From: spam@spam.com   
      
   On Sat, 02 Apr 2011 20:28:59 -0500, flipper  wrote:   
      
   >On Sat, 02 Apr 2011 20:33:33 GMT, spam@spam.com (Don Pearce) wrote:   
   >   
   >>On Sat, 02 Apr 2011 15:21:55 -0500, flipper  wrote:   
   >>   
   >>>On Sat, 02 Apr 2011 19:46:54 GMT, spam@spam.com (Don Pearce) wrote:   
   >>>   
   >>>>On Sat, 02 Apr 2011 14:38:18 -0500, flipper  wrote:   
   >>>>   
   >>>>>On Sat, 2 Apr 2011 02:55:54 -0700 (PDT), Patrick Turner   
   >>>>> wrote:   
   >>>>>   
   >>>>>>On Apr 2, 7:23 am, Newbie  wrote:   
   >>>>>>> It seems well known that negative feedback can reduce lower order   
   harmonics, but   
   >>>>>>> increase the higher order ones.   
   >>>>>>>   
   >>>>>>> Can anyone direct me to references that show how this happens with   
   mathematical   
   >>>>>>> analysis?  Perhaps a paper in the journal of the AES, or elsewhere; on   
   the web,   
   >>>>>>> perhaps?   
   >>>>>>   
   >>>>>>   
   >>>>>>During the last 40 years there have been at least two in depth   
   >>>>>>articles in Wireless World which later became Electronics World.  I   
   >>>>>>read all the WW and EW magazines from 1917 to about 1997 and you'll   
   >>>>>>probably find the articles you want to read if you go where there is   
   >>>>>>an archived set of the magazines like I did. In about 1993 I spent   
   >>>>>>days reading in several university library archives to see what had   
   >>>>>>been said about anything to do with audio engineering. Unfortunately I   
   >>>>>>don't have copies of all I read, but the phenomena of increasing   
   >>>>>>distortion spectra after applying NFB is well known, and remains   
   >>>>>>rivetted into my brain cells.   
   >>>>>>   
   >>>>>>The conditions required to "make matters worse" with NFB are about as   
   >>>>>>follows :-   
   >>>>>   
   >>>>>The only condition required to increase higher order harmonics is NFB.   
   >>>>>   
   >>>>Negative feedback can never make harmonics worse.   
   >>>   
   >>>I didn't say it made "harmonics worse." I said it increases *higher   
   >>>order* harmonics.   
   >>>   
   >>   
   >>Exactly - in terms of harmonics, increasing means making worse.   
   >   
   >No, not 'exactly' because you don't distinguish between *which*   
   >"harmonics."   
   >   
   >   
   >>>THD decreases because the reduction in low order harmonics is greater   
   >>>than the increase in high order harmonics.   
   >>>   
   >>>> Feedback can make   
   >>>>harmonics worse when the phase shifts far enough to make it positive.   
   >>>   
   >>>That will certainly screw things up but it has nothing to do with the   
   >>>basic principle of NFB always increasing higher order harmonics.   
   >>>   
   >>>Read Baxandall's paper.   
   >>>   
   >>I've read it. I suggest you read it again.   
   >   
   >I've read it. I suggest you read it again.   
   >   
   >I quote   
   >   
   >"Conclusions   
   >.   
   >.   
   >.   
   >A small amount of negative feedback (e.g. 6dB) in a single ended   
   >stage, though reducing the second-harmonic distortion, and also the   
   >total (unweighted) distortion, by about 6dB, will increase the   
   >higher-order distortion and the quality of reproduction may well   
   >become worse as judged subjectively.   
   >.   
   >.   
   >.   
   >The magnitude of harmonics of extremely high order will be increased   
   >by the application of negative feedback, no matter what practical   
   >amount of negative feedback is employed, but this is of no consequence   
   >if, when thus increased, they are, say, 120dB below the fundamental.   
   >.   
   >.   
   >."   
   >   
   >He also explains the mechanism producing the 'new' distortion as the   
   >modulator/mixer action of the non-linear amplifier, which we know is   
   >non-linear or else we would not be wrapping NFB around the thing   
   >trying to 'improve' it's linearity, acting on the fed back   
   >harmonic(s).   
   >   
   >To illustrate he uses the 'simple' case of an amplifier with a 'pure'   
   >square law transfer function so that it, sans NFB, produces 'only' the   
   >2'd harmonic.   
   >   
   >Again I quote   
   >   
   >"Thus while the amplifier without negative feedback gives nothing but   
   >second-harmonic distortion on a single sine-wave input, as soon as a   
   >little feedback is applied, a third harmonic output appears. This is   
   >not the end of the story, however, for this third harmonic, like the   
   >second harmonic, gets fed via the B network into the input circuit,   
   >where sum and difference signals are again generated. This time the   
   >sum products are at f+3f, which gives a fourth order harmonic, and at   
   >2f+3f, which gives a fifth harmonic. Clearly there is theoretically no   
   >end to this process - every new harmonic considered, when fed back,   
   >gives rise to harmonics of yet  higher order."   
   >   
   >The mechanism has nothing to do with slew rate limiting or lousy   
   >bandwidth, and he explicitly explains his analysis presumes the   
   >amplifier is flawless in that regard. It's inherent to NFB because the   
   >non-linear amplifier is a mixer.   
      
   Let me put this as few words as the subject will allow. Global NFB is   
   capable - through intermod - of generating tiny amounts of higher   
   harmonics where none existed. And I do mean tiny. These higher   
   harmonics are, in practice always swamped massively by naturally   
   occurring higher harmonics. These higher harmonics respond normally to   
   the application of NFB and are reduced proportionately to the ratio of   
   open loop to closed loop gain.   
      
   So no, NFB does not cause higher harmonics to increase.   
      
   d   
      
   --- SoupGate-Win32 v1.05   
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