- Total harmonic distortion
The

**total harmonic distortion**, or**THD**, of a signal is a measurement of theharmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of theFundamental frequency .Lesser THD, for example, allows the components in a loudspeaker, amplifier or microphone or other equipment to make aviolin sound like aviolin when played back, and not acello or simply adistorted noisedubious.**Explanation**In most cases, the transfer function of a system is linear and time-invariant. When a signal passes through a non-linear device, additional content is added at the harmonics of the original frequencies. THD is a measurement of the extent of that distortion.

The measurement is most commonly the ratio of the sum of the powers of all

harmonic frequencies "above" the fundamentalfrequency to the power of the fundamental::$mbox\{THD\}\; =\; \{sum\{mbox\{harmonic\; powers\; over\; mbox\{fundamental\; frequency\; power\; =$P_2 + P_3 + P_4 + cdots + P_n} over P_1}Other calculations for amplitudes, voltages, currents, and so forth are equivalent. For a voltage signal, for instance, the ratio of the squares of the

RMS voltages is equivalent to the power ratio::$mbox\{THD\}\; =$V_2^2 + V_3^2 + V_4^2 + cdots + V_n^2} over V_1^2}In this calculation, "V

_{n}" means the RMS voltage of harmonic "n", where n=1 is the fundamental harmonic. One can also calculate THD using all harmonics (n=∝)::$mbox\{THD\}\; =$V_{RMS}^2 - V_1^2} over V_1^2}Other definitions may be used. Many authors define THD as an amplitude ratio rather than a power ratio. This results in a definition of THD which is the square root of that given above. For example in terms of voltages the definition would be::$mbox\{THD\}\; =\; \{sqrt\{V\_2^2\; +\; V\_3^2\; +\; V\_4^2\; +\; cdots\; +\; V\_n^2\}\; over\; V\_1\}$

This latter definition is commonly used in audio distortion (percentage THD) specifications. It is unfortunate that these two conflicting definitions of THD (one as a power ratio and the other as an amplitude ratio) are both in common usage. Fortunately if the THD is expressed in dB then both definitions are equivalent. This is not the case if the THD is expressed as a percentage.The power THD can be higher than 100% and is known as IEEE, but for audio measurements 100% is preferred as maximum, thus the IEC version is used (Rohde & Schwartz, Bruel and Kjær use it).:$mbox\{THD\}\; =$V_{RMS}^2 - V_1^2} over V_{RMS}^2}

A measurement must also specify how it was measured. Measurements for calculating the THD are made at the

output of a device under specified conditions. The THD is usually expressed inpercent as distortion factor or in dB as distortion attenuation. A meaningful measurement must include the number of harmonics included.**THD+N****THD+N**means total harmonic distortion plus noise. This measurement is much more common and more comparable between devices. This is usually measured by inputting asine wave ,notch filter ing the output in question, and measuring the ratio between the output signal with and without the sine wave::$mbox\{THD+N\}\; =\; \{sum\{mbox\{harmonic\; powers$ + mbox{noise power} over mbox{total output powerA meaningful measurement must include the bandwidth of measurement. This measurement includes effects from

intermodulation distortion ,interference , and so on, instead of just harmonic distortion.For a given input frequency and amplitude, THD+N is equal to

SINAD , provided the bandwidth for the noise measurement is the same for both (the Nyquist bandwidth). [*http://www.analog.com/en/training-and-tutorials/tutorials/design-center/tutorials/CU_tutorials_MT-003/resources/fca.html MT-003: Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor*] —Analog Devices Tutorial MT-003 by Walt Kester]**See also***

Audio system measurements

*THD analyzer

*SINAD **References****External links*** [

*http://www.dogstar.dantimax.dk/tubestuf/thdconv.htm Explanation of THD measurements*]

* [*http://www.rane.com/note145.html Rane audio's definition of both THD and THD+N*]

* [*http://www.sengpielaudio.com/calculator-thd.htm Conversion: Distortion attenuation in dB to distortion factor THD in %*]

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