[SOLVED] Problem on LCR resonator

[Debdut]

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?

 

[jiripolivka]

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

 

[LvW]

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.

 

[godfreyl]

The problem is wrongly stated...

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%

 

[Debdut]

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

 

[godfreyl]

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.