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In Reply to: Re: transient test - Part II posted by mfc on July 31, 2003 at 10:42:57:
I felt the same way, at first. Walt Jung's articles on SID (TIM) convinced me that harmonic distortion is more practical. Please do a search on triple-tone IM, and then you should know more than I can offer here. I think that it is twice the equivalent harmonic amplitude, but I could be wrong. It is twice all the other IM tones for sure.
Follow Ups:
13DoW and anyone else who is interested,AddDistortion is now posted on my website. I'll be interested in people's reaction to it and the results they get listening to the distorted Wave files. Please note the importance of harmonic polarity in this - and the difficulty of obtaining this key information.
Regards to all,
Keith Howard
I meant to say triple beat IM distortion. Scott F. addressed this in May on this site. I just did a search myself, it is not easy to find a clear definition, but it is there somewhere.
Hi,I found something:
IM 2 =a 2 /a 1 *U, HD 2 =1/2*a 2 /a 1 *U
where a 2 , a 1 are coefficients.
U is signal amplitude.
and
IM 3 =3/4*a 3 /a 1 *U 2 , HD 3 =1/4*a 3 /a 1 *U 2
IM 2 =2HD 2 , IM 3 =3HD 3
Under low-distortion conditions, there is thus a one-to-one
correspondence between harmonic and intermodulation
distortion. It is thus sufficient to specify only one of them.
From Sansen, Distortion in Elementary Transistor Circuits
IEEE Transactions on Circuits and Systems Vol 46, No 3, March 1999Cool that we only need to worry about which ever is easiest to
measure and the other is related.
mfc,distortion is created by a non-linear transfer function. If you can model that transfer function by a series expansion then you can multiply it by as many Cosine inputs as your patience allows. If you apply one input then the output terms are the harmonics, if you apply two input tones you get the harmonics of each input plus the intermods between them and so on. The more tones you apply the more intermods generated but it all drives from the same transfer function.
In Willy Sansen's text the coefficients are the sum of all the same order terms left after doing all the math - and the exact value depends on the transfer function (quadratic, exponential etc). It also depends on how many terms you use in the expansion, for example a fifth order terms doesn't just generate fifth order products but lower order products also which must all be summed to give a2, a3 etc.Keith Howard wrote some interesting articles in recent Hi-Fi News's about this topic and showed how the number of intermods increase dramatically as the transfer function changes from 2nd order to 3rd order. This is nothing new but he does present it well.
Check out his most recent article about matching measured harmonic levels to transfer functions and that the phase of the harmonic is very important. He has web-site (see URL) but there's not too much there. He's promising a freeware program ("Adddistortion") that will add any defined non-linearity to a .WAV file - should make for interesting listening.Regards
13DoW
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