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| The '''total harmonic distortion''', or '''THD''', of a [[Signal (electronics)|signal]] is a measurement of the [[harmonic]] [[distortion]] present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the [[fundamental frequency]]. THD is used to characterize the linearity of audio systems and the power quality of electric power systems. '''Distortion factor''' is a closely related term, sometimes used as a synonym.
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| In audio systems, lower THD means the components in a loudspeaker, amplifier or microphone or other equipment produce a more accurate reproduction by reducing harmonics added by electronics and audio media.
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| In power systems, lower THD means reduction in peak currents, heating, emissions, and core loss in motors.<ref>[http://www.aspowertechnologies.com/resources/pdf/Total%20Harmonic%20Distortion.pdf Total Harmonic Distortion and Effects in Electrical Power Systems - Associated Power Technologies]</ref>
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| ==Definitions==
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| To understand a system with an input and an output, such as an audio amplifier, we start with an ideal system where the [[Transfer Function|transfer function]] is [[LTI system theory|linear and time-invariant]]. When a signal passes through a non-ideal, non-linear device, additional content is added at the harmonics of the original frequencies. THD is a measurement of the extent of that distortion.
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| When the input is a pure sine wave, the measurement is most commonly defined as the ratio of the RMS amplitude of a set of higher [[harmonic]] frequencies to the RMS amplitude of the first harmonic, or [[fundamental frequency|fundamental]], frequency:<ref>[http://www.eng.tau.ac.il/~shmilo/10.pdf On the Definition of Total Harmonic Distortion and Its Effect on Measurement Interpretation], Doron Shmilovitz</ref><ref>{{cite book
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| | last = Slone
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| | first = G. Randy
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| | title = The audiophile's project sourcebook
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| | publisher = McGraw-Hill/TAB Electronics
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| | year = 2001
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| | isbn = 0-07-137929-0
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| | page = 10
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| | quote = This is the ratio, usually expressed in percent, of the summation of the root mean square (RMS) voltage values for all harmonics present in the output of an audio system, as compared to the RMS voltage at the output for a pure sinewave test signal that is applied to the input of the audio system.}}
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| </ref><ref>[http://www.dogstar.dantimax.dk/tubestuf/thdconv.htm THD Measurement and Conversion] "This number indicates the RMS voltage equivalent of total harmonic distortion power, as a percentage of the total output RMS voltage."</ref><ref name="MT-003"/><ref>[http://www.aspowertechnologies.com/resources/pdf/Total%20Harmonic%20Distortion.pdf Total Harmonic Distortion and Effects in Electrical Power Systems - Associated Power Technologies]</ref><ref>IEEE 519 and other standards ([http://grouper.ieee.org/groups/harmonic/single/docs/P1495D2.doc draft]): "distortion factor: The ratio of the root-mean-square of the harmonic content to the root-mean-square
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| value of the fundamental quantity, often expressed as a percent of the fundamental. Also referred to as total harmonic distortion."</ref><ref>[http://static.schneider-electric.us/assets/consultingengineer/appguidedocs/section11_0307.pdf Section 11: Power Quality Considerations Bill Brown, P.E., Square D Engineering Services]</ref>
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| :<math>
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| \mathrm{THD_F} = \frac{ \sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} }{V_1}
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| </math>
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| where ''V<sub>i</sub>'' is the RMS voltage of ''i''th harmonic and ''i'' = 1 is the fundamental frequency.
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| This measurement is commonly used in audio distortion (percentage THD) specifications, however, THD is a non-standardized specification and the results between manufacturers are not easily comparable. Since individual harmonic amplitudes are measured, it is required that the manufacturer disclose the test signal frequency range, level and gain conditions, and number of measurements taken. It is possible to measure the full 20–20 kHz range using a sweep (though distortion for a fundamental above 10 kHz is inaudible). For all signal processing equipment, except [[Preamplifier|microphone preamplifiers]], the preferred gain setting is unity.{{citation needed|date=November 2013}} For microphone preamplifiers, standard practice is to use maximum gain.{{citation needed|date=November 2013}}
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| Measurements for calculating the THD are made at the [[output]] of a device under specified conditions. The THD is usually expressed in [[percent]] or in [[Decibel|dB]] relative to the fundamental as distortion attenuation.
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| A variant definition uses the fundamental plus harmonics as the reference, though usage is discouraged:<ref>[http://www.eng.tau.ac.il/~shmilo/10.pdf On the Definition of Total Harmonic Distortion and Its Effect on Measurement Interpretation], Doron Shmilovitz</ref><ref>[http://www.icrepq.com/pdfs/BAPTISTA317.pdf VOLTAGE WAVE QUALITY IN LOW VOLTAGE POWER SYSTEMS José M. R. Baptista, Manuel R. Cordeiro, and A. Machado e Moura]</ref><ref>[http://books.google.com/books?id=xxbvM40Wwa8C&dq=thdf+thdr&source=gbs_navlinks_s The Power Electronics Handbook] edited by Timothy L. Skvarenina "This definition is used by the Canadian Standards Association and the IEC"</ref>
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| :<math>
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| \mathrm{THD_R} = \frac{ \sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} }{\sqrt{V_1^2 + V_2^2 + V_3^2 + \cdots + V_n^2}}
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| </math>
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| These can be distinguished as '''THD<sub>F</sub>''' (for "fundamental"), and '''THD<sub>R</sub>''' (for "root mean square").<ref>[http://panelmeters.weschler.com/Asset/AEMC-605-UserManual.pdf AEMC 605 User Manual] "THDf: Total harmonic distortion with respect to the fundamental. THDr: Total harmonic distortion with respect to the true RMS value of the signal."</ref><ref>[http://www.atecorp.com/ATECorp/media/pdfs/data-sheets/Fluke-39-41B_Datasheet.pdf 39/41B Power Meter Glossary]</ref> THD<sub>R</sub> cannot exceed 100%. At low distortion levels, the difference between the two calculation methods is negligible. For instance, a signal with THD<sub>F</sub> of 10% has a very similar THD<sub>R</sub> of 9.95%. However, at higher distortion levels the discrepancy becomes large. For instance, a signal with THD<sub>F</sub> 266% has a THD<sub>R</sub> of 94%.
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| Some use the term "distortion factor" as a synonym for THD<sub>R</sub>,<ref>[http://www.amplifier.cd/Tutorial/Klirrfaktor/distortion_factor.htm Distortion factor]</ref> while others use it as a synonym for THD<sub>F</sub>.<ref>IEEE 519</ref><ref>[http://energylogix.ca/harmonics_and_ieee.pdf Harmonics and IEEE 519]</ref>
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| ==THD+N==
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| '''THD+N''' means total harmonic distortion plus noise. This measurement is much more common and more comparable between devices. It is usually measured by inputting a [[sine wave]], [[notch filter]]ing the output, and comparing the ratio between the output signal with and without the sine wave:<ref>[http://www.rane.com/note145.html Rane audio's definition of both THD and THD+N]</ref>
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| :<math>
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| \mathrm{THD+N} = \frac{\displaystyle\sum_{n=2}^\infty{\text{harmonics}} + \text{noise}}{\text{fundamental}}
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| </math>
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| Like the THD measurement, this is a ratio of RMS amplitudes.<ref name="MT-003"/><ref>http://www.analog.com/static/imported-files/tutorials/MT-053.pdf</ref>
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| A meaningful measurement must include the [[Bandwidth (signal processing)|bandwidth]] of measurement. This measurement includes effects from [[intermodulation distortion]], and so on, in addition to harmonic distortion. For psychoacoustic measurements, a weighting curve is applied such as [[A-weighting]] or [[ITU-R BS.468]], which is intended to accentuate what is most audible to the human ear, contributing to a more accurate measurement.
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| For a given input frequency and amplitude, THD+N is equal to [[SINAD]], provided that both measurements are made over the same bandwidth.<ref name="MT-003">{{cite web
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| | title = Tutorial MT-003: Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor
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| | first = Walt
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| | last = Kester
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| | url = http://www.analog.com/static/imported-files/tutorials/MT-003.pdf
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| | format = PDF
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| | publisher = [[Analog Devices]]
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| | accessdate = 1 April 2010}}
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| </ref>
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| ==Measurement==
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| The distortion of a waveform relative to a pure sinewave can be measured either by using a [[THD analyzer]] to [[Fourier analysis|analyse the output wave into its constituent harmonics]] and noting the amplitude of each relative to the fundamental; or by cancelling out the fundamental with a [[notch filter]] and measuring the remaining signal, which will be total aggregate harmonic distortion plus noise.
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| Given a sinewave generator of very low inherent distortion, it can be used as input to amplification equipment, whose distortion at different frequencies and signal levels can be measured by examining the output waveform.
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| There is electronic equipment both to generate sinewaves and to measure distortion; but a general-purpose [[digital computer]] equipped with a [[sound card]] can carry out harmonic analysis with suitable software. Different software can be used to generate sinewaves, but the inherent distortion may be too high for measurement of very low-distortion amplifiers.
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| === Interpretation ===
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| For many purposes different types of harmonics are not equivalent. For instance, crossover distortion at a given THD is much more audible than clipping distortion at the same THD, since the harmonics produced are at higher frequencies, which are not as easily [[Auditory masking|masked]] by the fundamental.<ref>[http://sound.westhost.com/valves/valve-trans.html#s33 Distortion - Valves vs. Transistors]</ref> A single THD number is inadequate to specify audibility, and must be interpreted with care. Taking THD measurements at different output levels would expose whether the distortion is clipping (which increases with level) or crossover (which decreases with level).
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| THD is an average of a number of harmonics equally weighted, even though research performed decades ago identifies that lower order harmonics are harder to hear at the same level, compared with higher order ones. In addition, even order harmonics are said to be generally harder to hear than odd order.{{Citation needed|date=April 2012}} A number of formulas that attempt to correlate THD with actual audibility have been published, however none have gained mainstream use.{{Citation needed|date=June 2011}}
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| ==See also==
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| * [[Audio system measurements]]
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| * [[Signal-to-noise ratio]]
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| * [[Timbre]]
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| ==References==
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| {{Reflist|30em}}
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| ==External links==
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| * [http://www.sengpielaudio.com/calculator-thd.htm Conversion: Distortion attenuation in dB to distortion factor THD in %]
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| * [http://www.rohde-schwarz.com/appnote/1GA56 Swept Harmonic Distortion Measurements]
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| * [http://www.rohde-schwarz.com/appnote/1GA55 Harmonic Distortion Measurements in the Presence of Noise]
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| [[Category:Electrical parameters]]
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My name: Enrique Blanchette
Age: 38 years old
Country: Germany
Home town: Berlin Marienfelde
Postal code: 12307
Address: Brandenburgische Stra?E 33
Feel free to surf to my homepage Fifa 15 Coin Generator (ownage.com.gridhosted.co.uk)