Experiment
Single and Double Sideband Amplitude Modulation
Experiment:
Single and Double Sideband Amplitude
Modulation
1 Introduction
Modulation is one of the basic principles in communications technology.
The purpose in using modulation is:
a) multiplexed operation of a transmission path,
b) transposition of the signals into a frequency band favorable for signal transfer,
c) obtaining favorable signal-to-noise ratios when source and noise power are given.
Depending upon the type of modulation, modifications can be done in
- amplitude (amplitude modulation, AM),
- phase angle (angular modulation), or
- both (quadrature-amplitude modulation ).
In detail, more distinctions can be made:
- types of amplitude modulation
double-sideband amplitude modulation suppressed carrier = linear AM, (SC-AM)
- double-sideband amplitude modulation with carrier
= DSB-AM (usual)
- single-sideband amplitude modulation without carrier
= SSB-AM (ESB-AM)
- vestigial (residual) sideband AM without carrier
= VSB-AM (RSB-AM)
- quadrature AM without carriers
= QAM
- types of angular modulation
- phase modulation
= PM
- frequency modulation = FM
In this experiment usual AM, DSB-AM and SSB-AM are treated.
1.1 Linear Amplitude Modulation
The amplitude Û of a sinusoidal carrier Û ⋅ sin (Ω0t + Φs) is modified in such a
manner that Û is a proportional to the signal s1(t), i.e.
Û → û(t) = k1 ⋅ s1 (t ) .
(1.1)
Thus the modulated signal can be written as
sM(t) == k1 ⋅ s1 (t ) ⋅ sin(Ω0 t + ΦS) .
A signal s1(t) is any function in time with a continuous spectrum [1]and k1 is a
constant
1
(1.2)
Experiment
Single and Double Sideband Amplitude Modulation
+∞
S1 (ω ) = ∫ s1 (t ) ⋅ e − jωt dt
(1.3)
−∞
The exponential form for the sine function from Eq. (1.2) is written as
1
1
sin(Ω 0 t ) = − j e jΩ0t + j e − jΩ0t ,
2
2
(l.4)
thus one receives the spectrum of the modulated signal
+∞
S M (ω ) = ∫ s M (t ) ⋅ e − jωt dt
−∞
=−j
k1
2
=−j
∫
+∞
−∞
s1 (t ) ⋅ e − j (ω −Ω 0 )t dt + j
k1
2
∫
+∞
−∞
s1 (t ) ⋅ e − j (ω + Ω0 ) t dt
k1
k
S 1 (ω − Ω 0 ) + j 1 S 1 (ω + Ω 0 ) .
2
2
(1.5)
The zero phase angle Φs of the carrier signal was assumed here to be zero. Proceeding
from signal with limited frequency band, then the amplitude spectrum from Eq. (1.5)
has for example the form represented in Fig. 1b.
Fig. 1: Amplitude spectrum
a) | S1 (ω) | : example for a band-limited signal
b) | SM (ω) | : with S1 (ω) modulated carrier
The spectral components of the carrier and the signal do not appear in the modulation
product. Sufficient information for rebuilding (or demodulating) the signal is
contained both in the upper and in the lower sideband of the modulated signal. Linear
AM therefore is also called double-sideband amplitude modulation (DSB-AM)
without carrier.
1.1.1 How to Modulate Signals
Following Eq. (1.2), linear amplitude modulation is in theory simply generated by
multiplying of the signal s1(t) with [ k1 ⋅ sin (Ω0 t)]. This means, that a modulator could
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Experiment
Single and Double Sideband Amplitude Modulation
be implemented by a multiplier circuit; its inputs have to be connected to the sine
carrier and the signal.
For high frequency applications, the implementation of linear semiconductor
multipliers causes difficulties. In some cases an approximation of the sine by a square
wave is sufficient. Using this, the modulated signal can be described as the signal
periodically reversed with the carrier frequency and multiplied by a factor. The
modulated signal then naturally contains parts in its frequency spectrum that have to
be removed by filtering.
In very high frequency applications, the semiconductor switches are implemented
using fast diodes. Such a circuit for linear AM is called a ring modulator or doublebalanced modulator. One setup for such a device is displayed within Fig. 2.
Fig. 2 Circuit diagram of a ring modulator
The amplitude of the carrier uT(t) has to be high enough to make the diodes
conducting, which means that the forward voltage of the diodes has to be exceeded. If
the amounts of the magnetic flux in the windings w2 and w3 or w4 and w5 are equal,
then no voltage is induced in windings w1 and w6. In w6 the signal s1(t) appears, only
switched in polarity in the same clock period as the carrier signal. As shown in [ 1 ],
this represents the linear modulated oscillation sM(t).
1.1.2 Synchronous or Coherent Demodulation
If the modulated signal is modulated again with the carrier
uT(t) = Û ⋅ sin(ΩE t + ΦE)
(1.6)
then the upper and lower sideband are shifted by +/-ΩE. The same occurs to the
negative upper and lower sideband. In case of ΩE = Ω0, the by -ΩE shifted upper and
lower sideband and the by +ΩE shifted negative upper and lower sideband are found
again in the baseband and add up following the cosine law. Signal components also
will be shifted around double the carrier frequency 2Ω0, which must be filtered out by
a low-pass.
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Experiment
Single and Double Sideband Amplitude Modulation
If the zero phase angles ΦS and ΦE of the carrier waves at the transmitter and receiver
are equal, then the signal s1(t) is transmitted at maximum receivable power. If the
phase angle is shifted by +/-90°, the power of the received signal reaches zero [1].
For the demodulation of the linear AM, the carrier must be supplied to the receiver,
corresponding the transmit carrier in frequency and phase. For the synchronization of
frequency and phase at the receiver, either the carrier rest or a subcarrier at a different
frequency has to be transmitted as well.
1.2 Single-sideband Amplitude Modulation (SSB-AM)
Since with linear AM the message is contained both in the lower sideband and in the
upper, the transfer of only one sideband is sufficient. This saves bandwidth in the
transfer system. Additionally, the demodulation of SSB-AM is simpler than for DSBAM without carrier.
1.2.1 How to Generate SSB-AM
For the generation of SSB-AM, DSB- AM is used, where one of the sidebands of the
modulated signal is filtered out (other procedures see [ 1 ]). Since filters are available
only with a finite edge steepness, SSB-AM can only be implemented for the signal
having a lower cut-off frequency not equal to zero. This is the case with speech
signals, where the frequency range spans from 0.3kHz < f < 3.4 kHz.
Many different filter methods can be used for the suppression of the unwanted
sideband. If a Nyquist-filter is used instead of a filter with a very good edge steepness,
the modulation method is called vestigial (residual) sideband AM. It enables the
transfer of signals with an only slightly higher bandwidth than as for example with
SSB-AM. The advantage is, that it can also carry DC voltage signals like TV video
signal.
SSB- modulation can be performed also by a so-called Hilbert-Transformer, which
flips the signal phase by - 90° for positive frequencies and + 90° for negative
frequencies. [1]. This procedure is of interest, if SSB- modulation is implemented by
digital signal processing.
1.2.2 Demodulation
Here the baseband can be recovered by modulating again with the carrier on the
receiver side.
(1.7)
uT(t) = Û ⋅ sin(ΩE t + ΦE)
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Experiment
Single and Double Sideband Amplitude Modulation
If Ω0= ΩE, the positive and negative upper and lower sideband are shifted by +/-ΩE.
Thereby the positive and negative baseband are reconstructed and additionally double
frequency components are generated. The higher frequency parts have to be removed
by appropriate filters, so that only the original signal remains. In Fig.3a, the amplitude
spectrum |SM(ω)| of the demodulated signal is represented. Only the upper sideband
was transferred. Fig. 3b shows the shift over +/-Ω with repeated linear modulation of
SSB-AM with Ω0=ΩE. The dashed line in the spectrum represents the modulated
signal which will not be contained in the spectrum |SE(ω)| of the resulting signal.
It easily can be shown that to demodulate SSB-AM the receiver only requires a carrier
with the same frequency. This means, that the carrier frequency on the receiver side
can also be produced by a separate generator (Beat Frequency Oscillator, BFO).
Fig. 3 Demodulation of SSB-AM
a) amplitude spectrum of the signal which can be demodulated
b) amplitude spectrum of the demodulated signal
With the use of vestigial sideband AM, the frequency-shifted sidebands supplement
themselves to form the baseband spectrum again, which is done by the symmetrical
copy of the sideband with the Nyquist filter edge. Obviously the important edge
symmetry requires more effort for the Nyquist filter.
1.3 Amplitude Modulation
Double sideband amplitude modulation with carrier is called (usual)AM. This
modulation is the oldest transmission method depending on a carrier-signal (Marcani,
1895) and allows very simple implementations by using nonlinear components. Long-,
medium- and short-wave broadcast uses AM due to minimal needs for the receivers.
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Experiment
Single and Double Sideband Amplitude Modulation
1.3.1 How to Generate AM Signals
The amplitude Û of a sinusoidal carrier is changed in accordance with
Û → û(t) = A0 + k1 ⋅ s1 (t ) ,
(1.8)
which means for the modulated signal
uT(t) = A0 ⋅ sin(Ω0 t + ΦS) + k1 ⋅ s1 (t ) ⋅ sin(Ω0 t + ΦS) .
(1.9)
Therefore, a carrier-frequency spectral line appears next to the two sidebands in the
spectrum. The peak value of the signal | S1 (t) | is called modulation factor m, and is
calculated by the quotient
k1 ⋅ Sˆ1
m=
.
(1.10)
A0
1.3.2 Envelope Demodulation
For m < 1, the envelope of the modulated signal sM(t) never crosses the zero line, see
Fig. 4, which permits the use of a very simple envelope detector.
Fig. 4 Envelope of AM
A rectifier cuts off the negative portions of sM(t), a low-pass smoothens high
frequency carrier components, and a high-pass eliminates the DC component A0. This
envelope demodulator can be implemented technically very easily with a diode and
RC elements, see Fig. 5.
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Experiment
Single and Double Sideband Amplitude Modulation
Fig. 5 Block diagram of an envelope detector
1.4 Description of the setup
In Fig. 6, the block diagram of the experimental setup is displayed. In the transmitter
modulator (multiplier) the signal s1(t) is linearly modulated and with a linear amplifier
magnified by factor 2.7. By substituting the band filters, both SSB-AM and DSB-AM
can be implemented. With additional amplification, the modulated signal is fed into
the transmission link. In the receiver amplifier, the transmission losses are
compensated. In the receiver modulator, the signal is demodulated where the carrier is
either taken from the transmitted signal itself and phase shifted by the phase shifting
device or is supplied separately onto the modulator. The low-pass filter on the receiver
side is suppressing the unwanted frequency band.
Fig. 6 Block diagram of the experimental setup
2 References
[1] K. Steinbuch, W. Rupprecht: Nachrichtentechnik Band I und II,
dritte, neubearbeitete Auflage, Springer-Verlag Berlin, Heidelberg, New York
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Experiment
Single and Double Sideband Amplitude Modulation
3 The Experiment
3.1 Measurement Equipment
Oscilloscope
Selective signal level meter
Level meter
Frequency generator
Frequency generator
Carrier frequency generator
loudspeaker amplifier
tape recorder
frequency counter
distortion generator
0.1Hz to 100kHz
0.1Hz to 20kHz
0.2Hz to 100kHz
20 Hz to 20kHz
20 kHz quartz-stabilized
Ri = 600Ω
3.2 Quantities in the experimental setup
The input and output resistances on the low frequency side of the experimental setup
are Ri=600 Ω; all other blocks have an input and output impedance of |Z|=150Ω. The
voltage level of the carrier signal at the transmitter- and receiver modulator is set up to
-9 dB. The carrier generator should have an internal resistance of approximately 0Ω,
and the signal generator has to have ”Ω.
3.3 Tasks
1.1) Build up the setup for DSB-AM. Use the same carrier for receiver and
transmitter. To simulate the transmission line a capacitor of 0.05µF has to be
applied.
l.2) A low frequency signal of 2 kHz and a voltage level of 0 dB is supplied to the
input of the transmission modulator. At the signal output of the receiver the
received level ( with Ri = 600Ω) has to be measured. For this, find out the optimal
adjustment of ΦE . Adjust the potentiometer at the low-pass of the receiver
amplifier at central position.
1.3) With the selective signal level meter, the residual carrier of the transmission
modulator can be measured, and has to be adjusted to the minimum. The achieved
carrier suppression in dB is to be written into a table.
1.4) Using the setup of task 1.2, the time signals at test points 1, 3, 4, 7 and 8 of the
experimental setup have to be measured with the oscilloscope. The pictures have
to be recorded and to be sketched in the block diagram of the experimental setup.
The oscilloscope is to be triggered with the LF signal via its second channel.
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Experiment
Single and Double Sideband Amplitude Modulation
1.5) The amplitude spectrum at the output of the transmission modulator has to be
recorded with a setup in accordance with task 1.2. Use a selective signal level
meter and display the result on logarithmically scaled paper (3 decades). The
result has to be described.
1.6) The amplitude spectrum of the output signal at the receiver modulator has to be
measured and displayed on logarithmically scaled paper (3 decades). Remove the
block “low-pass filter and amplifier" and insert the level meter instead(Ri=600Ω).
Then the block "low-pass filter and amplifier" has to be inserted again.
1.7) The frequency response of the entire transfer model has to be measured for a
direct connection between transmitter and receiver (no capacitor). The phase error
caused by the bandpass filter has to be compensated by adjusting the zero phase
angle ΦE of the receiver carrier. The frequency response measurement has to be
done for optimal adjustment of ΦE. The results of measurement have to be
depicted on logarithmically scaled paper.
2.1) The experiment for DSB-AM has to be built up. In addition, the receiver
demodulator has to be replaced by an envelope detector. The level of the 2 kHz
low frequency signal has to be lowered to -20 dB, and by superimposing a DC
offset at the transmission modulator, a modulation factor of approximately 0.5
has to be adjusted. As transmission circuit a direct connection between senders
and recievers is used. The receiver level has to be measured at Ri = 600Ω.
Compare the result with those of task 1.2 (discussion).
2.2) Like in task 1.4 the time signals at test points 3, 4, 7 and 8 of the experimental
setup have to be recorded.
3.1) The experimental setup for SSB-AM has to be built up. As transmission line a
direct connection between transmitter and receiver is used. The transmission
modulator is to be wired with a signal of the frequency 2 kHz and a level of 0 dB.
The receiver level is to be measured at Ri = 600Ω and compared with the result
of task 1.2.
3.2) Like in task 1.4, the time signals at test points 3, 4, 7 and 8 have to be recorded.
3.3) The frequency response of the transfer model has to be measured and drawn into
the diagram of task 1.7.
4.1) A disturbance generator has to be inserted into the transmission line in
accordance to Fig. 7.
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Experiment
Single and Double Sideband Amplitude Modulation
Fig. 7 A disturber in the transmission line
4.2) The signal-to-noise ratio (η) has to be measured for
a) SSB-AM
b) DSB-AM.
c) AM (usual), m = 0,5.
The signal-to-noise ratio η is calculated in accordance with
η = 10dB lg
PS
PN
For this, the signal power PS of the unimpaired system (disturbance “OFF”, Fig. 7) is
measured with a transmitter side wiring according to the task 1.2, 2.1 and 3.1.
Afterwards, the interference power PN in the disturbed system has to be measured
(disturbance “ON”, Fig. 7), whereby the low-frequency signal at the sender is
switched off and the transmission band filter is removed.
The signal-to-noise ratio is measured at the receiver input (test point 6) and at the
receiver output (test point 8).
4.3) The signal-to-noise ratio gain is determined between receiver input and output for
SSB -, DSB - and (usual)AM. These gains have to be compared with the
theoretical values in the references (i.e. [1]). How has the experimental setup to
be extended, so that the theoretical signal-to-noise ratio gains are obtained?
5.1) Perform an auditory test with SSB-AM without distortion. In addition the
transmitter side signal input has to be connected to the tape recorder with a
special cable. At the receiver output a loudspeaker amplifier is attached. As
transmission line a direct connection between transceiver and receiver is used.
a) the transmitter and receiver modulator use the same carrier frequency (splitting
jacks closed) and the tape recorder is started. What is observed during a phase
shift between transceiver and receiver carrier of 0°, 45°and 90°. What would be
observed for DSB-AM?
c) the splitting jack is opened and the receiver modulator is supplied by a separate
frequency generator (f = 20 kHz). After rewinding the tape the test is started again.
By slight changing the frequency of the receiver carrier (check with the frequency
counter) the influence of the frequency difference between transmitter and receiver
carrier have to be evaluated. The influence has to be described and explained.
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Experiment
Single and Double Sideband Amplitude Modulation
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Experiment
Single and Double Sideband Amplitude Modulation
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