Distortion factor

This article is about physical quantity. For the music group see distortion factor (band) .

The distortion , even harmonics - or distortion content is a measure of distortion of an originally sinusoidal alternating signal represented by non-linear behavior of a module ( amplifier , analog-to-digital converter , digital-to-analog converter ) or device ( speaker , microphone , tape recorder ) caused. The distortion factor is specified as the size of the number dimension ; alternatively, the logarithmic degree of harmonic distortion is used.

definition

Distortion factor

The harmonic distortion indicates the extent to which the harmonics, which are superimposed on a sinusoidal fundamental oscillation , contribute to the overall signal. ${\displaystyle k}$

One identifies

• the rms value of an electrical voltage ${\displaystyle U}$
• the effective value of their fundamental oscillation ${\displaystyle U_{1}}$
• the rms value of the harmonic with -fold frequency with , ${\displaystyle n}$ ${\displaystyle U_{n}}$

the distortion factor is defined by:

${\displaystyle k={\sqrt {\frac {U_{2}^{2}+U_{3}^{2}+U_{4}^{2}+\dots }{U_{1}^{2}+U_{2}^{2}+U_{3}^{2}+U_{4}^{2}+\dots }}}={\frac {\sqrt {U^{2}-U_{1}^{2}}}{U}}}$

The components of the individual harmonics in the distortion factor are often determined separately: ${\displaystyle k_{n}}$

${\displaystyle k_{n}={\sqrt {\frac {U_{n}^{2}}{U_{1}^{2}+U_{2}^{2}+U_{3}^{2}+U_{4}^{2}+\dots }}}\quad {\text{mit }}n\geq 2}$

${\displaystyle \Rightarrow k\ =\ {\sqrt {k_{2}^{2}+k_{3}^{2}+k_{4}^{2}+\dots }}}$

The equation for with = 1 gives the fundamental vibration content . ${\displaystyle k_{n}}$ ${\displaystyle n}$

Correspondingly, the distortion factor can also be used for the electrical current strength .

The distortion factor can have values ​​from zero to one and is therefore usually given in percent .

Distortion attenuation

Often, instead of the distortion factor, a logarithmic degree of distortion attenuation is given in decibels  (dB):

${\displaystyle L_{k}=20\cdot \lg {\frac {1}{k}}\ \mathrm {dB} }$

A distortion reduction measure of

• So 20 dB corresponds to a distortion factor of 10 ⁻¹ = 0.1 = 10%
• 40 dB corresponds to 10 ⁻² = 0.01 = 1%
• 60 dB means 10 ⁻³ = 0.001 = 0.1%.

The degree of distortion attenuation has a positive value; the harmonic distortion gain is measured negative (less common) with the same numerical value.

other sizes

In addition to the distortion factor, u. a. the terms fundamental vibration content, crest factor or in the English-speaking world Total Harmonic Distortion  (THD) are used in various definitions.

Total harmonic distortion and THD are not identical, but merge for small values: While the total harmonic distortion represents the ratio of the harmonic component of a signal to the total signal  , THD is the ratio of the harmonic component to the fundamental component  . In English-language specialist literature, the distortion factor is referred to as THD _R , for English THD root mean square . ${\displaystyle U}$ ${\displaystyle U_{1}}$

The clank

Origin of the word

Intermodulation caused by non-linear distortion in addition to the distortion factor is perceived as a 'rough' background noise that is reminiscent of a clink . The word clink is the attempt to reproduce a non-verbal noise as an onomatopoeic word ( onomatopoeia ).

causes

The rattling occurs in every assembly because the components used, especially semiconductors and electron tubes, have non-ideal properties (non-linearities). In the case of power amplifiers in particular , a compromise must be found between harmonic distortion and power loss or circuit complexity. Thermal processes due to self-heating and aging often play a role, which lead to distortions due to shifts in the operating point .

Example of non-linear transmission based on the characteristic curve of a field effect transistor :
Right (for example at 0… −1 V) almost linear: A sinusoidal course of a change generates a change without a visible deviation from the sine course. Left (e.g. at −1… −3 V) not linear: A sinusoidal course of a change produces a change with a recognizable non-sinusoidal course. ${\displaystyle \Delta U_{\mathrm {GS} }}$ ${\displaystyle \Delta I_{\mathrm {D} }}$
${\displaystyle \Delta U_{\mathrm {GS} }}$ ${\displaystyle \Delta I_{\mathrm {D} }}$

Components with strongly non-linear properties:

• Transistors (e.g. non-linear characteristic curve, temperature-dependent parameters)
• Transformers , coils with iron core (e.g. hysteresis with ferromagnetic core material)
• Varistors
• Diodes

Components with weak non-linear properties:

• Capacitors , especially electrolytic capacitors (e.g. field strength-dependent permittivity number )
• ironless inductors
• Wire and film resistances (e.g. frequency and temperature dependence of the resistance (see ohmic resistance , to which an idealized material property is assigned))

The influence of the non-linear components on the non-linearity of the assembly can be reduced by means of negative feedback .

practice

The human hearing is sensitive to distortion (distortion) , depending on the frequency . Distortions in the bass range (up to 150 Hz) with 5% distortion factor are mostly imperceptible; on the other hand, distortions in the presence or brilliance range (1 to 4 kHz), in which the hearing is most sensitive, can still be audible below 0.5% under certain conditions. The audibility of distortion in electroacoustic transmission ( hi-fi ), however, also depends heavily on the nature of the useful signal (music, speech) and its spectrum. Several sine-like sounds are considered to be the most sensitive to distortion. For example, when several flutes are played together, clink can be heard from 0.5%, as the sounds are very low in overtones. In the case of speech or other spectrally “dense” sounds and noises, such as drums, distortion is only audible with significantly greater distortion factors.

Electroacoustic devices produce different levels of distortion:

• Nowadays, hi-fi amplifiers are usually designed in such a way that the distortion factor they generate lies completely below the perception threshold (distortion factors below 0.1%), unless the amplifier is approaching its performance limit.
• Distortion mostly arises from the sound conversion in the loudspeaker. Depending on the frequency, these often generate audible distortion , especially at higher sound pressure levels (> 95 dB).
• Also pickup for long-playing records and the groove itself clink with values above the threshold of perception.

additional

The distortion factor remains low when an amplifier does not produce any background noise or signals. The distortion factor only describes "background noises" whose frequencies are integral multiples of the fundamental frequency. With audio amplifiers, advertising is made with very small distortion factors. Harmonic harmonics occur very frequently in nature and are very difficult to perceive or even perceive as pleasant by the human ear. With untrained hearing you can often no longer perceive a distortion factor of less than 5%, with a more sensitive one of less than 1%.

The non-linear behavior of an electroacoustic device generates not only distortion but also non-harmonic interference in the audio signal through intermodulation . If additional overtones are hardly noticeable with some instruments or even perceived positively, intermodulation distortion can be very noticeable. Depending on the situation (mode of operation of the devices, existing measurement options), the non-linear behavior can also be determined in other ways than by means of a distortion factor measurement. Depending on the situation, only one of the types of analysis is possible as a quality criterion. In the case of digitally operating devices such as CD or DVD, distortion measurement in the high frequency range is not possible at all. Particular interferences are determined by measuring the transient intermodulation (TIM) or the frequency intermodulation (FIM).

In the case of non-linear distortions, a distinction is made between

• the square portions by a non-symmetrical characteristic with the even-numbered units , , ..., and ${\displaystyle k_{2}}$ ${\displaystyle k_{4}}$
• the cubic units by a symmetrical characteristic with the odd-numbered portions , ... ${\displaystyle k_{3}}$ ${\displaystyle k_{5}}$

(For more information see web link).

literature

• Thomas Görne: Sound engineering. 1st edition, Carl Hanser Verlag, Leipzig, 2006, ISBN 3-446-40198-9
• Roland Enders: The home recording manual. 3rd edition, Carstensen Verlag, Munich, 2003, ISBN 3-910098-25-8
• Gustav Büscher, A. Wiegemann: Little ABC of electroacoustics. 6th edition, Franzis Verlag, Munich, 1972, ISBN 3-7723-0296-3
• Helmut Röder, Heinz Ruckriegel, Heinz Häberle: Electronics 3rd part, communications electronics. 5th edition, Verlag Europa-Lehrmittel, Wuppertal, 1980, ISBN 3-8085-3225-4
• Horst Clausert, Gunther Wiesemann: Basic areas of electrical engineering 2nd 9th edition, Oldenbourg Verlag, Munich, 2005, ISBN 3-486-27582-8

swell

1. ↑ DIN 40110-1 "Alternating current quantities; Two-wire circuits "
2. ↑ ^{a b} DIN 40148-3 "Transmission systems and four-pole"; Special damping dimensions "
3. ↑ Doron Shmilovitz: On the definition of Total Harmonic Distortion and Its Effect on Measurement interpretation . tape 20 , no. 1 . IEEE Transactions on Power Delivery, January 1, 2005, doi : 10.1109 / TPWRD.2004.839744 ( online [PDF]).

See also

• Cross modulation
• Listening condition
• Frequency spectrum
• Formant
• Audio analyzer

Web links

Wiktionary: Distortion factor  - explanations of meanings, word origins, synonyms, translations

• The distortion factor as a sound effect of 'artistic' distortion (PDF file; 255 kB)
• Example for calculating the distortion factor