Intermodulation product

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An intermodulation product (IMP) is a signal generated by the transit of two or more uncorrelated signals entering a nonlinear device, such as a nonlinear amplifier.

On musical instruments, it is the beat frequency produced when two other notes are produced.

On a radio, if two strong stations are there, they will appear in the wrong places on the dial on cheap radios.

[edit] Technical definitions

Consider, for instance, a number of three cosine signals at frequencies $f 1$ , $f 2$ , and $f 3$ , in the vicinity of a central frequency $f c$ , that are added and sent to the input of a nonlinear time-invariant system, i.e. a system for which the relationship

$y = T(x)\,$

applies, where $x$ and $y$ are the input and the output, respectively; $T(\cdot)$ is not a linear function and does not keep memory of the past values of the input. In this case, the output signal $y$ will contain the original tones, called fundamentals

$f_1, f_2, f_3\,$

and a number of noise-like terms, i.e. sine tones at different frequencies, interspersed among the fundamentals in the vicinity of $f c$ again. For example, there will be the so-called third-order IMPs, which can be either dominant

f 1 + f 2 - f 3, f 1 + f 3 - f 2, f 1 + f 2 - f 3

or specific

2 f 1 - f 2,2 f 1 - f 3,2 f 2 - f 1,2 f 2 - f 3,2 f 3 - f 1,2 f 3 - f 2 .

Distribution of third-order intermodulations: in blue the position of the fundamental carriers, in red the position of dominant IMPs, in green the position of specific IMPs.

More generally, given a number $N$ of carriers at frequencies $f_1, f_2, \ldots, f_N$ , with a reference centre frequency of $f c$ , we could find at the output an IMP which frequency is given by

$k_1 f_1 + k_2 f_2 + \cdots + k_N f_N,\,$

where the coefficients $k_1, k_2, \ldots, k_N$ are small integer numbers ( $k_i \in$ relative numbers). The order $O$ of the intermodulation product is given by the sum of the absolute values of these coefficients,

whereas the zone number $Z$ , sum of the coefficients,

$Z = k_1 + k_2 + \cdots + k_N\,$

gives the reference centre frequency, $Z f c$ . The dominant terms are those for which all $\left|k_i\right|$ '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 → $f 1 + f 2$
second-order, zero-zone (base-band) IMPs → $f 1 - f 2$
third-order, first-zone IMPs → $2 f 1 - f 2$ , $2 f_2 - f_1,\dots$
fifth-order, first-zone IMPs → $3 f 1 - 2 f 2$ , $3 f_2 - 2 f_1,\dots$
etc.,

and more sums and differences of the two frequencies and their harmonics.

It can be shown that the higher is the order of the product, the weaker is its power; moreover, only first-zone IMPs are really disturbing, since they fall in the vicinity of the original carriers and can overlap to them, whereas other zones' IMPs fall in the harmonics of $f c$ , which can be very far from the original carriers.

Categories: Cleanup from October 2006 | Waves | Radio | Electronics terms | Radio electronics

Intermodulation product

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[edit] Technical definitions

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