Peak Detector and/or Envelope Detector — A Detailed Analysis —

In this document, a simple circuit constructed using a diode, a resistor, and a capacitor, utilized as a peak detector and/or as an envelope detector is analyzed. The analysis is approached by applying approximate methods and by a mix of exact and numerical methods, aiming design guidelines and understanding of the circuit operation. Approximate and exact approaches are compared, and a region where the approximate analysis provides adequate answers is identified. Ability of the circuit to track the envelope variations is analyzed, and it is shown to depend both on the circuit time constant and the output voltage value, i.e. the modulation signal frequency and the modulation index. Relevant relations are derived and presented. Finally, distortion of the output voltage caused by the output voltage ripple is addressed, and averaged model of the circuit is derived. It is shown that average of the output voltage over the carrier period is increased about three times when filtering of the output voltage is applied. Transfer function for averaged waveforms of the envelope detector is derived, containing slight attenuation and a real pole at the double of the carrier frequency