Editing Intermodulation (section)

{{Short description|Non-linear effect in amplitude modulation}}
{{Use dmy dates|date=July 2022|cs1-dates=y}}
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{{about|signal processing|the album by Bill Evans and Jim Hall|Intermodulation (album)}}
[[File:RF Intermodulation at 280 MHz.jpg|thumb|upright=1.4|A [[frequency spectrum]] plot showing intermodulation between two injected signals at 270 and 275&nbsp;MHz (the large spikes).  Visible intermodulation products are seen as small spurs at 280&nbsp;MHz and 265&nbsp;MHz.]]
[[File:3rd order intermod animation (thumbnail).png|right|3rd order intermodulation products (D3 and D4) are the result of nonlinear behavior of an amplifier. The input power level into the amplifier is increased by 1&nbsp;dB in each successive frame. The output power of the two carriers (M1 and M2) increases by about 1&nbsp;dB in each frame, while the 3rd order intermodulation products (D3 and D4) grow by 3&nbsp;dB in each frame. Higher-order intermodulation products (5th order, 7th order, 9th order) are visible at very high input power levels as the amplifier is driven past saturation. Near saturation, each additional dB of input power results in proportionally less output power going into the amplified carriers and proportionally more output power going into the unwanted intermodulation products. At and above saturation, additional input power results in a ''decrease'' in output power, with most of that additional input power getting dissipated as heat and increasing the level of the non-linear intermodulation products with respect to the two carriers.]]

'''Intermodulation''' ('''IM''') or '''intermodulation distortion''' ('''IMD''') is the [[amplitude modulation]] of [[Signal (electrical engineering)|signals]] containing two or more different [[frequencies]], caused by [[non-linear|nonlinearities]] or time variance in a system.  The intermodulation between frequency components will form additional components at frequencies that are not just at [[harmonic]] frequencies ([[integer]] [[multiple (mathematics)|multiple]]s) of either, like [[harmonic distortion]], but also at the sum and difference frequencies of the original frequencies and at sums and differences of multiples of those frequencies.

Intermodulation is caused by non-linear behaviour of the [[signal processing]] (physical equipment or even algorithms) being used. The [[theoretical]] outcome of these non-linearities can be calculated by generating a [[Volterra series]] of the characteristic, or more approximately by a [[Taylor series]].<ref name="Rouphael_2014"/>

Practically all audio equipment has some non-linearity, so it will exhibit some amount of IMD, which however may be low enough to be imperceptible by humans. Due to the characteristics of the human [[auditory system]], the same percentage of IMD is perceived as more bothersome when compared to the same amount of harmonic distortion.<ref name="Rumsey-Mccormick_2012"/><ref name="Davis-Jones_1989"/>{{Dubious|date=May 2015|reason = harmonic distortion with high-order components (like crossover distortion) can be just as objectionable at a given percent}}

Intermodulation is also usually undesirable in radio, as it creates unwanted [[spurious emission]]s, often in the form of [[sidebands]]. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel [[interference (communication)|interference]], which can reduce audio clarity or increase spectrum usage.

IMD is only distinct from [[harmonic distortion]] in that the stimulus signal is different.  The same nonlinear system will produce both [[total harmonic distortion]] (with a solitary sine wave input) and IMD (with more complex tones).  In music, for instance, IMD is [[Distortion (music)|intentionally applied]] to electric guitars using overdriven [[Guitar amplifier|amplifiers]] or [[Effects unit|effects pedals]] to produce new tones at ''sub''harmonics of the tones being played on the instrument.  See [[Power chord#Analysis]].

IMD is also distinct from intentional modulation (such as a [[frequency mixer]] in [[superheterodyne receiver]]s) where signals to be modulated are presented to an intentional nonlinear element ([[Analog multiplier|multiplied]]).  See [[non-linear]] [[Electronic mixer#Product mixers|mixers]] such as mixer [[diode]]s and even single-[[transistor]] oscillator-mixer circuits. However, while the intermodulation products of the received signal with the local oscillator signal are intended, superheterodyne mixers can, at the same time, also produce unwanted intermodulation effects from strong signals near in frequency to the desired signal that fall within the passband of the receiver.