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Pt.4: Feedback versus distortion AT IS NEGA11VE Negative feedback can reduce distortion caused by non-linearities in amplifier circuits. The reduction depends on the ratio of open loop gain to closed loop gain at the frequency of the distortion component. We look at frequency components, harmonics and class B power output stages. By BRYAN MAHER Let's talk about distortion and audio amplifiers, especially power amplifiers, together with the AC signal voltages [and their waveforms) which we put in and get out. We start with a sinewave, as shown in Fig, 1. Sinewaves are widely used as test signals in electronic engineering but pure sinewaves rarely occur in speech or music. Speech or music signals have very complex waveforms but they can all be described in terms of one or more definite frequencies and repeating predictable waveforms. Furthermore, all can (if you wish) be described by equations and could all be generated by suitable linear circuits, or simulated on a digital computer. Non-linearity distortion Before discussing non-linearity distortion, we need to know more about sinewaves and the concepts of "frequency components" and "harmonics". The sinewave [including the cosine) is usually regarded as the fundamental "building block" of all cyclic waveforms. All periodic waveforms can be considered as being the sum of many sinewaves of different but related frequencies. Need convincing? Let's do a little experiment. We could take any number of sinewave generators, each giving output at a different frequency and combine those signals together in a linear operational adding circuit such as that depicted in Fig.2. For an example let's take four sine generators, each generating different frequencies as follows: (1). A lkHz sinewave at some reference amplitude; (2). A 3kHz sinewave, at 37.5% of the reference amplitude and inverted; ie, reversed in phase; (3). A 5kHz sinewave, at 8.125% of the reference amplitude and inphase with 1; (4). A 7kHz sinewave, at 3.125% of the reference amplitude and inverted. s Fig.1: a pure sinewave signal. Sinewave signals are widely used when testing audio amplifiers and loudspeakers, but pure sinewaves rarely occur in speech or music. Instead, the latter have quite complex waveforms. 82 SILICON CHIP "'SJNEWAVE GENERATORS Fig.2: this simple adder circuit can be used to combine four different sinewave signals (see text). Using the adder circuit of Fig.2, let's add those four signals together. If we had a 5-beam oscilloscope (CRO), we could view all four separate sine waveforms and their sum. Since a 5-beam oscilloscope is an extremely rare beast, we can simulate what will happen by drawing carefully on graph paper each of the four aforementioned sine waveforms. We take care to draw them to scale, all starting at the same point, and reversing the sign of those so indicated above. Fig.3 is the finished product. Listening test If we were to conduct the electronic experiment using four real synchronised sinewave generators and the adder of Fig.2, we really would see on the 5-beam oscilloscope all the separate sine waves (one on each beam) and on the fifth beam the sum waveform predicted in Fig.3. Using headphones you could listen to each sinewave separately and confirm that each had a different pitch [frequency). But the sum waveform voltage would have a quite different sound, though it would have the basic pitch of the lowest frequency sinewave. Musicians would say that the sum waveform sounds as if it contains ''harmonics''. Harmonics We call a 3kHz sinewave signal the "third harmonic" of a lkHz sinewave simply because it is three times the frequency. The expression came from the world of music, where the "second harmonic" of any note means " one octave higher" , the fourth two octaves higher, etc. Odd harmonics such as the third must then mean "one and a half" octaves higher. So how do harmonics relate to distortion in amplifiers? The relationship is simple. When an amplifier distorts a signal, due to its inherent non-linearities, it adds harmonics which weren't there before. Let's see why? FEEDBACK? i,..----- ONE CYCLE - - - - - - , - . i / Audio amplifiers 1kHz FUNDAMENTAL SINE WAVE TIME While every active device (ie, every transistor, FET etc) does contribute a share of distortion, the output stage usually contributes the largest share. In most audio amplifiers, the output stage usually operates in class-B mode or a variation, class AB, which is somewhere between class A and class B. We'll explain these modes before going further. An amplifier stage employing two transistors as in Fig.4 may be operated in either class A or class AB or class B, depending on the bias and drive used. (1). Class A: a transistor amplifier stage is operating in class A if that transistor is conducting current throughout the whole 360 degrees of the signal cycle (ie, all the time). All single transistor linear stages must operate in class A. +v INPUT BIAS PLUS DRIVE OUTPUT TIME 7kHz SEVENTH~- HARMONIC ,.-... ,.-... ,,-... ,,-... ,,-... ~~C>~~ I'"":) ,....._ ,.-... ,....._ ~<.::> . TIME Fig.3: the complex waveform reproduced in colour is the output from our adder circuit (Fig.2). The resultant waveform consists of a 1kHz fundamental combined with its third, fifth and seventh harmonics as shown. -v Fig.4: depending on the bias and drive used, a transistor amplifier can operate in class A, class B or class AB. SEPTEMBER 1988 83 distortion, but the lowest power efficiency; class B gives the most distortion and the highest efficiency; and class AB is a compromise. Output power stage + cuRiiNT 0 ~ - - - - r - - + - - - i . - - + - - ~ - - - - - - - - .. . - - - - - ~ (b) + OUTPUT CURRENT TIME (c) o· go• 1ao· 210· 350• Fig.5: when an amplifier is operated in class B, Qt conducts on the positive half of the sinewave signal (a) while Q2 conducts on the negative half (b). The resulting output current waveform is shown at (c). +3DV +3DV 01 INPUT 01 OUTPUT -30V RL Fig.6(a): in this circuit both Qt and Q2 are non-conducting for input signals between ± 0.6V. Fig.6(b): here, Dt, D2, R2 and R3 provide forward bias to Qt and Q2 to minimise crossover distortion. .,. -3DV A very basic class B complementary power output stage is shown in Fig.6(a). When the input drive signal is positive, Ql drives output current from the + 30V rail to the output, through the load R1 to ground. During that time Q2 is cutoff; ie, just loafing along doing nothing. A half cycle later when the input drive signal is negative , Ql becomes cut off and Q2 takes over the conduction process, allowing current to flow from ground, through the load R1 , to the negative rail. Fig.5 illustrates the current conduction of each transistor in turn when a test sinewave is used as signal. At (a) is the current waveform for Ql, at (b) the waveform for Q2, while at (c) is shown the output current which is simply the sum of current waveforms in the two output transistors; ie the sum of (a) and (b). A little thought convinces us that what Fig.5 demands is output transistors capable of switching instantaneously from cut-off state to conducting state and vice versa. That's a difficult demand to make of transistors, because their base region must contain more current carriers when in the conducting mode and less when in the cut-off mode. However, they try. Base-emitter voltage (2). Class B: when two transistors are operated in class B each transistor conducts in turn, meaning that, in Fig.4, Ql conducts only during the positive half cycle of a sinewave signal, with Q2 conducting only on the negative half. Fig.5 illustrates how each transistor delivers half the signal; there is no overlap, one transistor must cut off just as the other begins to conduct. As there are 360 degrees in one complete cycle we say that in class B operation, each transistor conducts for 180 degrees out of each cycle. (3). Class AB: an amplifier is 84 SILICON CHIP operating in class AB if the output transistors conduct for more than 180 degrees but less than 360 degrees of each cycle. So in class AB there is some overlap in transistor conduction times; ie, near the middle of the cycle there is some time during which both transistors are conducting. The class of operation for a circuit is decided by the value of bias voltage applied to the transistors (or FETs, valves etc) and how hard they are driven. Designers choose one of the three classes for an amplifier design, considering that: class A gives the least In any NPN junction transistor the base must be about 0.6 volts more positive than the emitter (and in PNPs 0.6 volts more negative) before the transistor can conduct. Therefore, in the simple circuit Fig.6(a), Ql would go out of conduction when the input signal voltage falls below + 0.6 volts but Q2 would wait until the input voltage falls down through zero and down to - 0.6 volts before taking over conduction. We would have a time when neither transistor is conducting, so the output current would be interrupted each side of the crossover COMPONENTS GALORE! _ ,_ ECONOMY TRANSFOR~f RS I ULTRASONIC lf~~J~Vr~rm ~~t 40kHz (L 19990) and receive at 40kHz (L 19991) with up to 20V I/P on the transmitter. 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No. Description 1·9 10 + P10620 8 pin $1.20 $1.10 P1 0624 14 pin S1 .60 $1.50 P10626 16 pin $1 .90 $1.80 P10628 18 pin S2 .00 S1.80 P1 0630 20 pin S2.20 S2.00 P10632 22 ptn S2.40 $2.20 P1 0634 24 p,n S2.60 S2.40 P10640 28 ptn S2.90 S2 .60 P10644 40 pm $3.00 S2.70 • TAG TANTALUM t~P~ C1Ifi?ft~p~g~C1"'1;~J R1 6124 R161 25 R1 6126 R161 28 R16216 R16220 R16222 R 16224 R 16228 R16300 R16302 R16304 R16306 R16308 R16310 R1631 1 R1631 2 R16314 R16316 R16318 R1 6320 R16322 R16324 R16326 R16328 16V 4.7u F .... 16V 10uF .. . 16V 15uF . 16V 22uF .. ... 25V 2.2uF . 25V 4.7uF .. 25V 6.8uF . 25V 10uF . 25V 22uF .... 35V 0.1uF .. 35V 0.15uF .. 35V 0.22uF.. 35V 0.33uF .. 35V 0.47uF . 35V 0. 68uF.. 35V 0.82uF .. 35V 1.0uF .. 35V 1.5uF . 35V 2.2uF .. 35V 3.3uF . 35V 4.7uF .. 35V 6. 8uF . 35V 10uF 35V 15uF .. . 35V 22uF . 0. 48 0 .52 0.75 0.85 0.40 0.70 0.70 0.60 2.40 0.30 0.30 0.30 0.30 0.30 0.35 0.35 0.30 0.50 0.50 0.35 0.70 0.80 0.80 1.40 3.50 1 Cat.R1 4405 .... ..... $45 .95 SPECIAL, $35.95 Numb,t,;'li)lil,~nV 1t 1- 11 Minor Scale Divi sion : 1150 turn Shatt Bore: 6.35mm ( 1/4 .. ) Finish : Clear Anodize Body Size : 22.2mm diameter (.875.. ) Depth : 22.2mm (.875" ) Weight : 19.8g (0.7oz.J Cat.R14400 ..... $26.95 SPECIAL, $21.50 Num,,,t,;'9'il.~n'.2,k 1-11 Minor Scale Division: 11100 turn Shatt Bore : 6.35mm ( 1/4") Finish: Satin Chrome Body Size : 46.04mm diameter (1.81 2") Depth : 25 .4mm (1 ") Weight : 85.g (3o z.J Cat.R14410 ... .... .. $46.95 SPECIAL, $37.50 ,I' • • • Rod Irving Electronics MELBOURNE : 48 A 'Beckett St. Phone (03) 663 6151 NORTHCOTE : 425 High St. Phone (03) 489 8866 CLAYTON : 56 Ren ver Rd . Phone (03) 543 7877 SOUTH AUSTRALI A; Electronic Di scounters PIL, 305 Morohett St, ADELAIDE 1 ~g~r:e,i ?! J..2! ~~ ?t!u> H•r •,',II•• 1,., 1, '1e,gh!COSl!>I MAIL ORDER : Local Orders: (03) 543 7877 Interstate Orders: (008) 33 5757 AU Inqu iries : (03) 543 7877 CORRESPONDENCE : P.O. Box 620. CLAYTON 3168 Telex: AA 151938 Fax : (03) 543 2648 - - MAIL ORDER HOTLINE 008 335757 SPECTROL MULTIDIALS Numbe"'/'li)lil,~nV 1i · l · 1 Minor Scale Division : 1/500 turn Shatt Bore: 6.35mm ( 1/4 .. ) Finish : Satin Chrome Body Size: 25.4 x 44 .45mm (1 X 13/4 ") Depth : 25.4mm (1.. ) Weight : 45.4g (1 602.) $0.18 :r·· ·:1•·:e·_··._ • ,4'.~~ 1 S.P.0 .T. 12VCoil 10A240VS 1411 4 $3.95 $0.20 DB 25 CRIMP SPECIALS! [!]0<at>] (z] ~ ~ (B[£]<at>) P10964 3 PIN LINE FEMALE P10966 3 PIN CHASIS FEMALE ,oo . s. P.D.T. 3A conneclors.. $1.95 DB25 CONNECTOR SPECIALS! $9.50 NEW TRANSISTORS Rod Irving Electronics have two new transistors which will replace a multitude ol common hard to gel devices. The PN 100is a NPN general purpose medium power amp and switch with continuous collector current up to SOOmA The PN200 is a PNP general purpose amp at collector currents to 1 Amp. Both are T0-82 plastic package PN100 REPLACES: PN2221 . PN 2222. PN2222A. PN3585. PN356S, PN3569. PN3643. PN5133, 2N2219A, 2N2222A. 2N3414 . 2N341 5, 2N3416 , 2N34 17. 2N3700 , 2N370 4, 2N3904 , 2N4 123. 2N4 124. 2N4401 . 2N5088. 2N52 10 PN200 REPLACES : PN2907. PN2907A, PN3638. PN3638A. PN3640, PN3644, PN4121 , PN4143, PN4248 , PN4249. PN4250. PN4355. PN491 6. PN4917. PN:5910, 2N2905A. 2N 3467. 2N3702. 2N3906, 2N4 125. 2N4 126. 2N4291 . 2N4402. 2N4403. 2N5086. 2N5087, 2N5447 PNIOO Cat. T90001 PN200 Cat. 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Suitable for Scotchcal, Eprom erasing etc. As used in ETI Eprom . $4.95ea $4.25ea $3.95ea fs~;;;;;;, SPECTROL 64Y ~/:IJ/IJ,~ p':', J f;l_!f.1P0,J!> Transmit: 4.0 (at 100dB) Receiver: 5.0 {al - 73d8 ) Impedance: Transmit : 500 Receiver: 5000 Cat. l 19990 (Transmitter) $6.95 Cat. L19991 (Receiver) .... $6.95 10 1 Cat. S1 2500 ......... Normally $7 .95 1·9 10 + 25 + =- ::_---...-.. WIRE WRAP IC SOCKETS These quality 3 level wire wrap sockets are tin-plated phosphor bronze. Cat.No. Description 1-9 1O.,. 8 p,n S1 .50 S1 .40 P10579 P10580 14 p,n $1.85 $1.70 P10585 16 pin S1.95 S1.80 P10587 18 pin S1.95 S1 .80 P10590 20 pin $2.95 $2.70 P10592 22 ptn $2.95 $2.70 P1 0594 24 pin $3.95 S3.50 P10596 28 pin $3.95 $3 .50 P 10598 40 p,n $4.95 S4.50 1s rn1tW~rfi::M~bNLYJ LOCAL ORDERS &INQUIRIES (03) 543 7877 POSTAGE RATES : S1 S9.99 S10 S24.99 S2 5 S49 .99 S50 S99.99 $100 S199 S200 S499 S500 pl us The above postage ra tes are for basic postage only . Road Freight . bulk y and fragile item s will be c harged al differen t ral es . Alt sa les ta x exempt order s and wholesale inqu iries to : RITRONICS WHOLESALE . 56 Renver Rd, Clayton . Ph . (03) 543 2166 (3 1ines) Errors and omissions excepted Pnces and spec1hcations sub1ect 10 change !~;~~:a~~ . x1;;11~~;,,,f~~.'.~~~~~.. M arh1ne~ · Apple ,1; a reqistered 11ac1cm.1, ~ ·oenolc!> rcg, s terrd ·radmar ~<. pt 1ht'" re!,pec1 1ve o w ner!> Fig.9: distortion can be measured using a harmonic wave analyser such as this H-P "Dynamic Signal Analyser". It displays relative amplitudes of the fundamental and each of the harmonics. Fig.7: input and output waveforms for the circuit shown in Fig.6(a). The output waveform shows severe crossover distortion because Ql and Q2 are non• conducting for signals between - 0.6V and + 0.6V. In Fig.8, the output from the circuit Fig.6(b), we notice the striking resemblance to the sum waveform "A" in Fig.3. Having previously demonstrated that the resultant waveform in Fig.3 is in fact the sum of a number of harmonic sine waves, we know that the voltage waveform photographed in Fig.8 is likewise. That is the justification for the use of the harmonic wave · analyser as a distortion measurement method. Enter negative feedback. Fig.8: the circuit shown in Fig.6(b) greatly reduces distortion. Even better results can be obtained by matching the diodes and transistors and trimming resistor values, but we need negative feedback for a really good amplifier. point as in the oscilloscope photo Fig. 7 where we are still using the test sinewave as an input signal. Clearly this produces a horribly distorted output current, especially on small signals (low volume). Distortion from this cause is, not surprisingly, called "crossover distortion". Many and wonderful are the circuits proposed and used to reduce this crossover distortion, one of the simplest being shown in Fig.6(b). The resultant output waveform is shown in Fig.8, an improvement on Fig. 7 but crossover distortion is still clearly evident. Without feedback, such improvements can reduce 86 SILICON CHIP crossover distortion, but cannot eliminate it. The distortion demonstrated in Fig.7 and Fig.8 could be measured using a harmonic wave analyser such as the Hewlett Packard "Dynamic Signal Analyser" model 3561A shown in Fig.9. Such an instrument displays on its screen the relative amplitudes of the fundamental frequency and each of the harmonics, as in Fig.10. We observe that crossover distortion creates an output signal rich in odd harmonics. Fig.10 shows the large fundamental (going well off screen) and also all measurable harmonics up to the 19th. Fig.11 is a block diagram of a complete amplifier, shown divided (for convenience of explanation) into two sections, the differential stage and the rest of the amplifier. We now proceed to enclose all that within one overall negative feedback loop. As before, the feedback signal is subtracted from the input voltage to give the error signal "E" which is the signal actually amplified (as explained in Pt.3 of this series, in the July 1988 issue). We call V(in) the test sinewave input to the power amplifier, and V(out) the output. Suppose we have chosen Rl = 4k0 and R2 = 1kn. This gives a voltage divider ratio of R2/(Rl + R2) = 0.2. The output from the amplifier will be an amplified version of the test sinewave V(in) plus the distortion harmonics introduced at the output stage. From our experience with Fig.3 and the harmonic analyser (Figs.8, 9 & 10), we expect the distortion generated in the output stage to consist of many sinewaves, all at odd multiples of ,.,.. l 008 Hz CAl.!JRAT!ON DISABLED RAHGE: ·S dB!/ F'REE RUN Off 98 a\lrH BAHll IMllltC SID£JAND ' aVras .,. ,.,.. /J)JY e Vns: I e Hz •1t1 Si!\RTI llt r,' r, ' ' J.1 : ll. Dtrntt NU" HARi! r;, BUI 190,97 Hz YI IH,I .Vru ... STOP: 20 809 Hz- THII 33,t l Fig.10: the output of the harmonic wave analyser here shows 33% THD (total harmonic distortion), mostly due to third and fifth harmonics in the output. the frequency of V(in), decreasing in strength as we go to higher orders. Let's label the the 3rd harmonic signal voltage VH3; the 5th, VH5; the 7th, VH7; the 9th, VH 9 ; the 11 th, Vm1; and the 13th, VH13· There will be more harmonics of still higher orders but the above is enough to make the operation of the system clear. Also we call "G" the open loop gain of the amplifier (ie, gain from E to the output). From Fig.11 we observe that: V(out) = G.E + VH3 + VH5 + VH7 + VHg + Vm1 + Vm3 E = (V(in) - FB) FB = 0.2V(out) FEEDBACK SIGNAL Thus V(out) = GV(in) - 0.2V(out) + VH3 + VH5 + VH7 + VHg + Vm1 + Vm3 (V(out))(l + 0.2G) = GV(in) + VH3 + VH5 + VH7 + VHg + Vm1 + VH13 If the open loop gain of our amplifier is 15,000 at low frequencies, we can write: V(out)(l + 0.2 x 15,000) = 15,000V(in) + VH3 + VH5 + VH7 + VHg + Vm 1 + Vm3 3001V(out) = 15,000V(in) + VH3 + VH5 + VH7 + VHg + Vm1 + Vm3 Thus V(out) = 4.998V(in) + VH3/3001 + VH5/3001 + VH7/3001 + VHg/3001 + Vmi/3001 + Vm3/3001. .,. Fig.11: by introducing negative feedback, harmonic distortion can be greatly reduced. If the open loop gain (G) is 15,000, harmonics generated by non-linearities in the output stage will be attenuated by a factor of 3001 (see text). We conclude from the above foray into a little algebra that at low frequencies the gain for the wanted input signal V(in) is 4.998 or approximately 5 but for the harmonics generated by the nonlinearities of the output stage, the gain is 1/3001; ie a severe attenuation. If you like you can regard it as a case of small distortion harmonics being fed back from the output to the inverting input, then amplified to the output stage where they (being inverted) almost cancel the distortion harmonics as they are produced by the output stage. Equilibrium is reached when the small fraction 1/3001 of each produced harmonic is heard in the output. Observe that the low frequency open loop gain of this amplifier is 15,000 but the feedback reduces the closed loop gain down to approximately 5. Therefore we say that we have applied 15,000/5 as a feedback "quantity". This is usually expressed in decibels; ie, approximately 70dB of feedback. The high frequency problem The above calculation holds good for all frequencies for which G = 15,000, and this will probably be true for frequencies up to about 3kHz, in a typical power amplifier. That presents a problem because harmonics at higher frequencies will have less feedback available to reduce them to low levels. Suppose the amplifier's open loop gain falls from 15,000 at low frequencies to 200 at 32kHz. This means that harmonics at 32kHz or thereabouts will no longer be reduced by a factor of 3000 but by the smaller factor of 41. You may argue "So what that's way above audibility". Ahah yes, but those less-reduced distortion harmonics will beat with every other music component present in the amplifier, producing sum-anddifference products which we call intermodulation. So even if you can't hear high distortion products, they can still make the sound unpleasant. Now we see the reason for making amplifiers with an open-loop frequency bandwidth extending as high as possible. ~ SEPTEMBER 1988 87