Calculate R and C in Envelope Detector Circuit (AM Modulation)

In summary, the conversation discusses the addition of impedance in parallel of a capacitor and resistor and Ohm's law for the relationship between input carrier and modulation frequencies. The main focus is on finding the best time constant for the circuit to smooth out the output while still being able to detect variations in the carrier amplitude. The proposed solution is to choose a time constant that results in a 3dB decrease in modulation amplitude at the modulation frequency.
  • #1
4
0
Homework Statement
Calculate the values for R and C on the envelope detector given below. Explain the role of the diode, resistor, and capacitor on the demodulation of the AM signal.
Relevant Equations
Zc = -j/wC, R=V/I
envelope_detector.png

1. Add impedance in parallel of capacitor and resistor
  • Z_rc = 1/((-wC/j) + 1/R) = (jR)/(j-wRC)
2. Ohm's law for relationship of i_d, Z_rc, and Vo
  • Vo = i_d * (jR)/(j-wRC)
Unsure how to do the rest?
Thanks.
 
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  • #2
What are input carrier and modulation frequencies?
 
  • #3
I think for this problem we are meant to assume w_c and w_m . Very theoretical.
 
  • #4
lottotlyl said:
I think for this problem we are meant to assume w_c and w_m . Very theoretical.
OK.
Basic idea: the time costant should be large enough to smooth out the output as much as possible.
BUT - at the same time it must be small enough to see variations in the carrier amplitude if that amplitude is varied by the modulation signal.
So there's a tradeoff here. How about picking the time constant such that the modulaton amplitude is down 3dB at ## \omega_m ##? What would be the ripple output voltage given ## \omega_c ##?
 

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