ECE 359-Simulink Experiment 3

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

I. Initialization: Copy the initialization files for the experiment into your Matlab working directory. Note that the initialization files have changed
The following constants should be set by the startup file. Use who in the matlab workspace to check if the constants are all there. Some additional constants may also be set, but you may ignore them
II. FM Modulation (Narrowband and Wideband)
1. Use the Message Signal (m(t)) from ece359lib . Pass this through an Integrator from ece359lib . Pass this signal through a gain block (ece359lib) of gain Kf.
2. Use the ramp block (ece359lib) to generate a ramp with slope F_CARR. Add the ramp output to the output in part (i). Take the cosine of the resulting signal using the cos block from ece359lib. This is the FM signal s(t). (Make sure you know why this is a FM signal.)
3. Use the Fourier Transformer from ece359lib to observe the spectra of s(t) and m(t). (You need to submit s(t) only.)
4. The value of Kf set by the constants file is for wideband FM. Now change Kf to 200 (in the workspace enter Kf=200) and plot the Fourier transforms of s(t) and m(t). (You need to submit s(t) only.)
5. Before going on to the next part make sure you run the script constants again. We want the value of Kf restored to 5000 for the next part.

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?

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