Talk:Total harmonic distortion

Removing my own edits since they are apparently not the standard:



\mbox{THD} = {\sum{\mbox{harmonic powers}} \over \sum{\mbox{harmonic powers}} + \mbox{fundamental frequency power}} $$
 * $$= {\sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} \over \sqrt{V_1^2 + V_2^2 + V_3^2 + \cdots + V_n^2}}

$$

FFT
I am going to try to figure out how to calculate this from the FFT. If anyone knows already, please add it. - Omegatron 20:58, Apr 29, 2005 (UTC)

Vandalism?
I reverted the edit by anonymous User:129.97.174.43, all of whose other 6-7 August 2005 edits were vandalism. Please vet my action. --Wetman 02:58, 20 September 2005 (UTC)

Clarifications
I think that THD can be defined for current THD_i, for voltage THD_v and other signals as well. Maybe this should be pointed out. I had the (misconception?) that THD is a general quantity that describes how well a load is matched in a circuit, and I thought that it is not neccesary to point out if it is THD_v, THD_i or even THD_p.

Also I would like to see specialized formulas for calculating THD_i when i(t) is known. This requires Fourier analysis.

Calculation based on Fourier series components
I'm not sure if the following rewrite of the THD-definition is 100% correct, so please add it if you also believe so:



\mbox{THD} = {I_{\mbox{distortion,rms}} \over I_{1,\mbox{rms}}} = { \sqrt{ I_{\mbox{rms}}  - I_{1,\mbox{rms}}  } \over  I_{1,\mbox{rms}} } $$

(A try to) proof:

Parsevals theorem

{1 \over T} \int_0^T|i(t)|^2 \, dt = \sum^\infty_{n=1} |I_n|^2 $$



\Downarrow $$



\sqrt{{1 \over T} \int_0^T|i(t)|^2 \, dt } = \sqrt{ \sum^\infty_{n=1} |I_n|^2} $$



\Downarrow $$



I_\mbox{rms} = \sqrt{I_1^2 + I_2^2 + \cdots + I_n^2} $$

and taking away the fundamental:



I_{\mbox{distortion,rms}} = \sqrt{I_2^2 + \cdots + I_n^2} $$


 * Is the I for current or intensity? — Omegatron 20:38, 3 December 2005 (UTC)

More here — Omegatron 19:32, 20 December 2005 (UTC)

Wrong definition
I didn't found any source - even the ones mentioned by the page on wikipedia - where the THD is defined without the square root. The right definition is this and it doesn't lead to any ambiguity.

\mbox{THD} = \sqrt {\mbox{Power in distortion} \over \mbox{Power in fundamental}} = \sqrt {\sum{\mbox{harmonic powers}} \over \mbox{fundamental frequency power}} $$ This, using the Parseval's theorem is equal to
 * $$\mbox{THD} = {\sqrt{V_2^2 + V_3^2 + V_4^2 + \cdots + V_n^2} \over V_1}

$$

I still think the definition is incorrect when it comes to current or voltage. Am I reading the wiki article incorrectly? Below is a direction quote from IEEE 519.

distortion factor (harmonic factor): The ratio of the root-mean-square of the harmonic content to the root-mean- square value of the fundamental quantity, expressed as a percent of the fundamental.

144.232.185.94 (talk) 20:42, 4 November 2008 (UTC)an engineer

The article was originally a dump of Federal Standard 1037C, which does in fact define it as a power ratio. If you're working in dB and following the rules of dB, it works out to the same thing. It does not work out the same if you're working in percent, though:

For instance, if the fundamental is 10 Vrms, while the harmonic content is 1 Vrms, and the load is 1 ohm, the power of the fundamental is then 10^2/1 = 100 W, and the power of the harmonic content is 1^2/1 = 1 W. The THD can then be calculated in decibels from either the power or voltage measurements:
 * power ratio: 10*log10(1/100) = -20 dB
 * voltage ratio: 10*log10(1^2/10^2) = 20*log10(1/10) = 20*log10(sqrt(1^2)/sqrt(10^2)) = -20 dB

However, if you calculate in percent directly from the ratio, it doesn't work:
 * power ratio: 1/100 = 1%
 * voltage ratio: 1/10 = 10%

I'm not sure how to make this clear in the article. 71.167.68.30 (talk) 16:36, 26 November 2013 (UTC)

Error in formula?
When measuring THD with B & K, Rohde & Schwarts the maximum distortion is 100%, with this definition it can go above 100% (if fundamental is lower than harmonics). We use the Vrms of harmonics, and divide by Vrms of all the signal. This way we get the same as professional equipment. Maybe someone can find a source for this formula? —Preceding unsigned comment added by 211.33.42.133 (talk) 05:51, 18 May 2008 (UTC)


 * Fixed. There are actually 2 definitions,  THDF and THDR.  Added references for both. 71.167.68.30 (talk) 16:47, 26 November 2013 (UTC)

Also the common THD% is 100*THD. There is a discussion on Hydrogenaudio about the whole question. --Mercurio81 07:43, 2 January 2007 (UTC)

THD+N includes IMD?
Under the THD+N heading it is stated "This measurement includes effects from intermodulation distortion, interference, and so on, instead of just harmonic distortion." The link to IMD then states that it is a measurement of signals that are non harmonic to the fundamental. This is very confusing and incorrect at worst and should be removed unless a source can be cited.10 Bit Garbage (talk) 03:14, 24 May 2009 (UTC)


 * This is correct. THD+N includes everything other than the fundamental, which means intermodulation products, interference, etc.  THD without N would only measure harmonics.  If you think it is confusing, please try to reword it.  —Preceding unsigned comment added by 71.167.69.82 (talk) 23:28, 17 July 2009 (UTC)

how much distortion is audible? —Preceding unsigned comment added by 71.167.68.198 (talk) 05:35, 23 November 2009 (UTC)

Non-audio THD
This page describes THD as used in audio testing, but it is also used heavily in power engineering. I would suggest separating the page into a definition part (which should be mostly consistent across all fields), and two application sections (audio, power), adding more if any other field uses it. I don't really know enough to write either of those sections though, so it would be helpful if someone could at least point me to some useful refs. GyroMagician (talk) 08:40, 9 March 2010 (UTC)


 * I agree. THD is integral to the design of ballasts in lighting fixtures and lighting systems in general, which I have to deal with on a regular basis.  This article does nothing to indicate how THD affects fluorescent lighting and things of that nature. 68.143.90.26 (talk) 14:51, 4 August 2010 (UTC)

The animation is distracting and irrelevant
The animation ("An animation illustrating harmonic summing") is not relevant enough to this article, I find it confusing. It would be better to have some simple diagram illustrating the fundamental VERSUS the harmonics.--mcld (talk) 13:22, 27 June 2011 (UTC)

Merging THD analyzer
Someone suggested merging THD analyzer into this article.


 * Oppose. Both articles can be reasonably sized. There are many who would be interested in this article but are not interested in the internal workings of a THD analyzer. Glrx (talk) 22:01, 21 April 2012 (UTC)
 * Support. The combined length of the merged article won't be excessive, and it's (IMO) quite likely that readers will be interested both in the mathematical basis of the measurement and the practical devices used to perform it. Tevildo (talk) 20:24, 13 May 2012 (UTC)
 * Oppose These are related but separate topics. Total harmonic distortion is a unit of measurement and THD analyzer is a piece of Electronic test equipment for measuring total harmonic distortion. -—Kvng 13:53, 21 December 2012 (UTC)

The merge proposal has been withdrawn by. ~KvnG 22:24, 2 December 2013 (UTC)

THD as defined by ratio of power/power (P/P), or Voltage/Voltage (V/V) or other.
The first paragraph states that THD is a ratio of power to power - The first formula(s) contradict this by computing voltage to voltage ratios - In my work in Television/Radio/Consulting if no units are given the assumption is (P/P) for audio devices unless different units are given - Since THD has no dimension (P/P) or (V/V) cannot be deduced - The units of the ratio should be stated clearly in this work - (V/V) ratios are simpler to measure in audio equipment since power at a given frequency is a product of voltage and current corrected for the angle between the two vectors - This is something that microprocessor based THD analyzers can do but nothing like this was available in my time. References: Electric Circuits, 2nd Edition, James W. Nilsson, Addison-Wesley Series in Electrical Engineering, June 1987 and who can overlook Horowitz and Hill's The Art of Electronics (currently on loan to an EE Major). RFRules (talk) 02:04, 28 January 2014 (UTC)


 * See https://en.wikipedia.org/wiki/Talk:Total_harmonic_distortion#Wrong_definition — Preceding unsigned comment added by 71.167.68.173 (talk) 03:55, 26 March 2014 (UTC)

What is Re
The quantity Re is used in connection with passing waves through a Butterworth filter but is not defined. Anyone know what this means? — Preceding unsigned comment added by 87.114.30.41 (talk) 13:49, 8 September 2014 (UTC)


 * Real part of a complex number. Glrx (talk) 19:16, 9 September 2014 (UTC)

THD+N and SINAD
I corrected the last paragraph of THD+N. But that removed an important reference, so I quote the previous text:

"For a given input frequency and amplitude, THD+N is equal to SINAD, provided that both measurements are made over the same bandwidth. "

Frlara (talk) 21:45, 4 December 2015 (UTC)