Intermodulation

plot showing intermodulation between two injected signals at 270 and 275 MHz (the large spikes). Visible intermodulation products are seen as small spurs at 280 MHz and 265 MHz. Intermodulation (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. 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.…

plot showing intermodulation between two injected signals at 270 and 275 MHz (the large spikes). Visible intermodulation products are seen as small spurs at 280 MHz and 265 MHz.]] Intermodulation (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. 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. Intermodulation is also usually undesirable in radio, as it creates unwanted spurious emissions, often in the form of sidebands. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel 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 intentionally applied to electric guitars using overdriven amplifiers or effects pedals to produce new tones at subharmonics 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 receivers) where signals to be modulated are presented to an intentional nonlinear element (multiplied). See non-linear mixers such as mixer diodes 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. ==Causes of intermodulation== A linear time-invariant 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_a, then the output is a signal which includes a number of integer multiples of the input frequency signal; (i.e. some of ~ f_a, 2f_a, 3f_a, 4f_a, \ldots ). Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider an input signal that contains three frequency components at ~f_a , ~ f_b , and ~f_c ; which may be expressed as \ x(t) = M_a \sin(2 \pi f_a t + \phi_a) + M_b \sin(2 \pi f_b t + \phi_b) + M_c \sin(2 \pi f_c t + \phi_c) where the \ M and \ \phi are the amplitudes and phases of the three components, respectively. We obtain our output signal, \ y(t) , by passing our input through a non-linear function G : \ y(t) = G\left(x(t)\right)\, \ y(t) will contain the three frequencies of the input signal, ~f_a , ~ f_b , and ~f_c (which are known as the fundamental frequencies), as well as a number of linear combinations of the fundamental frequencies, each in the form \ k_af_a + k_bf_b + k_cf_c where ~k_a , ~ k_b , and ~k_c are arbitrary integers which can assume positive or negative values. These are the intermodulation products (or IMPs). In general, each of these frequency components will have a different amplitude and phase, which depends on the specific non-linear function being used, and also on the amplitudes and phases of the original input components. More generally, given an input signal containing an arbitrary number N of frequency components f_a, f_b, \ldots, f_N , the output signal will contain a number of frequency components, each of which may be described by k_a f_a + k_b f_b + \cdots + k_N f_N,\, where the coefficients k_a, k_b, \ldots, k_N are arbitrary integer values. \ O = \left|k_a\right| + \left|k_b\right| + \cdots + \left|k_N\right|, For example, in our original example above, third-order intermodulation products (IMPs) occur where \ |k_a|+|k_b|+|k_c| = 3 : f_a + f_b + f_c f_a + f_b - f_c f_a + f_c - f_b f_b + f_c - f_a 2f_a - f_b 2f_a - f_c 2f_b - f_a 2f_b - f_c 2f_c - f_a 2f_c - f_b 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 waves, one at f_1 and one at f_2 . When you cube the sum of these sine waves you will get sine waves at various frequencies including 2\times f_2-f_1 and 2\times f_1-f_2 . If f_1 and f_2 are large but very close together then 2\times f_2-f_1 and 2\times f_1-f_2 will be very close to f_1 and f_2 . ==Passive intermodulation (PIM)== 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), however, occurs in passive devices (which may include cables, antennas etc.) that are subjected to two or more high power tones. The PIM product is the result of the two (or more) high power tones mixing at device nonlinearities such as junctions of dissimilar metals or metal-oxide junctions, such as loose corroded connectors. The higher the signal amplitudes, the more pronounced the effect of the nonlinearities, and the more prominent the intermodulation that occurs — even though upon initial inspection, the system would appear to be linear and unable to generate intermodulation. The requirement for "two or more high power tones" need not be discrete tones. Passive intermodulation can also occur between different frequencies (i.e. different "tones") within a single broadband carrier. These PIMs would show up as sidebands in a telecommunication signal, which interfere with adjacent channels and impede reception. Passive intermodulations are a major concern in modern communication systems in cases when a single antenna is used for both high power transmission signals as well as low power receive signals (or when a transmit antenna is in close proximity to a receive antenna). Although the power in the passive intermodulation signal is typically many orders of magnitude lower than the power of the transmit signal, the power in the passive intermodulation signal is oftentimes on the same order of magnitude (and possibly higher) than the power of the receive signal. Therefore, if a passive intermodulation finds its way to receive path, it cannot be filtered or separated from the receive signal. The receive signal would therefore be clobbered by the passive intermodulation signal. ==References==

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