Question E7E10:
How does a diode envelope detector function?  

Choices:  
A: By rectification and filtering of RF signals  
B: By breakdown of the Zener voltage  
C: By mixing signals with noise in the transition region of the diode  
D: By sensing the change of reactance in the diode with respect to frequency    

Correct Answer is  A: By rectification and filtering of RF signals  

To detect the AM envelope, a diode detector simply rectifies the RF and filters out the carrier, leaving the modulation (audio) as the output.

Why the correct answer is correct (A)
- A diode envelope detector is a rectifier (diode) followed by an RC low-pass filter.
- The AM signal can be written as:
  $$v_{AM}(t) = A_c[1 + m(t)]\cos(\omega_c t)$$
  where $m(t)$ is the modulation (audio).
- The diode conducts on RF peaks, charging the capacitor to track the crest (the envelope). Between peaks, the capacitor discharges slowly through the resistor, so the voltage across R follows $A_c[1 + m(t)]$ (the envelope).
- The RC time constant is chosen so it removes the RF but follows the audio:
  $$\frac{1}{f_c} \ll RC \ll \frac{1}{f_m}$$
  where $f_c$ is the carrier and $f_m$ is the highest audio frequency.

Why the other choices are incorrect
- B: Zener breakdown is used for voltage regulation or clipping, not for envelope detection.
- C: “Mixing signals with noise in the transition region” is not a detection method; envelope detectors do not rely on noise or diode transition-region effects.
- D: “Sensing reactance vs frequency” describes FM detectors (e.g., slope, Foster-Seeley, ratio detectors), not AM envelope detection.

Useful formulas and rules of thumb
- AM envelope (desired output): $|A_c[1 + m(t)]| \approx A_c[1 + m(t)]$ for normal modulation.
- RC choice guideline:
  - Suppress RF ripple: $RC \gg 1/(2\pi f_c)$
  - Follow audio without excessive distortion: $RC \lesssim 1/(2\pi f_m)$
- Ripple/droop estimate between peaks:
  $$\Delta V \approx \frac{V}{R}\frac{\Delta t}{C}, \quad \Delta t \approx \frac{1}{f_c}$$
  Keep $\Delta V$ small compared to the audio variation.