A frequency spectrum
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 or intermodulation distortion (IMD), or intermod for short, is the unwanted amplitude modulation of signals containing two or more different frequencies,
each component modulating other components, in a system with
nonlinearities. This will form additional signals at frequencies that
are not, in general, at harmonic frequencies (integer multiples) of either, but instead often at sum and difference frequencies of the original 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 conducting a Volterra series of the characteristic, while the usual approximation of those non-linearities is obtained by conducting a Taylor series.
Intermodulation is rarely desirable in radio or audio processing, as it essentially creates spurious emissions (sidebands; frequency components at the sum and difference of the input frequencies, and possibly more), which can create minor to severe interference to other operations on the signal (cross modulation). It should not be confused with general harmonic distortion (which does have widespread use in audio effects processing), nor confused with intentional modulation (such as a frequency mixer in superheterodyne receivers) where signals to be modulated (multiplied) are presented to different inputs of the mixing elements, although the distinction is difficult in non-linear mixers such as mixer diodes and even single-transistor
oscillator-mixer circuits. Intermodulation specifically creates
non-harmonic tones ("off-key" notes, in the audio case) due to unwanted
mixing of closely spaced frequencies.
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. However, non-linear systems generate harmonics, 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; (i.e some of ).
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 (which are known as the fundamental frequencies), 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 (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
More generally, given an input signal containing an arbitrary number N 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.
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 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 (IMPs) occur where :
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.
In a transmission path or device, intermodulation noise is noise, generated during modulation and demodulation, that results from nonlinear characteristics in the path or device. Intermodulation noise occurs when the frequency sum or difference of a particular signal, S1, interferes with the component frequency sum or difference of another signal, S2.
Someone listening to a car radio while driving close by an AM or FM radio transmission tower may hear two types of 'interference' / distortion:
- 'front-end overload', where the transmission from the near station overwhelms the car radio; and
- intermodulation, where the distortion products are heard.
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"). However, even passive components can perform in a
non-linear manner and cause intermodulation. Diodes
are widely known for their passive nonlinear effects, but parasitic
nonlinearity can arise in other components as well. For example, audio
transformers exhibit non-linear behavior near their saturation point,
electrolytic capacitors can start to behave as rectifiers under
large-signal conditions, and RF connectors and antennas
can exhibit non-linear characteristics. Even the air itself can behave
in a non-linear fashion, which can be exploited to produce audible sound from intermodulation of ultrasonic frequencies.
Passive intermodulation (PIM) occurs in passive systems (i.e. the
input signal is the only source of energy to the system) when the input
signal is very high power, and the system consists of junctions of
dis-similar metals or junctions of metals and oxides. These junctions
effectively form diodes,
which are non-linear. The higher the signal amplitude, the more
pronounced the effect of the non-linearities, and the more prominent
the intermodulation may occur, even though upon initial inspection, the
system would appear to be linear and unable to generate
PIM can also occur in connectors, or when conductors made of two galvanically
unmatched metals come in contact with each other. However, the most
common source of passive intermodulation in connectors comes from the
conduction of signal current through ferromagnetic metals such as
nickel, which has a nonlinear magnetization-inductance hysteresis. This
effect has been exploited to make reliable sources of PIM, which can be used to cancel unwanted PIM from a system.
Intermodulation in electronic circuits
Intermodulation can be caused by many common amplifier limitations, such as slew rate, crossover distortion and reduced transistor hFE or saturation of collector-emitter junctions near clipping. Slew-induced distortion (SID; also named slewing induced distortion or slew-rate induced distortion)
can produce intermodulation distortion (IMD) because the gain
reduction, during times when the first signal is slewing (changing
voltage) as fast as the amplifier's power bandwidth can drive it, partially amplitude-modulates the second signal. Similarly, transient intermodulation distortion (TIM or TID, and sometimes referred to as simply transient distortion or dynamic intermodulation distortion)
is the name given to intermodulation resulting from compression that
may come at the peaks of the signal, but often the transients are
accompanied by high slew rate so it is sometimes said that transient
intermodulation distortion is normally nothing more than SID.
Intermodulation in audio applications
Audio engineers usually strive to avoid intermodulation, as for
anything other than extremely simple input waveforms, it introduces
frequency components that are not harmonically related, which tends to
sound unmusical and unpleasant. However, certain audio effects rely on amplitude modulation; these include tremolo and ring modulation,
and one way to generate such effects is through deliberate
intermodulation in a non-linear device (although more often it may be
achieved by an analog multiplier without intermodulation). Harmonic distortion occurs through the same mechanism (non-linearity in an amplifier or loudspeaker
for instance) as intermodulation distortion, but involves an input
waveform containing only a single frequency component, or several
frequency components that are already harmonically related. All audio
devices give rise to distortion to some extent; harmonic distortion and intermodulaton distortion tests
highlight different aspects of imperfections, and one type of
distortion may be inaudibly low while the other is significantly high
for some equipment under certain conditions.
Intermodulation distortion in audio is usually specified as the Root Mean Square
(RMS) 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 Audio system measurements standard tests include SMPTE standard RP120-1994 
where two signals (at 70Hz and 6kHz, with 4:1 amplitude ratios) are
used for the test; many other standards (such as DIN, CCIF) use other
frequencies and amplitude ratios. Opinion varies over the ideal ratio
of test frequencies (e.g. 3:4, or almost -but not exactly - 3:1 for example).
After feeding the equipment under test with low distortion input sinewaves, the output distortion can be measured by using a 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.
- ^ Henrie, J., Christianson, A. and Chappell, W. Engineered passive nonlinearities for broadband passive intermodulation distortion mitigation, Microwave and Wireless Components Letters, Vol. 19, pp.614-616, 2009. Available online.
- ^ Henrie, J., Christianson, A. and Chappell, W. Cancellation of passive intermodulaiton distortion in microwave networks, in European Microwave Conference, Amsterdam, The Netherlands, IEEE, 2008. Available online.
- ^ http://www.rane.com/par-i.html#IM Rane Pro Audio Reference for IM
- ^ http://waltjung.org/PDFs/SID_TIM_TAA77_P1.pdf Slewing Induced Distortion in Audio Amplifiers, Part 1 by Walter Jung in The Audio Amateur Issue 1/1977
- ^ http://www.rane.com/par-i.html#IM Intermodulation at Rane
- ^ http://www.leonaudio.com.au/3-4.ratio.distortion.measurement.pdf John Cohen: 3-4 Ratio; A method of measuring distortion products
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).