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Pt.2: Why We Need Negative Feedback WHAT IS NEGXI'IVE In our second article on Negative Feedback, we see that open loop amplifiers, with their errors, distortions, uncertain gain, and erratic DC output level are just not good enough. Negative feedback is the answer. Open loop amplifier By BRYAN MAHER The story goes that in one quite "with-it" family a sister and brother, Krystie and Tyson, both avid SILICON CHIP readers, were interested in somewhat different applications of electronics in their spare time. Krystie wanted to build a small amplifier to drive some earphones, to be driven by her small cassette player. Two batteries would have to serve as the power supply for this project. Tyson, on the other hand, was more interested in using electronics to measure things, like some of the small voltages and currents he met in his experiments and working models. He already had a small cheap voltmeter, but yearned for a good DVM (digital voltmeter). In this direction he had a bright idea. He would buy one of those 4-digit panel-mount voltmeters (they're not too expensive) and then would build a little amplifier to go in front of it to raise the sensitivity. He thought that would be just as good as those expensive lowreading DVMs he had seen advertised. Not being endowed with much cash, both Krystie and Tyson needed the best results-per-dollar available. Krystie contemplated building a simple one-transistor amplifier with a gain of 30. That should be 10 SILICON CHIP sufficient for her needs. Wanting to keep it simple she thought she would do without this negative feedback idea she had been reading about - she just couldn't see why she needed it. Consulting a book on circuits, she drew up a simple single transistor stage powered by two 9-volt bat- + T 9V: ...L. C1 Vin teries, with one cheap transistor, three resistors and a couple of capacitors, as in Fig.l(a). She had learned that the symbol for such an open loop amplifier (ie, one without any feedback) is the simple triangle shown here as Fig.l(b) where G represents the amplifier open loop gain. Doing a few pages of calculations she figured G would be somewhere about 30. --1.--..,_----l'--I J T 9V : C2 ...I.. Fig.l(a): Krystie's little headphone amplifier. Rt, R2 provide the bias, while R4 helps to stabilise the DC levels and bias conditions. But the results are not good - the text tells why. ··- v- I N P U T ~ OUTPUT Vin ·· ·· Vout OPEN LOOP AMPLIFIER Fig.l(b): we use the triangle as the general symbol of any open loop amplifier. G represents the value of the open loop gain. We could callously term any open loop amplifier a " super optimist" amplifier where some applied input voltage produces an output which "we hope and pray" is a faithfully magnified image of the input. Unfortunately, Krystie found this simple amplifier was hopeless. Gain was not a critical factor in her application, as long as it was near enough, but distortion was rampant. Also the frequency range was disappointing; both very high and very low notes seemed pretty weak. Why? Let's see: Any electronic system, transistor or linear electronic amplifier without any feedback at all is called an open loop system. Its gain from input to output is called the open loop gain, and for this we use the symbol "G". G = open loop gain = output voltage 7 input voltage before any feedback is used. For an amplifier with an open loop gain which is not too large, we can measure G under any one set of conditions by measuring input and output voltage, keeping the input voltage small (to avoid false readings by overdriving). An example will illustrate this concept: Example 1: Open loop amplifier If input voltage Vin = 50 millivolts results in output voltage Vout = 1.5V [without any feedback), then input and output voltage. This is known as amplitude distortion, and is caused partly by the transistor's current gain, hFE, being a function of the collector current. Fig.2(a) shows the relation between hFE and collector cµrrent for one particular transistor, the 2N2891. Graphs for many transistors have this familar "hump" shape. FEEDBACK? Open Loop Gain G = Vout + Vin = 1.5V + 50mV = 30 We use the triangle symbol in Fig. l(b) as the universal symbol for all open loop amplifiers, large or small, single stage or multi-stage, and write "G" within to remind us that G stands for the value of the open loop gain. This leads to distortion. The output is not an image of the input. Changes in hFE The other component of amplitude distortion is caused by the value of hFE also being a function of transistor voltage Vce, the voltage from collector to emitter. As Fig.2(b) shows, Vee plus the voltage across the load V1 always add up to the constant supply voltage Vcc· At peaks of output, the current through (and voltage across) the collector load swings to its greatest value, leaving a minimum number of volts across the transistor, resulting in less gain due to decrease in hFE· This "collector non-linearity" is typical of all transistors. As well, if the circuit was designed so that at no signal the transistor operated at the peak of the hFE curve, then for both upward and downward signals we would be operating at higher and lower collector current, resulting in lower hFE as Fig.2(a) shows. Waveform comparison The output and input waveforms should be exactly the same shape, one an exact but magnified image of the other. By applying both input and output voltages to individual inputs of a dual trace CRO (cathode ray oscilloscope), and carefully adjusting the CRO gain controls of each channel, we can attempt to superimpose the output waveform upon the input waveform. If the output is an image of the input, the two can be made to exactly cover each other, no matter what the shape of the input waveform. If they cannot be made to coincide, then the output contains distortion. What's wrong with open loop? What was wrong with Krystie's single transistor amplifier? Why was the distortion so terrible? And the frequency range so poor? The trouble with all open loop systems is that inadequacies in the electronic system produce an output different from that desired. We find that: (1.) The value of G changes as temperature changes. (2.) G has different values at different frequencies. (3.) G has different values at different input signal voltages. Amplitude distortion One of the most serious faults in an open loop amplifier is the way the gain G varies depending on the 100 90 +vcc 2N2891 80 ( ;i; ~v- I'\ 70 ~,/' 60 C "'ffi ., 50 ... 40 30 I\ ... 0: \ \ / 0: ~ / ... ~ = 0: 1/ ...=~ \ 20 10 0 1mA 10mA 100mA 1A 10A COLLECTOR CURRENT (iC) Fig.2(a): nearly all transistors have a "bumpy" relationship between current gain hFE and collector current ilc, This is the graph for pulsed DC values of hFE for the 2N2891, when the collector-emitter voltage Vce is held constant at 5.0 volts. Fig.2{b): at the highest power output, most of the available voltage is expended across the load, leaving only a small voltage across the transistor. Such low values of Vce cause reduction in transistor current gain hFE at maximum collector current. w ~ = w ., "' "' Fig.2(c): the result of reduced gain with increasing collector current. The transistor fails to achieve maximum output swing, producing a distorted output waveform. ]UNE 1988 11 +12V 147.7uA t t 4.8746V 'I' 12V: ' Yin R1 ~ 03 .,. R3 -12V Fig.3(a): in this DC-coupled amplifier, Ql's collector voltage is a delicate balance. If a small drop in transistor temperature reduces collector current from 147.7,uA to 141.7,uA, the quiescent voltage would rise from 7.1254 volts to 7.3234 volts. This upwards DC drift in quiescent voltage would be amplified by all following stages. r----------------v+ Cc Cc Vin-lt-+---+-t .,. Fig.3(b): in an AC-coupled amplifier capacitors Cc and transformer T isolate any DC drift in one stage, preventing amplification of DC drift by following stages. Soft overload Fig.2(c) shows the output current waveform resulting when we try to swing the output transistor until it is practically "full on". The top of the current waveform looks compressed and finishes up with a different shape compared to the bottom. The rounded top of the waveform is sometimes referred to as a "soft overload characteristic". This lack of symmetry causes distortion rich in even harmonics. Music waveforms so mistreated have a kind of "squashed" or muffled distorted sound, lacking in any "brilliance". Odd harmonics No doubt you have heard the familiar saying "all transistors are non-linear". This results from the non-linear base voltage/base current diode characteristic in every 12 SILICON CHIP junction transistor. This causes considerable odd (particularly third) harmonic distortion. With open loop systems that's just too bad! Whether a simple onetransistor stage or the largest of open loop amplifiers, the results will always be distorted music. Quite disgusted by the distortion of her little open loop amplifier spoiling her favourite music, Krystie put it aside and wandered off to see her brother's progress with his voltmeter project. She found Tyson in deep dejection, staring unbelievingly at a small printed board sporting two transistors and a handful of resistors. Clearly everything was not right. Uncertain gain and DC level The story she heard, different from hers, was nevertheless just as sad. He had built up this tiny open loop amplifier which we show here as Fig.3(a), and while it worked and drove the DVM (digital voltmeter) he had purchased, the whole affair was useless because of errors. He couldn't quite understand it, as he had previously built another amplifier, shown as in Fig.3(b), which was more-or-less successful. His new circuit had three things wrong with it: (1.) The amplifier was supposed to have a gain of 100, but for his 4-digit DVM reading to be meaningful in all digits, that gain needed to be 100 ± 0.1 %. Though his gain was about 100, accurate it wasn't! (2.) The gain of the open loop amplifier was too hard to calculate. Even though Q3 of Fig.3(a) is an emitter follower, it does not have gain equal to one; actually its more like 0.95. As for the other stages, Ql and Q2, it was an awful lot of work calculating the two-stage gain, and even then his calculation didn't come out equal to the measured figure. (3.) Worst of all, his new DVM did not read zero when the amplifier input voltage was zero. Adding potentiometer VR1 as a DC level adjustment seemed like a good idea. But when he adjusted VR1 for a zero reading on the DVM (with the amplifier input zero and grounded), it did not stay at zero. If it couldn't do that no other reading of input voltage would have any real meaning. Instead of maintaining a steady reading of four zero digits (with zero input), the DVM reading varied all over the place, "like something crazy", as he put it! Consolation he deserved, but he needed to know how to fix it. Forgetting her own distortion problem for a moment, Krystie realized that Tyson's amplifier badly needed: (a) Gain that could be calculated and achieved with ease and accuracy; and (b) A DC output level that would stay put; ie, remain reading zero all day if necessary, as long as the input was zero volts. If he could achieve those two goals, his DVM would be an inexpensive, accurate and useful piece of equipment. Gain calculations The gain of a multi-stage open loop amplifier is quite difficult to calculate accurately. To do such a calculation all the component values, all the transistor parameters and many interconnected factors have to be known and taken into account. The output impedance is often higher than we would like, and the DC level is not sufficiently constant for some applications. Indeed, in some DC-coupled high gain open loop amplifiers it is quite usual for the DC output level to be positively erratic, drifting wildly. DC level in open loop Generally, in all open loop amplifiers, the actual DC output level depends for a start on whether the various stages are DCcoupled to each following stage. If they are all AC-coupled (ie, via a capacitor or transformer) as in the example of Fig.3(b), there isn't much of a problem. The coupling capacitors block all DC voltages while AC signals are passed to the next stage. In Fig.3(b) we have shown the use of coupling capacitors and also a transformer, either of which isolates DC levels. Though popular once upon a time, transformercoupling is little used these days because of the cost and the distortion introduced by the transformer itself. But a few applications still need transformers. Thermal DC drift If, on the other hand, the stages are all DC-coupled, as in Fig.3(a), then any drift in DC output level in the first stage becomes part of the signal seen by the second stage. Hence DC drifts of early stages are amplified by the following stages to become dangerously large at the final output. Tiny DC drifts in the first stage can be due to seemingly minor events. Typically, the breezes that blow through a room may cool the transistor slightly, reducing its hpE (and hence the collector current) just a tiny bit. This raises the collector voltage and hence the output voltage of that stage. But that small DC rise may be many times the size of the wanted signal at that point. Let's look at a second DC-coupled example: Example 2: if in Fig.3(a): Ql gain = 10 Q2 gain = 10.53 Q3 gain = 0.95 Load resistor R6 = 33kfl, then Ql collector current = 147.7µ,A, Ql collector voltage = + 7.1254 volts Wanted signal = 4.3 millivolts at Ql collector Now if a small drop in transistor temperature reduces hFE causing Ql 's collector current to fall by 6µ,A, then: Ql collector current = 141. 7µ,A, Ql collector voltage = 7.3234 volts. Thus, the DC drift in the collector voltage is Vdrift = 7.3234 - 7.1254 volts = 198 millivolts. Notice that the change in the collector voltage caused by the temperature drop is about 46 times bigger than the wanted signal at that point. Amplified DC drift As all stages are DC-coupled, this DC shift caused by the change in Ql's temperature will be amplified (along with the wanted signal) by later stages. In all stages, and in the output, the erroneous DC drift remains 46 times bigger than the wanted signal! To Krystie and Tyson it was obvious that the output of the last stage will be mostly the erroneous amplified DC drift of the first stage. They will have the ridiculous situation of an output signal with about 4600 o/o error. But help is at hand in the form of negative feedback. The application of that great friend, negative feedback, in the correct quantities can turn poor ugly duckling amplifiers into star performers! But wait, enthusiastic reader, first let's look into a few more details of open loop amplifiers. Amplifiers can have two types of input terminals. We call an input t e rminal "non inverting" or "positive" or "+" if the input signal to that terminal causes an output of the same polarity. But we call an input terminal "inverting" or "negative" or " - " if the input signal to that terminal produces an output of inverted (ie, opposite) polarity. Amplifiers with both types of terminals are said to have "differential inputs" and the absolute value of gain from either terminal to the output is the same. The symbol for such an open loop linear amplifier with differentiRl inputs is shown in Fig.4. Vin(1)=t>G I Yin (2) Vout - Fig.4: the symbol for a differential open loop amplifier. The two inputs are explained in the text. Gain with two inputs The output is proportional to the input signal applied to the noninverting terminal; and also proportional to 'the negative of the input signal' applied to the inverting terminal. That is (still with no feedback applied): Gain from non-inverting input terminal to output = G; and Gain from inverting input terminal to output = - G. In Fig.4 where we have named two inputs: if Vin(l) is the signal applied to the non-inverting input; Vin(2) the signal applied to the inverting input; and Vout is the output resulting from both inputs together, then Vout = G(Vin(l)) + ( -G)(Vin(2)) Vout = G(Vin(l) - Vin(2)) Differential polarities Two examples will illustrate a vital point. Example 3: if Vin(l) = 56.0mV Vin(2) = 51.0mV and G = 387; then V0 ut = 387(56 - 51)mV = 387(5)mV = 1935mV Vout = 1.9V JUNE 1988 13 Problems? ... and you don't have our 112 page catalogue ... Example 4: If Vin(l) = 47.0mV Vin(2) = 51.0mV and G = 387; then Vout = 387(47 - 51)mV -= 387(-4)mV = -1548mV Vout = -1.5V Polarities Notice that where both inputs are positive: if Vin(l)> Vin(2), the output is also positive but if Vin(l) <Vin(2), the output is negative. Keep that fact in mind. We will use it again soon. Notice another point in those two examples. We have expressed the answer to only two significant figures (and even feel tempted to use only one figure), because we know that the value of the open loop gain G is so unreliable. you've got real problems! ARISTA ... your one-stop problem solver. Audio leads ... Batteries ... Chargers ... Battery holders ... Cables ... Car accessories ... CD accessories ... Converters ... "Cutec" ... Earphones .. . Fuses ... Headphones .. . Intercoms ... Knobs .. . Microphones and accessories ... Mixers ... Multi meters ... Plugs/Sockets, etc ... Plug adaptors ... Power packs and leads ... PA ... Disc and Tape care ... Security equipment ... Signal modifiers ... Solderless terminals .. . Storage boxes ... Switches ... Telephone and TV accessories ... Tools and Technical aids .. . Video accessories ... Wiring accessories ... You name it and we're bound to have it ...Try us ... NOW! Get your catalogue... it'II solve a whole lot of your problems! Just send $2 + 50c p&h and your return address to: ARIST~ ELECTRONICS PTY LTD PO BOX 191, LIDCOMBE, NSW 2141 14 SILICON CHIP Variable open loop gain The value of open loop gain quoted in the above examples, 387, could be the value for some amplifier at one set of conditions. The pertinent conditions are the temperature of the transistor junctions, the values of Vin(l) and Vin(2) and the signal frequency . The change in hFE with temperature in all transistors, the temperature coefficient of the resistors used, and the circuit configuration all influence the sensitivity of the circuit gain G to thermal change. A wide ambient temperature rise could even slowly double the value of G! But the change in G could be quite fast by self-heating at the semiconductor junction if a large signal is applied to the tiny base of a very small transistor. Changes in any of those pertinent conditions will lead to distortion and errors in the output. So distortion and errors are inevitable with open loop amplifiers. The problem is that all open loop amplifiers, knowing nothing of the errors in the output, are content to go on merrily leaving us to put up with their distortions and other errors. As we saw last month, we can improve on this state of affairs if the first stage of the system could be "informed" of the output errors so that the system can compensate for its own "mistakes". Basic block diagram The general idea of how such "information about errors" can be conveyed back to the front end of the amplifier is illustrated in the basic block diagram of Fig.5. Of course the amplifier has to be so arranged that it will " act on" this information about errors in the output and do something to correct the situation. Vin FEEDBACK PATH Fig.5: the basic idea of all feedback amplifiers is that information about the state of the output is fed back to the amplifier input, to allow the amplifier to take action to compensate for its own faults. The operation of all negative feedback systems is simply that a sample of the output is "fed back" to the front end of the system to be compared with the input signal. The result of this comparison controls corrective action automatically taken by the system. Negative feedback action (1.) The input signal gives an idea of what the output should be. (2 .) The sample of the output fed back to the front end gives an indication of what the output actually is. (3.) The first is what you want, the second is what you've got. (4.) The two should be the same. (5 .) If they are not, we must arrange for the amplifier to take corrective action . (6.) This comparison is done by subtracting the fed-back output sample from the input, to give tp.e difference (Input - Feedback). (7.) This "difference" is the vital quantity which the self-correcting amplifier will use to compensate for all its errors and distortions. Then life will be beautiful. Exactly how this is done we must leave until next month. Bye for now. ~