Envelope detector

A signal and its envelope marked with red

This article is about the analog electronics technique. For the digital signal processing technique, see Envelope estimator.

An envelope detector (sometimes called a peak detector) is an electronic circuit that takes a (relatively) high-frequency amplitude modulated signal as input and provides an output, which is the demodulated envelope of the original signal.

Diode detector

Simple diode detector. The AM input (green) is first rectified by the diode. The output voltage (red) ripples around the input's envelope by alternatively charging and discharging the capacitor.

The simplest form of envelope detector is the diode detector. A diode detector is simply a diode between the input and output of a circuit, connected to a resistor and capacitor in parallel from the out of the circuit to the ground to form a low pass filter. Their RC time constant must be small enough to discharge the capacitor fast enough when the envelope is falling. Meanwhile, the filter's cutoff frequency should be well below the carrier wave's frequency to sufficiently attenuate the carrier. The output of this circuit approximates a voltage-shifted version of the original (baseband) signal. A simple high-pass filter may optionally then be applied to filter out the DC component.

Circuit operation

The capacitor stores charge on the rising edge and releases it slowly through the resistor when the input signal amplitude falls. The series diode performs half-wave rectification, allowing noticeable current flow only when the positive input terminal's electric potential is at least a diode drop higher than the negative input terminal.

AM Demodulation

Envelope detectors can be used to demodulate a previously amplitude modulated (AM) signal by removing all high frequency components of the signal. Such a device is often used to demodulate AM radio signals because the envelope of the modulated signal is equivalent to the baseband signal.

General considerations

Most practical envelope detectors use either half-wave or full-wave rectification of the signal to convert the AC audio input into a pulsed DC signal. Filtering is then used to smooth the final result. This filtering is rarely perfect and some "ripple" is likely to remain on the envelope follower output, particularly for low frequency inputs such as notes from a bass instrument. Reducing the filter cutoff frequency gives a smoother output, but decreases the high frequency response. Therefore, practical designs must reach a compromise.

Definition of the envelope

A signal in blue and the magnitude of its analytic signal in red, showing the envelope effect

Main article: Envelope (waves)

Any AM or FM signal $x(t)$ can be written in the following form

$x(t)=R(t)\cos(\omega t+\varphi (t))\,$

In the case of AM, φ(t) (the phase component of the signal) is constant and can be ignored. In AM, the carrier frequency $\omega$ is also constant. Thus, all the information in the AM signal is in R(t). R(t) is called the envelope of the signal. Hence an AM signal is given by the function

$x(t)=(C+m(t))\cos(\omega t)\,$

with m(t) representing the original audio frequency message, C the carrier amplitude and R(t) equal to C + m(t). So, if the envelope of the AM signal can be extracted, the original message can be recovered.

In the case of FM, the transmitted $x(t)$ has a constant envelope R(t) = R and can be ignored. However, many FM receivers measure the envelope anyway for received signal strength indication.

Precision detector

An envelope detector can also be constructed using a precision rectifier feeding into a low-pass filter.

Drawbacks

The envelope detector has several drawbacks:

• The input to the detector must be band-pass filtered around the desired signal, or else the detector will simultaneously demodulate several signals. The filtering can be done with a tunable filter or, more practically, a superheterodyne receiver
• It is more susceptible to noise than a product detector
• If the signal is overmodulated (i.e. modulation index > 1), distortion will occur

Most of these drawbacks are relatively minor and are usually acceptable tradeoffs for the simplicity and low cost of using an envelope detector.

Audio

See also: Noise gate § Trance gating

An envelope detector is sometimes referred to as an envelope follower in musical environments. It is still used to detect the amplitude variations of an incoming signal to produce a control signal that resembles those variations. However, in this case the input signal is made up of audible frequencies.

Envelope detectors are often a component of other circuits, such as a compressor or an auto-wah or envelope-followed filter. In these circuits, the envelope follower is part of what is known as the "side chain", a circuit which 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. Auto-wah uses the voltage to control the cutoff frequency of a filter. The voltage-controlled filter of an analog synthesizer is a similar circuit.

Modern envelope followers can be implemented:

1. directly as electronic hardware,
2. or as software using either a digital signal processor (DSP) or
3. on a general purpose CPU.

See also

• Analytic signal
• Attack-decay-sustain-release envelope

External links

• Envelope detector
• Envelope and envelope recovery