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

AI Thread Summary
The discussion focuses on calculating the resistance (R) and capacitance (C) in an envelope detector circuit for AM modulation. Participants highlight the importance of adding impedance in parallel with the capacitor and resistor, using the formula Z_rc = 1/((-wC/j) + 1/R). They emphasize the relationship between the input current (i_d), the impedance (Z_rc), and the output voltage (Vo) through Ohm's law. A key point is the need for a time constant that balances smoothing the output while still allowing for variations in the carrier amplitude due to modulation. The conversation suggests selecting the time constant to achieve a 3dB reduction in modulation amplitude at the modulation frequency (ω_m).
lottotlyl
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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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What are input carrier and modulation frequencies?
 
I think for this problem we are meant to assume w_c and w_m . Very theoretical.
 
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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