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'Intermodulation' or 'intermodulation distortion' ('IMD'), or 'intermod' for short, is the result of two or more signals of different frequencies being mixed together, forming additional signals at frequencies that are not, in general, at harmonic frequencies (integer multiples) of either.
Intermodulation is caused by non-linear behaviour of the signal processing being used. The theoretical outcome of these non-linearities can be calculated by conducting a Volterra series of the characteristic, while the usual approximation of those non-linearities is obtained by conducting a Taylor series.
Intermodulation is rarely desirable in radio, as it essentially creates spurious emissions, which can create minor to severe interference to other operations on the resulting frequency. Intermodulation may be desirable in audio if the intent is to create specific sound effects; for instance, intermodulation is the basis of the power chord technique in rock music.

Contents

Causes of intermodulation

Intermodulation order

Intermodulation noise

Use in music production

Problems in live audio

Passive intermodulation

References

See also

External links

Causes of intermodulation

By definition, a linear system cannot produce intermodulation. If the input of a linear system is a signal of a single frequency, then the output is a signal of the same frequency; only the amplitude and phase can differ from the input signal. However, non-linear systems generate harmonics, meaning that if the input of a non-linear system is a signal of a single frequency, $~f\_a$, then the output is a signal which includes a number of integer multiples of the input frequency; (i.e some of $~\; f\_a,\; 2f\_a,\; 3f\_a,\; 4f\_a,\; ldots$).
Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider, an input signal that contains three frequency components at$~f\_a$, $~\; f\_b$, and $~f\_c$; which may be expressed as
:$x(t)\; =\; M\_a\; sin(2\; pi\; f\_a\; t\; +\; phi\_a)\; +\; M\_b\; sin(2\; pi\; f\_b\; t\; +\; phi\_b)\; +\; M\_c\; sin(2\; pi\; f\_c\; t\; +\; phi\_c)$
where the $M$ and $phi$ are the amplitudes and phases of the three components, respectively.
We obtain our output signal, $y(t)$, by passing our input through a non-linear function:
:$y(t)\; =\; Gleft(x(t)$
ight),
$y(t)$ will contain the three frequencies of the input signal, $~f\_a$, $~\; f\_b$, and $~f\_c$ (which are known as the ''fundamental'' frequencies), as well as a number of linear combinations of the fundamental frequencies, each of the form
:$k\_af\_a\; +\; k\_bf\_b\; +\; k\_cf\_c$
where $~k\_a$, $~\; k\_b$, and $~k\_c$ are arbitrary integers which can assume positive or negative values. These are the 'intermodulation products' (or 'IMPs').
In general, each of these frequency components will have a different amplitude and phase, which depends on the specific non-linear function being used, and also on the amplitudes and phases of the original input components.
More generally, given an input signal containing an arbitrary number $N$ of frequency components $f\_a,\; f\_b,\; ldots,\; f\_N$, the output signal will contain a number of frequency components, each of which may be described by
:$k\_a\; f\_a\; +\; k\_b\; f\_b\; +\; cdots\; +\; k\_N\; f\_N,,$
where the coefficients $k\_a,\; k\_b,\; ldots,\; k\_N$ are arbitrary integer values.

Intermodulation order

The ''order'' $O$ of a given intermodulation product is the sum of the absolute values of the coefficients,
:$O\; =\; left|k\_a$
ight| + left|k_b
ight| + cdots + left|k_N
ight|,
For example, in our original example above, third-order intermodulation products (IMPs) occur where $|k\_a|+|k\_b|+|k\_c|\; =\; 3$:
:$f\_a\; +\; f\_b\; -\; f\_c,\; f\_a\; +\; f\_c\; -\; f\_b,\; f\_b\; +\; f\_c\; -\; f\_a$
:$2f\_a\; -\; f\_b,\; 2f\_a\; -\; f\_c,\; 2f\_b\; -\; f\_a,\; 2f\_b\; -\; f\_c,\; 2f\_c\; -\; f\_a,\; 2f\_c\; -\; f\_b.$
In many radio and audio applications, low-order IMPs of are most interest, as they fall within the vicinity of the original frequency components, and may therefore interfere with the desired behaviour.

Intermodulation noise

In a transmission path or device, intermodulation noise is noise, generated during modulation and demodulation, that results from nonlinear characteristics in the path or device. Intermodulation noise occurs when the frequency sum or difference of a particular signal, S1, interferes with the component frequency sum or difference of another signal, S2.
Someone listening to a car radio while driving close by an AM or FM radio transmission tower may hear two types of 'interference' / distortion:

★ 'break-through', where the transmission from the near station overwhelms the car radio; and

★ intermodulation, where another station entirely is heard.
On musical instruments, it is the beat frequency produced when two other notes are produced.

Use in music production

In modern record production, it is a commonplace technique to exploit the intermodulation distortion characteristics produced by vacuum-tube electronics and audio tape. For example; once a recording engineer has mixed the various tracks that make up a song into the stereo format, he may send the mix to a vacuum tube based stereo compressor and overload the vacuum tube electrical components. The resulting output will sound fuller and smoother due to the creation of second and third order harmonics.
This technique applies mostly to vacuum tube based equipment though some use electro-optical based compressors to similar effect. Solid-state or integrated-circuit based equipment is rarely used for this effect as its harmonic distortion character is not favorable.
A recording engineer may also record the mix to an audio tape format called reel to reel. In this technique, the engineer will increase the level at which the mix is recorded to audio tape far past the level recommended by the tape's manufacturer. This will result in a slight compressing of the dynamic (volume) range and the production of several second and third order harmonics.

Problems in live audio

RF technicians and audio engineers often experience problems with intermodulation distortion when setting up wireless equipment for live performances and events. Often, wireless equipment for performer’s in-ear monitors or wireless microphones operate on similar frequencies to digital televisions signals, creating harmonic frequencies that interfere with other equipment. With security, technical crew, performance and other wireless signals in use at larger live sporting or concert events, it has become common for hundreds of individual frequencies operating in the same area. Audio engineers have to rely on complex software to calculate all of the possible overlapping and distorted frequencies when setting up such a large live event.

Passive intermodulation

As explained in a previous section, intermodulation can only occur in non-linear systems. Non-linear systems are generally composed of ''active'' components, meaning that the components must be biased with an external power source which is not the input signal (i.e. the active components must be "turned on").
Passive intermodulation (PIM) occurs in passive systems (i.e. the input signal is the only source of energy to the system) when the input signal is very high power, and the system consists of junctions of dis-similar metals or junctions of metals and oxides. The junctions effectively form transistors, so if the input signals are of sufficiently high power, the "effective transistors" could be driven into their non-linear region of operation, and intermodulation may occur, even though upon initial inspection, the system would appear to be linear and unable to generate intermodulations.
PIMs can occur in connectors, or when conductors made of two galvanically unmatched metals come in contact with each other.

References

See also

★ Rusty bolt effect

★ Beat (acoustics)

★ Audio system measurements

External links

★ A program for the calculation of intermodulation products and for the search for free frequencies with wireless radio microphones.

★ Software that calculates possible intermodulation distortion at large live sound events.