# Total Harmonic Distortion, THN measurement

1. Nov 20, 2013

### FrankJ777

I have a couple of questions about what total harmonic distortion is, and what the measurement means. The definition I've read most places is:

$\frac{D}{S}$ × 100% , where S is the amplitude of the fundamental frequency, and D is the amplitude of the sum of all of the harmonics.

A common method I've read to measure THD is as follows.
1) Insert a sine wave (the fundamental frequency) into the input of the device under test.
2) Using an RMS AC voltmeter, measure the output signal, and call it V1.
3) Use a notch filter to notch out the fundamental frequency at the output.
4) Use the RMS AC voltmeter to measure the output with the fundamental frequency suppress This measures only the harmonic distortion, V2 + V3 + ... + Vn

THD = ( V2 + V3 + ... + Vn )/( V1 ) × 100% = $\frac{D}{S}$

The part that I question is does this give you $\frac{D}{S}$ ? It would seem to me that the first measurement V1 would be the total amplitude, not just the amplitude of the fundamental frequency, and so I would think that this method would actually give you $\frac{D}{S+D}$. Am I looking at this the wrong way?

Also I was wondering if the phase of the harmonics relative to the fundamental frequency makes a difference. If the fundamental and its harmonics are all in phase then it makes sense that they can be added arithmetically. If however there are phase disparities then measuring total amplitude with the voltmeter doesn't seem valid? Through a non linear device will the harmonics be in phase?

2. Nov 20, 2013

### AlephZero

There are several issues here.

The definition of THD is really in terms of the power contained in each harmonic, not its amplitude - though the quoted value may be referred back to a (fictitous) "amplitude". See http://en.wikipedia.org/wiki/Total_harmonic_distortion

The measurement method you describe won't give very accurate results. The notch filter will add its own distortion (and noise) into the signal. And you are right that the relative phase of the harmonics will affect a measurement with a standard DVM used on an AC range. DVM's actually measure the mean voltage and display the output as a RMS value assuming the signal is a pure sine wave, which is not likely to be the case when measuring distortion.

This measurement technique includes (broadband) noise as well as harmonic distortion.

You are right about D/(S-D), but given the other sources of error that is probably not too important.

There is a reason why "real" THD meters are expensive, e.g. this one - but for \$1000 you "only" get a meter that works at audio frequencies! http://www.rapidonline.com/Test-Mea...rce=googleps&gclid=CP25x9Hg87oCFafMtAodNwMAog

A different approach is to digitize the signal and do an FFT (e.g. with free software on a PC), which will tell you the contribution from each harmonic separately, not just the "total" distortion level.

3. Jun 22, 2014

### shoebelixir

Try < THD = 100*Sqrt(square(X))/Xamp >
Xamp= Amplitude value of current for e.g.
X= instantaneous current (or values)
since its a current we can use X(inst)=X(amp) * sin(ωt + ψ);
f- freq
t- time period 0-2 sec for this e.g.
ψ- power factor

ω=2∏f;

let me know if this works

Last edited: Jun 22, 2014
4. Jun 22, 2014

### MrSparkle

he probably figured everything out in the 7 months since he posted his question.

5. Jun 22, 2014

### shoebelixir

I know it wont work because I did not put it as a summation of the Numerator then the following expression goes as it is.