Distortion and Feedback

8/11/2019 Distortion and Feedback

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Audio, Distortion and Feedback

Nelson Pass 11/1/08

Introduction

Audiophiles seem to revel in minor controversies – vinyl vs CD's, tubes versus solid state,capacitor, ires, ma!ic dots""" and ne!ative #eedbac$"

At one e%treme, the position is that &#eedbac$ ma$es ampli#iers per#ect" At the othere%treme, &#eedbac$ is a menacin! succubus that suc$s the li#e out o# the music, leavin! adried hus$, devoid o# soul"

(he #ormer viepoint usually belon!s to so)called &ob*ectivists ho have a #ine appreciation#or electronic theory and measurements" (heir opposites ould be the &sub*ectivists hoemphasi+e the listenin! e%perience and o#ten on tube ampli#iers" Accusations areoccasionally made that ob*ectivists can't hear, and conversely that sub*ectivists hear thin!sthat aren't there" (his bein! the entertainment industry, hope everyone is havin! a !oodtime"

-eedbac$ is very lar!e sub*ect, and am !oin! to limit mysel# to some simple tutorialcomments and a discussion o# phenomena associated ith comple%ity in distortion created bynonlinear !ain sta!es, ne!ative #eedbac$, and the audio si!nal" (a$en sin!ly, thesephenomena seem simple enou!h, but hen they interact, they create distortions out o#proportion to hat you e%pect #rom the speci#ications #ound in product brochures"

(here are linear and non)linear #orms o# distortion" .inear distortions a##ect the amplitude andphase o# audio si!nals, but don't sho up on harmonic distortion analy+ers as added

#reuency components that eren't there in the #irst place" (one controls are a !ood e%ampleo# circuits ith linear distortion"

Nonlinear distortions are those hich add ne #reuency components to the ori!inal si!nal,either as harmonic multiples o# the ori!inal #reuencies or as sidebands resultin! #rom theirnon)linear interaction beteen the ori!inal #reuencies" Nonlinearities are o#ten deliberatelycreated in musical instruments themselves, but they are unanted in music reproduction" eill be tal$in! about nonlinear distortions"

e use ne!ative #eedbac$ in audio ampli#iers to stabili+e the !ain, increase the bandidth,loer the output impedance and loer the non)linear distortion" t is the aspect o# reducin!the distortion hich tends to !enerate the most controversy – ne!ative #eedbac$ is verysuccess#ul in loerin! distortion to very tiny numbers as measured by distortion analy+ers"

As r" 2poc$ said, &nstruments only measure hat they ere desi!ned to measure" 3 4iventhe complaints o# audiophiles over the sound o# hi!h)#eedbac$ type ampli#iers, it is reasonableto e%amine non)linear distortion in !reater depth than is possible ith a sin!le number"

3 2tar (re$, 5pisode 67, &(he Na$ed (ime



Nonlinear Distortion

-irst a little bac$!round" hen e tal$ about #eedbac$ and nonlinear distortion, e areinevitably tal$in! about !ain devices – (ubes, ipolar transistors, 9#ets and os#ets, andhen e tal$ about !ain devices, e usually !et around to nonlinear distortion" :ere are thebasic players shon in simple circuits;

All o# these e%amples have current #loin! #rom pin 1 to pin < as a #unction o# the volta!ebeteen pin = and pin <" n the e%ample o# the tube, the current #rom Plate to Cathode islar!ely determined by the volta!e beteen the 4rid and the Cathode" (he other e%ampleshave similar relationships, but vary in the details" e thin$ o# pin = as the control pin, andsi!nal presented here is ampli#ied to a lar!er si!nal passin! throu!h the other to pins"

All !ain devices have imper#ections in their !ain" >ut o# the bo% you can measure their !ain,

and #or a !iven test each ill have a di##erent value" # you ta$e a sin!le device and measurethe !ain, you ill #ind that the it varies ith the current #loin! throu!h the device" t alsovaries ith the volta!e across the device as ell as the temperature o# the device" All three o#these ill create nonlinear distortion"

Distortion is hat you !et hen the !ain is not constant" # the devices had per#ectly constant!ain under all conditions, they ould have no distortion" e are mostly concerned abouthat happens to an audio si!nal hen it is ampli#ied by a device hose !ain #i!ure ischan!in! in response to the si!nal" (he si!nal !oes in and comes out ith a di##erent shape"(he !ain is not per#ectly strai!ht ) it is bent, or nonlinear"

An important thin! about distortion – hen you run a si!nal throu!h a device hich is evensli!htly non)linear, you have chan!ed the si!nal #orever" ?ou can use various techniues toreduce distortion a#ter the #act, but you can't !o bac$"

(he problem is !reatly compounded hen comple% si!nals consistin! o# many #reuencies alltravel throu!h the !ain device at the same time, or hen a simple si!nal is passed throu!h anumber o# nonlinear !ain sta!es in series" ># course you can do both, and as e'll see later,these can add up to a perfect storm o# distortion"



Harmonics

hen you ampli#y a sin!le tone @sine ave and the !ain device distorts it, the output containsthe ori!inal tone plus a series o# harmonic tones hich are hole multiples o# the ori!inal#reuency" # the ori!inal tone is 1 B:+, then the output ill contain 1 B:+ plus maybe some <B:+ @second harmonic, = B:+ @third harmonic, Bh+ @#ourth harmonic, and so on"

Audio si!nal alternates beteen positive and ne!ative values" # the nonlinearity o# thetrans#er curve is symmetric ith respect to positive and ne!ative, then the harmonics ill beodd – third, #i#th, seventh and so on" # the trans#er curve is bent non)symmetrically, theharmonics ill be even – second, #ourth, si%th, etc" -i!ure < shos a sine ave ith a hi!h<nd harmonic content" (his variety o# distortion is o#ten seen in overdriven tubes operated insin!le)ended Class A mode"

-i!ure = shos a sine ave ith a hi!h =rd harmonic content, reco!ni+able as a &so#t clip,occasionally seen in overdriven push)pull Class A tube circuits"

A !ain device's trans#er curve can be e%pressed as a polynomial; E a F bG F cG< F dG="""(he &a term is a DC o##set component and the &b is the linear coe##icient, re#lectin! thedistortion)#ree per#ormance, hich ould be a strai!ht line" (he c, d and etc" are coe##icientsto a poer series representin! the &bent nonlinear portions o# the curve"

2imilarly, a volta!e ave#orm can be e%pressed as a sum o# harmonic #reuencies, each ithits on amplitude and phase coe##icients" (hese to ays o# loo$in! at thin!s nicelycorrespond to each other"



Harmonic Distortion and Sound

any audiophiles believe that <nd harmonic is to be pre#erred over = rd harmonic" Certainly it issimpler in character, and it is ell a!reed that orders hi!her than third are more audible andless musical" :oever hen !iven a choice beteen the sound o# an ampli#ier hosecharacteristic is dominantly <nd harmonic versus =rd harmonic, a !ood percenta!e o# listeners

choose the =rd

"

have built many e%amples o# simple <nd and =rd harmonic &types o# ampli#iers over the last=H years" hen say &types mean that they used simple Class A circuits described as&sin!le)ended versus &push)pull and so tended to have a <nd harmonic versus =rd harmonic inthe character o# their distortion, but ere not made to deliberately distort"

Anecdotally, it appears that pre#erences brea$ out rou!hly into a third o# customers li$in! <nd

harmonic types, a third li$in! =rd harmonic, and the remainder li$in! neither or both"Customers have also been $non to chan!e their mind over a period o# time"

:oever the issue is partially obscured by the #act that the =

rd

harmonic type ampli#iersusually have loer total distortion" (hird harmonic usually appears ith a ne!ative coe##icient,resultin! in hat e thin$ o# as &compressive ) the e%ample in #i!ure =" t's orth notin! thatodd orders on nonlinearity also can be seen alterin! the amplitude o# the #undamental tone)somethin! a distortion analy+er doesn't ordinarily display"

Audiophiles have been accused o# usin! <nd or =rd harmonic distortion as tone controls todeliberately alter the sound" suppose that there are people ho li$e it that ay, but don'tthin$ this is !enerally the case" -or reasons hich ill become clearer hen e tal$ aboutinter)modulation distortion, hi!h levels o# any harmonic become problematic ith musicalmaterial havin! multiple instruments, and the ar!ument that <nd or =rd adds &musicality doesn't

uite hold up"

(he sound o# <nd order type circuits is o#ten praised as &arm and by comparison =rd ordertype circuits are o#ten noted #or &dynamic contrast" <nd order type ampli#iers seem to doparticularly ell ith simple musical material, and =rd order types !enerally seem to be betterat more comple% music" -i!ure shos a distortion curve o# to poer sta!es operatedithout #eedbac$ – the blue is sin!le)ended Class A, the red is a push)pull Class A"



n -i!ure e see that the <nd order type declines inversely to the output volta!e @the suareroot o# poer, and the =rd order type declines inversely to the suare o# the volta!e @inverselyproportional to poer" (here may be also a relation beteen this and the perception o#&armth versus &dynamics, but it is not clear to me at this time"

Nevertheless, hether you pre#er <nd or =rd order type ampli#iers, let's a!ree that e ish to

minimi+e the total amount o# distortion" And assumin! that e have to put up ith somedistortion let's also a!ree that e pre#er <nd and =rd harmonic components over th, Hth, Ith, 7th

and so on"

(o !et loer order harmonic character e ant smoother &bends on the device's trans#ercurve" (his usually means Class A operation" -i!ure H shos a harmonic comparisonbeteen the same push)pull circuit operated Class A versus Class ith a H00 :+ si!nal" nthe case o# Class A operation e trade ener!y e##iciency o## #or a smoother trans#er curve,ith both halves o# the push)pull !ain sta!e smoothly sharin! the load and mutuallyconductin! current at all times" n Class , there is no time hen both halves share the load"

A popular compromise desi!n, Class A, smooths the transition out beteen the to halvesby havin! them both share the load #or a portion o# the trans#er curve"

(he hi!h harmonic content o# Class ampli#iers brin!s us to the ord monotonicity.onotonicity describes the relationship beteen the distortion level and the output level"

(he smooth trans#er curves o# Class A ampli#iers have a characteristic hich is monotonic,that is to say the distortion !oes don as the output declines" t implies lo order harmoniccharacteristic, hich e have previously a!reed is sonically pre#erred"

# you see a curve ith distortion level climbin! as the output !oes don, it implies crossoverdistortion caused by the !ap beteen the to push)pull !ain elements, and this implies hi!horder harmonics"



(he e%amples o# -i!ure shoed distortion declinin! smoothly ith poer in Class Aampli#iers, but -i!ure I compares a push)pull Class A ampli#ier @red ith a Class @blue"

n real li#e, o# course, the distortion o# the blue ampli#ier ould li$ely be reduced throu!h theuse o# ne!ative #eedbac$, and the mar$etin! department ould be able to say that thedistortion is &less than "0HJ" @(o avoid any con#usion, please note that !raphics that you seein this paper sho per#ormance ithout #eedbac$ unless otherise noted

Inter-modulation Distortion

# you li$e to listen to simple music as played by an unaccompanied sac$butt, harmonicdistortion #i!ures mi!ht be per#ectly relevant to you, but ith a lot o# music you ill #ind thatinter)modulation distortion becomes the elephant on the dance #loor"

:armonic distortion is closely related to inter)modulation distortion in that both result #rom thesame nonlinear distortion o# the !ain device, but distortion re#lects hat happens henthere is more than one tone involved, and that describes most music" ith a sin!le tone,loer order harmonics such as <nd and =rd are not as discernible, and in real li#e mostinstruments @includin! vocal contain a #airly rich set o# these harmonics anyay" (hey areconsidered musical"

ut hen to tones are passed throu!h a non)linear device, the amplitude o# each o# thetones is altered, or modulated by the other tone" (he result is a series o# &sidebands,additional tones occurrin! at the sum and di##erence o# the ori!inal #reuencies" (heseadditional tones are not !enerally musically related"

orse, real music consists o# very many tones passin! throu!h the nonlinear !ain device,and each o# these interacts ith each o# the others" (he result ill be very comple%, and veryunmusical"



-i!ure 7 shos a distortion ave#orm resultin! #rom to tones passin! throu!h a !ain sta!eith both <nd and =rd order nonlinearities havin! 1J coe##icients" (he to tones have eualamplitude and they are one octave apart" (he si!nal pea$s are about 1"8 volts, and thedistortion pea$s are about "0K volts, or HJ, and the ratio o# rms avera!ed distortion divided bythe rms si!nal is about J

(his distortion doesn't loo$ so bad, but it is obviously hi!her and more comple% than sin!le)tone distortion" .et's see hat happens hen there are lots o# #reuencies involved" n-i!ure 8 e see a ave#orm consistin! o# 7 non)harmonically related tones o# eualamplitude #rom 100 :+ to <800 :+" # e run this si!nal throu!h the same !ain sta!e andsubtract the ori!inal si!nal e !et the distortion seen in -i! 8;

Not very pretty is itL No the distortion is !ettin! really comple%, ith lots o# harmonics, andthe pea$s are up around "K volts" (hat's 11 times the "08 volt #i!ure o# the sin!le tone, and theratio o# the rms distortion to the rms input si!nal is about 8J"

y pointL distortion is the elephant on the dance #loor"

uch o# the time distortion simply #orms a comple% &noise #loor hich mas$s musicaldetail" At loer levels, it ta$es the li#e out o# the music and ma$es it uninterestin!, evenirritatin!" t isn't as noticeable ith very simple music, but it stands out ith orchestralmaterial as i# the instruments ere covered by a veil"

At hi!h distortion levels, the sound simply turns to mud, and e turn it don"

>r o##"



Negative Feedback

n 1K<7 :arold lac$ invented the ne!ative #eedbac$ ampli#ier in hich the output si!nal o# ananalo! !ain circuit is compared ith the input si!nal so as to improve the per#ormance" (hereare many ays to achieve this e##ect, all involvin! ne!atively ampli#yin! the di##erencebeteen the input and output so as to minimi+e this di##erence"

A simple version can be made #rom a = pin device li$e the parts #rom -i!ure 1, in a circuit thatloo$s li$e this;

:ere e see a sin!le part @os#et in a netor$ o# #our resistors #ormin! an invertin! ampli#ierith some !ain" M= and M set up the &open loop !ain @the !ain you !et ithout ne!ative#eedbac$ and M1 and M< set up a ne!ative #eedbac$ loop"

# e remove M< so that there is no #eedbac$, and assume that the os#et is a hi!h !ain part,then e ould see an &open loop !ain o# appro%imately the ratio M= / M" t is not di##icult toma$e M= / M a #airly hi!h #i!ure, !ivin! an open loop !ain o# maybe 10 times @<0 d or even100 times @0 d lar!er than input volta!e" A typical e%ample o# 100 times ould be M= at avalue o# 1 Bohm and M at 10 ohms"

# you put M< bac$ in the circuit, you ill #ind the !ain reduced" # the ratio o# M< / M1 is much

less than the open loop !ain, and i# the value o# M< is much hi!her than M=, then the !ain o#the hole sta!e becomes uite close to M< / M1" 5%amples #or this ould be M< at 100 Bohmand M1 at =1"I Bohm, #or an output !ain o# appro%imately ="1I times @10 d"

2imply put, the di##erence beteen the to !ain #i!ures is considered the amount o# #eedbac$ – # the open loop !ain is 0 d and the !ain ith #eedbac$ is 10 d, then the amount o##eedbac$ is =0 d" n actual audio circuits, the amount o# #eedbac$ can ran!e beteen 0 d@none at all and as much as 100 d @100,000 times" 2ometimes you don't need that much,but a typical inte!rated circuit op)amp comes ith that much open loop, so there it is"



Ne!ative #eedbac$ is !ood at reducin! all #orms o# distortion, linear and nonlinear" As aconcept, it's pretty strai!ht)#orard; ?ou create one o# more !ain sta!es in series in order to!et enou!h !ain to eual the #inal !ain #i!ure you ant plus the amount o# #eedbac$ you thin$you ant to use"

As the #eedbac$ #i!ure e%ceeds <0 d or so, you #ind that all the measurements ill improve

by the amount o# additional #eedbac$" # the open loop distortion o# the ampli#ier is HJ, thenI0 d o# #eedbac$ should ma$e it about "00HJ" t's relatively easy to construct additionalsta!es or to mil$ e%istin! sta!es #or more open loop !ain, so hy not 80 d #or "000HJL

2ounds li$e somethin! #or nothin!, doesn't itL

Not uite" thin$ it's a bit more li$e a credit card – convenient i# used isely, but carryin!interest payments and penalties hen it's not"

Negative Feedback and Higher Order Harmonics

?ears a!o Peter a%andall pointed out that hile ne!ative #eedbac$ reduces distortion, itcreates additional hi!her order harmonics in the process" >thers have con#irmed thisphenomenon e%perimentally and in computer simulations" #ound -i!ure 10 on the internet,attributed to 9ohn .insley):ood;

:ere e see that as lo #eedbac$ #i!ures are applied to a sin!le !ain sta!e the < nd harmonicdeclines linearly ith #eedbac$, but increased amounts o# hi!her order harmonics are created"

As #eedbac$ increases above about 1H d or so, all these #orms o# distortion declinin! inproportion to increased #eedbac$"

Ne!ative loop #eedbac$ creates hi!her order distortion harmonics, and there seems to be animplication that you mi!ht ant to use lots o# #eedbac$ i# you plan on usin! any at all" 2omedesi!ners loo$ at it this ay, others to use #eedbac$ sparin!ly, and some re#use to use it at all"



per#ormed my on version o# the e%periment, usin! a poer os#et in a sin!le)ended Class A !ain sta!e drivin! 1 att into an 8 ohm load;

-i!ure 11 clearly shos the increase in hi!her order harmonics ith the application o#ne!ative #eedbac$" n this !raphic, the amplitudes are e%pressed in d, and the #reuency o#each curve as sli!htly o##set #or clarity"

2o it's pretty clear that hile loerin! the total amount o# distortion, ne!ative #eedbac$ doesincrease the distortion comple%ity"

Wait! heres "ore###

e have seen that distortion comple%ity results hen you pass a simple si!nal throu!h a !ainsta!e ith hi!h order nonlinearities, as in the e%ample o# the distortion spectrum o# a Class Aversus Class output sta!e @-i!ure H"

e have also seen that distortion comple%ity results hen a comple% si!nal is passedthrou!h a !ain sta!e ith relatively simple lo order non)linearities @-i!ure 8"

And #inally e have seen that distortion comple%ity is increased henever you use ne!ative#eedbac$ @-i!ure 11"

can thin$ o# one more source o# distortion comple%ity, that hich results #rom passin! asi!nal throu!h successive !ain sta!es" (his is uite common because it is popular to usemultiple sta!es in an ampli#ier in an e##ort to !enerate enou!h open loop !ain so as to haveplenty o# #eedbac$"

Parado%ically, you can visuali+e instances o# #eedbac$ pyramid schemes, in hich more !ainsta!es are added to !enerate more #eedbac$ to partially correct #or the distortions !eneratedby the additional !ain sta!e"



-i!ure 1< illustrates the result o# cascadin! multiple sta!es" :ere there are #our sta!es, eachhavin! a 1J coe##icient o# <nd and =rd harmonic ampli#yin! a sin!le tone;

(he indo o# #i!ure 1< represents 1 sinusoidal cycle and you can see the K th harmonic

components at the bottom o# the !raph" ?ou can also see that much o# the distortion isconcentrated into lar!e pea$s"

?ou ill recall the comple% e%ample o# #i!ure 8 in hich seven tones ere passed throu!ha sin!le sta!e" -i! 1= shos hat they loo$ li$e passin! them throu!h the #our !ain sta!es o##i!ure 1<, ith the same 1J coe##icients #or <nd and =rd harmonic;

:mmm" (he distortion *ust $eeps !ettin! orse ) it mi!ht ta$e a lot o# #eedbac$ to !et this

don to a reasonable level" (he rms value o# this distortion is very much loer than thepea$s ) on the order o# 100J" (here is appro%imately as much distortion as ori!inal si!nal"

2o no e have #our scenarios by hich distortion is made more comple%, and they can allbe e%perienced ith an ordinary audio ampli#ier" e have seen that these comple%distortions can be concentrated into intense pea$s, #ar more poer#ul than the avera!e valuesthat e mi!ht measure ith a voltmeter"



$onclusion

(ime #lies, and there is still much to learn" haven't really touched on hat these picturesmean to an audiophile, perhaps not hat 2ra*an had in mind hen he as$ed #or this piece"

n #act, apart #rom assumin! the pre#erence #or lo amounts o# simple #orms o# distortion, e

haven't discussed the listener at all" Nevertheless, am tryin! to ma$e a point that relatesstron!ly to the apparent disconnect beteen sub*ective e%perience and simple measurementso# distortion"

e have seen that nonlinear distortion becomes lar!er and more comple% dependin! on thenonlinear characteristic o# the sta!es, the number o# cascaded sta!es, and the number o#spectral elements in the music"

Ne!ative #eedbac$ can reduce the total uantity o# distortion, but it adds ne components onits on, and tempts the desi!ner to use more cascaded !ain sta!es in search o# betternumbers, accompanied by !reater #eedbac$ #reuency stability issues"

(he resultin! comple%ity creates distortion hich is unli$e the simple harmonics associatedith musical instruments, and e see that these comple% aves can !ather to create theoccasional tsunami o# distortion, pea$in! at values #ar above those ima!ined by the distortionspeci#ications"

# you ant the pea$ distortion o# the circuit o# #i!ure 1= to remain belo "1J ith a comple%si!nal, then you need to reduce it by a #actor o# about =000" 70 d o# #eedbac$ ould do it,but that does seems li$e a lot"

y contrast, it appears that i# you can ma$e a sin!le sta!e operate at "01J < nd harmonic ith

a sin!le tone ithout #eedbac$, you could also achieve the "1J pea$ in the comple% test"

li$e to thin$ the latter ould sound better"

Nelson Pass, <008

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Distortion and Feedback

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