Experiment 3
Objective: FM modulation and demodulation
Description: In this experiment you will design a FM
modulator and a derivative based FM demodulator. You will also study
the influence of the frequency deviation constant on the signal
bandwidth.
Instructions
III. Demodulation (Wideband FM) Kf=5000
You need not use the Fourier transform blocks for this part (to save on
simulation time)
- Pass the signal through a differentiator from ece359lib
. The resulting signal (call it q(t))
passed through a conventional AM demodulator.
- Implement the AM demodulator shown in the figure
below. Recall from class that a differentiator followed by an
AM demodulator can demodulate FM.
Use the Rectifier(half cycle) from ece359lib. Use an
order 5 Butterworth lowpass filter with cutoff F_CUTOFF.
For the DC stop use a Butterworth high-pass filter (help
butter for help on high pass filters) of order 3 and lower
cutoff F_DC_STOP. Let the output be v(t).
- Observe m(t), v(t) using
scopes. If possible, get these plots on the same matlab
figure using the subplot command. The signals
will not look identical for the first 1-2 ms, so be sure to plot till
at least 4ms.
Use the scope from ece359lib. This scope has its
parameters set properly for viewing signals in this
experiment. If you want to see the modulated high
frequency signal(not required), use the HF scope, also in ece359lib. Scope help
Questions
- Submit a block diagram for the entire Modulator/Demodulator system.
- Give equations to show that the signal s(t) is indeed a FM signal.
- Using appropriate equations, compute the bandwidth of the
modulated signal s(t) for the wideband
case. Assume that the peak amplitude of m(t) is 150. Does the computed bandwidth match
what you observe? Submit a plot of the spectrum of s(t) in II.3.
- Using appropriate equations, compute the bandwidth of the
modulated signal s(t) for the
narrowband case. Does it match what you observe?
Submit a plot of the spectrum of s(t) in
II.4.
- Give the equation for the differentiator output q(t). Also give the equation for the demodulator
output, v(t) in terms of the input signal
m(t).
- Submit the plots of the signals seen in III.3. Use values of Kf
for the wideband case to predict the amplitude gain for the
demodulated signal. Compare the peak amplitudes of m(t) and v(t) and
verify the amplitude gain predicted by theory.
- Notice that there is distortion in the initial portion of m(t), but
after a few ms, v(t) begins to track m(t) closely. Explain this
phenomenon (hint: it is linked to one of the filters in the
demodulator).
- This demodulation scheme filters out any DC present in the
original signal. Do you think this would be a problem for a real voice
broadcast system?
ECE 359 home