Editing Envelope detector

{{Short description|Electronic circuit}}
{{More sources needed|date=June 2024}}
[[Image:C Envelope follower.png|thumb|An envelope (red) outlines a signal (black)]]
{{About|the analog electronics technique|the digital signal processing technique|Envelope estimator}}

An '''envelope detector''' (sometimes called a '''peak detector''') is an electronic circuit that takes a (relatively) high-frequency signal as input and outputs the ''[[Envelope (waves)|envelope]]'' of the original signal.

== Diode detector ==
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| footer            = Simple diode detector. An input voltage (the green [[Amplitude modulation|AM]] signal) is first [[Half-wave rectification|rectified]] by the [[diode]]. The output voltage (red) ripples just below the input's upper envelope by charging and discharging the [[capacitor]].
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A simple form of envelope detector used in [[Detector (radio)|detectors]] for early [[Radio|radios]] is the '''diode detector'''. Its output approximates a voltage-shifted version of the input's upper envelope.

Between the circuit's input and output is a [[diode]] that performs [[half-wave rectification]], allowing substantial current flow only when the input voltage is around a [[Diode forward voltage drop|diode drop]] higher than the output terminal.

The output is connected to a [[capacitor]] of value <math>C</math> and [[resistor]] of value <math>R</math> in parallel to [[ground (electricity)|ground]]. The capacitor is charged as the input voltage approaches its positive peaks. At other times, the capacitor is gradually discharged through the [[resistor]]. The resistor and capacitor form a 1st-order [[low pass filter]], which attenuates higher frequencies at a rate of -6 dB per octave above its [[cutoff frequency]] of <math>\tfrac{1}{2 \pi R C}</math>. The filter's [[RC time constant]] <math>(\tau {=} R C)</math> must be small enough to track quickly-falling envelope slopes and "top up" the envelope's voltage every peak to prevent ''negative peak clipping''.<ref name=":0">{{Cite web |last=Lesurf |first=Jim |date=2000-05-18 |title=The Envelope Detector |url=https://www.winlab.rutgers.edu/~crose/322_html/envelope_detector.html |url-status=live |archive-url=https://web.archive.org/web/20230326153521/https://www.winlab.rutgers.edu/~crose/322_html/envelope_detector.html |archive-date=2023-03-26 |access-date=2024-06-09 |website=www.winlab.rutgers.edu}}</ref>

=== AM demodulation ===
Envelope detectors can be used to [[demodulate]] an [[amplitude modulated]] (AM) signal. Such a device is often used to demodulate AM [[radio signal]]s because the envelope of the modulated signal is equivalent to the [[baseband]] signal. To sufficiently attenuate the frequency of the [[carrier wave]] frequency <math>f_\text{carrier}</math>, the cutoff frequency of the low-pass filter should be well-below the carrier wave's frequency. To avoid negative peak clipping, the original signal that is modulated is usually limited to a maximum frequency <math>f_\text{max}</math> to limit the maximum rate of fall of the AM signal. To minimize distortions from both ripple and negative peak clipping, the following inequality should be observed:<ref name=":0" />

<math display="block"> \frac{1}{f_\text{carrier}} \ll \tau \ll \frac{1}{f_\text{max}} \; .</math>

Next, to filter out the DC component, the output could pass through a simple high-pass filter, such as a DC-blocking capacitor.

== General considerations ==
Most practical envelope detectors use either half-wave or full-wave [[Rectifier|rectification]] of the signal to convert the [[alternating current|AC]] audio input into a pulsed [[Direct current|DC]] signal. Full-wave rectification traces both positive and negative peaks of the envelope. Half-wave rectification ignores negative peaks, which may be acceptable based on the application, particularly if the input signal is symmetric about the horizontal axis. Low [[Diode#Threshold voltage|threshold voltage]] diodes (e.g. [[germanium]] or [[Schottky diode|Schottky diodes]]) may be preferable for tracking very small envelopes.

The [[Electronic filter|filtering]] for smoothing the final result is rarely perfect and some "ripple" is likely to remain on the output, particularly for low frequency inputs such from a [[bass instrument]]. Reducing the filter cutoff frequency gives a smoother output, but designers must compromise this with the circuit's high frequency response.

== Definition of the envelope ==
[[Image:analytic.svg|thumb|300px|right|A signal in blue and the magnitude of its [[analytic signal]] in red, showing the envelope effect]]
{{Main|Envelope (waves)}}

Any [[amplitude modulation|AM]] or [[frequency modulation|FM]] signal <math>x(t)</math> can be written in the following form
: <math>x(t) = R(t) \cos ( \omega t + \varphi(t) ) \,</math>

In the case of AM, φ(''t'') (the phase component of the signal) is constant and can be ignored. In AM, the [[carrier frequency]] <math>\omega</math> 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
: <math>x(t) = (C + m(t)) \cos(\omega t) \,</math>
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 <math>x(t)</math> 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 filter]]ed 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 [[overmodulation|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 [[music]]al 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 [[Audio level compression|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 (sound)|side chain]]", a circuit which describes some characteristic of the input, in this case its volume.

Both [[dynamic range compression|expanders]] and [[audio level compression|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: 
# directly as [[electronic hardware]],
# or as software using either a [[digital signal processor]] (DSP) or
# on a general-purpose CPU.

== See also ==
* [[Analytic signal]]
* [[Envelope (music)|Attack–decay–sustain–release envelope]]

== References ==
{{reflist}}

== External links ==
* [https://web.archive.org/web/20071105091112/http://seniord.ee.iastate.edu/SSOL/RADAR/prjpln99/detector3.html Envelope detector]
* [https://www.ele.uri.edu/Courses/ele436/labs/expA4.pdf Envelope and envelope recovery]

[[Category:Electronic music]]
[[Category:Audio engineering]]
[[Category:Communication circuits]]
[[Category:Detectors]]
[[Category:Demodulation]]