Total Harmonic Distortion

Question

Hello,
i have a question to .four 1k 10 -1 v(out).
In the log-file I can find
Partial Harmonic Distortion: 4.335049%
Total Harmonic Distortion: 4.810931%
The Partial Harmonic Distortion match to result of 1+9 harmonic ( = sprt ((U2^2+...+U9^2)/(U1^2)).
But how can I calculate the Total Harmonic Distortion?
How is the Total Harmonic Distortion defined?

MStokowski · Answer

Hi JOMEAH , Denspa , 
 THD is calculated from Vrms of the signal. using: 
 
 Interesting note: I went back to some older versions of LTspice that reported as thus: 
 Total Harmonic Distortion: PHD value ( THD value ) 
 The THD was noted in parentheses for some reason. 
 mike

MStokowski · Answer

Hi Denspa , 
 Denspa said: In this case, it seems to imply that if the observation interval (the .tran stop time) is not an integer multiple of the signal period (1/f), the result may not be calculated correctly. My reason is that when calculating V1rms, if the time window does not contain an integer number of cycles, 
 Well, yes and no. LTspice will do exactly what you tell it to do. As View FFT and .four are two different functions, let's start with .four, where I've set Nperiods to 10. 
 .four {fundamental} 40 10 V(sine) V(triangle):

Denspa said: the result may not be calculated correctly 
 Wll, "may not be calculated correctly" is debatable, as LTsice will do exactly what you tell it to do. To wit&hellip; 
 I ran this simple test for N=10.33 in LTspice 17.1.9, (that version just 'cause I was testing something else) but with Nperiods set to -1 (see the help) : 
 
 In contrast, setting the .tran time to exactly 10 cycles: 
 
 Using my handbuilt windowing function: 
 
 Denspa said: However, if THD implicitly uses the entire observation interval, then in order to obtain an accurate FFT of V1, is it correct that we should choose the observation interval (.tran stop time) so that it is an integer multiple of the signal period? 
 In short, no, yes, and "up to you". Turns out the actual FFT feature allows you to specify the interval after the fact: 
 
 Circling back to the top of this message, Nperiods in the .four directive will not affect the FFT used in View FFT, but does affect the calculation of Vrms used to report THD in the log. 
 Hope this helps. 
 mike