Intermodulation
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Intermodulation or intermod 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. The largest intermodulation products appear at 
or 
(second-order intermodulation), and less so at 
or 
(third order intermodulation).
The cause for intermodulation is the existence of non-linear characteristics of the according equipment. The theoretical outcome of these nonlinearities can be calculated by conducting a Volterra series of the characteristic, while the usual approximation of those nonlinearities is obtained by conducting a Taylor series. According to the summands in those series, the above numbering of orders is counted.
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.
Since intermodulations require non-linearities, they usually occurs only in ‘active’ circuit elements, such as amplifiers and diodes. However ‘passive’ structures can produce passive intermodulations, which are identical to intermodulation produced by ‘active’ circuit elements.
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[edit] Intermodulation and non-linear systems
By definition, a linear system cannot produce intermodulations. If the input of a linear system is a signal of a single frequency, then the output is a signal of the same frequency and only the output amplitude and output phase can vary from the input signal. Non-linear systems generate harmonics, meaning if the input of a non-linear system is a signal of a single frequency, 
, the output is a signal which includes an infinite number of integer multiples of the input frequency 
(albight higher order harmonics carry less energy, and asymptotically approach zero, since the principal of energy conservation requires that the total energy of the output signal must be less than or equal to the energy of the input signal).
Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider, for instance, a number of three cosine signals at frequencies 
, in the vicinity of a central frequency 
, that are added and sent to the input of a nonlinear time-invariant system, i.e. a system for which the relationship
applies, where 
and 
are the input and the output, respectively; 
is a non-linear function independent of previous input values. In this case, the output signal will contain the three frequencies of the input signal, (which are called the fundamental frequencies), as well as an infinite number of linear combinations of the fundamental frequencies
where 
are arbitrary integers which can assume positive or negative values. The frequencies which are of most interest are those in the vicinity of again. For example, there will be the so-called third-order Intermodulation Products (IMPs), which can be either dominant
or specific
More generally, given a number N of carriers at frequencies 
, with a reference centre frequency of , we could find at the output an IMP which frequency is given by
where the coefficients 
are small integer numbers (
relative numbers). The order 
of the intermodulation product is given by the sum of the absolute values of these coefficients,
whereas the zone number 
, sum of the coefficients,
gives the reference centre frequency, 
. The dominant terms are those for which all 
's are unity: all the other combinations will be considered specific. The name dominant comes from the fact that these terms are either more powerful or more numeorus than the specific ones.
Given two different input frequencies, we can have
- second-order, second-zone IMPs
- second-order, zero-zone (base-band) IMPs
- third-order, first-zone IMPs
- fifth-order, first-zone IMPs
- etc.,
Conservation of power requires that the total power of the output signal must be less than or equal to the total power of the input signal. Since the output signal of a non-linear system is composed of an infinite sum of an intermodulation products, power in higher order products must be less than the power of lower order products, and asymptotically approach zero for infinite order products.
Generally, the first-zone IMPs require more attention, since they fall in the vicinity of the original carriers and can overlap to them, whereas other zones' IMPs fall in the harmonics of , which can be very far from the original carriers.
[edit] 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.
[edit] Intermodulation distortion
Intermodulation distortion is nonlinear distortion characterized by the appearance, in the output of a device, of frequencies that are linear combinations of the fundamental frequencies and all harmonics present in the input signals.
Harmonic components themselves are not usually considered to characterize intermodulation distortion. When the harmonics are included as part of the distortion, a statement to that effect should be made. This is usually considered Total harmonic distortion.
IMD in its most basic and most testable form shows up as presence of frequencies not in the input signal. If the sum of two pure tones is the input to the system, IMD shows up as the presence of new tones in the output whose frequencies are the sum and difference of the input tone frequencies.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] References
This article contains material from the Federal Standard 1037C (in support of MIL-STD-188), which, as a work of the United States Government, is in the public domain.
