Web: http://www.pearl-hifi.com 86008, 2106 33 Ave. SW, Calgary, AB; CAN T2T 1Z6 E-mail: [email protected] Ph: +.1.403.244.4434 Fx: +.1.403.245.4456 Inc. Perkins Electro-Acoustic Research Lab, Inc. ❦ Engineering and Intuition Serving the Soul of Music

Please note that the links in the PEARL logotype above are “live” and can be used to direct your web browser to our site or to open an e-mail message window addressed to ourselves. To view our item listings on eBay, click here. To see the feedback we have left for our customers, click here.

This document has been prepared as a public service . Any and all trademarks and logotypes used herein are the property of their owners. It is our intent to provide this document in accordance with the stipulations with respect to “fair use” as delineated in Copyrights - Chapter 1: Subject Matter and Scope of Copyright; Sec. 107. Limitations on exclusive rights: Fair Use. Public access to copy of this document is provided on the website of Cornell Law School at http://www4.law.cornell.edu/uscode/17/107.html and is here reproduced below:

Sec. 107. - Limitations on exclusive rights: Fair Use

Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, includ- ing such use by reproduction in copies or phono records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for class- room use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include:

1 - the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;

2 - the nature of the copyrighted work;

3 - the amount and substantiality of the portion used in relation to the copy- righted work as a whole; and

4 - the effect of the use upon the potential market for or value of the copy- righted work.

The fact that a work is unpublished shall not itself bar a finding of fair use if such finding is made upon consideration of all the above factors

♦ PDF Cover Page ♦ ♦ Verso Filler Page ♦ AUDIO-HIGH FIDELITY

Type.r Of o,rcil/atioll, ronditiOIl.r p rodll cillg tilell1, tile .ftahilitv criterioll

By NOI\Mi\N II. CHOWHURST

o ' A VOID confusion between kinds be evident because the blocking capac­ the results Can be slightly dilferent­ of instability let's start by defining itor may stop the low-frequency compo­ although thel'e may be eases where Tthe different things that can con­ nent from registering on the scope this difi'el'enee is so marginal that it stitute instabilitv, The one most displacement. It may just be noted tha,t cannot be used to discover whi('h kind ' evident is cOlltinuous oscillation, In the clipping point on the top and bottom of instability is o('cul'I'ing, feedbac k amplifiers, particularly, this of the wave seems to fluctuate in some One way is to run into overload, usually oecu 1'5 outside the audio spec­ erratic manner, This means that the amplifier behaves b'um, either at a ve ry hig'h 01' very low A way in which this forl11 of irt­ normally all the while the pl'ogram frequency, stability can be spotted, sometimes, is level stays inside the clipping point. If the high-frequency oscillation is by taking' de reading's at various points But as soon as the progTam runs into of sufficient amplitude to load fully ill the amplifier: plate, cathode, etc, clipping, the amplifier bursts into os­ some 01' all amplifier stag'es, it results The dc J'eading's will go up and down cillation and nothing will stop it ex­ in hi,ljli-fl'eqllenC1! hlocf..-i1liJ' This is with a slow fluctuation at the Slime I'ate cept turning the unit otf and starting chara('tel'ized by the output of the as the low-frequency instability, And over again, a The second way usuallv ditl'el's in the amplifiel' seeming exeeptionally quiet instead of moving' with ticking 01' ' � until one tries to pass an audio signal sawtooth ,waveform, whieh is respon­' means by which it is initiated not thro�lg'h it. Then the audio signal break!:; sible for 1110torboating, the instrument by going up to the ('lipping level, but through in varying- degrees, according pointer will wave up and down sinu­ by a somewhat smaller signal (but to the strength of the high-fl'equency soidally. not a very low one), This means that blocking', in an extt'emely distorted form, So much for the continuous types the amplitier may be all right while The sound resembles what one would of instability, They are more definite playing very quietly, But as soon as a imagine it to be like if the audio volt­ than the others, The remaining kinds slightly louder program is passed ages had to break down a spark gap are parasitic and conditional oscillation, through it, oscillation begins, before they got through, Low-intensity Supel'tically there is not mllch differ­ sounds don't get throug'h at all, but Parasitic oscillation enee between these forms and in prac­ larg'e ones break the gap down and This occurs at some point on a wave­ ti('al cases also the margin may be manage to carry some other small ones forlll and may be ha I'd to detect as an nnrl'o,v,', Bllf in cause there are tWII di/fel'ent cases To explain these through with them, Then, when the level entity audibly because the parasitic ' here! drops, everything becomes quiet ag'ain, frequency is inaudible-it does not fo;'ms of instability in feedback ampli­ The waveform, as seen on a scope, is show up audibly on a sinusoidal wave, fiers and find ways and means of CUI'­ shown in Fig, 1. However, it Illay well interfere with ing them, w� need to understalld why Low-frequency oscillation results some of the highel' frequencies on the they OCClil'. either in audible motorboating (since same wave and produce a form of in­ the oscillation is not sinusoidal), the terlllodulation distortion that sounds Stability criterion variety most easily recognized, 01' in muddy, The waveform for sine-wave A feedback amplifier is stable pro­

an approximately sinuso'idal low-fre­ input looks on the scope like Fig, 3, vided that the feedback does not get quelH'y waveforll1 which is inaudible The amplifier generally breaks into to being positive and of sufficient am­ because it is subsonic, oscillation at one point on a larg:e­ plitude to cause oscillation at any fre­ However, the latter may result in amplitude wavefonll and then dies out. quency within the rang'e of the ampli­ intermodulation distortion because it fier, Considerin),!: the overall gain carries peaks of the true audio signal Conditional oscillation around the feedback loop, rolloffs are beyond the output limit of the amplifier, The third variety of instability t:all bound to occur at the end of the re­

as shown at Fig: , 2, If you use an ac be called conditional oscillation, There sponse-in direet-('ollpled amplifiers at

input to a scope, the real cause may not are two ways this can be caused and the hig'h-f requency end only; in the

Fig. I, left-High-frt'quency hlocking. Fig'. 2, ct'ntt'r-Scolle display when an amillilier oscillates inaudihly at a very low fre­ quency. Circled numhers show start of trace and corresllonding uncircled nU'Alhers show the trace ends. Fig, :1. right-sine­ wav(' inlHlt Ilroduced hy Ilarasitic oscillation.

34 RADIOJELECTRONICS AUDIO-HIGH FIDELITY

more u:;ual R-C-e:oupled amplifiers at both ends of the response. Associated with the progressive attenuation that --- -...... these ro)loffs introduce is a phase delay -...... at the high�frequeney end and a phase ...... advance at the low-fl'equency end. I'.. The problem in achieving stability ..... is one of insuring' that the attenuation around tile loop-that is, through the ; � amplifier and back through the feed­ I "- .. back to the input point again-becomes -l " sufficient so that the fed-back signal ---j-- I--- is less than the input signal before the 0 THIS LINE REP�rNTS UNITY GAIN I ,t phase shift reaches 180°. '\. " GAIN When the phase shift reaches 180°, HARGIll the feedback has chang'ed from nega­ i I'\.. --_. tive completely over to positive so that, I� I I' if the fed-back sig'nal is equal to the 10 "- I input signal, we have the condition I necessary to maintain oscillation. To jl '-I I determine whether this happens at any -�� -r- frequency we can draw the gain and 6f1 � l-r-+ phase characteristics of the amplifier - K loops (Fig. 4) and spot the point whel'e the gain has dropped to unity, i"o",,� IJIJ. ------� then check on the lower' diagram to . j � I� .Ii see that the phase is less th�n 180�. H PIIASE f-- -r HAIIGIN , Or el�e, we can spot the point where I- "- f the phase reaches 180° and check to see 1', that the overall gain has dropped to 21 less than unity, (A mal'g'in of about ;{OO, 24 at unity gain, as shown, is desirable for i-j 270 I excellent stability,) This entl!\ls looking lie 2 3 4 5 6 � 10 l 50 40 SO 6 � at two curves, so the Nyquist diagram FREQ Fig g

.--- FREQ - KC ______Nyquist diagram 0: J' This consists of plotting a polar curve of the response so that the dis­ tance of a point on the curve from the origin represents the gain a round the loop at any particular frequency and the angle of this line from the origin represents the phase shift. This presentation is illustrated in Fig. 5. U sing this form of presentation the condition for stability can be expressed by stating that the must ��, L--1---1--1-���--4--4I---�--�I---�� simply curve 10 987654 l pass inside the point representing a GAIN RATIO SCALE " gain of unity in the negative direction, GAIN MARGIN as sho wn ilt Fig. 5-a. ( N ote that gain ORIGIN in Fig', 5 is a straight voltag� ratio, wherehs it is ex p l'e ssed in decibels in Fig. 4. ) If the curve passes outside this point, as at Fig. 5-b, the amplifier is unstable �I because the amount of feedback at 180° C, Rp ••• R phase shift is greater than unity. Hence L the a fier will osci ate good and mpli ll ,, hard at the frequency represented by Fig. 5-N) Q'uist .L diagrams: a this poi.nt on the cu I've. B-t- TCs roepre·· , senta.tion of i-no There a I'e advantag'es to each metbod ACTUAL CKT formation in Fig. of presenting this information, but we It "; b. ("une encircles will not go into a discussion of this the critical point. right here or we will not fulfill the signifying i nstabili ­ Jlurpose of this article. More detail on ty. For simplicity. the Nyquist diagTam appeal's in High­ only response aho\'e Fidelity Ci?'cuit Desiyn (see footnote) 1 kc is shown. if any reader wishes to pursue the t" subject further. \Vhat we want to see �T ", is how the loop ga in presented in either EQUIY fOR LOW'fREQ RESPONSE EaVIV fOR HIGH-fREQ RESI'OO!£ of these method controlled and in s is 6 c what way practical parametel'S in the a mplifiel' brings about such conditions. As was explained in the series of Fig. 6-Typical interstage coupling. articles by George Fletcher Cooper on

DECEMBER, 1956 35 AUDIO-HIGH FIDELITY

"Feedback Amplifier Design"'" the 1'011- off l'e�ponse at each end of the spectrum _ ... .. -- - - - is contributed to by each of the cou­ I J piing- networks in the amplifier and also by various subsidiary circuitry " [I . BI( �I=- such as decoupling arrangements. \Vhat / " has not been too cleal'!y explained is / � I how the quantities so contributed can / �'1 vary with the charadeI' of the signal j II J� [ J I � - -- -- passed through the amplilier in such il [ I r<.IJ 'I a manner as to produce some of the 'I _. - kinds of oscillation described. [I J � �!7H' j� r If J If I- r) Take the simple coupling alTange­ r��� ment of Fig .. 6-a. Here the relevant J II f-- i-V I quantitics are the plate resistance R", :/ [I f-II- ' - fJ lj L the plate loau resistor RL, the coupling l-t f capal"itance and the resisto r J 1/ V II. It -- �V J.I C grid 'I. j i/ � -lZ � L V V R. of a following stag·e. The high­ PLA TE VOLT E fl'eq uellCY response is controlled by the total stnlY capacitanl"e C,. The low-fl'equency response is con­ trolled by the relation of the reactance C to the total resistance with which it appeal'S to be in series. This con­ sists o f R. on one side and the pnrallel combination of RI, and Rl. on the other side. This is sh� wn at Fig. 6-b. The high-frequency response is con­ trolled by the relation of the reactance of tot�l stray capacitance C, to the total cil'cuit l'esistance with whil"h it appears in parallel. This consists of R", R, and R. all in parallel (Fig G-c). If the amplifier has been designed . f- - --f- for minimum distol·tion, the amplifica­ PLATE VOLTAGE tion at all points on a waveform is Fig. i-I'late-l'u rrent, pial ('-"oltage curves for tYllica I t rilldc uniform. Hence the stray capacitance and Ilentode. due to Miller effect will be constant so one can regard the reactance COI11- - ponent C, for the high-frequency rol1- off as remaining constant under all I I I conditions. The reactance C.' for the ...... I 1""'0 r I low-frequency is naturally constant. I The quantity that varies is RI" This �.sc. % is illustrated in Fig. for both the �+,. � "i � pentode and triode. At different points �s. 1'''J: I ��tr... along a load line the value of R" is z :it l'epresented by the slope at which the co � characteristics, representing plate cur­ rent and plate voltage variation fol' different fixed values of grid voltage, MJMEN,TARY EXCESS GAIN � , " cross the load line. Although the load �" line has been chosen for minimum dis­

36 RADIO-ELECTRONICS AUDIO-HIGH FIDELITY

the primary inductance oC a trans­ the g'ain during' the whole period of fonner since it is not constant as the the square-wave oscillation averages l"urrent through it varies. This par­ out so as to keep the !liyquist curve in ticularly applies to an output trans­ a position to maintain oscillation. former where the instantaneous values Viewed otherwise, the gain chang'es of inductance may change throughout during this square-wave oscillation, an audio waveform. being' at a maximum during the steep side and falling a way at the top be­ From cause to effect cause of the saturation condition. This Now how does this explain the dif­ fluctuation oC gain throughout the ferent phenomena that we have listed? waveform maintains the peculiar form First the case of the parasitic oscilla­ of oscillation that results. tion shown in Fig. 3. However you explain it. the result Fig. 9-lnformation of Fig. 8 converted This is usually caused by the chang'e is that the amplifier breaks into oscil­ , into Nyquist diagram form. of plate resistance that occurs in some lation as soon as clipping' occurs he­ sing'le-ended part of the amplifier. It e:tuse, during: the instant of clipping'. will shift the time constants of the the gain of the amplifier momentarily hig'h-frequency rolloff at various points disappears and this is all that is needed in the waveform and the response will to initiate this kind of instability. g-o beyond the stability criterion in one direction of the audio sig-nal fluctu­ The cure ation. This causes oscillation at a hig'h The remedy for all these kinds of frequency to appeal' at this point on Instability is much the same as for the the waveform. the frequency being con­ continuous kind: Attention to the dif­ trolled by the Iloint at which the Ny­ ferent circuits of the amplifier to pro­ quist diagram goes beyond the stabil­ duce a condition where the whole sys­ ity criterion. As the waveform causing tem is 111Iie)'elltl!l stable. Any kind of �, this variation in transfer response re­ ('onditional or parasitic oscillation is . ,. turns toward the quiescent zero of really a marginal condition that does to-Nyquist illustrates the systcm, the loop gain characteristic not quite succeed in being continuously Fig. diagram form of conditional stahility : a, a m pli ­ returns to the stable side of the stabil­ unstable. What is needed is a safer fier is stahle because loop goes insidl' ity eriterion and the oscillation dies. working margin. -I point ; b, reducing gain of amplifier The next case is the amplifier that The approach to this is to change to one-half makes it unstahle. oscillates when more than a small sig­ the circuit values so as to obtain a g)'eater spread in the time constants nal is passed through it. ductanee of the tuned circuit and the contributed by all the components that This can happen in an amplifier resistance must be placed between the cause the rolloff attenuation und phase that uses tetrodes and pentodes in class­ tube and the inductance that causes shift. This makes the rolloff more A B push-pull for the output stag-e. the trouble. The capacitance is built gradual so that a gTeater degree of Here the plate resbtance, du ring the into the tube so it cannot be isolated. attenuation can occu I' before the phase quieseent condition, is very much hig'her Motorboating usually is due to de­ shift becomes as big. than when a signal passes through, coupling ci)·cuits. The inaudible type There are a variety of ways to eausing the plate CUITents to swing up of motorboating, however, may be due tackle this. But unless we want to into the working range of each tube. to a bad choice of coupling components gE't into u complete desig'n problem This means that, not only does the which can cause an almost perfect sine the simplest way is to just try changing value of RI• change during the wave­ wave at a very low frequency due to various values and see which ones ap­ form, but its average value throug'hout the amplifier's becoming' unstable. This the entire waveform falls. Thus the peal' critical and which do not seem is not uncommon in feedback amplifiers. to help appreciably. The ones that ap­ average response throughout the wave­ The eure for this is changing various pear critical are the best bets to pro­ form changes. This may well result in coupling capacitor values until a suit­ ceed with to find a value that gives the overall loop gain curve moving' a able combination is found that gives good margin of sufety. over to an average condition where it sufficient spread to get rid of the gain encircles the critical point at which The high-frequency blocking' form of before the phase shift gets too big-. instability begins. Once this happens oscillation mar not be due to instu­ The audible variety of motorboating' the hig'h-frequency oscillation main­ bility around the complete loop. It can that g'oes plop, plop is more often due tains this operating- condition within often happen just in the output stage to bad decoupling arrangements some­ the amplifier and the oscillation con­ or in any single stag'e of the amplifier, where. The best cure is to try various tinues indefinitely or until the ampli­ due to a tuned-plate tuned-grid ef­ decoupling capacitor values. If this fier is switched off. fect. This occurs at some very high does not correct the trouble, try a dif­ The other form of oscillation caused frequency, the inductance of the plate ferent decoupling alTangement. in this way is one that has been lead with the plate capacitance form­ Remember that two stages together described before and is ascribed to a in/!: one tuned circuit while the induct­ cannot be unstable by themselves. In­ ('ondition demonstrated with the Ny­ ance of the grid lead with its effective stability of this kind occurs due to quist diagram as 'being conditional sta­ capacitance to ground forms the other. the fluctuations in the third-stage plate bility. If the attenuation and phase This is particularly liable to happen circuit feeding back to the plate cir­ chal'acteristics are such (Fig. 10) that with many of the high-efficiency tubes, cuit of the first stage, or some similar the response goes around the point and the best remedy is a well known alTangement. This means that, com­ without ellclosing. it, the amplifier, one: inserting suitable antiparasitic bining- the decoupling of the second while operating under this condition, resistors in the g)'id and plate circuits. and third stages of a three-stage am­ cannot oscillate. But if the gain is re­ Suitable values are from 5,000 to 50,- plifier, or maybe operating them both duced by any cause so the amplitude 000 ohms in the grid circuit and from without decoupling and using decou­ of the whole curve drops, the curve 100 to 500 ohms in the plate circuit. pIing just for the first stag'e, may give will then enclose the critical point for Similar resistors sometimes help in the best cure for this kind of instability. stability and oscillation starts. the screen circuit. Sometimes the more elaborate the Once oscillation commences there is The important thing is that the precautions taken to safeguard the sufficient gain in this amplifier to set resistors be connected as close as pos­ situation, the more unexpectedly oscil­ up a saturating oscillation. This pro­ sible to the tube pins themselves-it lation turns up. The simplest circuit duces something like square waves and is the actual lead that forms the in- is usually the .best circuit. END

DECEMBER. 1956 37