Editing Intermodulation (section)

=== Intermodulation order ===
[[Image:Imps thirdorder.png|thumb|upright=1.8|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.]]

The ''order'' <math>\ O</math> of a given intermodulation product is the sum of the absolute values of the coefficients,

:<math>\ O = \left|k_a\right| + \left|k_b\right| + \cdots + \left|k_N\right|,</math>

For example, in our original example above, third-order intermodulation products (IMPs) occur where <math>\ |k_a|+|k_b|+|k_c| = 3</math>:

* <math>f_a + f_b + f_c</math>
* <math>f_a + f_b - f_c</math>
* <math>f_a + f_c - f_b</math>
* <math>f_b + f_c - f_a</math>
* <math>2f_a - f_b</math>
* <math>2f_a - f_c</math>
* <math>2f_b - f_a</math>
* <math>2f_b - f_c</math>
* <math>2f_c - f_a</math>
* <math>2f_c - f_b</math>

In many radio and audio applications, odd-order IMPs are of most interest, as they fall within the vicinity of the original frequency components, and may therefore interfere with the desired behaviour. For example, intermodulation distortion from the third order ('''IMD3''') of a circuit can be seen by looking at a signal that is made up of two [[sine wave]]s, one at <math>f_1</math> and one at <math>f_2</math>.  When you cube the sum of these sine waves you will get sine waves at various [[frequency|frequencies]] including <math>2\times f_2-f_1</math> and <math>2\times f_1-f_2</math>.  If <math>f_1</math> and <math>f_2</math> are large but very close together then <math>2\times f_2-f_1</math> and <math>2\times f_1-f_2</math> will be very close to <math>f_1</math> and <math>f_2</math>.