Envelope detector
Circuit that extracts the envelope of a high-frequency signal.
An envelope detector, also known as a peak detector, is an electronic circuit that accepts a relatively high-frequency input signal and produces the envelope of that signal as its output. A common application is demodulating amplitude modulated (AM) radio signals, since the modulated signal's envelope matches the original baseband signal. The simplest version, the diode detector, employs a forward-biased diode for half-wave rectification, followed by a parallel resistor-capacitor (RC) low-pass filter that smooths the output.
In a diode detector, the diode allows current to flow only when the input voltage exceeds the output voltage by roughly a diode drop, effectively charging the capacitor to the input's positive peaks. Between peaks, the capacitor discharges through the resistor. The RC time constant must be chosen carefully: too short and the output tracks the carrier's rapid fluctuations; too long and the capacitor cannot recharge quickly enough, causing negative peak clipping. The RC combination acts as a first-order low-pass filter, attenuating frequencies above its cutoff (1/(2πRC)) at a rate of -6 dB per octave.
For AM demodulation, the low-pass filter's cutoff must be well below the carrier frequency to sufficiently suppress it. To avoid clipping, the modulating signal's maximum frequency (f_max) must be limited, ensuring the envelope does not fall too quickly. The design constraint is: 1/f_carrier ≪ τ ≪ 1/f_max, where τ = RC. A subsequent high-pass filter, such as a DC-blocking capacitor, can remove any DC component from the output.
Most practical envelope detectors use either half-wave or full-wave rectification. Full-wave rectification captures both positive and negative peaks, while half-wave ignores negative peaks—acceptable if the input signal is symmetric about zero. For very small envelopes, diodes with low threshold voltages (e.g., germanium or Schottky) are preferable. Filtering is never perfect, so some ripple remains, especially for low-frequency inputs like bass notes. Lowering the filter cutoff reduces ripple but compromises high-frequency response.
Mathematically, any AM or FM signal x(t) can be written as x(t) = R(t) cos(ωt + φ(t)). For AM, φ(t) is constant, and the carrier frequency ω is fixed, so all information resides in R(t), the envelope.
- Cutoff frequency formula
- 1/(2πRC)
- Rc time constant
- τ = RC
- Ripple attenuation rate
- -6 dB per octave above cutoff
- Inequality for minimizing distortion
- 1/f_carrier ≪ τ ≪ 1/f_max
Lore & Background
The envelope detector's most common form is the diode detector, which performs half-wave rectification by allowing current flow only when the input voltage is around a diode drop higher than the output terminal. The output is connected to a capacitor and resistor in parallel to ground; the capacitor charges near the positive peaks and discharges through the resistor at other times. The RC time constant must be small enough to track quickly-falling envelope slopes and 'top up' the envelope's voltage every peak to prevent negative peak clipping. In AM demodulation, the cutoff frequency of the low-pass filter should be well below the carrier wave frequency to sufficiently attenuate it. To avoid negative peak clipping, the original modulated signal is usually limited to a maximum frequency. The inequality 1/f_carrier ≪ τ ≪ 1/f_max should be observed to minimize distortions from both ripple and negative peak clipping. A DC-blocking capacitor can be used to filter out the DC component. Full-wave rectification traces both positive and negative peaks, while half-wave rectification ignores negative peaks, which may be acceptable if the input signal is symmetric about the horizontal axis. Low threshold voltage diodes (e.g., germanium or Schottky diodes) may be preferable for tracking very small envelopes.
Reader's Guide
The envelope detector is notable for its simplicity and low cost, making it a common choice for AM radio demodulation despite several drawbacks. The input must be band-pass filtered around the desired signal, or the detector will simultaneously demodulate several signals; this filtering can be done with a tunable filter or, more practically, a superheterodyne receiver. It is more susceptible to noise than a product detector, and if the signal is overmodulated (modulation index > 1), distortion will occur. These drawbacks are usually acceptable tradeoffs for the circuit's simplicity.
In musical environments, an envelope detector is sometimes called an envelope follower and is used to detect amplitude variations of an incoming signal to produce a control signal. It is often a component of other circuits such as compressors, auto-wah, or envelope-followed filters, where the envelope follower is part of the 'side chain' that describes some characteristic of the input, in this case its volume. Both expanders and compressors use the envelope's output voltage to control the gain of an amplifier, while auto-wah uses the voltage to control the cutoff frequency of a filter. Modern envelope followers can be implemented as electronic hardware, as software using a digital signal processor (DSP), or on a general-purpose CPU.
Did You Know?
- The envelope detector is sometimes called a peak detector.
- A simple form is the diode detector, which uses a forward biased diode for half-wave rectification.
- The RC time constant must satisfy 1/f_carrier ≪ τ ≪ 1/f_max to minimize ripple and negative peak clipping.
- In musical environments, an envelope detector is referred to as an envelope follower.
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