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

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Discussion Overview

The discussion revolves around calculating the resistor (R) and capacitor (C) values in an envelope detector circuit used for amplitude modulation (AM). Participants explore theoretical aspects of the circuit's behavior, including impedance, frequency considerations, and the trade-offs involved in selecting time constants.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a formula for the impedance of the resistor and capacitor in parallel, suggesting a relationship involving the output voltage and current.
  • Another participant inquires about the input carrier and modulation frequencies, indicating a need for clarification on these parameters.
  • A participant suggests that the problem assumes specific values for the carrier and modulation frequencies, emphasizing the theoretical nature of the discussion.
  • Another participant reiterates the assumption about the carrier and modulation frequencies and introduces the concept of a time constant that balances smoothing the output while allowing for variations in carrier amplitude due to modulation.
  • This participant proposes selecting the time constant such that the modulation amplitude is down 3dB at the modulation frequency, raising a question about the ripple output voltage given the carrier frequency.

Areas of Agreement / Disagreement

Participants express varying assumptions about the frequencies involved and the implications for the time constant, indicating that multiple competing views remain regarding the optimal approach to selecting R and C values.

Contextual Notes

Limitations include assumptions about the carrier and modulation frequencies, as well as the dependence on the chosen time constant and its impact on the output voltage ripple.

Who May Find This Useful

Individuals interested in circuit design, particularly in the context of AM modulation and envelope detection, may find this discussion relevant.

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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