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MathsDude69
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Homework Statement
An SSB-AM modulator is shown in fig 1 (please see attached), where the SSB filter removes the lower sideband.
A synchronous demodulator is shown in fig 2 (please see attached). Show that by setting the frequency of the local oscillator to the carrier frequency the output of the demodulator will contain the original message.
Homework Equations
Trigononmetric itdentities:
cos(u).cos(v) = 0.5cos(u-v) + 0.5cos(u+v)
cos2(a) = 0.5(1 + cos2a)
The Attempt at a Solution
We can state that:
V1(t) = 8 + 4cos(2π5x103t)
V2(t) = 8cos(2π105t) + 2cos(2πx105x103t) + 2cos(2πx95x103t)
V2(t) = 8cos(2π105t) + 2cos(2πx105x103t)
in which case at the demodulation stage we would get:
(8cos(2π105t) + 2cos(2πx105x103t)) x cos(2π105t)
which is:
4(1+cos(4π105t) + cos(2πx5x103t) + cos(2πx205x103t)
All the information I have on this illustrates that the demodulated signal should have a baseband component of the original message at half the magnitude and a component at twice the carrier frequency with a magnitude a quarter of the original. Can anyone see where I have gone wrong here??