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# Intermodulationbasics

ntermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies, caused by 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 multiples) 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. For details please refer to intermodulation.

A linear system cannot produce intermodulation. If the input of a linear time-invariant 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.

Non-linear systems generate harmonics in response to sinusoidal input, meaning that if the input of a non-linear system is a signal of a single frequency f, then the output is a signal which includes a number of integer multiples of the input frequency signal, i.e. n·f with n ∈ 0, 1, 2, 3, 4, ....

Let denote a input signal that comtains n frequency components of f1, f2, ..., fn. After passing through a non-linear system, the output signal is .

y(t) contains frequency components that are the linear combinations of the fundamental frequencies, in the form of , where ki is an arbitary integer.

Intermodulation order

The order O of a given intermodulation product (IMP) is the sum of the absolute values of its frequency coefficients: . E.g., the third-order products of two frequency components f1 and f2 are (note: f and -f are considered as indentical frequency components, only positive frequency is):

Toolbox: intermodulation product (IMP) calculator
Order f1=f2=f3=f4=
IMP5, 20, 30, 35, 40, 45
Plot
Details2f1-f2 = 5
-f1+2f2 = 20
3f1 = 30
2f1+f2 = 35
f1+2f2 = 40
3f2 = 45