Nonlinear distortion

Last updated April 28, 2019

Nonlinear distortion is a term used (in fields such as electronics, audio and telecommunications) to describe the phenomenon of a non-linear relationship between the "input" and "output" signals of - for example - an electronic device.

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. The identification of the electron in 1897, along with the invention of the vacuum tube, which could amplify and rectify small electrical signals, inaugurated the field of electronics and the electron age.

Model

For many devices, a linear model is accurate only for small signal levels. For example, at 2 volts input, a typical audio amplifier might put out 20 V, meaning the linear gain is 10 V/V. For 3 V input, it might then output 30 V. However, the model implies that at 50 V input it would produce 500 V, which is not possible with most amplifiers.

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.

Mathematically, the input-output relationship of many devices should be described by a polynomial or Taylor series, as shown below.

Polynomial In mathematics, sum of products of variables, power of variables, and coefficients

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, $x$ , is $x 2 - 4 x + 7$ . An example in three variables is $x 3 + 2 xyz 2 - yz + 1$ .

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

$v=\sum _{k=1}^{\infty }a_{k}u^{k}$

For larger values of u, the higher order coefficients such as $a_{2}$ and $a_{3}$ come into play.

Effects of nonlinearity

Nonlinearity can have several effects, which are unwanted in typical situations. The $a_{3}$ term for example would, when the input is a sine wave with frequency $\omega$ , result in an extra sine wave at $3\omega$ , as shown below.

In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle.

$v=(a_{1}+{\frac {3}{4}}a_{3})sin(\omega t)-{\frac {1}{4}}a_{3}sin(3\omega t)$

In certain situations, this spurious signal can be filtered away because the "harmonic" $3\omega$ lies far outside the frequency range used, but in cable television, for example, third order distortion could cause a 200 MHz signal to interfere with the regular channel at 600 MHz.

A harmonic is any member of the harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves. A harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz, 150 Hz, 200 Hz and any addition of waves with these frequencies is periodic at 50 Hz.

An n^th characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at $L and L, where L is the length of the string. In fact, each n th characteristic mode, for n not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions L and L . If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the n th characteristic modes, where n is a multiple of 3, will be made relatively more prominent.$

Nonlinear distortion applied to a superposition of two signals at different frequencies causes the circuit to act as a frequency mixer, creating intermodulation distortion.

Frequency mixer nonlinear electrical circuit that creates new frequencies from two signals applied to it

In electronics, a mixer, or frequency mixer, is a nonlinear 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 difference of the original frequencies. Other frequency components may also be produced in a practical frequency mixer.

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Related Research Articles

An electronic mixer is a device that combines two or more electrical or electronic signals into one or two composite output signals. There are two basic circuits that both use the term mixer, but they are very different types of circuits: additive mixers and multiplicative mixers. Additive mixers are also known as "analog adders" to distinguish from the related digital adder circuits.

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (values of atomic electric fields, typically 10⁸ V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.

In engineering, a transfer function of an electronic or control system component is a mathematical function which theoretically models the device's output for each possible input. In its simplest form, this function is a two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.

Distortion is the alteration of the original shape of something. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal representing sound or a video signal representing images, in an electronic device or communication channel.

An electro-optic modulator (EOM) is an optical device in which a signal-controlled element exhibiting the electro-optic effect is used to modulate a beam of light. The modulation may be imposed on the phase, frequency, amplitude, or polarization of the beam. Modulation bandwidths extending into the gigahertz range are possible with the use of laser-controlled modulators.

In signal processing, group delay is the time delay of the amplitude envelopes of the various sinusoidal components of a signal through a device under test, and is a function of frequency for each component. Phase delay, in contrast, is the time delay of the phase as opposed to the time delay of the amplitude envelope.

Heterodyning is a signal processing technique invented by Canadian inventor-engineer Reginald Fessenden that creates new frequencies by combining or mixing two frequencies. Heterodyning is used to shift one frequency range into another, new one, and is also involved in the processes of modulation and demodulation. The two frequencies are combined in a nonlinear signal-processing device such as a vacuum tube, transistor, or diode, usually called a mixer. In the most common application, two signals at frequencies $f 1$ and $f 2$ are mixed, creating two new signals, one at the sum $f 1 + f 2$ of the two frequencies, and the other at the difference $f 1 - f 2$ . These frequencies are called heterodynes. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. Heterodyne frequencies are related to the phenomenon of "beats" in acoustics.

In telecommunications, a third-order intercept point (IP₃) is a specific figure of merit associated with the more general Third Order Intermodulation (TOI) distortion, which is a measure for weakly nonlinear systems and devices, for example receivers, linear amplifiers and mixers. It is based on the idea that the device nonlinearity can be modeled using a low-order polynomial, derived by means of Taylor series expansion. The third-order intercept point relates nonlinear products caused by the third-order nonlinear term to the linearly amplified signal, in contrast to the second-order intercept point that uses second-order terms. (IP₃) is the generally accepted unambiguous term for the third-order intercept point, although one occasionally sees the use of TOI for this figure-of-merit, such use is considered as incorrect by experts in the field.

The total harmonic distortion (THD) is a measurement of the harmonic distortion present in a signal and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. Distortion factor, a closely related term, is sometimes used as a synonym.

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 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.

Linear electronic oscillator circuits, which generate a sinusoidal output signal, are composed of an amplifier and a frequency selective element, a filter. A linear oscillator circuit which uses an RC network, a combination of resistors and capacitors, for its frequency selective part is called an RC oscillator.

A function generator is usually a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies. Some of the most common waveforms produced by the function generator are the sine wave, square wave, triangular wave and sawtooth shapes. These waveforms can be either repetitive or single-shot. Integrated circuits used to generate waveforms may also be described as function generator ICs.

In electronics, a frequency multiplier is an electronic circuit that generates an output signal whose output frequency is a harmonic (multiple) of its input frequency. Frequency multipliers consist of a nonlinear circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent bandpass filter selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output.

In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior. The describing function is one of the few widely applicable methods for designing nonlinear systems, and is very widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such as industrial process controls, servomechanisms, and electronic oscillators.

Gain compression is a reduction in "differential" or "slope" gain caused by nonlinearity of the transfer function of the amplifying device. This nonlinearity may be caused by heat due to power dissipation or by overdriving the active device beyond its linear region. It is a large-signal phenomenon of circuits.

Ripple in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.

A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The "pump" motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency $and damping .$

In electronic music waveshaping is a type of distortion synthesis in which complex spectra are produced from simple tones by altering the shape of the waveforms.

In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal. The term complex is used because mathematically this effect can be expressed as a complex number.

Differential gain is a kind of linearity distortion which affects the color saturation in TV broadcasting.