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
lottotlyl
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 ##?
 

1. How do I calculate the value of R in an envelope detector circuit?

To calculate the value of R in an envelope detector circuit, you will need to know the desired output voltage and the input signal voltage. The formula for R is R = Vout / I, where Vout is the desired output voltage and I is the input signal voltage. You will also need to consider the type of diode used in the circuit and its forward voltage drop.

2. What is the purpose of the capacitor in an envelope detector circuit?

The capacitor in an envelope detector circuit serves to smooth out the output voltage by storing and releasing charge. This helps to eliminate any high-frequency noise or fluctuations in the output signal.

3. How do I calculate the value of C in an envelope detector circuit?

The value of C in an envelope detector circuit can be calculated using the formula C = I / (2πfR), where I is the input signal voltage, f is the frequency of the input signal, and R is the value of the resistor in the circuit. This formula ensures that the capacitor is able to effectively store and release charge to smooth out the output voltage.

4. What is the ideal value for R in an envelope detector circuit?

The ideal value for R in an envelope detector circuit depends on the desired output voltage and the input signal voltage. Generally, a higher value of R will result in a larger output voltage, but it may also introduce more distortion to the signal. It is important to choose a value of R that balances the desired output voltage with minimal distortion.

5. How does the envelope detector circuit work?

The envelope detector circuit works by using a diode and a capacitor to rectify and smooth out an amplitude-modulated (AM) signal. The diode only allows the positive half of the signal to pass through, while the capacitor stores and releases charge to create a smooth output voltage. This results in an envelope of the original signal being detected, hence the name "envelope detector".

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