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In Reply to: 3rd harmonic distortion posted by MAD MAN HARJU on December 28, 2004 at 07:53:17:
I don't have Baxandall's article, but I would assume that it is related. The math is derived in full in advanced non-linear design college courses, at least at UCB.
Follow Ups:
Hi John.The fig in Baxandall's article that I'm refering to is similar to Fig 2-16 (Calculated Distortion versus feedback level)on page62 in Cheever's Thesis whith the dip in the 3:d harmonic, but whith actual measurments up to the 6:th harmonic included.
BTW Cheever has ript of a large part of his math from this article.
I remember that you credited Cheever for his for his idea and history, I belive that it's a good idea BUT as several others have mentioned I don't belive that we should "aim" to fit the distortion in our systems to the ears natural aural harmonic distortion.Instead aim should be that the distortion in the system is "low enough" (I can't and don't wan't to give a specific number... It's a difficult task, I hawe studied this for several years and been learning how our hearing works in regard to distortion. But if someone forces me to put out a number it would be less than 0.1% for amplifiers and less than 0.01% for preamps at full power/signal-level when all aspekts SID and EMF etc is included.)
And the most inportant aspect is that the distortion falls of faster or at least as fast as the ears natural aural harmonic distortion whith rising harmonics. Where the 7:th and higher absolutley should be down at vanishing small levels.
I ran across a wery intresting paper from AES whith very god distortion-measurment histoty and conclusions:
"Multitone Testing of Sound System Components-
Some Results and Conclusions" JAES Vol 49 No 11 2001 Nowember.
Wery good readingI have been "fideling around" whith electronics and loudspeakers for some 20 years now and I am an electric engineer working whith both tubes and transistors (low (20 to 30 dB) or no global feedback), but ower the yerars by learning more I'we discoverd that there is more and more to learn and that I know less beause there are more and more questions to answer. I'we read the articles written by You, Walt, Otala, Baxandall and others. Done a lot of tesing and measurments of my own but ewery time you learn something new there are also new questions.
To come back to the issue here, I known that the dips in the harmonic distortion stucture is there whith bjt's (There are sewerall present in the higher harmonics) But I haven't got the real grasp on why they are there and why fet's don't have them. What function is in work here? Ofcourse fet's have a near parabolic transter function and bjt's have close to a exponential transter function and this is a part of the answer (Or the key point actually?)
Enjoy creating / MAD MAN HARJU
MMH, I could FAX you the info, if you have a fax #. It is too difficult to post here, and my E-mail send isn't working properly. You can, however, e-mail me your fax #, if you have one.
Thanks John!I will mail the fax # to you
Enjoy creating / MAD MAN HARJU
Rolf, I received your E-mail. I will attempt to send you the info I have. The analysis was developed for an advanced course by Dr. R.G. Meyer and Dr. Don Pederson, (and perhaps others as well) as working notes for a course in nonlinear circuit analysis in the early 1970's. Subsequently, Dr. Meyer wrote the book: 'Analysis and Design of Analog Integrated Circuits' , a very good textbook, BUT it is for an other course and it covers only the usual aspects of negative feedback, known to almost everyone interested in this subject.
The cancellation of 3'rd harmonic distortion by local feedback is, however, on page 94 of 'Analog Integrated Circuits for Communication' by Don Pederson and K. Mayaram. You might find this textbook in your university library.
In 1973, I did ask Dr. Meyer, privately, whether higher orders were easily cancelled as well, but he said that he did not know of any approach at the time. I am not surprised at this time after rereading the class notes on the subject, because:
"The term involving a(3) in (1.42) is due to third order distortion in the forward amplifier. The term involving a(2) is due to second order distortion in the forward amplifier being fed back and combining with the fundamental signals to produce third order distortion. Thus the error signal S(e) contains second order distortion as well as linear terms. These two combine in the second order nonlinearity to produce third order distortion. This process is called second order interaction. It is interesting to note that if a(3) is zero, but a(2) is non-zero, then b(3) will be finite. That is, even if the original amplifier had no third order distortion, the application of feedback can create third order distortion via second order interaction. ..."
The basic equation relating to the above commentary is:b(3) = {a(3)[ 1+a(1)f ] - 2a(2)squared times f } / [ 1+a(1) times f ] to the fifth power
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