Gain compression
Encyclopedia
Gain compression is a reduction in 'differential' or 'slope' gain caused by nonlinearity
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

of the transfer function
Transfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

of the amplifying device. This nonlinearity may be caused by heat due to power dissipation, or by overdriving the active device beyond its linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

region. It is a large signal
Large-signal model
Large-signal modeling is a common analysis method used in electrical engineering to describe nonlinear devices in terms of the underlying nonlinear equations....

phenomenon of circuits.

## Relevance

Gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...

compression is relevant in any system with a wide dynamic range, such as audio or RF
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

. It is more common in tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

circuits than transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

circuits, due to topology differences, possibly causing the differences in audio performance called "valve sound
Tube sound
Tube sound is the characteristic sound associated with a vacuum tube-based audio amplifier. The audible significance of tube amplification on audio signals is a subject of continuing debate among audio enthusiasts....

". The front-end RF amps
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

A radio receiver converts signals from a radio antenna to a usable form. It uses electronic filters to separate a wanted radio frequency signal from all other signals, the electronic amplifier increases the level suitable for further processing, and finally recovers the desired information through...

s are particularly susceptible to this phenomenon when overloaded by a strong unwanted signal.

## Audio effects

A tube radio or tube amplifier will increase in volume to a point, and then as the input signal extends beyond the linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

range of the device, the effective gain is reduced, altering the shape of the waveform. The effect is also present in transistor circuits. The extent of the effect depends on the topology of the amplifier.

## Differences between clipping and compression

Clipping, as a form of signal compression, differs from the operation of the typical studio audio level compressor
Audio level compression
Dynamic range compression, also called DRC or simply compression reduces the volume of loud sounds or amplifies quiet sounds by narrowing or "compressing" an audio signal's dynamic range...

, in which gain compression is not instantaneous (delayed in time via attack and release settings).

### Limiting or clipping

Gain is a linear operation. "Gain compression" is not linear and, as such, its effect is one of distortion, due to the nonlinearity
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

of the transfer characteristic which also causes a loss of 'slope' or 'differential' gain. So the output is less than expected using the small signal
Small signal model
Small-signal modeling is a common analysis technique in electrical engineering which is used to approximate the behavior of nonlinear devices with linear equations...

gain of the amplifier.

In clipping
Clipping (audio)
Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability...

, the signal is abruptly limited to a certain amplitude and is thereby distorted in keeping under that level. This creates extra harmonics that are not present in the original signal.

"Soft" clipping or limiting means there isn't a sharp "knee point" in the transfer characteristic. A sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

that has been softly clipped will become more like a square wave
Square wave
A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels...

, with more rounded edges, but will still have many extra harmonics.

### Compression

Compression of gain is caused by non-linear characteristics of the device when run at high levels. With any signal, as the input level is increased beyond the linear range of the amplifier, gain compression will occur.

A transistor's operating point may move with temperature, so higher power output may lead to compression due to collector dissipation. But it's not a change in gain; it's non-linear distortion. The output level stays relatively the same as the input level goes higher. Once the non-linear
Nonlinearity
In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable to be solved for cannot be...

portion of the transfer characteristic of any amplifier is reached, any increase in input will not be matched by a proportional increase in output. Thus there is compression of gain. Also, at this time because the transfer function is no longer linear, harmonic distortion will result.

#### Intentional compression

In intentional compression (sometimes called automatic gain control
Automatic gain control
Automatic gain control is an adaptive system found in many electronic devices. The average output signal level is fed back to adjust the gain to an appropriate level for a range of input signal levels...

or audio level compression
Audio level compression
Dynamic range compression, also called DRC or simply compression reduces the volume of loud sounds or amplifies quiet sounds by narrowing or "compressing" an audio signal's dynamic range...

) as used in devices called 'dynamic range compressors', the overall gain of the circuit is actively changed in response to the level of the input over time, so the transfer function remains linear over a short period of time. A sine wave into such a system will still look like a sine wave at the output, but the overall gain is varied, depending on the level of that sine wave. Above a certain input level, the output sine wave will always be the same amplitude.

"Gain compression" in RF amps is similar to soft clipping. However, in narrowband
Narrowband
In radio, narrowband describes a channel in which the bandwidth of the message does not significantly exceed the channel's coherence bandwidth. It is a common misconception that narrowband refers to a channel which occupies only a "small" amount of space on the radio spectrum.The opposite of...

systems, the effect "looks" more like gain compression simply because the harmonics are filtered out after amplification. Many data sheets for RF amplifiers list gain compression rather than distortion figures because it's easier to measure and is more important than distortion figures in non linear RF amplifiers.

In wideband
Wideband
In communications, wideband is a relative term used to describe a wide range of frequencies in a spectrum. A system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth....

and low frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

systems, the non-linear effects are readily visible, e.g. the output is clipped
Clipping (signal processing)
Clipping is a form of distortion that limits a signal once it exceeds a threshold. Clipping may occur when a signal is recorded by a sensor that has constraints on the range of data it can measure, it can occur when a signal is digitized, or it can occur any other time an analog or digital signal...

. To see the same thing at one GHz
GHZ
GHZ or GHz may refer to:# Gigahertz .# Greenberger-Horne-Zeilinger state — a quantum entanglement of three particles.# Galactic Habitable Zone — the region of a galaxy that is favorable to the formation of life....

, an oscilloscope
Oscilloscope
An oscilloscope is a type of electronic test instrument that allows observation of constantly varying signal voltages, usually as a two-dimensional graph of one or more electrical potential differences using the vertical or 'Y' axis, plotted as a function of time,...

with a bandwidth of at least 10 GHz is needed. Observing with a spectrum analyzer
Spectrum analyzer
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals...

, the fundamental compressed and the harmonic
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

s picking up.

### Examples of RF compression

A low-noise RF amplifier
Linear amplifier
A linear amplifier is an electronic circuit whose output is proportional to its input, but capable of delivering more power into a load. The term usually refers to a type of radio-frequency power amplifier, some of which have output power measured in kilowatts, and are used in amateur radio...

if fed by a directional antenna
Directional antenna
A directional antenna or beam antenna is an antenna which radiates greater power in one or more directions allowing for increased performance on transmit and receive and reduced interference from unwanted sources....

to a consumer 900 MHz receiver should improve the transmission range. It works, but the receiver may also pick up a couple of UHF
Ultra high frequency
Ultra-High Frequency designates the ITU Radio frequency range of electromagnetic waves between 300 MHz and 3 GHz , also known as the decimetre band or decimetre wave as the wavelengths range from one to ten decimetres...

stations around 700 MHz.

For example, if channel 54 is transmitting 6 MW of AM
Amplitude modulation
Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent...

, FM
Frequency modulation
In telecommunications and signal processing, frequency modulation conveys information over a carrier wave by varying its instantaneous frequency. This contrasts with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant...

, and PM
Phase modulation
Phase modulation is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.Unlike its more popular counterpart, frequency modulation , PM is not very widely used for radio transmissions...

, the RF front end, expecting −80 dBm
DBm
dBm is an abbreviation for the power ratio in decibels of the measured power referenced to one milliwatt . It is used in radio, microwave and fiber optic networks as a convenient measure of absolute power because of its capability to express both very large and very small values in a short form...

, would be grossly overloaded and generate mixing products. This is a typical effect of gain compression.

## High power loudspeakers

A form of gain compression also takes place in loudspeaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...

voice coil
Voice coil
A voice coil is the coil of wire attached to the apex of a loudspeaker cone. It provides the motive force to the cone by the reaction of a magnetic field to the current passing through it...

s when they heat up and increase their resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

. This causes less power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

to be drawn from the amplifier and a reduction in SPL.