# Harmonic Distortion of Sine Wave

#### bipin

Joined Mar 21, 2004
80
Hi All,
Can someone help me out in visualizing the total harmonic distortion measurement in dB ? and how to quantify a distorted wave form with respect to a non distorted wave form.

Thanks
bipin

#### Battousai

Joined Nov 14, 2003
141
What do you mean by "visualizing?"

Total harmonic distortion (THD) = squareroot(HD2^2 + HD3^2 + HD4^2 + ... )

Distortion is a result of non-linearity in the transfer function of an amplifier. The more non-linear a transfer function, the more distortion.

The higher the frequency of operation, the higher the non-linearity in the circuits and the higher the distortion.

At low frequencies a taylor series can be used to model the voltage at a given node in a circuit and from the taylor series the distortion at the node can be calculated.

At higher frequencies a Volterra series must be used to take into account all the higher frequency nonlinearity.

Hope this helps.

#### bipin

Joined Mar 21, 2004
80
hi Battousai,
Thanks for the reply. I was trying to understand this distortion in terms of wave shape rather than the multiples (harmonics) of the fundemental. thats y the term visualization came in .
I came across an instrument which is used to measure the THD of power lines.
It basically takes the sine wave, samples it and calculate the THD of that wave.
It gives a read out in terms of %. (eg: 20%).
Could you give some comments on the algorithms or the calculation methode which probably this instrument would be using.
mean while let me have a "google" on this taylor series and voltara series.
Thanks once again for the new informations.

#### Battousai

Joined Nov 14, 2003
141
If you have an input signal at a frequency f, the nonlinearities in the transfer function result in frequencies at the output of f, 2f, 3f, etc...

HD2 is a measure of the strength of the second harmonic component (2f) at the output relative to the desired output component (f).

Same thing for HD3, HD4, etc...

In my opinion, THD is a poor measurement of distortion. This is because each order of distortion is given equal weighting, and depending on the application certain distortion is more noticeable than others.

I'm not too big on distortion in audio systems, but I'm sure if you're an audio expert you may find say HD3 to be worse than HD2. THD doesn't tell you anything about which component is the worst, it just gives you a general level of distortion. So you can have terrible HD3 and good HD2 but not know it from the THD indication.

The taylor/volterra series calculation methods are kind of similar. Basically the idea is to model the output waveform as a power series. So you write the voltage/current at each node as a power series that depends on the input signal of the circuit. And you keep progressing through each node until you reach the output and then you should have one large series from which you can pluck the voltage/current magnitudes of the desired distortion components.

I hope this isn't too confusing... but it is getting late... I'm off to bed....