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[SOLVED] Problem on LCR resonator

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Debdut

Debdut

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Hello :roll:, can you help me solve this problem. Its from An Introduction to Analog and Digital Communications - Simon Haykin

A carrier wave of frequency 1 MHz is modulated 50% by a sinusoidal wave of frequency 5 kHz. The resulting AM wave is transmitted through the resonant circuit of the Fig. below, which is tuned to the carrier frequency and has a Q factor of 175. Determine the modulated wave after transmission through this circuit. What is the percentage modulation of the modulated wave?

Untitled.jpg
 

The problem is wrongly stated: there is no resonator-coupling circuit, nor source impedance.
I would fire your professor for giving you such nonsense!
 

Jiripolivka - I am afraid you didn`t notice that the signal source symbol in the diagram represents a CURRENT source.
In this case, there is of course a filtering effect.
 

jiripolivka said:
The problem is wrongly stated...
Click to expand...
Looks OK to me, the input is an AC current source.

3dB bandwidth = 1MHz/175 = 5.7 KHz
i.e. sidebands are attenuated by 3dB at +-2.85KHz from carrier.

Thus the sidebands at +- 5KHz are attenuated by a factor of SQRT((2.85^2) / (2.85^2 + 5^2)) = 0.5,
so the modulation will be 50% * 0.5 = 25%
 
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    LvW

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godfreyl, could you explain a bit. I didn't understand : SQRT((2.85^2) / (2.85^2 + 5^2)) = 0.5
 

The calculation is the same as if you have a simple first order RC low pass filter with corner frequency = 2.85 KHz, and you want to find the attenuation at 5 KHz.
 
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