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Demodulator for FM Stereo Signals

Multiplication of a carrier by a modulating signal generates an AM waveform known as DSB-SC, the waveform is

v(t) DSB-SC = Ac cos W ct x Vm cos Wmt
Where W = is the angular velocity

a. Make a sketch of the DSB-SC waveform with Vm = 1 V and Ac = 10 V for a carrier frequency of 10 kHz and a modulating signal frequency of 1 kHz. Show one cycle of the modulating signal frequency. Make sure you label your axes correctly!
b. Draw a single sided spectral diagram for the DSB-SC waveform in part (a) above.
c. DSB-SC signals cannot be demodulated with an envelope detector. Describe one way in which a DSB-SC signal can be demodulated.
d. Why is DSB-SC modulation used to transmit stereo information in FM broadcast signals rather than DSB-LC AM?
e. Stereo information is transmitted in the baseband of FM broadcasts using DSB-SC modulation of a 38 kHz sub-carrier. A diagram of the demodulator that recovers L+R and L-R audio channels is show in slide 33 of the power point file of Module 10. How is the 38 kHz locally generated signal that is used to drive the DSB-SC multiplier derived from the baseband signal at the output of the FM demodulator?

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Solution Preview

Please see attached solutions.

a. A DSB-SC waveform is given by the expression

A sketch of the waveform over one cycle ( 0.seconds) of the modulating signal whose modulating frequency is ,
, amplitude on a carrier of frequency ,
, amplitude is shown below. I have used the resource found here [1] to graph this

b. To sketch the single sided power spectrum for DSB-SC we need to note that the spectrum consists of both lower and upper side bands containing redundant information. These sidebands are centred around the original carrier component frequency and are at the following frequencies

Lower sideband frequency
Upper sideband frequency
In terms of power magnitude these lower rand upper components have power magnitude determined from

Where is the modulation index.
For our scheme we have a modulation index and meaning we get power magnitudes for each sideband component (assuming 1Ω resistance reference) of

Converting to this is a power magnitude of

Thus the single sided power spectrum for the DSB-SC signal will consist of two spectral components with power one at a lower sideband frequency of the other at an upper sideband frequency of as shown in the plot below

c. A DSB-SC ...

Solution Summary

The expert examines demodulator for FM stereo signals.