Intermodulation
Intermodulation or intermodulation distortion 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 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 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 and IMD. 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 where signals to be modulated are presented to an intentional nonlinear element. 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 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, then the output is a signal which includes a number of integer multiples of the input frequency signal;.
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,, and ; which may be expressed as
where the and are the amplitudes and phases of the three components, respectively.
We obtain our output signal,, by passing our input through a non-linear function :
will contain the three frequencies of the input signal,,, and , as well as a number of linear combinations of the fundamental frequencies, each of the form
where,, and are arbitrary integers which can assume positive or negative values. These are the intermodulation products.
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 of frequency components, the output signal will contain a number of frequency components, each of which may be described by
where the coefficients are arbitrary integer values.
Intermodulation order
The order of a given intermodulation product is the sum of the absolute values of the coefficients,For example, in our original example above, third-order intermodulation products occur where :
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.Passive intermodulation, however, occurs in passive devices that are subjected to two or more high power tones. The PIM product is the result of the two 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.
It is also possible for a single broadband carrier to generate PIM if it passes through a PIM generating surface or defect. These distortions would show up as side lobes in a telecommunication signal and interfere with adjacent channels and impede reception.
PIM can be severe problem in modern communication systems. Paths that share both high power transmission and the receive signal are most susceptible to this kind of interference. Once PIM interference finds its way to receive path, it can not be filtered or separated.
PIM Testing
IEC 62037 is the international standard for PIM testing and gives specific details as to PIM measurement setups. The standard specifies the use of two +43 dBm tones for the test signals for PIM testing. This power level has been used by RF equipment manufacturers for more than a decade to establish PASS / FAIL specifications for RF components.Intermodulation in electronic circuits
can produce intermodulation distortion when the first signal is slewing at the limit of the amplifier's power bandwidth product. This induces an effective reduction in gain, partially amplitude-modulating the second signal. If SID only occurs for a portion of the signal, it is called "transient" intermodulation distortion.Measurement
Intermodulation distortion in audio is usually specified as the root mean square value of the various sum-and-difference signals as a percentage of the original signal's RMS voltage, although it may be specified in terms of individual component strengths, in decibels, as is common with RF work. Audio IMD standard tests include SMPTE standard RP120-1994 where two signals are used for the test; many other standards use other frequencies and amplitude ratios. Opinion varies over the ideal ratio of test frequencies.After feeding the equipment under test with low distortion input sinewaves, the output distortion can be measured by using an electronic filter to remove the original frequencies, or spectral analysis may be made using Fourier Transformations in software or a dedicated spectrum analyser, or when determining intermodulation effects in communications equipment, may be made using the receiver under test itself.
In radio applications, intermodulation may be measured as adjacent channel power ratio. Hard to test are intermodulation signals in the GHz-range generated from passive devices. Manufacturers of these scalar PIM-instruments are Summitek and Rosenberger. The newest developments are PIM-instruments to measure also the distance to the PIM-source. Anritsu offers a radar-based solution with low accuracy and Heuermann offers a frequency converting vector network analyzer solution with high accuracy.