB SC : Double sideband AM with suppressed carrier<br />
BP : Bandpass<br />
b : Bandwidth<br />
d : Attenuation<br />
SSB : Single sideband AM<br />
f : Frequency<br />
f M : Frequency of the modulating signal<br />
m : <strong>Modulation</strong> index<br />
USL : Upper sideline<br />
R : Frequency resolution<br />
s(t) : Signal function in the time domain, general<br />
s D (t) : Demodulated signal<br />
s M (t) : Information signal, modulating signal<br />
s C (t) : Carrier signal<br />
S(n) : <strong>Amplitude</strong> spectrum, general<br />
S AM (n) : Spectrum of the AM signal<br />
s AM (t) : Dynamic characteristic of the AM signal<br />
S R (n) : Spectrum of the square-wave signal<br />
T : Period duration<br />
LP : Lowpass filter<br />
LSL : Lower sideline<br />
η : Efficiency<br />
DSB : Double sideband AM<br />
Bibliography<br />
E. Stadler <strong>Modulation</strong>sverfahren<br />
Vogel Buchverlag, Würzburg<br />
3rd edition 1983<br />
Herter, Röcker,Lörcher<br />
Nachrichtentechnik, Übertragung, Vermittlung, Verarbeitung<br />
Hanser, München, Wien<br />
3rd edition 1984<br />
G. Kennedy Electronic Communication Systems,<br />
McGraw Hill Book Company, Singapore,<br />
3rd edition 1985<br />
D.G. Fink D. Christiansen<br />
Electronic Engineer’s Handbook<br />
McGraw Hill Book Company<br />
2nd edition 1982<br />
D. Roddy, J. Coolen Electronic Communications<br />
Prentice Hall International, Reston Verginia,<br />
3rd edition 1984<br />
Hewlett Packard Measurement, Computation, Systems, catalog 1986,<br />
Palo Alto California<br />
Dipl. Ing. Klaus Breidenbach<br />
Hürth, February 1997<br />
8
TPS <strong>7.2.1.3</strong><br />
Introduction<br />
1 Introduction<br />
Signals<br />
In electrical telecommunications engineering,<br />
messages are usually in the form of time-dependent<br />
electrical quantities, for example, voltage u(t)<br />
or current i(t). These kinds of quantities which are<br />
described by time functions are called signals. In<br />
order to transmit messages a parameter of the<br />
electrical signal must be suitably influenced. In<br />
cases where a signal defined as a time function is<br />
known and the signal value can be determined<br />
exactly at any given point in time, then the signal<br />
is called deterministic. Examples of deterministic<br />
signals are:<br />
1. Harmonic oscillation<br />
u(t) = A · sin (2 π ft + φ) (1.1)<br />
2. Symmetrical square wave<br />
u(t) = u(t + nT) n = 1, 2, 3... (1.2)<br />
A t T<br />
u()= t<br />
⎧ for 0 < < / 2<br />
⎨<br />
⎩ 0 for T/ 2 < t< T .<br />
Deterministic telecommunications is useless from<br />
the point of view of information theory. Only unknown,<br />
i.e. unpredictable messages are important<br />
for the message receiver. Nevertheless, when discussing<br />
modulation methods it is standard procedure<br />
to work with harmonic signals. The results<br />
which can be obtained are then clearer and more<br />
straightforward. If the signal value for any given<br />
point in time cannot be given because the signal<br />
curve appears totally erratic, then the signal is<br />
called stochastic. An example for a stochastic signal<br />
is noise. Stochastic signals can be described<br />
using methods of probability mathematics, but<br />
they will not be taken into consideration here. Signals<br />
are distinguished according to the characteristic<br />
curves of their time and signal coordinates. If<br />
the signal function s(t) produces a signal value at<br />
any random point in time, the signal function is<br />
called time-continuous (continuous w.r.t. time).<br />
In contrast, if the signal values differ from 0 only<br />
at definite, countable points in time, i.e. its time<br />
characteristic shows “gaps”, then this is referred<br />
to as time-discrete (discrete w.r.t. time). What is<br />
true for the time coordinate, can also be applied to<br />
the signal coordinates. Accordingly, a signal is<br />
called level-continuous, if it can assume any<br />
given value within the system limits. It is called<br />
value-discrete or n-level, if only a finite number<br />
Fig 1-1: Classification of signals<br />
(a) time- and level-continuous<br />
(b) time-discrete (sampled), level-continuous<br />
(c) time-continuous, level-discrete (quantized)<br />
(d) time- and level-discrete<br />
9
TPS <strong>7.2.1.3</strong><br />
Introduction<br />
of signal values are permitted. Two important signal<br />
classes can be defined using these 4 terms:<br />
Analog signals<br />
A signal is called analog if it is both time as well<br />
as value-continuous.<br />
Digital signals<br />
A signal is called digital, if it is both time as well<br />
as value-discrete.<br />
Fig. 1-1 shows the various kinds of signals.<br />
Time and spectral domain<br />
In the technical sciences there exists, in addition<br />
to the “time domain”, signal representation in the<br />
“frequency” or “spectral domain”. The equivalence<br />
of the two types of representation can be<br />
seen in the depictions in Fig. 1-2.<br />
If you first consider the harmonic function as<br />
specified in (1.1), then a display on the oscilloscope<br />
results in the familiar, dynamic (time) characteristic<br />
according to Fig. 1-2-A. The sinusoidal<br />
time function is described by the amplitude A and<br />
the period duration T. However, a totally equivalent<br />
representation of this function is reproduced<br />
when the variables A and f = 1/T are used instead<br />
of the parameters A and T. If the amplitude is displayed<br />
on the frequency axis, then this form of<br />
representation is called the amplitude spectrum.<br />
Time domain<br />
Thus, a single line can depict a harmonic function.<br />
Now, after Fourier, every non-harmonic, periodic<br />
function can be represented as the superimposition<br />
of harmonic oscillations with fixed<br />
amplitudes S(n). As an example Fig. 1-2-B<br />
presents a symmetrical square-wave signal with<br />
the amplitude A R and the period of oscillation T R .<br />
We can see from the corresponding amplitude<br />
spectrum S R (n) in Fig. 1-2-D that the squarewave<br />
function is produced from the superposition<br />
of many (an infinite number of) harmonic oscillations.<br />
Their frequencies are odd numbered multiples<br />
of<br />
f = 1/T R and their amplitudes decrease as a function<br />
of the ordinal number n, see Table on pg. 11.<br />
Note: Any precise and comprehensive discussion<br />
of the spectra not only takes the amplitude<br />
spectrum S(n) into consideration<br />
but also the phase spectrum φ(n). However,<br />
in many practical exercises it suffices<br />
to determine the amplitude spectrum.<br />
<strong>Modulation</strong><br />
When speaking of modulation, one generally refers<br />
to the conversion of a modulation signal s M (t)<br />
into a time function with altered characteristics<br />
using a carrier signal. The message signal influences<br />
a parameter of the carrier in a suitable fash-<br />
Spectral domain<br />
(A)<br />
(C)<br />
(B)<br />
(D)<br />
Fig. 1-2:<br />
Time and spectral representation<br />
(A) Harmonic function, time representation (C) Harmonic function, spectral representation<br />
(B) Symmetrical square-wave oscillation, (D) Symmetrical square-wave oscillation,<br />
time representation<br />
spectral representation<br />
10
TPS <strong>7.2.1.3</strong><br />
Introduction<br />
Harmonic Frequency <strong>Amplitude</strong><br />
1<br />
2<br />
3<br />
4<br />
n<br />
f R = 1/T R SR(1)= 4 A<br />
π<br />
3 f R<br />
5 f R<br />
7 f R<br />
(2 n – 1) f R<br />
S R (1)<br />
3<br />
S R (1)<br />
5<br />
S R (1)<br />
7<br />
SR (1)<br />
2n<br />
−1<br />
<strong>Amplitude</strong> spectrum of a symmetrical squarewave<br />
signal n = 1, 2, 3, 4, ...<br />
ion. Either harmonic oscillations or pulse trains<br />
are used as carrier signals. If, for example, a harmonic<br />
carrier is used with the form:<br />
s C<br />
(t) = A C<br />
cos (2 f C<br />
t + φ ), (1.3)<br />
then the message signal s M (t) can have an effect<br />
either on the amplitude A C , the carrier frequency<br />
f C or the zero phase angle φ. These effects result in<br />
the analog modulation methods:<br />
– <strong>Amplitude</strong> modulations (AM)<br />
– Frequency modulation (FM)<br />
– Phase modulation (PM).<br />
In the case of analog modulation methods, the<br />
modulation process means a continuous conversion<br />
of the modulating signal s M (t) into a higher<br />
frequency band (frequency conversion). The mod-<br />
R<br />
ulating signal is shifted from the baseband (AF<br />
range, original frequency band), into an RF frequency<br />
band. It no longer appears in the spectrum<br />
of the modulated oscillation. A modulation always<br />
requires that the carrier and the modulation<br />
signal interact. Both of these signals are fed into a<br />
modulator. The original signal s M (t) is recovered<br />
from the modulated signal through demodulation.<br />
Consequently, modulation and demodulation are<br />
mutually related, inverse processes. The complexities<br />
involved in modulation and demodulation are<br />
considerable. The following reasons explain why<br />
modulation is worthwhile:<br />
1. <strong>Modulation</strong> enables the matching of the<br />
modulating signal to the characteristics of the<br />
transmission channel. (radio links e.g. are<br />
only possible above a certain frequency.)<br />
2. Existing transmission channels can be multiply<br />
exploited using modulation, (frequency<br />
or time division multiplex systems).<br />
3. Improved signal-to-noise ratios can be obtained<br />
using modulation.<br />
The communications system according to Shannon<br />
Electrical communications engineering is divided<br />
into three classical subfunctions:<br />
1. Transmission of the message<br />
2. Processing of the message<br />
3. Relaying the message (telephone technology)<br />
If only a single transmission channel is examined,<br />
(i.e. no telephone technology), then we can concentrate<br />
on the remaining functions illustrated by<br />
the scheme in Fig. 1-3.<br />
Fig. 1-3: The telecommunications system<br />
(A) The telecommunications system<br />
(B) Message transmission<br />
(C) Message processing<br />
1 Message source<br />
(human being, measurment sensor etc.)<br />
2 Converter (microphone,<br />
television camera,<br />
strain gauges, thermo sensor etc.)<br />
3 Transmitter<br />
4 Transmission channel (radio link,<br />
transmission cable, data storage system)<br />
5 Receiver<br />
6 Converter<br />
7 Message recipient<br />
8 Interference source<br />
11
TPS <strong>7.2.1.3</strong><br />
Introduction<br />
The telecommunication system (A) consists of<br />
equipment used for message transmission (B) and<br />
message processing (C). The message source (1)<br />
generates the information, which is to be made<br />
available to the message recipient (7). The signals<br />
generated are of the most varied physical nature,<br />
e.g. sound, light, pressure, temperature, etc. It is<br />
the function of the converter (2) to convert the<br />
non-electrical signal of the source into an electrical<br />
one. The transmitter (3) converts the converter<br />
signal into one better suited for transmission via<br />
the channel. Thus the modulation process takes<br />
place in (3). The transmission channel (4) serves<br />
either to bridge a spatial distance, or to overcome<br />
a period of time. The modulated signal, generally<br />
distorted by the interference source (8), reaches<br />
the receiver (5), where it is then reconverted into<br />
its original electrical signal there (demodulation).<br />
Finally, the converter (6) transforms the electrical<br />
signal back into the physical signal required by<br />
the message recipient (7). The message recipient<br />
can take the form of the human being with eyes<br />
and ears or a machine in a process control loop.<br />
12
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
2 Measuring instruments<br />
2.1 Oscilloscope and spectrum analyzer<br />
The oscilloscope<br />
The oscilloscope is amongst the most important<br />
measuring instruments used in electrical engineering.<br />
It is used to graphically display signal<br />
voltages u(t) in the time domain. It can also be<br />
regarded as a two dimensional voltmeter. The signal<br />
is displayed in the form of Cartesian coordinates.<br />
The abcissa (x-axis) shows the time scale,<br />
(e.g. ms/Div) and the y-axis shows the voltage<br />
scale (e.g. V/Div). The oscilloscope provides immediate<br />
information on the signal shape and is<br />
therefore superior to moving coil instruments or<br />
digital voltmeters. The prerequisite for all forms<br />
of pointer instruments and multimeters is that the<br />
time characteristic or curve of the electrical signals<br />
is known. As a rule only DC voltages or harmonic<br />
AC voltages can be measured using these<br />
kinds of instruments. The oscilloscope is used for<br />
the voltage measurement of signals with unknown,<br />
random time characteristics. Here a distinction<br />
is drawn between two different cases:<br />
1. The voltage signal is non-sinusoidal, but periodic<br />
with “higher” frequency.<br />
The oscilloscope is operated in repeating real time<br />
mode. This operating mode is the most frequently<br />
one used. A sawtooth generator is started each<br />
time the signal to be measured has exceeded an<br />
adjustable level (trigger level). This produces a<br />
time-linear voltage used for the horizontal deflection<br />
of the cathode ray tube. The sawtooth generator<br />
is part of the time base. The vertical deflection<br />
is controlled by the measurement signal itself. The<br />
result is a standing image of the voltage signal on<br />
the screen. In real time operation the oscilloscope<br />
has a slow-motion function. Thus, processes<br />
which are too fast for the human eye can be made<br />
visible.<br />
2. The voltage signal to be measured is non-periodic,<br />
or has a very long period duration.<br />
The signal to be measured is digitalized and input<br />
into a storage system. The contents of the storage<br />
unit can then be output periodically. Processes<br />
which are too long can be displayed in the storage<br />
mode.<br />
The oscilloscope masks out the amplitude and<br />
time windows from the signal characteristic, see<br />
Fig. 2.1-1.<br />
Fig. 2.1-1:Functioning of the oscilloscope<br />
(A) <strong>Amplitude</strong> window<br />
(T) Time window<br />
The spectrum analyzer<br />
Spectrum analyzers are used to display signals in<br />
the spectral domain. These analyzers operate<br />
either digitally with the aid of mathematical algorithms<br />
(Fast Fourier Transformation) or in analog<br />
mode as a filter bank i.e. according to the principle<br />
of frequency conversion. The latter principle<br />
is implemented in the spectrum analyzer 726 94<br />
training panel. For that reason we shall study this<br />
in more detail with the aid of Fig. 2.1-2.<br />
The harmonic signal supplied by the VCO is fed<br />
into the mixer with the input signal. Depending on<br />
its spectral quality and the oscillator frequency, an<br />
AC voltage signal appears at the mixer output<br />
which lies in the passband of the bandpass filter.<br />
The IF signal at the output of the bandpass filter is<br />
produced for the individual spectral components<br />
of the input signal for correspondingly different<br />
VCO frequencies. If its frequency is linearly dependent<br />
on its control voltage, then this can be<br />
used for the X-deflection of a display unit. Thus<br />
the X-axis also achieves linear frequency scaling.<br />
The rectified, amplified output voltage of the IF<br />
filter is used for Y-deflection. Consequently each<br />
spectral amplitude of the input signal can be measured<br />
by adjusting the VCO. The spectrum<br />
analyzer thus constitutes an application of the superheterodyne<br />
principle used in radio technology,<br />
whereby the bandfilter can be regarded as a<br />
spectral window. The position of this window in<br />
the frequency domain is determined by the VCO<br />
13
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
Fig. 2.1-2: Design of a spectrum analyzer according to the superheterodyne principle<br />
(A) Signal path<br />
1Input amplfier/ attenuator V 1<br />
2Mixer<br />
3Bandpass (BP)<br />
4Rectifier<br />
5Output amplifier V 2<br />
(B) Oscillator<br />
6VCO<br />
7Sawtooth generator<br />
(C) Display unit<br />
frequency. The width of the window is determined<br />
by the selected bandwidth of the bandpass filter,<br />
see Fig. 2.1-3.<br />
The time law of electrical telecommunications<br />
engineering<br />
The use of analyzers according to the<br />
superhetrodyne principle requires that the time<br />
law of electrical telecommunications be observed.<br />
According to this law, the pulse response of a<br />
lowpass system becomes longer, the smaller its<br />
bandwidth b is, see Fig. 2.1-4.<br />
This statement can also be applied to the<br />
bandpasses present in the spectrum analyzer. The<br />
time law is similar to the uncertainty relation in<br />
nuclear physics. It states that it is impossible to<br />
decrease both the duration T as well as the bandwidth<br />
b of a signal. When tuning the VCO, the<br />
slower it takes for the VCO frequency to change,<br />
the longer the mixer output signal is in the<br />
passband of the downstream bandpass (BP). The<br />
frequency change with respect to the time unit<br />
depends on:<br />
1. (Periods of the sawtooth generator (SCAN<br />
TIME)<br />
2. Absolute frequency domain passed through<br />
by the VCO (SPAN).<br />
Fig. 2.1-3:The functioning principle of a spectrum<br />
analyzer<br />
1 Bandpass with bandwidth b<br />
(spectral window)<br />
2 Signal spectrum<br />
14
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
Fig. 2.1-4:The time law of electrical telecommunications engineering<br />
(A): Input signals: pulses with equal amplitude A and period T<br />
(B): Lowpasses with critical frequencies f c1<br />
and f c2<br />
; f c1<br />
< f c2<br />
(C): Output signals: pulse of varying period and amplitude<br />
If, for example, a spectrum analysis has to be performed<br />
over a wide frequency domain, and, in<br />
addition, a very short sawtooth period is selected,<br />
then the result of this is a very large change in frequency<br />
per unit time. The mixer output signal<br />
passes through the mid-frequencies of the BPF<br />
with corresponding speed. According to the time<br />
law the selected bandwidth of the BPF now has to<br />
be “sufficiently” large if the BPF is to attain the<br />
input amplitude. However, at greater bandwidth<br />
of the bandpass filter the analyzer's spectral resolution<br />
capacity drops. For that reason, work with<br />
the spectrum analyzer always involves the compromise<br />
between spectral RESOLUTION and<br />
fault-free reproduction of the amplitude. For the<br />
relationship between the SCAN TIME T, bandwidth<br />
b and frequency window SPAN the following<br />
approximately applies:<br />
b = 20 ( f − f )<br />
T<br />
max min (2.1)<br />
Where:<br />
f max : maximum frequency<br />
f min : minimum frequency<br />
b : bandwidth of the filter<br />
T : sawtooth period SCAN TIME.<br />
The difference f max – f min is called frequency<br />
window = SPAN.<br />
15
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
2.2 Equipment descriptions<br />
726 94 Spectrum analyzer<br />
The spectrum analyzer is depicted in Fig. 2.2-1.<br />
A. Setting the signal path<br />
Always set the gain settings V 1 and V 2 as high as<br />
possible to increase the sensitivity of the signal<br />
path. However, overdrive - recognizable by the<br />
lighting up of the OVER-LEDs, must be avoided<br />
(overdrive falsifies the measurement results).<br />
B. Setting the oscillator component<br />
Frequency tuning is performed with the aid of a<br />
sawtooth-controlled VCO. The sawtooth generator<br />
is set with the controllers SCAN TIME and<br />
SCAN MODE. The selection of the SCAN TIME<br />
depends on the time law of electrical telecommunications<br />
engineering (2.1).<br />
1. Setting the upper limit of the frequency: This<br />
is carried out in SCAN MODE f max using the<br />
corresponding controller.<br />
2. Setting the lower frequency limit: This is carried<br />
out in SCAN MODE f min using the corresponding<br />
controller.<br />
The frequencies can be read off directly at the<br />
connected COUNTER (TTL). In SCAN MODE<br />
RUN the VCO runs through the set frequency<br />
range once (important when using the XY recorder).<br />
An LED indicates when the upper frequency<br />
limit is reached.<br />
Only in the SCAN MODE STOP is the locking<br />
mechanism of the RESET function disabled. In<br />
this setting manual operation using a toggle<br />
switch is possible. The setting “UP” of the toggle<br />
switch enables the VCO to run in the f max direction,<br />
while the setting “DOWN” causes a corresponding<br />
reduction in frequency.<br />
Attention:For the run through time T = 1/25 s the<br />
set frequency window is passed through<br />
in RUN auto-repeat mode. This enables<br />
us to also use the spectrum<br />
analyzer as a sweep generator.<br />
C. Connection of the display unit<br />
The following external measuring instruments can<br />
be used as display units:<br />
– Analog voltmeter<br />
– Storage oscilloscope<br />
– XY recorder.<br />
Fig. 2.2-1:The spectrum analyzer<br />
Note:<br />
The analyzer operates in manual mode as<br />
a frequency-selective voltmeter. This operating<br />
mode is particularly suitable for<br />
quantitative evaluations. Due to the beat<br />
effects in the analyzer the output signal<br />
can start oscillating particularly when<br />
working with V 2 = 10. To obtain as accurate<br />
a reading of the output voltage S(n) as<br />
possible, a slight frequency adjustment is<br />
recommended if this should occur.<br />
16
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
726 961 Function generator 200kHz<br />
1. Safety instruction:<br />
Read the instruction sheet provided with the device!<br />
The function generator is illustrated in Fig. 2-1.<br />
Where:<br />
1 Mains switch<br />
2 FUNCTION: selection of the output signal<br />
3 MODE: selection of the signal parameter adjustable<br />
using the control knob<br />
4 Control knob for the selected signal parameters<br />
5 TTL output<br />
6 Output (50 Ω)<br />
7 Toggle switch for output attenuator<br />
8 Multifunction display in LCD technology<br />
8 Power bus lines and ground<br />
Multifunction display in LCD technology with:<br />
- Function symbols and signs<br />
- Numerical display with decimal points<br />
- Signal parameter<br />
Putting the system into operation<br />
Connect the mains plug into the socket. Actuate<br />
mains switch 1. When the device is on the mains<br />
switch lights up. The desired output signal is set<br />
by actuating the FUNCTION button. By<br />
repeatedly pressing the FUNCTION button you<br />
shuttle cyclically through the sequence of output<br />
signals available, sinussoidal, triangular, squarewave,<br />
DC. With the MODE pushbutton the<br />
following signal parameters are selected:<br />
– Frequency<br />
– <strong>Amplitude</strong> (peak-to-peak value)<br />
– DC offset<br />
– Duty cycle (only for square-wave)<br />
You can shuttle cyclically through the program<br />
menus by pressing the MODE pushbutton repeatedly.<br />
After the desired signal parameter has been<br />
set its magnitude can be varied by turning the control<br />
knob. The maximum output voltage of the device<br />
lies at approx. ±12 V.<br />
Fig. 2.2-2:<br />
DC<br />
FUNCTION<br />
MODE<br />
726 961<br />
FUNKTIONSGENERATOR 200 kHz<br />
FUNCTION GENERATOR 200 kHz<br />
The function generator and the multifunction<br />
display<br />
Storing the last setting<br />
After switch off all of the settings are retained.<br />
They are at your disposal unchanged after you<br />
switch the unit back on.<br />
Calling up the base setting<br />
If you simultaneously press either the MODE or<br />
FUNCTION buttons with the device switched on,<br />
the function generator supplies a sinusoidal signal<br />
with 1 kHz and 10 V PP , DC = 0 V. The base setting<br />
for the duty cycle (for square-wave signal) is<br />
50%.<br />
kHz<br />
V<br />
pp<br />
=<br />
%<br />
ATT<br />
dB<br />
0<br />
20<br />
40<br />
OUT<br />
TTL<br />
17
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
726 99 Frequency counter 0..10 MHz<br />
1 8-digit 7-segment display<br />
2 TTL inputs (Channel A), f max = 10 MHz.<br />
3 Analog input (Channel A), f max = 10 MHz.<br />
4 TTL input (Channel B), f max = 2 MHz.<br />
5 Toggle switch for switchover between TTL<br />
and analog input of channel A<br />
6 Function switch<br />
FREQ.A<br />
: Frequency measurement of channel<br />
A, display in kHz.<br />
PERIOD A : Period duration channel A,<br />
display µs. The last respective<br />
measurement value is stored<br />
f max = 2 MHz.<br />
RATIO A/B : Frequency ratio f A /f B . Signal<br />
B with TTL level! f max = 2 MHz.<br />
TIME A-B<br />
: Time interval between a negative<br />
edge of signal A and the<br />
next negative edge of the signal<br />
B, f max = 2 MHz.<br />
COUNT A : Event counting in channel A<br />
from 0 - 10.000.000.<br />
7 Gate : Gate time (meas. duration)<br />
0.01s/0.10s/1.00s/10.0s<br />
Note:<br />
The analog input is coupled with AC power. Due<br />
to an unfavorable set up (long connecting leads)<br />
of the experiment and despite shielding, a display<br />
might appear even without an input signal, if a signal<br />
is applied in TTL channel A. This crosstalk<br />
can be attributed to the high sensitivity of the analog<br />
input and the spatial proximity of the input<br />
sockets. For that reason always connect the analog<br />
input to a signal source using a short connection<br />
cable after switching to ANALOG.<br />
736 201 CF transmitter 20 kHz<br />
The training panel contains the following components:<br />
1. Input filter<br />
The input filter sets the upper critical frequency<br />
limit of the modulating signal to f c = 3.4 kHz. Gain<br />
in the bandpass: +1.<br />
2. Modulator M2<br />
Product modulator with 2 freely accessible inputs:<br />
– Input for the modulating signal (LF-input)<br />
0,1s<br />
0,01s<br />
GATE<br />
1s<br />
10s<br />
RATIO A/B<br />
PERIOD A<br />
FREQ A<br />
FUNCTION<br />
TIME A-B<br />
COUNT A<br />
CHECK<br />
TTL - IN(A)<br />
TTL - IN(A)<br />
TTL - IN(B)<br />
ANALOG (A)<br />
726 99<br />
FREQUENZZAEHLER 0-10MHz<br />
FREQUENCY COUNTER 0-10MHz<br />
Fig. 2.2-3: The frequency counter<br />
Fig. 2.2-4: The CF transmitter 20 kHz<br />
18
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
– Input for the carrier oscillation (RF input)<br />
In addition, the carrier in the output signal of the<br />
modulator can be enabled or disabled using a toggle<br />
switch. (CARRIER, ON-OFF)<br />
3. Channel filter CH2<br />
The channel filter is needed for the generation of<br />
SSB-AM. It suppresses the lower sideband. The<br />
passband range of approx. 20 kHz...30 kHz extends<br />
beyond the upper sideband.<br />
Gain in the passband: +1.<br />
Both filters (1 and 3) are equipped with freely accessible<br />
inputs and outputs, which permits the recording<br />
of amplitude frequency responses.<br />
4. Output summer<br />
The output summer (4) has two inputs with the<br />
gain levels +1. The component is used to linearly<br />
superimpose signal components of the AM signal.<br />
At the output of the summing unit you have at<br />
your disposal the complete AM signal, i.e.<br />
including any existing pilot tone or, in the case of<br />
FMUX operation, the multiplex signal for<br />
transmission via the transmission channel.<br />
736 221 CF receiver 20 kHz<br />
The training panel is used for the demodulation of<br />
amplitude-modulated signals. The auxiliary carrier<br />
required for synchronous demodulation can<br />
be forwarded either directly via an external source<br />
e.g. to the corresponding CF transmitter or<br />
internally from the subassembly “carrier<br />
recovery”.<br />
Design:<br />
The device contains the following components:<br />
1. Channel filter CH2<br />
Bandpass filter for the filtering out of the wanted<br />
SSB signals. The passband from approx.<br />
20...30 kHz extends beyond the upper sideband.<br />
Gain in the passband: +1. For the demodulation of<br />
single sideband-AM (SSB) a bridging plug is<br />
needed between the output of the channel filter<br />
CH2 (1) and the input of the demodulator D2 (2).<br />
Should the CF receiver demodulate the double<br />
sideband-AM (DSB), then the SSB-signal has to<br />
Subassembly for “carrier generation”<br />
(CARRIER)<br />
Frequency division f 0 /8 (5) is used to generate the<br />
carrier frequency of 20 kHz out of the pilot tone.<br />
The unipolar TTL signal is converted into a bipolar<br />
square-wave signal with 4 V PP in the TTL/<br />
square-wave converter (6). Conversion into a bipolar<br />
sine oscillation also with 4 V PP is performed<br />
in the square-wave/sine converter (7). The adjustable<br />
phase-shifter (8) φ = 0 0 ...150 0 introduces a<br />
defined phase-shift between the carrier on the<br />
modulator side (M2) and the auxiliary carrier on<br />
the demodulator side. The phase-shifter permits<br />
the features of coharent demodulation to be examined.<br />
Furthermore, together with the CF transmitter<br />
16 kHz (736 211), it is able to generate<br />
quadrature modulation.<br />
Subassembly “pilot tone generation”<br />
(PILOT TONE)<br />
The quartz oscillator (9) generates the primary<br />
master clock pulse, symmetrical square-wave,<br />
TTL with a frequency of 160 kHz. The converter<br />
(10) and the attenuator (11) connected in series<br />
form an attenuated unipolar square-wave signal<br />
of approx. 200 mV pp out of the TTL signal, which<br />
is transmitted to the CF receiver to recover the<br />
carrier signal.<br />
Fig. 2.2-5: The CF receiver 20 kHz<br />
19
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
+15V<br />
(+5V)<br />
kHz<br />
V<br />
pp<br />
=<br />
DC<br />
%<br />
I ><br />
FUNCTION<br />
MODE<br />
OUT<br />
U<br />
ATT<br />
dB<br />
0<br />
U<br />
20<br />
40<br />
I ><br />
M1<br />
TTL<br />
0V<br />
Fig. 2.3-1: Experiment setup for learning to handle the spectrum analyzer<br />
be fed directly into the input of the demodulator<br />
D2 after the bridging plug has been removed.<br />
2. Synchronous demodulator D2<br />
A multiplier IC takes over the function of the synchronous<br />
demodulator. The AM signal (DSB or<br />
SSB) and an auxiliary carrier are supplied to the<br />
demodulator. In addition to the wanted LF signal,<br />
higher frequency signal components also appear<br />
in its output signal.<br />
3. Lowpass filter<br />
Synchronous demodulation requires a subsequent<br />
filtering for the suppression of the higher frequency<br />
signal components. The filter (3) used<br />
here has an upper critical limit f c = 3.4 kHz and a<br />
gain of +1.<br />
Subassembly "carrier recovery"<br />
Carrier recovery is performed using a PLL circuit<br />
with subsequent frequency division. The synchronization<br />
of the PLL circuit is performed by a pilot<br />
tone of 160 Hz sent by the CF transmitter, which<br />
is processed in the receiver by a bandpass filter (4)<br />
and an amplitude limiter (5). The PLL circuit consists<br />
of the phase comparator (6), the loop filter<br />
(7) and the VCO (8). In standard operation the<br />
output of the loop filter is connected directly to<br />
the input of the VCO using a bridging plug.<br />
However, the VCO can also be tuned using an<br />
external DC voltage 0...+5 V. After locking into<br />
the pilot tone a recovered auxiliary oscillation f 0 =<br />
160 kHz is available at the output of the PLL. This<br />
signal is then divided down to the required carrier<br />
frequency f T = 20 kHz in a frequency divider (9).<br />
2.3 A measurement example<br />
Required equipment and material<br />
1 Spectrum analyzer 726 94<br />
1 Frequency counter 0...10 MHz 726 99<br />
1 Analog multimeter C. A 406 531 16<br />
Additionally required:<br />
1 Function generator 0...200 kHz 726 961<br />
1 DC power supply ±15 V, 3 A 726 86<br />
1 Digital storage oscilloscope 305 575 292<br />
2 Probes 100 MHz, 1:1/10:1 575 231<br />
1 Set of 10 bridging plugs, black 501 511<br />
2 Cable pairs, black 100 cm 501 461<br />
Additionally recommended:<br />
1 XY recorder e.g. 575 663<br />
Preliminary remark<br />
The measurement station described here consists<br />
of a spectrum analyzer, oscilloscope and frequency<br />
counter. Using this measurement station<br />
signals can be measured in the time and spectral<br />
20
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
domain. This will be used a lot in the following<br />
experiments.<br />
Experiment procedure<br />
Set up the experiment as specified in Fig. 2.3-1.<br />
Set a square-wave signal with A R = 5 V and<br />
f R = 2 kHz on the function generator. The TTL input<br />
A of the frequency counter remains permanently<br />
connected to the analyzer via bridging<br />
plugs. In order to test the signal frequency f R plug<br />
a connecting lead into the analog input and actuate<br />
the toggle switch.<br />
Record the spectrum of the square-wave signal in<br />
the frequency range of approx. 1.5 kHz....20 kHz.<br />
1. Manual operation with the analog voltmeter.<br />
Connect an analog voltmeter 10 V DC to the<br />
analyzer output.<br />
V 1 : 1<br />
V 2 : 5, 10<br />
Analyzer settings<br />
f r / kHz: 20 b/Hz: 500<br />
Tabelle 2.3-1: Spectrum square wave signal<br />
Signal parameter<br />
A R : V<br />
τ/T P :<br />
f R : kHz<br />
n<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
8<br />
f<br />
kHz<br />
Measurements<br />
S(n)<br />
V<br />
Analyzer settings<br />
V 1 :<br />
b : Hz<br />
f r : kHz<br />
T : s<br />
S R (n)<br />
V 2<br />
V<br />
Theory<br />
S<br />
R<br />
V<br />
(n)<br />
SPAN/kHz: 0.5...20<br />
T/s: 20<br />
9<br />
10<br />
When V 1 = 2, 5, 10 the input stage is overdriven,<br />
the OVER LED lights up and the<br />
measurement results are falsified.<br />
Now record the spectrum of the square-wave<br />
signal by starting the VCO in SCAN MODE<br />
RUN. In the spectral energy range the output<br />
signal demonstrates a brief increase. Then<br />
stop the VCO and manually adjust it around<br />
the frequency of the spectral line using the<br />
pushbutton up/down. Read off the spectral<br />
amplitude S(n) on the voltmeter. In this manner<br />
enter all the amplitudes S(n), the index n<br />
and the corresponding frequencies f into the<br />
Table 2.3-1. Also the analyzer settings are to<br />
be noted down there. Plot the spectrum in a<br />
graph in Diagram 2.3-1.<br />
Discuss your results.<br />
2. Automatic operation with the XY recorder<br />
or the storage oscilloscope.<br />
In automatic operation the scanning process<br />
is performed without interruption. Also the<br />
gain settings V 1 , V 2 remain unchanged.<br />
Diagram 2.3-1:<br />
Spectrum of the square-wave signal<br />
τ<br />
A R<br />
= 5 V, = 0.5<br />
T P<br />
2.1 Using an XY recorder<br />
Connect the X+ input of the recorder to the X<br />
socket of the analyzer. Connect the Y+ input<br />
of the recorder to the analyzer output; X–,<br />
Y– to earth. Both recorder axes have to be<br />
calibrated. The X-axis is set to f max . The Y-<br />
axis is aligned to the highest spectral amplitude<br />
(test it out!). The analyzer cycle is<br />
21
TPS <strong>7.2.1.3</strong><br />
Measuring instruments<br />
triggered by switching to SCAN MODE<br />
RUN.<br />
2.2 Using the storage oscilloscope<br />
The simplest operation is the recording of<br />
spectra with the storage oscilloscope in the<br />
ROLL mode. Then all of the problems involving<br />
triggering are avoided. The holding<br />
time base is set so that its period is greater<br />
than the SCAN TIME set on the analyzer.<br />
The analyzer output is connected to a Y-input<br />
of the oscilloscope. By selecting a suitable Y-<br />
gain setting the screen surface is optimally<br />
exploited for the spectral display. Once the<br />
spectrum is completely reproduced on the<br />
screen, the ROLL modus can be disabled by<br />
pressing the SINGLE pushbutton. The screen<br />
contents are then “frozen”. When in SINGLE<br />
storage mode you have to trigger externally<br />
on the falling edge of the sawtooth signal<br />
(socket X). Try out the most effective trigger<br />
filter.<br />
Repeat the recording of the spectra one after<br />
the other for the bandwidths b = 100 Hz,<br />
b = 50 Hz, b = 10 Hz, b = 5 Hz. What do you<br />
observe?<br />
22
TPS <strong>7.2.1.3</strong><br />
Review<br />
3 Review of amplitude modulation<br />
In amplitude modulation (AM) the momentary<br />
value of the message signal s M (t) has an<br />
immediate effect on the amplitude of the carrier<br />
oscillation s C (t). This takes place in a modulator,<br />
see Fig.3-1.<br />
Here it would be:<br />
s C<br />
(t) = A C<br />
cos (2 π f C<br />
t) (3-1)<br />
for the high-frequency carrier and:<br />
1. s M<br />
(t) = A M<br />
cos (2 π f M<br />
t) (3-2)<br />
for the low frequency message signal. The combining<br />
of the carrier and message signal in the<br />
modulator then provides the following modulation<br />
product:<br />
s AM<br />
(t) = [A C<br />
+ α s M<br />
(t)] cos (2 π f C<br />
t) (3-3)<br />
= [A C<br />
+ α A M<br />
cos (2 π f M<br />
t)]<br />
cos (2 π f C<br />
t).<br />
Where α stands for the modulator constant, which<br />
expresses the affect of the message signal s M (t)<br />
on the amplitude A C of the carrier. Normally (3-3)<br />
is described in more general terms. For this you<br />
need the following definitions:<br />
∆A C<br />
= α A M<br />
<strong>Amplitude</strong> deviation (3-4)<br />
A<br />
m = ∆ C<br />
A<br />
C<br />
<strong>Modulation</strong> index (3-5)<br />
<strong>Amplitude</strong> deviation ∆A C describes the maximum<br />
change away from the original value A C in the carrier<br />
amplitude. The modulation index m reproduces<br />
the ratio of the amplitude deviation to the carrier<br />
Fig. 3-1: Generation of amplitude modulation<br />
amplitude. Thus it is possible to convert (3-3) as<br />
follows:<br />
⎡ ∆A<br />
⎤<br />
C<br />
sAM<br />
( t) = A ⎢<br />
C 1+ cos( 2π<br />
fMt)<br />
⎥cos<br />
2π<br />
fCt<br />
⎢<br />
⎣<br />
A<br />
⎥<br />
C<br />
⎦<br />
A 1 mcos<br />
2π<br />
f t cos 2π<br />
f t<br />
C M C<br />
( )<br />
[ ] ( )<br />
= + ( )<br />
(3-6)<br />
Fig. 3-2 shows the amplitude modulated signal according<br />
to (3-6). The modulating signal s M (t) can<br />
be recognized in the envelope curve.<br />
Normally the following holds true: 0 < m < 1.<br />
The following limiting cases for m are interesting:<br />
m = 0 : no modulation effect<br />
m = 1 : full modulation, the envelopes bordering<br />
the modulating signal just touch at their<br />
minimum values<br />
m > 1 : overmodulation, the envelopes permeate<br />
each other, modulation distortion arises.<br />
m = 0%<br />
A C<br />
s AM<br />
T C<br />
Envelope<br />
∆A C<br />
∆A C<br />
m = 100%<br />
T M<br />
Envelope<br />
m > 100%<br />
Fig. 3-2: The amplitude modulated signal<br />
Fig. 3-3: Limiting cases for the modulation factor<br />
23
TPS <strong>7.2.1.3</strong><br />
Review<br />
Special cases are depicted in Fig. 3-3.<br />
The spectrum of amplitude modulation<br />
The expression in the brackets of (3-6) describes<br />
the envelope of amplitude modulation. If you<br />
multiply the dynamic (time) characteristic of the<br />
carrier oscillation in this expression, you obtain:<br />
s AM<br />
(t) = A C<br />
[cos (2 π f C<br />
t)<br />
+ m cos (2 π f T<br />
t) cos (2 π f M<br />
t)] (3-7)<br />
The application of the addition theorem:<br />
1<br />
cos x⋅ cos y= cos( x−y)+ cos x+<br />
y<br />
2<br />
provides:<br />
s ( t) A cos 2π<br />
f t<br />
AM C C<br />
[ ( )]<br />
= ( )<br />
m<br />
+ cos 2π<br />
( fC<br />
− fM<br />
) t<br />
2<br />
[ ]<br />
m<br />
+ cos 2π<br />
( fC<br />
+ fM<br />
) t<br />
2<br />
[ ]<br />
(3-8)<br />
From (3-8) you can see the spectral composition of<br />
amplitude modulation, see Fig. 3-4.<br />
From the spectrum we can see that besides the<br />
carrier oscillation with the frequency f C , there are<br />
also 2 side oscillations with the frequencies f C + f M<br />
and f C – f M contained in s AM (t). According to (3-8)<br />
the amplitudes of the equal side oscillations depend<br />
on the modulation index. The oscillation with the<br />
lower frequency f C – f M is called the lower sideline,<br />
the one with the higher frequency is the upper<br />
sideline f C + f M . The lower sideline (LSL) slips further<br />
into the range of lower frequencies as the<br />
signal frequency f M increases. This frequency response<br />
of the LSL is referred to as inverted position.<br />
The upper sideline (USL) shifts into the<br />
higher range of frequencies with increasing signal<br />
frequency. It lies in the normal position. In Fig. 3-<br />
5 the terms are in standard representation for the<br />
transmission of an information band, which extends<br />
from a lower frequency limit f u up to the<br />
upper frequency limit f o .<br />
The representation according to Fig. 3-5 is standard<br />
particularly in carrier frequency technology.<br />
The bandwidth requirement of AM equals twice<br />
the maximum message frequency f Mmax :<br />
b = 2 f Mmax<br />
(3-9)<br />
Representing amplitude modulation with a<br />
vector diagram<br />
The vector diagram constitutes an important tool in<br />
the representation of modulation methods. It frequently<br />
permits the immediate assessment of interference<br />
effects or manipulations during modulation.<br />
For example, asymmetrical attenuation of the<br />
sideband oscillations in AM can lead to the<br />
formation of parasitic angular modulation.<br />
From Fig. 3-6 the following features of amplitude<br />
modulation can be read off directly:<br />
An AM signal can be represented by 3 complex<br />
vectors ( 2 sideband vectors and a vector for the<br />
carrier). The 3 vectors are displayed in a joint diagram<br />
for any given point in time, see Fig. 3-6.<br />
S AM<br />
S AM<br />
A C<br />
m/2<br />
A C<br />
m/2<br />
f M f C<br />
(f)<br />
f C – f M<br />
Fig. 3-4: The spectrum of amplitude modulation<br />
s M<br />
f u f o<br />
s AM<br />
f C – f o f C f C + f o<br />
1<br />
1<br />
f C<br />
f C + f M<br />
(f)<br />
f<br />
Fig. 3-5: Normal and inverted position<br />
f<br />
24
TPS <strong>7.2.1.3</strong><br />
Review<br />
t = t 1<br />
s AM<br />
USL<br />
USL<br />
t = t 2<br />
LSL<br />
LSL<br />
s C<br />
s C<br />
s AM<br />
Fig. 3-6: <strong>Amplitude</strong> modulation in a vector diagram Fig. 3-7: Relationship between envelope and vector<br />
representation<br />
1. The carrier oscillation is depicted with a constant<br />
direction (normally perpendicular upwards),<br />
although in absolute terms it rotates in<br />
counterclockwise rotation with 2 π f C .<br />
2. The length of the carrier vector remains constant.<br />
3. The sideband vectors are symmetrical with<br />
respect to the carrier. The vector of the USL<br />
rotates counterclockwise around the tip of the<br />
carrier vector. The vector of the LSL rotates<br />
in clockwise rotation.<br />
4. The vector for the amplitude modulated oscillation<br />
is obtained through vector addition, i.e.<br />
construction of the vector parallelogram,<br />
made up of the vector of the carrier and the<br />
side oscillations. The resulting vector always<br />
has the direction of the carrier vector.<br />
As you can see from Fig. 3-7, the tips of the resulting<br />
vectors, if you draw them as a function of time,<br />
again produce the envelope of the amplitude<br />
modulated oscillation.<br />
1. A DC voltage component<br />
2. The original signal with the frequency f M .<br />
3. Components with higher frequencies f C ,<br />
f C + f M , 2 f C + f M , etc.<br />
Fourier expansion shows that rectification of the<br />
AM signal produces many new spectral components<br />
which are not present at the input of the rectifier.<br />
A suitable filter is used to suppress these<br />
unwanted spectral components. Envelope demodulation<br />
belongs to the so-called incoherent<br />
demodulation methods, as neither the carrier phase<br />
nor the carrier frequency are of any importance.<br />
Fig. 3-9 reproduces the possible circuit configuration<br />
of an envelope demodulator.<br />
AM demodulation<br />
Envelopes and synchronous demodulation<br />
1st envelope demodulation<br />
First the AM signal is rectified, see Fig. 3-8.<br />
The dynamic characteristic of the current passing<br />
through the recifier can be subjected to Fourier<br />
series expansion. It can be shown that a rectified<br />
AM signal contains the following signal components:<br />
Fig. 3-8: Envelope curve demodulation<br />
25
TPS <strong>7.2.1.3</strong><br />
Review<br />
s AM (t) C 1 R 1 s D (t)<br />
S AM (t)<br />
S D (t)<br />
S H (t)<br />
Fig. 3-9: The envelope demodulator<br />
Fig. 3-10: Synchronous demodulation<br />
Envelope demodulation always requires the carrier.<br />
After rectification this produces a DC voltage,<br />
which establishes the working point of the diode. In<br />
practice envelope demodulation is frequently used<br />
in AM radio communications due to its simple<br />
circuitry.<br />
2. Synchronous demodulation<br />
In principle synchronous demodulation is simply<br />
another modulation process. To carry it out, you<br />
need an auxiliary oscillation in the receiver, which<br />
in terms of frequency and phase corresponds exactly<br />
to the carrier oscillation in the modulator. The<br />
auxiliary carrier s Aux (t) and the modulated signal<br />
s AM (t) are supplied to a circuit with multiplying capabilities,<br />
see. Fig. 3-10:<br />
Three cases can be distinguished DSB, DSB sc and<br />
SSB:<br />
1. Demodulation of DSB<br />
⎧⎪<br />
m<br />
sAM ( t) = AC⎨cos( 2π<br />
fC t)+ cos 2π( fC − fM<br />
) t<br />
⎩⎪<br />
2<br />
m<br />
+ cos 2π<br />
( fC<br />
+ fM<br />
) t<br />
2<br />
s t cos 2π<br />
f t φ<br />
( 3 10)<br />
Aux<br />
( ) = +<br />
[ ] ⎫ ⎬ ⎪ ⎭ ⎪<br />
Aux<br />
[ ]<br />
( ) −<br />
The amplitude of the auxiliary oscillation is negligible,<br />
furthermore it is true that f C = f Aux (i.e. frequency<br />
equality prevails between carrier and<br />
auxiliary carrier). After lowpass filtering we obtain<br />
the demodulated signal:<br />
AC<br />
m<br />
sD( t) = ACcosφ+ cos( 2 π fMt)<br />
cosφ<br />
(3-11)<br />
2<br />
2. Demodulation of DSB sc .<br />
The constant DC voltage component A C cos φ is<br />
omitted:<br />
A m<br />
s D ( t ) = C<br />
cos ( 2π f t ) M cosφ (3-12)<br />
2<br />
3. Demodulation of SSB SC .<br />
s D ( t )<br />
= AC<br />
m<br />
cos(<br />
2π f ± ) M φ (3-13)<br />
4<br />
In the synchronous demodulation of DSB a phase<br />
error φ reduces the amplitude of the demodulated<br />
signal by the factor cos φ. In the case of SSB, the<br />
phase error leads to a shift in the demodulated signal.<br />
In both cases the phase between the carrier<br />
and the auxiliary carrier has a noticeable effect on<br />
the demodulation process. Due to this phase sensitivity<br />
synchronous demodulation is also called coherent<br />
demodulation.<br />
Questions<br />
3.1 What is meant by modulation? Mixing?<br />
3.2 Name the reasons for performing modulation!<br />
3.3 In DSB the carrier's peak values are affected<br />
by the instantaneous value of the message<br />
signal, but the spectrum shows that the<br />
carrier amplitude remains constant! How do<br />
you explain the apparent contradiction?<br />
3.4 Which are the characteristic features of a<br />
beat?<br />
3.5 Define amplitude deviation and the modulation<br />
index.<br />
3.6 Which methods of AM demodulation are<br />
you familiar with and how do they differ?<br />
26
TPS <strong>7.2.1.3</strong><br />
Review<br />
3.7 In radio links the carrier is normally attenuated<br />
to 5%...10%. What advantages does this<br />
have compared to transmission with 100%<br />
carrier amplitude? Why isn't the carrier<br />
completely suppressed?<br />
3.8 How high is the maximum efficiency in<br />
DSB? How can the efficiency be increased?<br />
3.9 Which methods of carrier suppression are<br />
there?<br />
3.10 Which demodulation method is used for AM<br />
with supressed carrier?<br />
27
TPS <strong>7.2.1.3</strong><br />
Review<br />
4 Required equipment and accessories<br />
1 CF transmitter 20 kHz 736 201<br />
1 CF receiver 20 kHz 736 211<br />
Additionally required<br />
1 Spectrum analyzer 726 94<br />
1 Function generator 0...200 kHz 726 961<br />
1 Frequency counter 0-10 MHz 726 99<br />
1 DC power supply ±15 V, 3 A 726 86<br />
1 Digital storage oscilloscope 305 575 292<br />
2 Probes 100 MHz, 1:1/10:1 575 231<br />
1 Analog multimeter C.A. 406 531 16<br />
2 Sets of 10 bridging plugs, black 501 511<br />
1 Cable pair, black, 100 cm 501 461<br />
Additionally recommended<br />
1 XY-Yt recorder e.g. 575 663<br />
Training objectives:<br />
Distinguish between modulation and linear<br />
superpositioning.<br />
The investigation of line spectra in AM.<br />
The AM as linear modulation (normal position and<br />
inverted position of sidebands)<br />
The bandwidth requirement for AM<br />
<strong>Amplitude</strong> deviation and modulation index are determined.<br />
The residual carrier can be measured out.<br />
Synchronous demodulation is investigated.<br />
Problems regarding carrier recovery in synchronous<br />
demodulation are looked at in detail.<br />
The dynamic characteristic of the output signal at<br />
the ring modulator is investigated.<br />
The frequency-periodic structure of the output<br />
spectra at a ring modulator can be recognized.<br />
28
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
5 Double Sideband AM<br />
OSL<br />
s AM<br />
1<br />
USL<br />
m/2<br />
s C<br />
f C<br />
(f)<br />
Fig. 5-1: Representation of DSB<br />
f C – f M<br />
f C + f M<br />
The features of the DSB are summarized in Fig. 5-<br />
1.<br />
s DSB<br />
(t) = [A C<br />
+ αs M<br />
(t)] cos (2π f C<br />
t) (5-1)<br />
Demodulation methods : Envelope<br />
demodulation<br />
: Synchronous<br />
demodulation<br />
Bandwidth : b = 2 · f Mmax (5-2)<br />
Application<br />
: Radio technology<br />
The DSB SC<br />
.<br />
If in (5-1) the constant component A C inside the<br />
brackets is suppressed, then we obtain:<br />
s αs t cos 2π<br />
f t<br />
= ( ) ( )<br />
DSBSC M C<br />
= α AM cos( 2π fM t) cos( 2π<br />
fC<br />
t )<br />
α AM<br />
= cos[ 2π<br />
( fC<br />
− fM<br />
) t]<br />
(5-3)<br />
2<br />
α AM<br />
+ cos[ 2π<br />
( fC<br />
+ fM<br />
) t]<br />
2<br />
The DSB SC consists of the superimposition of 2<br />
harmonic oscillations, whose frequencies f C + f M ,<br />
resp. f C – f M are in direct proximity due to the fact<br />
that f C >> f M . Therefore, the dynamic characteristic<br />
of the DSB sc is a beat. Here the side oscillations<br />
arise on account of the frequency conversion<br />
from f M to f C – f M resp. f C + f M . Since there is no<br />
carrier, the modulation depth m cannot be defined.<br />
Overmodulation is not possible. The amplitude of<br />
the modulation product s DSBSC (t) is directly proportional<br />
to the instantaneous value of the modulating<br />
signal s M (t). The upper and lower envelope curves<br />
have the abcissa as a joint reference line, instead<br />
of the positive or negative carrier amplitude. The<br />
features of the DSB SC are summarized in Fig. 5-2.<br />
Clear to be seen in the dynamic characteristic is<br />
the abrupt phase change of 180° at the zero<br />
crossover of the envelope curve.<br />
The envelope curve contains sinusoidal halfwaves<br />
of double the signal frequency.<br />
Demodulation methods<br />
: Synchronous<br />
demodulation<br />
Bandwidth : b = 2 · f Mmax (5-4)<br />
Application<br />
: Radio transmission<br />
USL<br />
s AM<br />
1<br />
LSL<br />
m/2<br />
s C<br />
f C<br />
(f)<br />
Fig. 5-2: Representation of the DSB SC<br />
.<br />
f C – f M<br />
f C + f M<br />
29
%<br />
0<br />
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Experiment procedure<br />
Assemble the experiment as specified in Fig. 5-3.<br />
Switch on the carrier. Connect the output of the<br />
function generator directly to the modulator input.<br />
Set the function generator to: sine, A M = 2 V and<br />
f M = 2 kHz.<br />
5.1 Investigations on the dynamic<br />
characteristic of the DSB<br />
5.1.1 DSB<br />
Set toggle switch to CARRIER ON setting. Display<br />
the output signal of the modulator M2 on the<br />
oscilloscope (this signal is called the modulation<br />
product) and the modulating signal s M (t) of the<br />
function generator and sketch them. (<strong>Modulation</strong><br />
product on channel 2, modulating signal on channel<br />
1 of the oscilloscope). Use Diagram 5.1.1-1.<br />
GATE<br />
1s<br />
10s<br />
0,1s<br />
0,01s<br />
TIME A-B<br />
COUNT A<br />
CHECK<br />
FUNCTION<br />
RATIO A/B<br />
PERIOD A<br />
FREQ A<br />
TTL - IN(A) TTL - IN(A)<br />
ANALOG (A)<br />
TTL - IN(B)<br />
Diagram 5.1.1-1: Dynamic (time) characteristic of the DSB<br />
signal<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output M2<br />
Shift the AF signal to the upper or lower envelope<br />
curve of the AM signal. Vary the frequency f M<br />
and the amplitude A M of the modulating signal.<br />
What do you observe?<br />
Settings on the Oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
2V/DIV<br />
2V/DIV<br />
kHz<br />
V pp<br />
=<br />
MODE<br />
OUT<br />
ATT<br />
dB<br />
20<br />
40<br />
TTL<br />
Time base<br />
Trigger<br />
200 µs/DIV<br />
s M (t)<br />
DC<br />
FUNCTION<br />
Trigger to the modulating signal s M (t). Reduce the<br />
A M signal to approx. 1 V. Determine the modulation<br />
depth m. The following applies for the modulation<br />
depth m:<br />
∆ A D d<br />
m = C −<br />
=<br />
(5.1.1-1)<br />
A D + d<br />
C<br />
+15V<br />
(+5V)<br />
I ><br />
U<br />
U<br />
Fig. 5-3: Experiment set-up for DSB<br />
I ><br />
M1<br />
0V<br />
30
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Diagram 5.1.1-2: The modulation trapezoid<br />
Where:<br />
D: Peak-to-peak value of the maximum of the<br />
AM signal<br />
d: Peak-to-peak value of the minimum of the<br />
AM signal.<br />
Use Diagram 5.1.1-1 to determine m. Distortion<br />
can only be detected with difficulty when determining<br />
the modulation depth directly from the modulated<br />
signal. A better approach is to determine m<br />
from the modulation trapezoid. For this the oscilloscope<br />
is operated in XY modus and the message<br />
signal s M (t) is used for horizontal deflection. The<br />
result obtained on the screen is a trapezoid which<br />
opens to the left. Sketch the modulation trapezoid<br />
in Diagram 5.1.1-2.<br />
Explain how the modulation trapezoid is generated.<br />
5.1.2 DSB SC<br />
Set the toggle switch to CARRIER OFF. Set the<br />
oscilloscope as specified in the Table.<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / external<br />
2V/DIV<br />
2V/DIV<br />
200 µs/DIV<br />
mod. signal<br />
Proceed as described under point 5.1.1. Use Diagram<br />
5.1.2-1. What is this kind of signal called?<br />
What characteristics does it have? Display the<br />
modulation trapezoid im Diagram 5.1.2-2, assess<br />
the modulation distortion. Repeat the experiment.<br />
This time feed the modulating signal s M (t) via the<br />
LP filter in modulator M2. Vary f M . What do you<br />
observe?<br />
Diagram 5.1.2-1: Dynamic characteristic of the DSB SC<br />
signal<br />
Diagram 5.1.2-2: The modulation trapezoid<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output M2<br />
5.2 Spectrum of the DSB<br />
5.2.1 DSB<br />
Set the toggle switch to the CARRIER ON position.<br />
Set the spectrum analyzer as shown in the<br />
Table.<br />
V 1 :1<br />
V 2 :10<br />
SPAN/kHz:1.5 ... 20<br />
Analyzer settings<br />
f r /kHz: 50 b/Hz: 100<br />
T/s:40<br />
Connect its input to the output of the modulator<br />
M2. Use a sinusoidal signal with A M = 2 V and<br />
f M = 2 kHz as the modulating signal s M (t). Feed<br />
the modulating signal into the input filter of the CF<br />
transmitter. Measure the AM spectrum in the<br />
range from approx. 15 kHz up to 25 kHz. Enter the<br />
measurement values S(n) from the output of the<br />
analyzer with the corresponding frequencies in<br />
31
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Table 5.2.1-1. The amplitude values of the desired<br />
spectral components are obtained from:<br />
S<br />
AM<br />
S(n)<br />
(n) =<br />
V ⋅ V<br />
1 2<br />
Calculate the spectral components S AM (n) with the<br />
aid of (3-8). Also enter the calculated values for<br />
S AM (n) into Table 5.2.1-1. Plot the curve of the<br />
AM spectrum in a graph. Mark the lower and upper<br />
sidelines appropriately with LSL and USL.<br />
Repeat the experiment for s M (t): Sinusoidal, A M =<br />
1 V and f M = 3 kHz. Feed the modulating signal<br />
s M (t) directly into the modulator M2 (why?). Keep<br />
the analyzer settings unchanged. Use Table 5.2.1-<br />
2 and Diagram 5.2.1-2.<br />
Table 5.2.1-1: DSB spectrum<br />
Signal parameter Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
Table 5.2.1-2: DSB spectrum<br />
Signal parameter Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
Measurements<br />
Theory<br />
Measurements<br />
Theory<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
Diagram 5.2.1-1: DSB spectrum<br />
Diagram 5.2.1-2: DSB spectrum<br />
32
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Compare the results. How does the USL respond<br />
as a function of the signal frequency f M ? What<br />
about the LSL? What is the frequency response of<br />
the LSL and USL? Determine the transmission<br />
bandwidth of the AM signal based on the measurements.<br />
Generalize your results for a randomly taken<br />
modulating signal. Determine the modulation<br />
depth m from the various spectra.<br />
5.2.2 DSB SC<br />
Set the toggle switch to CARRIER OFF. Use a<br />
sinusoidal signal with A M = 2 V and f M = 2 kHz as<br />
a modulating signal. Measure the spectrum as in<br />
point 5.2.1. Enter all your results in Table 5.2.2-1<br />
and Diagram 5.2.2-1.<br />
Table 5.2.2-1: DSB SC Spectrum<br />
Signal parameter<br />
Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
s AM<br />
f g f C – f g f C f C + f g<br />
Fig. 5.2-1:<br />
AM for randomly taken spectrum of the<br />
modulating signal.<br />
5.2.3 The AM spectrum for modulation with<br />
a square-wave signal<br />
The AM spectrum is linear. For that reason we<br />
can draw direct conclusions as to the AM spectrum<br />
based on our knowledge of the spectrum of<br />
the input signal. Now let us assume that the input<br />
signal s(t) consists of a frequency mix, whose<br />
spectrum S(f) is shown in Fig. 5.2-1. What should<br />
the corresponding AM spectrum look like?<br />
Repeat the recording of the spectrum for a modulating<br />
square-wave signal with A M = 2 V and<br />
f M = 2.0 kHz. Feed the square-wave signal directly<br />
into the modulator M2. Use Table 5.2.3-1.<br />
Display the spectrum in Diagram 5.2.3-1. Elucidate<br />
your findings.<br />
f<br />
V 2<br />
f<br />
KHz<br />
Measurements<br />
S( n)<br />
Name<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
V<br />
V 1 :2<br />
V 2 :1<br />
Analyzer settings<br />
f r /kHz: 50 b/Hz: 100<br />
SPAN/kHz: 1 ... 25<br />
T/s:40<br />
Diagram 5.2.2-1: DSB SC<br />
spectrum<br />
33
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
V 2<br />
Table 5.2.3-1: AM spectrum for<br />
square-wave modulation<br />
Signal parameter<br />
f<br />
KHz<br />
Measuerements<br />
Name<br />
S( n)<br />
V<br />
Analyzer settings<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
V<br />
5.3 AM demodulation (synchronous<br />
demodulation)<br />
5.3.1 DSB<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / external<br />
1 V/DIV<br />
1 V/DIV<br />
200 µs/DIV<br />
s M (t)<br />
Start with the settings from point 5.1. Set the phase<br />
controller on the CF transmitter to far left limit.<br />
Feed the DSB signal from the output of the<br />
modulator M2 directly into the demodulator D2<br />
(do not use channel filter CH2!) Using a connecting<br />
lead feed the carrier signal (f C = 20 kHz) of the<br />
CF transmitter into the auxiliary carrier input of the<br />
demodulator D2. What have you achieved by this?<br />
Display the modulating signal s M (t) on the oscilloscope<br />
as well as the demodulated signal s D (t) at the<br />
output of the LP filter of the CF receiver. Sketch<br />
the curve of the modulating signal and the demodulated<br />
signal in Diagram 5.3.1-1.<br />
Tap the auxiliary carrier for the demodulator D2 in<br />
front of the phase shifter of the CF transmitter.<br />
Diagram 5.2.3-1: AM spectrum for square-wave modulation<br />
Diagram 5.3.1-1: Modulating and demodulated signal for<br />
the DSB, fixed phase relation<br />
(1): Modulating signal s M (t)<br />
(2): Demodulated signal s D<br />
(t)<br />
34
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Using the oscilloscope set the phase-shifts between<br />
the carrier of the transmitter and the carrier<br />
of the receiver as entered in Table 5.3.1-1. Measure<br />
the amplitude A D of the demodulated signal as<br />
a function of the phase φ. Complete Table 5.3.1-1.<br />
Plot the curve of A D /A Dmax in Diagram 5.3.1-1.<br />
Table 5.3.1-1: Phase response of the DSB<br />
φ<br />
degrees<br />
0<br />
18<br />
36<br />
54<br />
72<br />
90<br />
108<br />
s M (t): Sine A M = 2 V, f M = 2 kHz<br />
A D<br />
V<br />
A<br />
A<br />
D<br />
Dmax<br />
cos φ<br />
5.3.2 Carrier recovery<br />
Carrier recovery is performed in the CF receiver<br />
using a PLL circuit. The PLL circuit is a control<br />
loop whose function is to match the frequency and<br />
phase of an oscillator to the reference oscillation.<br />
Fig. 5.3.2-1 illustrates the structure of a PLL circuit.<br />
Let's assume that the input signal s 1 (t) is supplied<br />
with the frequency f 1 to the phase detector. You<br />
can be fairly certain that the VCO is not going to<br />
be so friendly as to oscillate precisely at the same<br />
frequency. So its frequency f 2 will initially differ<br />
from f 1 . At the output of the phase detector an AC<br />
voltage is generated whose frequency is equal to<br />
the difference f 2 – f 1 . This AC voltage is now supplied<br />
to the input of the VCO via the loop filter.<br />
The VCO will respond to an AC voltage at its input<br />
with a corresponding change in frequency. In<br />
turn the VCO's changing frequency is detected by<br />
the phase detector. With a little luck the PLL locks<br />
into the frequency of the input signal. The PLL<br />
corrects the VCO until the input frequency and the<br />
VCO frequency coincide. A voltage U Φ arises<br />
behind the PD based on the phase shift. This is<br />
supplied to the VCO free of interfering AC components<br />
(U F ) through the loop filter. The following<br />
relationship prevails between the control voltage<br />
U F and the frequency f VCO of the VCO:<br />
f VCO<br />
= k F<br />
· U F<br />
(5.3.2-1)<br />
Diagram 5.3.1-1:<br />
Demodulated signal A D<br />
/A Dmax<br />
as a function of the phase φ<br />
Note:<br />
The synchronous demodulation is performed<br />
according to Equation (3-11),<br />
or (3-12)<br />
The control characteristic of the VCO (CF<br />
receiver)<br />
Remove the bridging plug between the loop filter<br />
and VCO input at the PLL. Feed a variable DC<br />
voltage U 1 from the function generator into the<br />
VCO input. Use this variable DC voltage to control<br />
the frequency of the VCO. Note down your measurement<br />
results in Table 5.3.2-1. Sketch the results<br />
in Diagram 5.3.2-1.<br />
Attention: 0 V< U F<br />
< 5 V<br />
W<br />
S 1 (t)<br />
X<br />
U Φ<br />
U F<br />
Fig. 5.3.2-1:<br />
Design of a PLL<br />
1 Phase detector PD<br />
2 Loop filter LF<br />
3 VCO<br />
35
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Synchronous demodulation with the aid of a<br />
free-wheeling VCO.<br />
Table 5.3.2-1:<br />
Control characteristic of the VCO<br />
U F<br />
V<br />
0.5<br />
1.0<br />
1.5<br />
2.0<br />
2.5<br />
3.0<br />
3.5<br />
4.0<br />
f VCO<br />
kHz<br />
Option: This experiment requires a second<br />
function generator 726 961.<br />
Feed an AM signal into the input of the CF receiver.<br />
The modulating signal is harmonic and has<br />
approximately a frequency of f M = 1000 Hz. Display<br />
the signal present at the output of the receiver<br />
on the oscilloscope. Connect the counter in parallel<br />
to the output. By tuning the controlling DC voltage<br />
U F of the VCO it is possible to achieve f M = f D !<br />
Attention: the tuning has to be carried out with<br />
care! This is critical!<br />
Synchronous demodulation with the aid of a<br />
PLL-controlled VCO.<br />
Remove the cable connected to the auxilary carrier<br />
input of the demodulator D2. For this insert the<br />
bridging plug between the CARRIER RECOV-<br />
ERY and auxiliary carrier input of D2. Use now<br />
for demodulation the recovered auxilary carrier<br />
from the PLL CARRIER RECOVERY. Sketch<br />
the pilot tone of the transmitter and the recovered<br />
signal in the receiver at the output of the PLL circuit<br />
in Diagram 5.3.2-2.<br />
4.5<br />
5.0<br />
Diagram 5.3.2-1:<br />
The control characteristic of the VCO in the PLL circuit of<br />
the CF receiver<br />
Diagram 5.3.2-2:<br />
Pilot tone and recovered signal of the receiver<br />
(1): Pilot tone at the CF transmitter<br />
(2). Recovered pilot at the output of the PLL (receiver)<br />
Hint:<br />
The required auxiliary carrier oscillation is generated<br />
out of the pilot tone recovered in the PLL<br />
circuit by means of frequency division f/8. Depending<br />
on the initial state of the frequency divider<br />
this creates a fixed phase shift between the auxiliary<br />
carrier and carrier oscillation. Consequently,<br />
the demodulated signal shows an amplitude<br />
error. (For the sake of testing connect and disconnect<br />
the bridging plug in the PLL-circuit of the CF<br />
receiver and observe the amplitude of the demodulated<br />
signal.<br />
36
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Sketch the 20 kHz square-wave carrier of the<br />
transmitter at the output of the divider and the corresponding<br />
recovered signal in the receiver in Diagram<br />
5.3.2-3. Disconnect and reconnect the<br />
bridging plug at the receiver between the VCO input<br />
and the output of the loop filter on the PLL circuit.<br />
Diagram 5.3.2-3:<br />
(1): 20 kHz - carrier at the transmitter<br />
(2): The recovered auxiliary carrier at the receiver<br />
Discuss the results.<br />
5.3.3 DSB SC<br />
Demodulation<br />
Set the toggle switch to CARRIER OFF. Repeat<br />
the experiment in accordance with point 5.3.1.<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / AC<br />
2 V/DIV<br />
2 V/DIV<br />
200 µs/DIV<br />
mod. signal<br />
Summarize the requirements made on the auxiliary<br />
carrier in synchronous demodulation.<br />
5.4 Beats<br />
<strong>Modulation</strong> is only produced if the carrier s C (t) and<br />
modulating signal s M (t) are combined by a non-linear<br />
element. The following experiment describes<br />
the linear superimposition of harmonic signals. For<br />
this the carrier and the message signal are fed to a<br />
linear quadripole. This is available in the form of an<br />
summing amplifier on the CF transmitter. Set up<br />
the experiment as specified in Fig. 5-4. Use the<br />
connecting lead to feed the sinusoidal carrier of the<br />
CF transmitter (A 2 = 2 V) into an input of the output<br />
summer and feed a sine signal from the function<br />
generator with f 1 = 2.0 kHz, A 1 = 2 V into the<br />
other input. Display the addition of both signals at<br />
the output of the summing amplifier (Σ) on the oscilloscope.<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / AC<br />
2 V/DIV<br />
_____<br />
500 µs/DIV<br />
Sketch the curve of the modulating signal and the<br />
demodulated signal in Diagram 5.3.3-1. Discuss<br />
the results.<br />
Diagram 5.4-1:<br />
Additive superpositioning of 2 sinusoidal signals with the<br />
same amplitudes but very different frequencies.<br />
Sketch the signal curve in Diagram 5.4-1. Record<br />
the spectrum of the superpositioned signal at the<br />
output of the summer (summing amplifier). Use<br />
Table 5.4-1. Depict the spectrum in Diagram 5.4-<br />
2.<br />
Diagram 5.3.3-1:<br />
Modulating and demodulated signal in DSB SC<br />
(1): Demodulated signal s D (t)<br />
(2): Modulating signal s M<br />
(t)<br />
37
%<br />
0<br />
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
2 V/DIV<br />
GATE<br />
1s<br />
10s<br />
0,1s<br />
0,01s<br />
TIME A-B<br />
COUNT A<br />
CHECK<br />
FUNCTION<br />
RATIO A/B<br />
PERIOD A<br />
FREQ A<br />
TTL - IN(A) TTL - IN(A)<br />
ANALOG (A)<br />
TTL - IN(B)<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / AC<br />
______<br />
500 µs/DIV<br />
Table 5.4-1: Spectrum of a beat<br />
Signal parameter<br />
Analyzer settings<br />
A 2 : V V 1 :<br />
f 2 : kHz b : Hz<br />
f r : kHz<br />
A 1 : V T : s<br />
f 1 : kHz SPAN : kHz<br />
Measurements<br />
Theory<br />
n<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V2<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
kHz<br />
V pp<br />
=<br />
MODE<br />
OUT<br />
ATT<br />
dB<br />
20<br />
40<br />
TTL<br />
DC<br />
FUNCTION<br />
I ><br />
I ><br />
U<br />
U<br />
+15V<br />
(+5V)<br />
0V<br />
M1<br />
Fig. 5-4: Experiment set-up for beats<br />
Diagram 5.4-2: Spectrum of the beat<br />
38
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
Repeat the experiment for the message signal of<br />
f 1 = approx. 20 kHz. Sketch the result in Diagram<br />
5.4-3.<br />
Diagram 5.4-3:<br />
Additive superimposing of 2 sinusoidal signals with equal<br />
amplitudes and approx. equal frequencies<br />
Depict the spectrum in Diagram 5.4-4.<br />
Table 5.4-2: Spectrum of a beat<br />
Signal parameter<br />
Analyzer settings<br />
A 2 : V V 1 :<br />
f 2 : kHz b : Hz<br />
f r : kHz<br />
A 1 : V T : s<br />
f 1 : kHz SPAN : kHz<br />
Measurements<br />
Theory<br />
n<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V2<br />
S(n)<br />
V<br />
S(n)<br />
V<br />
Diagram 5.4-4: Spectrum of a beat<br />
39
TPS <strong>7.2.1.3</strong><br />
Double Sideband AM<br />
40
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
6 The Single Sideband AM (SSB)<br />
1<br />
m/2<br />
f C<br />
f C + f M<br />
(f)<br />
Fig. 6-1: Representation of SSB<br />
In DSB each sideband carries all of the information<br />
contents. The transmission bandwidth could<br />
thus be reduced by half, if one sideband is suppressed.<br />
It does not matter which sideband is used<br />
for transmission and which one is suppressed. The<br />
upper sideband appears in the normal position, the<br />
lower one in the inverted position. If, for example,<br />
we suppress the lower sideband in (3-8) then we<br />
obtain:<br />
s ( t) A cos 2π<br />
f t<br />
= ( )<br />
SSB C C<br />
m<br />
+ cos 2π<br />
( fC<br />
+ fM<br />
) t<br />
2<br />
[ ]<br />
(6-1)<br />
To suppress a sideband, a bandpass filter with<br />
sharp cutoff is used which only allows the desired<br />
spectral components to pass.<br />
The dynamic characteristic of SSB resembles that<br />
of the DSB SC . However the envelope curve is<br />
somewhat more distorted.<br />
Demodulation method : Synchronous demodulation<br />
Bandwidth requirement : b = f Mmax (6-2)<br />
Application<br />
: Line-bound transmission<br />
of telephone<br />
signals in frequencydivision<br />
multiplex<br />
technology<br />
The SSB with residual carrier<br />
If instead of the unattenuated carrier only a defined<br />
fraction k of the carrier amplitude is transmitted,<br />
then you obtain the SSB with residual carrier:<br />
⎡<br />
m<br />
sESB,T ( t)= ⎢ AC kcos( 2π<br />
fC<br />
t) +<br />
⎣⎢<br />
2<br />
cos[ 2π<br />
( fC<br />
+ fM<br />
) t]]<br />
Demodulation method : Synchronous demodulation<br />
Bandwidth requirement : b = f Mmax .<br />
Application<br />
: SSB radio links<br />
(6-3)<br />
The vestigial sideband AM (VSB)<br />
In message or information signals with very low<br />
frequency components bandpass filters with very<br />
sharp cutoffs are required for the filtering out of<br />
the unwanted sideband. Since this leads to phase<br />
distortion, part of the unwanted sideband is also<br />
transmitted. Then the filters used may have cutoffs<br />
which are less sharp, on the other hand, the slope<br />
characteristic has to be precisely defined (Nyquist<br />
slope).<br />
USL<br />
1<br />
m/2<br />
s C<br />
f C<br />
f C + f M<br />
(f)<br />
Fig. 6-2: SSB with residual carrier<br />
41
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
The overlapping transmission range has to run<br />
symmetrically with respect to the carrier frequency.<br />
Demodulation method : Synchronous<br />
demodulation<br />
Bandwidth requirement : f Mmax < b < 2 f Mmax<br />
Application<br />
: TV technology<br />
s<br />
f C + f M<br />
f C<br />
f C + f M<br />
(f)<br />
Experiment procedure<br />
Set up the experiment as specified in Fig. 6-4.<br />
Connect the output of the function generator directly<br />
to the AF input of the modulator M2. Set the<br />
function generator to: sinusoidal, A M = 2 V and f M<br />
= 2 kHz.<br />
6.1 Investigations on the dynamic<br />
characteristic of the SSB<br />
6.1.1 SSB RC<br />
Set the toggle switch to CARRIER ON. Display<br />
the output signal of the channel filter CH2 and the<br />
modulating signal s M (t) of the function generator<br />
on the oscilloscope and sketch the signals. (<strong>Modulation</strong><br />
product on channel 2, modulating signal on<br />
channel 1 of the oscilloscope). Use Diagram 6.1.1-<br />
1. Shift the AF signal to the upper or lower<br />
envelope curve of the AM signal. Vary the frequency<br />
f M and the amplitude A M of the modulating<br />
signal. What do you observe?<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger<br />
2 V/DIV<br />
1 V/DIV<br />
200 µs/DIV<br />
mod. signal<br />
Fig. 6-3: Filter characteristic with Nyquist slope for VSB<br />
Trigger to the modulating signal s M (t). Switch the<br />
modulating signal off. Measure the unattenuated<br />
carrier amplitude A C at the input of the channel<br />
filter, as well as the amplitude A RC of the attenuated<br />
carrier at the output of the channel filter.<br />
Calculate the ratio k = A RC /A C . Determine the carrier<br />
suppression t in dB according to (6-4):<br />
m<br />
t = 20 log (6-4)<br />
2 k<br />
6.1.2 SSB SC<br />
Set the toggle switch to CARRIER OFF. Set the<br />
oscilloscope as specified in the Table.<br />
Proceed as described in point 6.1.1. Use Diagram<br />
6.1.2-1. What features does the SSB SC signal<br />
have?<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / external<br />
2 V/DIV<br />
1 V/DIV<br />
200 µs/DIV<br />
mod. signal<br />
Diagram 6.1.1-1: Dynamic characteristic of the SSB RC<br />
Signals<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output of CH2<br />
Diagram 6.1.2-1: Dynamic characteristic of the SSB SC<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output of CH2<br />
42
%<br />
0<br />
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
6.2 Spectrum of the SSB<br />
6.2.1 SSB RC<br />
Set the toggle switch to CARRIER ON.<br />
GATE<br />
1s<br />
10s<br />
0,1s<br />
0,01s<br />
TIME A-B<br />
COUNT A<br />
CHECK<br />
FUNCTION<br />
RATIO A/B<br />
PERIOD A<br />
FREQ A<br />
TTL - IN(A) TTL - IN(A)<br />
ANALOG (A)<br />
TTL - IN(B)<br />
Analyzer settings<br />
V 1 :1<br />
V 2 :10<br />
f r /kHz: 50 b/Hz: 100<br />
SPAN/kHz:1.5 ... 20<br />
T/s:40<br />
Set the spectrum analyzer as specified in the Table.<br />
Connect its input to the output of the modulator<br />
M2. As the modulating signal use a sinusoidal<br />
signal with A M = 2 V and f M = 2 kHz. Feed the<br />
modulating signal into the input filter of the CF<br />
transmitter. Measure the SSB spectrum in the<br />
range of approx. 15 kHz up to 25 kHz and enter the<br />
measured values S(n) from the output of the<br />
analyzer with their corresponding frequencies in<br />
Table 6.2.1-1. The amplitude values of the wanted<br />
spectral components are obtained from:<br />
S<br />
AM<br />
S(n)<br />
(n) =<br />
V ⋅ V<br />
1 2<br />
Calculate the spectral components S AM (n) with the<br />
aid of (3-8). Also enter the calculated values for<br />
S AM (n) in Table 6.2.1-1. Plot the curve of the<br />
spectrum in Diagram 6.2.1-1. Label the spectral<br />
lines.<br />
Determine the transmission bandwidth of the AM<br />
signal based on the measurements. Generalize the<br />
results for the case of any modulating signals.<br />
kHz<br />
V pp<br />
=<br />
DC<br />
MODE<br />
FUNCTION<br />
OUT<br />
ATT<br />
dB<br />
20<br />
40<br />
TTL<br />
6.2.2 SSB SC<br />
Set the toggle switch to CARRIER OFF. Use a<br />
sinusoidal signal with A M = 2 V and f M = 2 kHz as<br />
a modulating signal. Measure the spectrum as described<br />
in point 6.2.1. Enter your results in Table<br />
6.2.2-1 and Diagram 6.2.2-1.<br />
Evaluate your measurement results as shown in<br />
point 6.2.1.<br />
I ><br />
I ><br />
U<br />
U<br />
+15V<br />
(+5V)<br />
0V<br />
M1<br />
Fig. 6-4: Experiment setup for SSB<br />
43
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
Table 6.2.1-1: SSB RC spectrum<br />
Signal parameter Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
Table 6.2.2-1: SSB SC spectrum<br />
Signal parameter Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
Measurements<br />
Theory<br />
Measurements<br />
Theory<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
Diagram 6.2.1-1: SSB RC<br />
spectrum f M<br />
= 2 kHz<br />
Diagram 6.2.2-1: SSB SC<br />
spectrum f M<br />
= 2 kHz<br />
6.3 SSB demodulation<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger<br />
2 V/DIV<br />
1 V/DIV<br />
200 µs/DIV<br />
mod. signal<br />
Start with the settings given in point 6.1. With the<br />
aid of a connecting lead feed the carrier signal<br />
(f C = 20 kHz) of the CF transmitter directly into<br />
the RF input of the demodulator D2. What have<br />
you achieved by this?<br />
Display the modulating signal s M (t) on the oscilloscope<br />
as well as the demodulated signal s D (t) at the<br />
output of the LP filter of the CF receiver. Sketch<br />
the curve of the modulating signal and the demodulated<br />
signal in Diagram 6.3-1. Adjust the phase<br />
between the original carrier of the transmitter and<br />
the auxiliary carrier of the receiver. What do you<br />
observe? Remove the connecting lead between<br />
the CF transmitter and the demodulator. Now for<br />
demodulation use the recovered auxilary carrier<br />
from the PLL circuit to recover the carrier. For<br />
this connect the bridging plug between CARRIER<br />
44
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
Diagram 6.3-1: Modulating and demodulated signal in SSB<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Demodulated signal s D<br />
(t)<br />
Diagram 6.3-2: Modulating and demodulated signal in<br />
SSB SC<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Demodulated signal s D<br />
(t)<br />
RECOVERY and the auxiliary carrier input of D2.<br />
Discuss your findings.<br />
Set the toggle switch to CARRIER OFF. This time<br />
repeat the experiment for SSB SC .<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger<br />
2 V/DIV<br />
1 V/DIV<br />
100 µs/DIV<br />
mod. signal<br />
45
TPS <strong>7.2.1.3</strong><br />
Single Sideband AM<br />
46
TPS <strong>7.2.1.3</strong><br />
Ring Modulator<br />
7 The Ring Modulator<br />
s M<br />
s T<br />
s M<br />
s M<br />
+<br />
–<br />
D1<br />
D3<br />
D4<br />
D2<br />
s C<br />
s C<br />
s C<br />
Fig. 7-1: Ring modulator in diode technology<br />
s AM<br />
s AM<br />
s AM<br />
Up until now the modulation process has been<br />
described as a multiplication of a harmonic carrier<br />
s C (t) with an equally harmonic message signal<br />
s M (t) using a multiplier IC (e.g. AD632). This is<br />
how the wanted modulation product is directly<br />
obtained without any undesired sidelines. However,<br />
in practice product modulators in the form of<br />
integrated circuits are of no importance because<br />
they can only be used at relatively low frequencies.<br />
Consequently, modulation is performed using discrete<br />
components with non-linear characteristics<br />
on account of the high frequencies used in communications<br />
engineering. A group of modulators important<br />
in practice is known under the name of<br />
balanced modulators. These types of balanced<br />
modulators include the push-pull and ring modulators.<br />
The response of the ring modulator can also<br />
be investigated using the training panel 736 201 CF<br />
transmitter 20 kHz. Ring modulators are generally<br />
designed with special diode and transistor<br />
concepts. An example for this is illustrated in Fig.<br />
7-1.<br />
The bipolar carrier signal s C (t) is fed into the center<br />
taps of the two symmetrical differential transformers.<br />
The diodes are supposed to perform a<br />
pure switching operation, which is triggered exclusively<br />
by the carrier amplitude. For this the<br />
carrier amplitude has to be high enough. During the<br />
positive half-oscillations of the carrier 2 diodes are<br />
fully triggered in the forward direction (D1 and<br />
D2). They function like closed switches while the<br />
two other diodes are blocked. During this period<br />
the modulating signal s M (t) fed into the transformer<br />
on the left flows through to the output<br />
transformer. In the time in which the carrier's polarity<br />
is reversed, the previously blocked diodes<br />
(D3 and D4) perform the job of transmitting the<br />
modulating signal to the output transformer. However,<br />
this time the current of the modulating signal<br />
flows in the reverse direction.<br />
A symmetrical differential transformer is needed<br />
for the carrier current to be able to switch the diodes<br />
without influencing the output signal. Its function<br />
is explained in Fig. 7-2.<br />
The total flux Φ C magnetically induced by the carrier<br />
current is equal to zero when the transformer<br />
is perfectly symmetrical. Depending on the switching<br />
state of the diode pairs the current of the modu-<br />
47
TPS <strong>7.2.1.3</strong><br />
Ring Modulator<br />
s M<br />
i<br />
i<br />
C<br />
2<br />
C<br />
2<br />
^↑Φ<br />
^↓Φ<br />
T / 2<br />
T / 2<br />
⎫<br />
⎪<br />
⎪<br />
⎬ΣΦ<br />
⎪<br />
⎪<br />
⎭<br />
C<br />
Φ C Φ<br />
=+ −<br />
2 2<br />
C<br />
! 0<br />
0<br />
f T<br />
3 f T<br />
5 f T f<br />
Fig. 7-2: The principle of the differential transformer<br />
Fig. 7-3: Dynamic characteristic and spectrum for the ring<br />
modulator<br />
lating signal alternates its flow through the output<br />
transformer. The transformers have to be suitable<br />
to process radio frequencies (RF). For that reason<br />
ferrite is used as the core material. Earlier ring<br />
modulators were manufactured exclusively with<br />
differential transformers. Today they are being<br />
overtaken more and more by ICs which operate<br />
without transformers. Fig. 7-3 shows the dynamic<br />
characteristic and the spectrum at the output of the<br />
ring modulator. The AF signal is cancelled out in<br />
the envelope of the modulated signal. Therefore,<br />
the line at f = f M is missing in the spectrum<br />
The following holds true for the spectrum of the<br />
ring modulator:<br />
4<br />
1<br />
1<br />
sAM t [cos 2π fCt cos 2π3fCt cos 2π5fCt<br />
π<br />
3<br />
5<br />
( ) = ( ) − ( ) + ( )<br />
−+ ...] A cos( 2π<br />
f t)<br />
M<br />
M<br />
2<br />
2<br />
= AM cos[ 2π<br />
( fC − fM ) t]+ AM cos 2π<br />
( fC + fM<br />
) t<br />
π<br />
π<br />
[ ]<br />
2<br />
2<br />
− AM cos[ 2π<br />
( 3fC − fM<br />
) t]−<br />
AM cos 2π ( 3 fC + fM<br />
) t<br />
3π<br />
3π<br />
+−<br />
[ ]<br />
(7-2)<br />
If you consider the spectrum of the ring modulator,<br />
it becomes clear that suitable filters have to be<br />
used to separate the wanted sidebands from the<br />
interfering sidebands.<br />
Questions<br />
7.1 What features does the ring modulator have?<br />
7.2 What circuit techniques and measures are<br />
additionally required, if you want to generate a<br />
narrow band AM signal with a balanced<br />
modulator?<br />
7.3 Which feature is common to all modulating<br />
components?<br />
48
TPS <strong>7.2.1.3</strong><br />
Ring Modulator<br />
+15V<br />
(+5V)<br />
kHz<br />
V<br />
pp<br />
=<br />
DC<br />
%<br />
I ><br />
FUNCTION<br />
MODE<br />
ATT<br />
dB<br />
OUT<br />
0,1s<br />
0,01s<br />
GATE<br />
1s<br />
10s<br />
U<br />
0<br />
20<br />
40<br />
U<br />
FUNCTION<br />
I ><br />
RATIO A/B<br />
PERIOD A<br />
FREQ A<br />
TIME A-B<br />
COUNT A<br />
CHECK<br />
M1<br />
TTL<br />
TTL - IN(A)<br />
TTL - IN(A)<br />
0V<br />
TTL - IN(B)<br />
ANALOG (A)<br />
Fig. 7-4:<br />
Experiment setup to examine signal characteristics at the ring modulator<br />
Experiment procedure<br />
Operating the CF transmitter as a ring<br />
modulator<br />
Set up the experiment as specified in Fig. 7-4 auf.<br />
Set the toggle switch to CARRIER OFF. Use the<br />
bridging plug to feed the square-wave carrier into<br />
the RF input of the modulator. Feed a sinusoidal<br />
signal with f M = 2.0 kHz and A M = 2 V as the<br />
modulating signal into the AF input of the modulator.<br />
7.1 Dynamic response of the ring<br />
modulator<br />
Display the modulating AF signal and the output<br />
signal of the modulator on the oscilloscope. Sketch<br />
the signal in Diagram 7.1-1.<br />
Diagram 7.1-1: Dynamic characteristic of the modulating<br />
and modulated signal (CARRIER OFF)<br />
(1): Modulating signal s M (t)<br />
(2): Modulated signal<br />
Settings on the oscilloscope<br />
Input attenuator channel 1<br />
Input attenuator channel 2<br />
Time base<br />
Trigger / AC<br />
1 V/DIV<br />
1 V/DIV–––<br />
200 µs/DIV<br />
mod. signal<br />
Note: The use of a storage oscilloscope simplifies<br />
this procedure. If only a real time oscilloscope<br />
is available, you have to trigger to the<br />
AF signal and, if necessary, carefully adjust<br />
its frequency, in order to obtain a standing<br />
image.<br />
Repeat the experiment with CARRIER ON.<br />
Diagram 7.1-2: Dynamic characteristic of the modulating<br />
signal and modulated signal (CARRIER ON)<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Modulated signal<br />
49
TPS <strong>7.2.1.3</strong><br />
Ring Modulator<br />
7.2 Spectrum at the output of the ring modulator<br />
CARRIER OFF! Record the spectrum of the<br />
modulation product at the output of the modulator<br />
M2 in the range 0.5 kHz...100 kHz.<br />
Analyzer settings<br />
V 1 :2<br />
V 2 :2<br />
f r /kHz: 200 b/Hz: 500<br />
SPAN/kHz: 1 ... 25 T/s:40<br />
Table 7.2-1: Spectrum of the ring modulator<br />
Signal parameter Analyzer settings<br />
A C : V V 1 :<br />
f C : kHz b : Hz<br />
f r : kHz<br />
A M : V T : s<br />
f M : kHz<br />
Note:<br />
In the frequency range f r =200 kHz you<br />
will not come that far under f min = 10<br />
kHz. Consequently, you will have to<br />
measure the lower frequency range<br />
from approx. 0.5 kHz...10 kHz separately<br />
in the range f r = 20 kHz. For this<br />
use Table 7.2-1.<br />
V 2<br />
f<br />
KHz<br />
Measurements<br />
S( n)<br />
Name<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
V<br />
Plot the spectrum in a graph in Diagram 7.2-1.<br />
Sketch the position of the suppressed carrier lines<br />
with a dashed line.<br />
Diagram 7.2-1: Spectrum of the ring modulator<br />
50
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
Solutions<br />
2.3 A measurement example<br />
1. Manual operation with analog voltmeter<br />
The amplitude S R (1) of the fundamental harmonic<br />
is greater than the square-wave amplitude A R by a<br />
factor 4/π = 1.27. The formation law for the spectrum<br />
of a symmetrical square-wave signal is:<br />
S<br />
R<br />
4 AR<br />
( n)<br />
=<br />
π ( 2n<br />
−1)<br />
n: 1, 2, 3...<br />
Diagram 2.3-1:<br />
Spectrum of the square-wave signal A R<br />
= 5 V, τ/T P<br />
= 0.5<br />
Table 2.3-1: Spectrum square wave signal<br />
Signal parameter<br />
A R : 5 V<br />
τ/T P : 5/10<br />
f R : 2.00 kHz<br />
n<br />
f<br />
kHz<br />
Analyzer settings<br />
V 1 : 1<br />
b : 500 Hz<br />
f r : 20 kHz<br />
T : 20 s<br />
Measurement<br />
S(n) S R (n)<br />
V 2<br />
V<br />
V<br />
Theory<br />
S (n)<br />
R<br />
V<br />
1 2.0 6.6 1 6.6 6.37<br />
2 4.0 ---- - ---- ----<br />
3 6.0 2.1 1 2.1 2.12<br />
4 8.0 ---- - ---- ----<br />
5 10.0 6.6 5 1.32 1.27<br />
6 12.0 ---- - ---- ----<br />
7 14.0 4.7 5 0.94 0.91<br />
8 16.0 ---- - ---- ----<br />
9 18.0 3.6 5 0.72 0.71<br />
10 20.0 ---- - ---- ----<br />
2. Automatic operation with the XY recorder<br />
or the storage oscilloscope<br />
The reduction in the bandwidth b narrows the<br />
spectral window. The manual frequency setting<br />
thus becomes increasingly difficult, while at the<br />
same time the spectral lines become clearer.<br />
Even when using an oscilloscope as a display unit<br />
which operates (almost) without any inertia, the<br />
spectrum is no longer reproduced with full amplitude.<br />
The reason for this lies in the time law of<br />
electrical communications engineering. The filters<br />
of the analyzer no longer reach the transient<br />
recovery state. If mechanical measuring instruments<br />
subject to inertia are used as display units,<br />
e.g. a multimeter instrument or an XY recorder,<br />
then the lowpass response of the entire system is<br />
further improved. There is practically no pointer<br />
deflection. The following general statements can<br />
be made about the spectrum of the symmetrical<br />
square-wave signal:<br />
– The spectrum has a line structure.<br />
– The spectral lines occur at odd numbered multiples<br />
of the fundamental frequency f R . (3 f R ,<br />
5 f R , 7 f R , ...)<br />
– The amplitudes S R (n) respond inversely proportional<br />
to the odd numbered multiples of the<br />
fundamental frequency.(1/3, 1/5, 1/7, ...). The<br />
envelope curve has the characteristic 1/f.<br />
51
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
3 Review of amplitude modulation<br />
Answers<br />
3.1 <strong>Modulation</strong> means the frequency conversion<br />
of an information signal from the AF position<br />
of the baseband into the RF band of the<br />
carrier. Here, the modulating signal<br />
influences an appropriate parameter of the<br />
carrier oscillation, e.g. the amplitude or frequency.<br />
While f C >> f M always holds true in<br />
modulation, mixing entails frequency<br />
conversion being generated between signals<br />
with comparable frequencies.<br />
3.2 <strong>Modulation</strong> offers the following advantages:<br />
– Matching to the features of the transmission<br />
channel, i.e. improved efficiency<br />
during transmission of information signals.<br />
– Multiple utilization of transmission channels,<br />
e.g. in frequency multiplexing<br />
methods.<br />
– Improved signal-to-noise ratios (modulation<br />
gain)<br />
3.3 The DSB is something "new" produced by<br />
combining the carrier oscillation and the<br />
modulating signal. While the dynamic characteristic<br />
of the AM signal can be observed<br />
as a whole on the oscilloscope the spectrum<br />
analyzer shows the AM broken down into its<br />
components. With constant modulation<br />
signal these components have amplitudes<br />
contstant with respect to time.<br />
3.4 In the dynamic characteristic of the beat a<br />
phase shift of 180° arises in the envelope<br />
curve. The frequency of the envelope curve<br />
is approx. half the differential frequency of<br />
the oscillation components involved. The<br />
beat frequency corresponds to the arithmetic<br />
mean value.<br />
3.5 The amplitude deviation ∆A C indicates the<br />
maximum change permissible for the carrier<br />
amplitude A C . It is dependent on the<br />
modulator constant α and the amplitude A M<br />
of the modulating signal. The modulation<br />
index m is the quotient formed out of the<br />
amplitude deviation and the carrier amplitude.<br />
The modulation index m can assume<br />
values between 0 and 1. Overmodulation<br />
occurs for m > 1.<br />
3.6 In addition to envelope demodulation, synchronous<br />
or coherent demodulation are<br />
common demodulation methods particularly<br />
in commercial communications systems. In<br />
contrast to envelope demodulation, it requires<br />
an auxiliary carrier which is stable in<br />
terms of frequency, phase and amplitude.<br />
3.7 The reduction in carrier power means an<br />
improvement in the transmission efficiency.<br />
The amount of power and amplifier circuitry<br />
in the transmitter can be reduced.<br />
Bandwidth is saved by limiting modulation to<br />
one sideband. However, coherent demodulation<br />
becomes problematic when the carrier<br />
is completely suppressed. For that reason a<br />
residual carrier is transmitted with which the<br />
receiver is synchronized.<br />
3.8 The following applies for the efficiency η:<br />
useful power<br />
η =<br />
total power<br />
Expressed by the modulation index m the<br />
following holds true:<br />
η =<br />
m 2<br />
2+ m 2<br />
For the maximum modulation index<br />
m = 100% you obtain the best efficiency of<br />
the DSB when η = 33%! Regarding the<br />
power needed in DSB at least 2/3 is “squandered”<br />
in the carrier. Since the carrier contains<br />
no information it can be suppressed to<br />
increase the efficiency.<br />
3.9 Methods of carrier suppression<br />
– Suppress the carrier using a bandpass filter<br />
with very sharp cutoffs.<br />
– Addition of a carrier in phase opposition<br />
and of equal amplitude to the modulated<br />
signal.<br />
– Use of a modulation method which does<br />
not permit the carrier to reach the modulation<br />
product, e.g. balanced or ring<br />
modulator.<br />
3.10 Here only coherent demodulation still constitutes<br />
a viable alternative. For this an auxiliary<br />
oscillation is needed in the receiver,<br />
which is in agreement with the original carrier<br />
in terms of frequency and phase and<br />
whose amplitude remains constant.<br />
52
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
5 The Double Sideband AM<br />
Experiment results<br />
5.1 Investigating the dynamic characteristic<br />
of the DSB<br />
5.1.1 DSB<br />
modulation signal. At the same time the amplitude<br />
of the modulated signal drops. Consequently in XY<br />
display modus a trapezoid is produced which the its<br />
broad side on the left.<br />
5.1.2 DSB SC<br />
Diagram 5.1.1-1: Dynamic characteristic of the DSB signal<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output M2<br />
The envelope curve of the AM signal nearly coincides<br />
completely with the modulating signal and<br />
immediately follows its changes in frequency and<br />
amplitude.<br />
Diagram 5.1.2-1: Dynamic characteristic of the DSB SC<br />
signal<br />
(1): Modulating signal s M (t)<br />
(2): <strong>Modulation</strong> product at output M2<br />
The DSB SC signal has the characteristic of a beat,<br />
i.e. it is the linear superpositioning of 2 harmonic<br />
oscillations with very close frequencies. The envelope<br />
curve of the beat shows zero crossings. There<br />
the beat signal experiences phase shifts of 180°.<br />
Also the DSB SC signal follows the frequency<br />
changes of the AF signal without any visible phase<br />
delay. There is no overmodulation caused by<br />
amplitude changes in the modulating signal, as in<br />
the case of DSB.<br />
The modulation trapezoid for DSB SC<br />
.<br />
Diagram 5.1.1-2: The modulation trapezoid<br />
m D − d 65 . − 2<br />
= ≈ ≈ 53%<br />
D+<br />
d 65 . + 2<br />
The modulation index amounts to approx.<br />
m = 53%. Observation: the trapezoid chords are<br />
distorted "cigar-shaped". This is an indication for a<br />
phase shift between the signals at the X and Y<br />
input. These kinds of distortions can scarcely be<br />
seen in Diagrams like 5.1.1-1.<br />
Generating the modulation trapezoid<br />
Oscilloscope set to XY mode. Set the coordinate<br />
origin in the middle of the screen using the X-position<br />
and Y-position controllers. If the modulating<br />
AF signal reaches its negative maximum value,<br />
then the X-deviation is at the far left. From there it<br />
increases horizontally to the right with a rising<br />
Diagram 5.1.2-2: The modulation trapezoid<br />
Observations:<br />
In the display of the modulation trapezoid in XY<br />
mode Lissajous figures appear resembling a double<br />
conic section depending on the modulation frequency<br />
f M . These figures rotate as a function of<br />
the frequency f M . The modulation trapezoid is bet-<br />
53
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
ter suited for the assessment of moduation distortions<br />
than direct display of the modulated signal in<br />
YT modus. Between the modulating and the<br />
modulated signal there arise, e.g. severe phase<br />
delay distortions, if the modulation is performed<br />
using the LP filter connected in series. These visible<br />
distortions on the oscilloscope are frequencydependent.<br />
They belong to the group of linear distortions<br />
and are caused by the phase response of<br />
the electronic components (especially the LP filter).<br />
5.2 Spectrum of the DSB<br />
5.2.1 DSB<br />
Table 5.2.1-1: DSB spectrum<br />
Signal parameter Analyzer settings<br />
A C : 2.0 V V 1 : 2<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2.0 V T : 40 s<br />
f M : 2 kHz<br />
Table 5.2.1-2: DSB spectrum<br />
Signal parameter Analyzer settings<br />
A C : 2.0 V V 1 : 2<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 1 V T : 40 s<br />
f M : 3 kHz<br />
Measurements<br />
Theory<br />
Measurements<br />
Theory<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
2 18.00 LSL 4,5 1.1 1<br />
2 20.01 carrier 8.5 2.1 2<br />
2 22.01 USL 4.5 1.1 1.00<br />
2 17.00 LSL 2.1 0.52 0.5<br />
2 20.01 carrier 8.4 2.2 2.00<br />
2 23.01 USL 2.2 0.55 0.50<br />
Diagram 5.2.1-1: DSB spectrum<br />
Diagram 5.2.1-2: DSB spectrum<br />
With f M = 3 kHz the frequency of the modulating<br />
signal s M (t) already lies in the cutoff range of the<br />
LP filter. For that reason using a filter can lead to<br />
the attenuation of the amplitude at the modulator<br />
input and thus to a reduction in the modulation<br />
index.<br />
From the spectra it follows that:<br />
– With increasing signal frequency f M the<br />
USLs are shifted away from the carrier in<br />
the direction of higher frequencies. This frequency<br />
response of the USL is called the<br />
normal position, high signal frequencies also<br />
lie in the modulation spectrum at high<br />
frequencies.<br />
– With increasing signal frequency f M the LSLs<br />
shift further away from the carrier into the<br />
lower frequencies. The frequency response<br />
of the LSLs is thus called the inverted position<br />
54
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
because high signal frequencies lie in the<br />
modulation spectrum at low frequencies.<br />
Basically the following applies: The upper<br />
sideband is in the normal position, the lower<br />
sideband is in the inverted position.<br />
The modulation index m amounts to approx. 60%.<br />
Calculate the transmission bandwidths in DSB<br />
based on the spectra. For f M = 2 kHz:<br />
b = (22 – 18) kHz = 4 kHz = 2 · f M<br />
.<br />
For f M = 3 kHz:<br />
b = (23 – 17) kHz = 6 kHz = 2 · f M<br />
.<br />
In general:<br />
b = 2 f Mmax<br />
(3-9)<br />
5.2.3 The AM spectrum for modulation with a<br />
square-wave signal<br />
5.2.2 DSB SC<br />
Signal parameter Analyzer settings<br />
Table 5.2.2-1: DSB SC spectrum<br />
Signal parameter Analyzer settings<br />
A C : 2.0 V V 1 : 2<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2.0 V T : 40 s<br />
f M : 2 kHz<br />
V 2<br />
f<br />
KHz<br />
Measurement<br />
S( n)<br />
Name<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
2 18.00 LSL 4.5 1.1 1.00<br />
2 ____ ____ ____ ____ _____<br />
2 22.01 USL 4.5 1.1 1.00<br />
V<br />
V 2<br />
Table 5.2.3-1: AM spectrum for<br />
square-wave modulation<br />
A C : 2 V V 1 : 2<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2 V T : 40 s<br />
f M : 2 kHz<br />
f<br />
KHz<br />
Measurement<br />
Name<br />
S( n)<br />
5 10 LSL 3 3.2 0.32<br />
5 14 LSL 2 5,0 0.50<br />
2 18 LSL 1 5.6 1.40<br />
2 20 carrier 8.4 2.10<br />
2 22 USL 1<br />
5.5 1.38<br />
5 26 USL 2<br />
4.6 0.46<br />
5 30 USL 3 2.7 0.27<br />
5 34 USL 4 2.0 0.20<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
V<br />
Diagram 5.2.2-1: DSB SC<br />
spectrum<br />
Diagram 5.2.3-1: AM spectrum for square-wave modulation<br />
55
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
The USL 1 is taken as a reference for the calculation<br />
of the spectrum. Corresponding to the known<br />
characteristic curve of the square-wave spectrum<br />
the LSL and USL have to be located symmetrically<br />
to the suppressed carrier, where the amplitudes<br />
decrease inversely to the ordinal number n. The<br />
deviations between the theory and the measurements<br />
increase with rising frequency due to the finite<br />
upper frequency cutoff of the modulator IC.<br />
Transmission bandwidth based on the spectrum<br />
b = (22.01 – 18.00) kHz ≈ 4 kHz = 2 f M<br />
.<br />
The following is true in the general case of a modulating<br />
signal with the maximum frequency limit<br />
f Mmax :<br />
b = 2 f Mmax<br />
(3-9)<br />
5.3 AM demodulation<br />
(synchronous demodulation)<br />
5.3.1 DSB<br />
Table 5.3.1-1: Phase response of the DSB<br />
s M (t): Sine A M = 2 V, f M = 2 kHz<br />
φ<br />
degrees<br />
A D<br />
V<br />
A<br />
A<br />
D<br />
Dmax<br />
cos φ<br />
0 2.1 1.00 1.00<br />
18 1.9 0.91 0.95<br />
36 1.6 0.79 0.81<br />
54 1.1 0.55 0.59<br />
Diagram 5.3.1-1: Modulating and demodulated signal with<br />
DSB, fixed phase relation<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Demodulated signal s D<br />
(t)<br />
72 0.6 0.28 0.31<br />
90 0.13 0.06 0.00<br />
108 0.76 0.37 –0.31<br />
Observation:<br />
With the exception of a constant amplitude factor<br />
the modulating signal s M (t) and the demodulated<br />
signal s D (t) are in agreement.<br />
Diagram 5.3.1-1:<br />
Demodulated signal A D /A Dmax as a function of the phase φ<br />
56
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
5.3.2 Carrier recovery<br />
Table 5.3.2-1:<br />
Control characteristic of the VCO<br />
U F<br />
V<br />
f VCO<br />
kHz<br />
0.5 0.0<br />
corresponds precisely to the frequency difference<br />
between the carrier and the auxiliary oscillation.<br />
The frequency shift in the demodulated signal disappears<br />
completely for f C = f Aux .<br />
Synchronous demodulation with the aid of a<br />
PLL-controlled VCO.<br />
1.0 0.0<br />
1.5 0.3<br />
2.0 14.5<br />
2.5 41.3<br />
3.0 69.1<br />
3.5 96.3<br />
4.0 121.8<br />
4.5 148.7<br />
5.0 167.5<br />
Diagram 5.3.2-2:<br />
(1): Pilot tone at the CF transmitter<br />
(2): Recovered pilot at the output of the PLL (receiver)<br />
After lock-in of the PLL the original pilot signal<br />
and the recovered signal have exactly the same<br />
frequency. A fixed phase-shift occurs between<br />
the two signals. This leads to a (constant)<br />
amplitude error during synchronous demodulation.<br />
Diagram 5.3.2-1: The control characteristic of the VCO in<br />
the PLL circuit of the receiver<br />
The synchronous demodulation is performed<br />
with the aid of a free-wheeling VCO.<br />
In the demodulated signal a constant frequency<br />
shift occurs for f C ≈ f Aux . This is maintained during<br />
variation of the signal frequency f M . It is only dependent<br />
on the control voltage U F of the VCO,<br />
which determines the frequency f Aux of the auxiliary<br />
carrier. The frequency phase-shift between<br />
the modulating signal and the demodulated signal<br />
Diagram 5.3.2-3:<br />
(1): 20 kHz original carrier at the transmitter<br />
(2): The recovered auxiliary carrier at the receiver<br />
A fixed phase-shift exists between the two carriers.<br />
This phase-shift can assume 8 various values<br />
due to the undefined starting conditions of the frequency<br />
divider (f/8). These phase-shifts are associated<br />
with amplitude errors in the demodulated<br />
signal.<br />
57
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
5.3.3 DSB SC<br />
demodulation<br />
Table 5.4-1: Spectrum of a beat<br />
Signal parameter<br />
Analyzer settings<br />
A 2 : 2 V V 1 : 5<br />
f 2 : 20.0 kHz b : 500 Hz<br />
f r : 50 kHz<br />
A 1 : 2 V T : 20 s<br />
f 1 : 2 kHz SPAN: 1...25 kHz<br />
Diagram 5.3.3-1: Modulating and demodulated signal for<br />
DSB SC<br />
(1): Demodulated signal s D<br />
(t)<br />
(2): Modulating signal s M<br />
(t)<br />
The DSB SC shows the same phase-dependency as<br />
the DSB<br />
Requirements for the auxiliary carrier in synchronous<br />
demodulation:<br />
1. Frequency stability and frequency equality<br />
with the original carrier frequency.<br />
2. Constant phase angle < 90°. Ideally φ€= 0°.<br />
3. <strong>Amplitude</strong> stability of the auxiliary carrier<br />
n<br />
f<br />
KHz<br />
Measurement<br />
Name<br />
S( n)<br />
V2<br />
S AM (n)<br />
Theory<br />
1 2 10.5 2.1 2<br />
1 20 10.5 2.1 2<br />
V<br />
S AM (n)<br />
V<br />
5.4 Beats<br />
Diagram 5.4-2: Spectrum of the beat<br />
Diagram 5.4-1: Additive superpositioning of 2 sinusoidal<br />
signals with the same amplitudes but very different<br />
frequencies.<br />
Linear superpositioning of 2 harmonic signals, here<br />
with extremely different frequencies f 1 = 2.0 kHz<br />
and f 2 = 20 kHz, generates a beat. The two<br />
frequency components are easily distinguishable.<br />
There is no frequency conversion for beats<br />
Diagram 5.4-3: Additive superimposing of 2 sinusoidal<br />
signals with the same amplitudes and almost the same<br />
frequencies.<br />
58
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
If harmonic signals with approximately the same<br />
frequencies are additively superimposed, then the<br />
beat takes on a totally different appearance.<br />
f 1 = 20.01 kHz<br />
f 2 = 20.03 kHz<br />
Table 5.4-2: Spectrum of a beat<br />
Signal parameter<br />
Analyzer settings<br />
A 2 : 2 V V 1 : 5<br />
f 2 :20.03 kHz b : 500 Hz<br />
f r : 50 kHz<br />
A 1 : 2 V T : 20 s<br />
f 1 :20.01 kHz SPAN: 1...25 kHz<br />
Diagram 5.4-4: Spectrum of a beat<br />
Measurement<br />
Theory<br />
n<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V2<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
*<br />
*<br />
* Spectral lines cannot be resolved (discriminated)<br />
because they are packed so closely to<br />
each other.<br />
Diagram 5-4-4 shows the spectrum of a beat for<br />
f 1 ≈ f 2 . The resolution of the analyzer is too low.<br />
The closely-packed spectral lines of the beat are<br />
no longer reproduced separately. The amplitude<br />
display is invalidated.<br />
Interpretation<br />
The simple addition of the carrier and information<br />
signal is not suited for the generation of frequency<br />
conversion (modulation). Both unmodulated signals<br />
remain separate. There is no frequency shift<br />
of the AF signal into the range of higher frequencies,<br />
as is the standard case for modulation. In<br />
order to maintain modulation, the carrier and the<br />
modulating signal have to be supplied to an element<br />
with non-linear characteristic.<br />
59
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
6 The Single Sideband AM (SSB)<br />
Experiment results<br />
6.1 Investigating the dynamic characteristic<br />
of the SSB<br />
6.2 Spectrum of the SSB<br />
6.2.1 SSB RC<br />
6.1.1 SSB RT<br />
Table 6.2.1-1: SSB RC spectrum<br />
Signal parameter Analyzer settings<br />
A C : 0.32 V V 1 : 5<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2 V T : 40 s<br />
f M : 2 kHz<br />
Diagram 6.1.1-1: Dynamic characteristic of the SSB RC<br />
signal<br />
(1): Modulating signal s M<br />
(t)<br />
(2): <strong>Modulation</strong> product at the output of CH2<br />
The SSB RC signal resembles the DSB signal in<br />
terms of its dynamic characteristic.<br />
ARC<br />
045 .<br />
k = = = 021 .<br />
A 21 .<br />
C<br />
20log<br />
m<br />
t =<br />
2 k<br />
(6-4)<br />
V 2<br />
f<br />
KHz<br />
Measurement<br />
S( n)<br />
Name<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
10 18 LSL 3.0 0.06 0.00<br />
2 20 carrier 4.5 0.45 0.00<br />
2 22 USL 8.0 0.80 1.00<br />
V<br />
6.1.2 SSB SC<br />
Diagram 6.2.1-1: SSB RC<br />
spectrum f M<br />
= 2 kHz<br />
Diagram 6.1.2-1. SSB SC<br />
time characteristic<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Modulated signal s SSBsc (t)<br />
The modulated SSB SC signal is a pure sinusoidal<br />
signal when the carrier and the unwanted sideband<br />
have been completely suppressed.<br />
60
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
6.2.2 SSB sc<br />
6.3 SSB demodulation<br />
Table 6.2.2-1: SSB SC spectrum<br />
Signal parameter Analyzer settings<br />
A C : 0.32 V V 1 : 5<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2 V T : 40 s<br />
f M : 2 kHz<br />
V 2<br />
f<br />
KHz<br />
Measurement<br />
S( n)<br />
Name<br />
V<br />
S AM (n)<br />
V<br />
Theory<br />
S AM (n)<br />
10 18 LSL 3.0 0.06 0.00<br />
2 22 USL 8.0 0.80 1.00<br />
V<br />
Diagram 6.3-1: Modulating and demodulated signal in SSB<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Demodulated signal s D<br />
(t)<br />
The synchronous demodulation of a SSB RC signal<br />
provides a perfectly suitable demodulated signal.<br />
The phase-shift set by the phase controller of the<br />
CF transmitter occurs between the modulating signal<br />
s M (t) and demodulated signal s D (t). Any<br />
influence on the amplitude of the demodulated<br />
signal cannot be detected. The following applies<br />
for the demodulated signal:<br />
s<br />
D<br />
AC<br />
m<br />
( t ) = cos 2π fM<br />
t±<br />
φ<br />
4<br />
( )<br />
Diagram 6.2.2-1: SSB SC<br />
spectrum f M<br />
= 2 kHz<br />
Diagram 6.3-2: Modulating and demodulated signal for<br />
SSB SC<br />
(1): Modulating signal s M<br />
(t)<br />
(2): Demodulated signal s D (t)<br />
Also in the case of SSB signals the carrier has no<br />
influence on synchronous demodulation. It can be<br />
switched on and off at will.<br />
61
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
7 The ring modulator<br />
Answers<br />
7.1 The ring modulator provides an AM signal<br />
with carrier suppression. The line of the<br />
modulating signal is missing in the output<br />
spectrum for f = f M .<br />
7.2 In balanced modulators frequency-periodic<br />
modulation spectra are produced.<br />
Consequentily the wanted bands have to be<br />
filtered out, i.e. the interfering sidebands<br />
have to be suppressed for the sake of a narrow<br />
transmission bandwidth.<br />
7.3 All of the circuits which have been used for<br />
modulation have one feature in common: a<br />
non-linear characteristic. This is true in particular<br />
for the mixer, multiplier, ring modulators<br />
etc. A switch can be seen as a very<br />
extreme case, its characteristic has abrupt<br />
step changes.<br />
Experiment results<br />
Diagram 7.1-2: Dynamic characteristic of modulating signal<br />
and modulated signal (CARRIER ON)<br />
(1): modulating signal s M<br />
(t)<br />
(2): modulated signal<br />
7.2 Spectrum at the output of the ring modulator<br />
Table 7.2-1: Spectrum of the ring modulator<br />
Signal parameter<br />
Analyzer settings<br />
A C : V V 1 : 2<br />
f C : 20.0 kHz b : 100 Hz<br />
f r : 50 kHz<br />
A M : 2 V T : 40 s<br />
f M : 2 kHz<br />
Measurement<br />
Theory<br />
V 2<br />
f<br />
KHz<br />
Name<br />
S( n)<br />
V<br />
S AM (n)<br />
V<br />
S AM (n)<br />
V<br />
2 18 LSL2 5.20 1.30<br />
2 22 LSL1 5.30 1.32<br />
Diagram 7.1-1: Dynamic characteristic of modulating signal<br />
and modulated signal (CARRIER OFF)<br />
(1): modulating signal s M<br />
(t)<br />
(2): modulated signal<br />
2 58 USL1 1.60 0.4<br />
2 62 USL2 1.70 0.43<br />
The modulation product has a certain similarity to<br />
the PAM signal for the special case of a symmetrical<br />
duty cycle t/T P = 50%.<br />
Diagram 7.2-1: Spectrum of the ring modulator<br />
62
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
Observation:<br />
Balanced modulators have an extended amplitude<br />
spectrum. A double line appears for odd number<br />
multiples of the carrier frequency. When comparing<br />
theory with the measurement results it is conspicuous<br />
that the measured spectral amplitudes<br />
turn out to be smaller as the frequency increases.<br />
The reason for this lies in the low cutoff frequency<br />
of the modulator ICs. High frequency spectral<br />
components are more severely attenuated by the<br />
modulator than lower frequency components.<br />
When the carrier is switched on (CARRIER ON)<br />
additional lines appear for odd numbered multiples<br />
of the carrier frequency.<br />
63
TPS <strong>7.2.1.3</strong><br />
Solutions<br />
64
TPS <strong>7.2.1.3</strong><br />
Keywords<br />
Keywords<br />
AM demodulation ............................................................................................................................25<br />
amplitude deviation ..........................................................................................................................23<br />
amplitude error .................................................................................................................................57<br />
amplitude spectrum ..........................................................................................................................10<br />
auxiliary oscillation ..........................................................................................................................26<br />
baseband ...........................................................................................................................................11<br />
beat ............................................................................................................................................ 37, 59<br />
carrier frequency technology............................................................................................................24<br />
carrier recovery ................................................................................................................................20<br />
carrier suppression............................................................................................................... 42, 52, 62<br />
channel filter .....................................................................................................................................19<br />
control characteristic ........................................................................................................................35<br />
phase delay .......................................................................................................................................53<br />
demodulation, coherent ....................................................................................................................26<br />
differential transformer ....................................................................................................................47<br />
double sideband AM ........................................................................................................................29<br />
efficiency ..........................................................................................................................................52<br />
envelope curve ........................................................................................................................... 23, 29<br />
envelop curve modulation ................................................................................................................25<br />
frequency conversion .......................................................................................................................29<br />
frequency conversion .......................................................................................................................52<br />
index .................................................................................................................................................21<br />
input filter .........................................................................................................................................18<br />
interfering sideband ..........................................................................................................................48<br />
inverted position ........................................................................................................................ 24, 54<br />
line structure .....................................................................................................................................51<br />
linear distortion ................................................................................................................................54<br />
Lissajous-figure ................................................................................................................................53<br />
loop filter ................................................................................................................................... 20, 35<br />
lowpass filter ....................................................................................................................................20<br />
message signal ..................................................................................................................................10<br />
mixing ...............................................................................................................................................52<br />
modulation ........................................................................................................................................10<br />
modulation index ....................................................................................................................... 23, 53<br />
modulation product ..........................................................................................................................23<br />
modulation trapezoid ................................................................................................................. 31, 53<br />
modulator..........................................................................................................................................11<br />
modulator constant ...........................................................................................................................23<br />
multiplex signal ................................................................................................................................19<br />
normal position .......................................................................................................................... 24, 54<br />
Nyquist slope ....................................................................................................................................41<br />
original frequency band....................................................................................................................11<br />
oscilloscope ......................................................................................................................................13<br />
overmodulation .................................................................................................................................52<br />
phase change.....................................................................................................................................29<br />
phase detector ...................................................................................................................................35<br />
phase error ........................................................................................................................................26<br />
phase shift .........................................................................................................................................57<br />
phase shifter......................................................................................................................................19<br />
65
TPS <strong>7.2.1.3</strong><br />
Keywords<br />
PLL circuit........................................................................................................................................20<br />
processing of the message ................................................................................................................12<br />
product modulator ..................................................................................................................... 18, 47<br />
push-pull modulator .........................................................................................................................47<br />
relaying the message ........................................................................................................................12<br />
residual carrier ..................................................................................................................................41<br />
ring modulator ..................................................................................................................................47<br />
side oscillation ..................................................................................................................................24<br />
sideband vector .................................................................................................................................25<br />
signal, analog ....................................................................................................................................10<br />
signal, deterministic ...........................................................................................................................9<br />
signal, digital ....................................................................................................................................10<br />
signal, stochastic.................................................................................................................................9<br />
single sideband AM..........................................................................................................................41<br />
spectral domain ................................................................................................................................10<br />
spectrum analyzer .............................................................................................................................13<br />
square-wave signal ...........................................................................................................................10<br />
superheterodyne ................................................................................................................................13<br />
switching operation ..........................................................................................................................47<br />
synchronous demodulation ...............................................................................................................26<br />
synchronous demodulator ................................................................................................................20<br />
telecommunication system ...............................................................................................................12<br />
time continuous ..................................................................................................................................9<br />
time domain ......................................................................................................................................10<br />
time function ......................................................................................................................................9<br />
time law ............................................................................................................................................14<br />
time law of electrical communications engineering ........................................................................51<br />
transmission bandwith ............................................................................................................... 43, 56<br />
transmission channel ........................................................................................................................12<br />
transmission of the message.............................................................................................................12<br />
uncertainty relation ...........................................................................................................................14<br />
VCO ..................................................................................................................................................35<br />
vector diagram ..................................................................................................................................24<br />
wanted sideband ...............................................................................................................................48<br />
66