
Intermodulation (IM) or intermodulation distortion (IMD) is the
amplitude modulation
Amplitude modulation (AM) is a signal modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the instantaneous amplitude of the wave is varied in proportion t ...
of
signals
A signal is both the process and the result of Signal transmission, transmission of data over some transmission media, media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processin ...
containing two or more different
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, 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
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
frequencies (
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
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
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...
(physical equipment or even algorithms) being used. The
theoretical outcome of these non-linearities can be calculated by generating a
Volterra series
The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system t ...
of the characteristic, or more approximately by a
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
.
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 auditory system is the sensory system for the sense of hearing. It includes both the ear, sensory organs (the ears) and the auditory parts of the sensory system.
System overview
The outer ear funnels sound vibrations to the eardrum, incre ...
, 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 emission
In radio communication, a spurious emission is any component of a radiated radio frequency signal, the complete suppression of which, would not impair the integrity of the modulation type, or the information being transmitted. A radiated signal ...
s, often in the form of
sidebands. For radio transmissions this increases the occupied bandwidth, leading to adjacent channel
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
, 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
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It is a two-port electronic circuit that uses electric power from a power suppl ...
or
effects pedals
An effects unit, effects processor, or effects pedal is an electronic device that alters the sound of a musical instrument or other audio source through audio signal processing.
Common effects include distortion (music), distortion/overdrive, ...
to produce new tones at ''sub''harmonics 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 electronics, a mixer, or frequency mixer, is an electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals are applied to a mixer, and it produces new signals at the sum and di ...
in
superheterodyne receiver
A superheterodyne receiver, often shortened to superhet, is a type of radio receiver that uses frequency mixing to convert a received signal to a fixed intermediate frequency (IF) which can be more conveniently processed than the original car ...
s) where signals to be modulated are presented to an intentional nonlinear element (
multiplied). See
non-linear
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...
mixers such as mixer
diode
A diode is a two-Terminal (electronics), terminal electronic component that conducts electric current primarily in One-way traffic, one direction (asymmetric electrical conductance, conductance). It has low (ideally zero) Electrical resistance ...
s and even single-
transistor
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
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
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
and
phase can differ from the input signal.
Non-linear systems generate
harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
s 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; (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 combination
In mathematics, a linear combination or superposition is an Expression (mathematics), expression constructed from a Set (mathematics), set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of ''x'' a ...
s of the fundamental frequencies, each in 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 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 (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. 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
A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...
s, one at
and one at
. When you cube the sum of these sine waves you will get sine waves at various
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
including
and
. If
and
are large but very close together then
and
will be very close to
and
.
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
sideband
In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, that are the result of the modulation process. The sidebands carry the information transmitted by the radio signal. The sidebands c ...
s 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 often times 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.
Sources of passive intermodulation
Ferromagnetic materials are the most common materials to avoid and include ferrites, nickel, (including nickel plating) and steels (including some stainless steels). These materials exhibit
hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
when exposed to reversing magnetic fields, resulting in PIM generation.
Passive intermodulation can also be generated in components with manufacturing or workmanship defects, such as cold or cracked solder joints or poorly made mechanical contacts. If these defects are exposed to high radio frequency currents, passive intermodulation can be generated. As a result, radio frequency equipment manufacturers perform factory PIM tests on components, to eliminate passive intermodulation caused by these design and manufacturing defects.
Passive intermodulation can also be inherent in the design of a high power radio frequency component where radio frequency current is forced to narrow channels or restricted.
In the field, passive intermodulation can be caused by components that were damaged in transit to the cell site, installation workmanship issues and by external passive intermodulation sources. Some of these include:
* Contaminated surfaces or contacts due to dirt, dust, moisture or oxidation.
* Loose mechanical junctions due to inadequate torque, poor alignment or poorly prepared contact surfaces.
* Loose mechanical junctions caused during transportation, shock or vibration.
* Metal flakes or shavings inside radio frequency connections.
* Inconsistent metal-to-metal contact between radio frequency connector surfaces caused by any of the following:
** Trapped dielectric materials (adhesives, foam, etc.), cracks or distortions at the end of the outer conductor of coaxial cables, often caused by overtightening the back nut during installation, solid inner conductors distorted in the preparation process, hollow inner conductors excessively enlarged or made oval during the preparation process.
* Passive intermodulation can also occur in connectors, or when conductors made of two
galvanically unmatched metals come in contact with each other.
* Nearby metallic objects in the direct beam and side lobes of the transmit antenna including rusty bolts, roof flashing, vent pipes, guy wires, etc.
Passive intermodulation testing
IEC 62037 is the international standard for passive intermodulation testing and gives specific details as to passive intermodulation measurement setups. The standard specifies the use of two +43 dBm (20 W) tones for the test signals for passive intermodulation testing. This power level has been used by radio frequency equipment manufacturers for more than a decade to establish PASS / FAIL specifications for radio frequency components.
Intermodulation in electronic circuits
Slew-induced distortion (SID) can produce intermodulation distortion (IMD) when the first signal is slewing (changing voltage) 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
In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square.
Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denote ...
(RMS) value of the various sum-and-difference signals as a percentage of the original signal's root mean square voltage, although it may be specified in terms of individual component strengths, in
decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
s, as is common with
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...
work.
Audio system measurements
Audio system measurements are used to quantify audio system performance. These measurements are made for several purposes. Designers take measurements to specify the performance of a piece of equipment. Maintenance engineers make them to ensur ...
(Audio IMD) include SMPTE standard RP120-1994
where two signals (at 60 Hz and 7 kHz, 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 an
electronic filter
Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped-element model, lumped electronic components, as opposed to distributed-element filters. That ...
to remove the original frequencies, or spectral analysis may be made using
Fourier transformations in software or a dedicated
spectrum analyzer
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most co ...
, or when determining intermodulation effects in communications equipment, may be made using the receiver under test itself.
In
radio
Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
applications, intermodulation may be measured as
adjacent channel power ratio. Hard to test are intermodulation signals in the GHz-range generated from passive devices (PIM: passive intermodulation). 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.
See also
*
Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, ''perceived'' as a periodic variation in volume whose rate is the difference of the two frequencies.
With tuning instruments that can produc ...
*
Audio system measurements
Audio system measurements are used to quantify audio system performance. These measurements are made for several purposes. Designers take measurements to specify the performance of a piece of equipment. Maintenance engineers make them to ensur ...
*
Second-order intercept point
The Second-order intercept point, also known as the SOI, IP2, or IIP2 (Input intercept point), is a measure of linearity that quantifies the second-order distortion generated by nonlinear systems and devices. Examples of frequently used devices th ...
(SOI)
*
Third-order intercept point
In telecommunications, a third-order intercept point (IP3 or TOI) is a specific figure of merit associated with the more general third-order intermodulation distortion (IMD3), which is a measure for weakly nonlinear systems and devices, for exa ...
(TOI), a metric of an amplifier or system related to intermodulation
*
Luxemburg–Gorky effect
References
*
Further reading
* {{cite magazine , title=Intermodulation Performance and Measurement of Intermodulation Components , author-first=Lloyd , author-last=Butler , date=August 1997 , id=VK5BR , magazine=Amateur Radio , volume= , number= , publisher= , pages= , url=http://users.tpg.com.au/ldbutler/Intermodulation.htm , access-date=2012-01-30
Audio amplifier specifications
Waves
Radio electronics