PAPERS

Feedforward Error Correction in Power ~ m ~ l i f i e r s *

JOHN \ IANDER KOOY Al

University of Waterloo, Waterloo, 'on?. , Canada

PAPERS

Feedforward Error Correction in power ~ m ~ l i f i e r s *

JOHN VANDERKOOY AND STANLEY P. LlPSHlTZ

University of Waterloo, Waterloo, Ont., Canada

The engineering community is presently putting much effort into designing low-distortion amplifiers with techniques more sophisticated than ordinary feedback. To guide this effort a detailed exposition of feedforward error nulling techniques is presented. and a recent commer- cial design is analyzed with an illustration of significant modifications. The paper thus consists of: 1 ) a brief history of errorfeedforward, why i t was eclipsed by feedback, and why the time is now ripe to exploit its possibilities for total error nulling; 2) an analysis of Black's feedforward configuration and how i t relates to more recent circuit concepts such as Macdonald's active error feedback. Sandman's error takeoff, Walker's "current dumping," and several new topologies; 3) an illustration of the only commercially available error feedfonvard circuit. the Quad "current dumping" amplifier; 4) significant modifications to the latter scheme using practical amplifiers, and generalizations of the bridge system incorporated in this concept; 5) an incorporation of error correction intoclass-D switching amplifiers with resulting relaxed design criteria.

0 INTRODUCTION audio industry in particular? These are some of the ques-

V e year 1977 marked the fiftieth anniversary of the invention of negative feedback, as we know it today, by Harold S. Black in 1927. So contrary to intuition were the

8 made in his patent application, and so far-reaching in rnplications, that it took nine years before the patent

was nnally granted in 1937 [I]. It is enlightening to read the inventor's own account [2] for the historical perspective in which it places the discovery. This is something that is very difficult to appreciate nowadays, since negative feedback as an error-reduction or control mechanism is now all-per-

:n for gn IS of appl nore esotc ~tive feedt

tions which we shall attempt to answer in the sequel. It is our belief, and we trust that we shall be able to substantiate it below. that error feedforward can bestow considerable advantages, and that the time is now ripe to begin to reap some of these benefits. To our knowledge there is at present only one feedforward audio amplifier on the market, name- ly, the Quad 405 "current dumping" power amplifier [4]- [6], and we shall therefore use its design principle to il- lustrate the latter portion of this discussion. We also show wavs in which the principle can be extended to include

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systems, sucn as their'stabll~ty cnterla, are. riow well un stood as a result of the work of Nyquist and Bode, am others; In fact, error feedforward as a distortion reduc nrnppss distinct from negative feedback is now virtu

wn, and it is sobering to real s inventio (and patenting in 1928 [3]), 4arold Bl; es that of negative feedback vr ears. Wh.

ue1- long 1 ,tion F a l lv

The negatlve teeaback prlnclple 1s now so well known iat it is sufficient to refer to Fig. I for features. iy feeding back to the input of amplifier ~n fl of its lutput e, in antiphase to the input siglldl el . ~ ~ i e overall ignal gain of the system is reduced by a factor ( 1 + GP) elow the open-loop gain G of the amplifier; that is, an xcess gain factor of (1 + GP) is required in the amplifier.

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1 ENGINEEF

. . ,- , . . - - . - . , UMBER 1/2 - JOURNAL OF THE AUDIC 3ING SOCIETY. 1980 JANUARY/FEBRUARY. VOLUME 28, N

PERS 4RD ERROR

tages. The i signal g a I/P for larg ss gain, c reduction by u ~ e leeuoacn ractor ( I + Gp), arlo aoove all

lm our present point of view, a reduction in the distortion the overall amplifier by the same factor over that of the lplifier without feedback. Unfortunately these advan-

ages are available on s, not by engineerin :onsiderations which i

:. 1 . The open-loop gain G of any amplifier is frc pendent [that is,G = G(w)] in both magnitude an( d so the vanishing of the denominator, that is, I -

0, warns of the potential instability with which one 1s flirting when negative feedback is being used. For stable performance the magnitude and phase of the loop gain GP must be carefully controlled, that is, JGPI must be reduced to unity before <(GP) becomes 180". At high frequencies the open-loop amplifier phase shift will increase due to poles or propagation delay -so that the output will even- tually be in antiphase with its input, at which frequencies the loop gain must be less than unity, and feedback cannot correct any errors. Below these ultimate limiting frequen- cies there are generally two regimes, in both of which the open-loop gain exceeds the closed-loop gain, and feedback error reduction is possible. First, at frequencies below the open-loop bandwidth, the error is simply reduced by the low-frequency loop gain. Although there will be delay error due to the low-pass filter that describes the &en-loop bandwidth, at these frequencies a signal pulse, bandlimited to this open-loop bandwidth, will cause almost totally over- lapping butput and error pulses. There is no problem (as

11 1> 11

error rema

I princlurr I I I C U I C L I L ~ I I ~ I I I I ~ U S ~ I D I ~ 10 totally null tne b! )f negative feedback. We should perhaps rk hall use the term "error" in the sense of

Black [L, p. JUJ and Sandman [7], [8] to include not onlv ;nal components introduced by nonlineariiies irr 3 hum, noise, and gain, frequency response, 2

rrors present in the output signal. For example, a! 1 Fig. 1, tl gain stabil parture of gain from ~lariations le of G) cc

as an error to be corrected. In contradistinction to Fi

feedforward' is exemplifit moment the delay lines 7, ana 7,. tne concept 1s as orlglna described by Black [3]. The attenuated output p e l of 1

main amplifier A, is subtracted from the input signal leaving only an "error" signal to be amplified by auxiliary amplifier A,. This amplified error e, is then co bined with the output of the main amplifier to produce output signal e,, in which the errors due to A, have bc totally canceled. This immediately emphasizes one prim, difference between error feedforward and negative fei back. In error feedforward it is in principle possible completely null all errors due to the main amp1 only those due to the auxiliary amplifier, v "errors of the error signal," are second-order negative feedback no error null is even theoretically achi able. A second fundamental difference is also apparc There is no closed loop to form a potential instability. 1 sum/difference networks are assumed to be true biconjugare networks, so that closing the feedforward path does not

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mentioned in some circles) that the output cannot be syn- I We shall use the term feedforward- to

chronized with the input to provide proper error reduction. feedfonvard error correction in Black's sense from "signal feed- Second, the open-loop bandwidth is generally determined fonvard." a technique frequently used in operational amplifier

design as a compensation technique to improve closed-loop stabil- One pole- and at higher frequencies* the for- ity when negative feedback is applied, but having nothing to do

ward am~lifier eain has an integrating characteristic. A witherrorcorrection. u u u

signal input step will still cause a proportional insranfane- Clearly, a number.of distinct permutations of amplifier and sum/difference network polarities is possible in practice. Fig. 2 ous output slope change (except for true propagation de- illustrates just one such possibility,

lays, which only have appreciable effect at the ultimate frequencies referred to earlier). There will be significant reduction of linear and nonlinear errors due to the speed resulting from the reserve loop gain, even though the error ed signal is substantial in this frequency region. The loop gain must be reduced below unity at the ultimate frequencies where the period is comparable to the propagation delay. Thus only a finite amount of error reduction is possible, and

I f 7 , = 7 , = 0 : e ,=e ,+e ,

- - - if{ either G , P = I

P and/or G a = I Fig. 1. Standard negative feedback amplifier with forward gain

I

G ( o ) and feedback attenuation P. The signal gain Gfb tends to I/P Fig. 2. Error feedfonvard principle, with main amplifier A, as the loop gain G/3 tends to infinity. The distortion of A is reduced whose errors are nulled by the auxiliary amplifier A, provided G d by the factor ( l + GP). , = I . The signal gain Gn is then also I/P.

JOURNAL OF THE AUDIO ENGINEERING SOCIETY, 1980 JANUARY/FEBRUARY, VOLUME 28. NUMBER 1/2 3

VANDERKOOY AND LlPSHlTZ PAPERS

introduce the potential regeneration present in negative feedback, 'b i r~ui ts~here is no stability criterion to be sat- ,

, isfied,:~ird, ,no excess gain or bandwidth is required in the ,main amplifier.. he delay line (or phase correction network) 7, is designed ,to ,correct for the time delay of the main amplifier channel A, ,in order tq alloy proper synchronous subtraction of its attenuated butput ,signal from the input signal. similarly, I., corrects for the time delay of the auxiliary amplifier A,. It is important to note, however, that the absence of time-delay correction does not introduce any form of potential instability into the circuit. It merely leads to less accurate error detection and cancellation than would otherwise be possible. In this sense, it is,totally different from phase compensation as used in, a negative feedback amplifier.to enhance stability. Another important distinc- tion between error feedforward and negative feedback is that, . . since . the former acts additively, whereas the latter correctsby a multiplicative process, gain matching accu- Facy in,the various paths in an error feedforward amplifier is of,paramount importance. This is apparent from.Fig. 2 and the overall system's gain formula.. Let us suppose that at aii,ins'tant there is present at the output Pof amplifier A,, in addition, to the linearly amplified portion G,e, of the input sign,al e,,adisto~ion,component &,,say, so that e l = Gle, + 6, The error term is attenuated. by a factor P , but does not cancel in the input summing network, and so appears at the output . , . of A, ase, = :-G,P&. It thus follows thatthe 6 terms wil],exactly. cancel i n theoutput summing-network, and e, will be free of d is to~ion due to A,, provided that G& = I , a . . . . .

condition.which ye.shall refer to as,.'-'output path balance.:' .I; this, condition,is satisfied,:we areguaranteed that, within the accuracy of amplifie; A,, all errors caused by amplifier A will. be nulled at the output. egl, Another independent

.;.,.!11 ,:,,I:; , ,,.. . , : , .. , . . < . I ' .. ' cer)&,tiqq relat~'the.gaiii'~f,~hplifier.~l to th=jttenuation 6; If,forexample, we'choose G,P =- 1 ; that is, P = .I/G,; *;ti a l l@m~, ; ig? i l components w,ill be cinceledin the input.s"m&ifig network; andLily errdr components will be left to pass through the auxiliary amplifier A,. We'shall call ihi$;'condition "inputpath balance." 1t"ensures . ._. . . that , . . , the auxiliary channel carries only "'pure dihtbAidn7'and not primary signal, and so minimizes the load on A,. If, how- ever, we set the input path.balance somewhat differently fro&'G1/3 = 1, say,tocorrect the overall amplifier gainto a value different fro;n' that of A, itself, then A, will carry some primary (gain error correction) signal in addition to the distortion components. Its 'signal-hanaling capability must now be proportionately greater, a s it is i;ow being used, not solely as a distortion-nulling amplifier, but also for gain re~iormalization,.,With practical output summing networks for power arnplifi$$~&e may be good reasons (as we shall see) for unbalancing input path. Note, at this stage, that it is pbHsible to ichieirebiitA!input and output path balances simultaneously by setting G, = G2 = 1/P. It should be clear that the maintenance ofrpath balance is a crucial requirement of an y m r feedforwhd amplifier, as its

ulling accuracy, is vitally dependent on proper sub- I and subsequent addition.,-11s overall gain stability

ur;~ends on these same conditions, as we shall see. We should 'fee h ko,

error n tractio~ nlorr rln

ste'that th ~lifier is n~

e of 'an er egative, fe

back amplifier, while a measure of redundancy is intro- duced, in that the failure of either Al or A, does not render the amplifier inoperative, but merely lets i t revert to the same performance as a single (unstabilized) amplifier of about the same gain but of reduced output capability. This ''fail safe" advantage can be of considerable importance in certain applications.

It is instructive at this juncture to examine in somewhat greater detail the nature of the gain stabilization and distor- tion reduction furnished by both error feedforward and negative feedback systems. For instance, it may not be obvious that an error feedforward amplifier even affords gain stabilization. As usual, the sensitivity of the overall gain G, to a parameter x, denoted by S,"l, is defined by

It represents the percentage change in G, caused by a 1% change in x. In terms of these sensitivities, the actual change AGn in Gff caused by changes AG, in the gain G I of amplifier A, and AG, in the gain G,of amplifier A, in Fig. 2 is given by

. . I . . I ,

to first order,. using the overall gain formula f r o ' m , ~ i ~ . 2. we find (see Klaassen et al. [9]) that fbr the feedforward

. . I , . i II case. : .. : . I . .. 1 4 ! ,.

ollow$.,th~ I ) output . . .----

I " it: path bala . . ." .....-.- 1

e to borh :I, under tl In,-

G, and C ~ e s e condi

r ;

. .

nce (̂ G# = I) mak& S,,,ff= 0 (that is, gall1 I I I S C I ~ ~ I L ~ V C LO GI) . . . - -/

2) Input path balance ( G I P .=,I) makes SczGff = 0 (that is, gain insensitive to- G2),.- ,

.

3) Both paths balanced makes the overall gain insensi- . tivi ler, AGfr = 0. In fac vn that, to second

Mi. 4 ed-

so that, .

~tions, it c; -,:,. :,,,!I,

to first orc an be shov

IUARY. VOLl - WBER 1/2 -

VAN PAPER

ject

... L

is 1' Powe icramento 'oltage - C -

awa, "Hi ,r(...- .

211 "Threshold Model 'Stasi :r Amplifier Pro- Brief," Threshold Corp., S: I, CA.

221 N. S. Pass, "Constant \i :onstant Current ,h Fidelity Amplifier," U.S. Patent 4 107 619 (1978 :. 15). 231 N. Sano, T. Hayashi, a!

ficiency Class A Audio Power Ampl~ne r (uass n- ier)," presented at the 61st Co :ering Society, New York, 1' ~t 1382. 241 W. W. Macalpine, "Distortionless ransn tem," U.S. Patent 2 043 587 (1936 Jun 251 R. W. Ketchledge. " Distonionles:

, ~er," U.S. Patent 2 751 442 (1956 June . _, . [26] "Class-B Output Stages without Quiescent Current

(Adjustment)," Elektor, iss. 20, pp. 26- 27 (1976 Dec.). [27] G. Schmidt, "Current Dumping Amplifier," Elek-

tor, iss. 51/52, p. 37 (1979 July/Aug.). [28] G. Stocchino, "Feedforward Amp1

World, vol. 84, p. 70 ( 1978 May). [29] J. C. H. Davis, "Total Differentla1 reeuoacn,

Electron. & Radio Eng., vol. 35, pp. 40-44 (l958 Feb.). [30] A. M. Sandman, Wireless World (Letters to the.

Editor), vol . 82, p. 54 ( 1976 Apr.) . [31] J. G. Bennett, Wireless World (Letters to the

Editor), vol. 82, p. 55 (1976 Apr.). [32] J. Halliday, Wireless World (Leners to the Editor),

vol. 82, p. 55 (1976 Apr.). [33] B. G. Olsson, Wireless World (Letters to the

Editor), vol. 82, pp. 61 - 62 (1976 July).

of the Auc mber 3 - I

be 9). s Feedbac 19).

lifier," W,

. :-I n.-->I

gh Ef- I- Arn- . - ---- lie En- 6, pre-

llsslon

k Am-

ireless

. - - I . 9 9

IV.). ate, Wire 1977 Apr . . ,-

ters to th

less Worl .I.

[34] P. J. Baxanaal~, Wireless World (Let] Editor), vol. 82, pp. 60-61 (1976 July).

[35] T. C. Stancliffe, Wireless World (Letters ru m Editor), vol. 82, pp. 52- 53 (1976 No

[36] D. M. Divan and V. V. Gh d (Letters to the Editor), vol. 83, p. 76 (

[37] D. T. Ovens, Wireless Woria (Letters to trip

Editor), vol. 83, p. 49 (197; [38] "Quadi-Complimer

1220- 1222 (1975 Dec.). [39] "Quadi-Complimentary Complemented." Elek-

tor, iss. 21, p. 39 (1977 Jan.). [40] "Quad 405," Funkschau, vol. 48, pp. 2

( 1976 July 30). [41] L. Le Quinquis, "Analyse d'un SchCma pa

comme les Autres: le Quad 405," L'Audiophile, pp 53-60(1977O~t.).

[42] J . Vanderkooy and S. P. Lipshitz, "Current Dumping --Does It Really Work? Parts 1 and 2," Wireless World, vol. 84, pp. 38- 40 (1978 June); pp. 83- 85 (1978 July):

[43] T. Hevreng, "Distortionless Current Dumping,' Wireless World (Letters to the Editor), vol. 85, p. 7 1 ( 197 May).

[44] J. Vanderkooy and S. P. Lipshitz, reply to T. Hev- reng, "Distortionless Current Dumping," Wireless World (Letters to the Editor), vol. 85, p. 7 1 ( 1979 May).

[45] -D. M. Divan and V. V. Ghate,,"A Novel ro roach to Switching Regulator Design," Wireless World, vol. 84, pp. 42-44 (1978 May).

THE AUTHORS

J. Vanderkooy

John Vanderkooy was born in Maasland, the Nether- lands in 1941. He and his family emigrated to Canada in 1947. He was educated in Hamilton. Ontario. receiving an undergraduate degree in engineering physics, and went on to obtain a Ph.D. in physics from McMaster University in 1967, studying low temperature magnetic properties of metals. He spent two years in Cambridge, England, on a postdoctoral fellowship in the same area of research, and since then he has been at the University of Waterloo in the Department of Physics, now as an associate professor. His interest in high fidelity has developed in these latter' years, and he has always been involved in electronic tink- ering and design.

Dr. Vanderkooy is amember of the Canadian Associa- tion of Physics, and has published papers dealing with low temperature metals research. He has contributed some arti- cles on electronics dealing with oscillators and compan- ders. Currently he is teaching a course on the physical principles involved in audio and he is interested in the

S. P. Lipshitz

ever-changing nature of audio electronics and in recording techniques.

Stanley P. Lipshitz was born in Cape Town, South Af- rica, in 1943. He was educated in Durban and Pretoria. and received his Ph.D. in mathematics from the University of the Witwatersrand. Johannesburg, in 1970. Since then he has been assistant professor in the Department of Applied Mathematics at the University of Waterloo. Waterloo, On- tario. He has always had a keen interest in the whole field of audio and electroacoustics, and has recently become in- terested in some of the mathematical problems raised by the subject.

Dr.' Lipshitz is a member of the Audio Engineering Society, and is the author of a previous Journal paper on pickup arm dynamics. Other current research ranges over a wide area, including error feed-fonvard audio amplifier circuit analysis, the improved characterization of amplifier distortions, and stereophonic recording techniques.

JOURNAL 1 bF THE AUDIO ENGINEERING SOCIETY, 1980 JANUARY/FEBRUARY, VOLUME 28, NUMBER 1/2