Download Lab 1: AMPLITUDE MODULATION

TELE3013 TELECOMMUNICATION SYSTEMS 1
Lab 1: AMPLITUDE MODULATION
1. INTRODUCTION
A sinusoidal carrier (Ac cos ωc t) which is amplitude modulated by a message signal, m(t), is
represented by
s(t) = [A
[A c + m(t)] cos ω c t ,
ω c = 2π
2π f c
(1)
where Ac is the carrier amplitude, fc is the carrier frequency.
When the modulating message is also a sinusoidal signal, ie. m(t) = Am sin ωm t, ωm = 2π fm ,
the corresponding AM signal may be expressed in simple form
s(t) = A c [1 + m sin ω m t] cos ω c t,
(2)
where m is the modulation index.
2. PREPARATION
P1.
Using trigonometry write down a Fourier series representation for the AM signal with
a message as given in equation (2)
P2.
From the result in question P1 give an expression for the AM signal s(t) as the real part
of complex exponentials.
Sketch a rotating phasor diagram for s(t) using the carrier frequency as a reference.
P3.
Write down the Fourier transform of s(t) in question P1. Sketch the amplitude of the
AM signal frequency spectrum.
P4.
Determine the average power (i.e. find its mean–square value) of the AM signal
assuming it is a voltage across a 1 ohm resistor.
What is the power of each frequency components?
Determine an expression for the fraction of power in the sidebands.
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3. EXPERIMENTS
EQUIPMENT
MODULES
Audio Oscillator
Adder
Multiplier
Utilities Modules
Tuneable Low Pass Filter
QTY
1
1
2
1
1
TRUNK SIGNALS
Signal #1 16.6 kHz sine wave
Signal #2 10 kHz sine wave
Signal #3 Speech
3.1 Generation and Characteristics of AM Signals
The signal of equation (2) can be conveniently modelled by the TIMS system using the block
diagram below.
Audio
Osc.
m cos ωmt
(Message)
Adder
Multiplier
1 volt dc
A c cos ωct
(Carrier)
AM
Signal s(t)
Using a 2 kHz sinusoidal (tone) signal and the 100 kHz sinusoidal signal both from the Master
Signals panel as the carrier, generate an AM signal and investigate the following characteristics.
Record the results in your laboratory notebook.
3.1.1 Time Domain Waveform
Investigate the time domain waveform of the AM signal for m = 0.7 and 1.5. Sketch the
waveforms observed and compare their envelopes with the message waveform. Replace the 100
kHz carrier with the 16.6 kHz carrier available from the trunks panel. What is the effect of
decreasing the carrier frequency? Now use the Audio Oscillator for the message signal and note
the effect of increasing the message frequency.
3.1.2 Frequency Domain
Keep the 16.6 kHz carrier source from the trunks panel to assure that your frequency spectra are
within the range of the Spectrum Analyser. Investigate the frequency spectrum of the AM signal
for m = 0.7 and 1.5. Sketch the spectra observed. What is the effect of increasing the message
frequency? Replace the 16.6 kHz with the 100 kHz carrier available from the trunks.
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3.1.3 Power in the Sidebands
Determine the fraction of the total signal power that is in the sidebands for the cases m = 0.7 and
1.5. Calculate your answer from the relative heights of the spectral components in the frequency
spectrum and compare your answers to the predictions from the formula that, for sinusoidal
signals, the fraction of power in the sidebands is given by the expression:
Q =
m2
2 + m2
Draw up a suitable table for your results.
3.2 Demodulation by Envelope Detection
The envelope of the AM signal can be recovered using an envelope detector. Implement a simple
envelope detector using the half–wave rectifier in the Utilities module followed by the Tuneable
Lowpass Filter. Note that to obtain the envelope the bandwidth of the Lowpass Filter must be
wide enough to pass all significant frequency components of the envelope, but less that the
carrier frequency (strictly, less than the carrier frequency minus the higher message frequency).
Recovered
message
~
m(t)
Tuneable
Lowpass
Filter
AM
Signal
(100 kHz carrier)
Demodulate the AM signal for the cases m = 0.7 and 1.5. In each case sketch the envelope
detector input and output waveforms and note the Lowpass Filter bandwidth.
Does the AM signal envelope waveform correspond to the message in both cases? To help
explain your results sketch a half–wave rectified cosine wave and write down the first three terms
of its Fourier series representation.
3.3 Demodulation by Coherent Detection
The AM signal can also be recovered using a coherent (synchronous) detector.
LPF
AM signal
(100 kHz carrier)
~
m (t)
Recovered
message
(100 kHz LO)
Also demodulate the AM signal for the cases m = 0.7 and 1.5. In each case sketch the envelope
detector input and output waveforms and note the Lowpass Filter bandwidth. Does the AM
signal envelope waveform correspond to the message in both cases? Compare the results with
those from envelope detection.
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3.4 AM Modulation and Demodulation of Speech Signals
Generate an AM signal using the speech signal available from the Trunks Panel as your message.
Observe the time domain waveform. The frequency spectrum will extend for about 3 kHz either
side of the carrier. Since this is a stochastic (random) signal, the spectrum analyser may not give
you much response apart from the carrier.
Demodulate the signal by both envelope detection and coherent detection, and use the headphone
amplifier to listen to the recovered speech. Observe and record the effect of increasing the
modulation index in both cases.
3.5 Demodulation of Unknown Signals
There are two unknown AM signals at the coaxial cable sockets on the coloured panel. Observe
their time domain waveforms and spectra. Sketch the spectra and demodulate the signals to
determine the message signals and their frequency components.
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