Amplifiers with Negative Feedback

Transcription

1 13 Amplifiers with Negatie Feedback 335 Amplifiers with Negatie Feedback 13.1 Feedback 13.2 Principles of Negatie Voltage Feedback In Amplifiers 13.3 Gain of Negatie Voltage Feedback Amplifier 13.4 Adantages of Negatie Voltage Feedback 13.5 Feedback Circuit 13.6 Principles of Negatie Current Feedback 13.7 Current Gain with Negatie Current Feedback 13.8 Effects of Negatie Current Feedback 13.9 Emitter Follower D.C. Analysis of Emitter Follower Voltage Gain of Emitter Follower Input Impedance of Emitter Follower Output Impedance of Emitter Follower Applications of Emitter Follower Darlington Amplifier INTRODUCTION Apractical amplifier has a gain of nearly one million i.e. its output is one million times the input. Consequently, een a casual disturbance at the input will appear in the amplified form in the output. There is a strong tendency in amplifiers to introduce hum due to sudden temperature changes or stray electric and magnetic fields. Therefore, eery high gain amplifier tends to gie noise along with signal in its output. The noise in the output of an amplifier is undesirable and must be kept to as small a leel as possible. The noise leel in amplifiers can be reduced considerably by the use of negatie feedback i.e. by injecting a fraction of output in phase opposition to the input signal. The object of this chapter is to consider the effects and methods of proiding negatie feedback in transistor amplifiers Feedback The process of injecting a fraction of output energy of

2 336 Principles of Electronics some deice back to the input is known as feedback. The principle of feedback is probably as old as the inention of first machine but it is only some 50 years ago that feedback has come into use in connection with electronic circuits. It has been found ery useful in reducing noise in amplifiers and making amplifier operation stable. Depending upon whether the feedback energy aids or opposes the input signal, there are two basic types of feedback in amplifiers iz positie feedback and negatie feedback. (i Positie feedback. When the feedback energy (oltage or current is in phase with the input signal and thus aids it, it is called positie feedback. This is illustrated in Fig Both amplifier and feedback network introduce a phase shift of 180. The result is a 360 phase shift around the loop, causing the feedback oltage V f to be in phase with the input signal V in. Fig The positie feedback increases the gain of the amplifier. Howeer, it has the disadantages of increased distortion and instability. Therefore, positie feedback is seldom employed in amplifiers. One important use of positie feedback is in oscillators. As we shall see in the next chapter, if positie feedback is sufficiently large, it leads to oscillations. As a matter of fact, an oscillator is a deice that conerts d.c. power into a.c. power of any desired frequency. (ii Negatie feedback. When the feedback energy (oltage or current is out of phase with the input signal and thus opposes it, it is called negatie feedback. This is illustrated in Fig As you can see, the amplifier introduces a phase shift of 180 into the circuit while the feedback network is so designed that it introduces no phase shift (i.e., 0 phase shift. The result is that the feedback oltage V f is 180 out of phase with the input signal V in. Fig Negatie feedback reduces the gain of the amplifier. Howeer, the adantages of negatie feedback are: reduction in distortion, stability in gain, increased bandwidth and improed input and output impedances. It is due to these adantages that negatie feedback is frequently employed in amplifiers.

3 Amplifiers with Negatie Feedback Principles of Negatie Voltage Feedback In Amplifiers A feedback amplifier has two parts iz an amplifier and a feedback circuit. The feedback circuit usually consists of resistors and returns a fraction of output energy back to the input. Fig *shows the principles of negatie oltage feedback in an amplifier. Typical alues hae been assumed to make the treatment more illustratie. The output of the amplifier is 10 V. The fraction m of this output i.e. 100 mv is fedback to the input where it is applied in series with the input signal of 101 mv. As the feedback is negatie, therefore, only 1 mv appears at the input terminals of the amplifier. Referring to Fig. 13.3, we hae, Gain of amplifier without feedback, A 10 V 10, 000 1mV Fig Fraction of output oltage fedback, m 100 mv V 10 V Gain of amplifier with negatie feedback, A f mv The following points are worth noting : (i When negatie oltage feedback is applied, the gain of the amplifier is **reduced. Thus, the gain of aboe amplifier without feedback is 10,000 whereas with negatie feedback, it is only 100. (ii When negatie oltage feedback is employed, the oltage actually applied to the amplifier is extremely small. In this case, the signal oltage is 101 mv and the negatie feedback is 100 mv so that oltage applied at the input of the amplifier is only 1 mv. (iii In a negatie oltage feedback circuit, the feedback fraction m is always between 0 and 1. (i The gain with feedback is sometimes called closed-loop gain while the gain without feedback is called open-loop gain. These terms come from the fact that amplifier and feedback circuits form a loop. When the loop is opened by disconnecting the feedback circuit from the input, the amplifier's gain is A, the open-loop gain. When the loop is closed by connecting the feedback circuit, the gain decreases to A f, the closed-loop gain. * Note that amplifier and feedback circuits are connected in series-parallel. The inputs of amplifier and feedback circuits are in series but the outputs are in parallel. In practice, this circuit is widely used. ** Since with negatie oltage feedback the oltage gain is decreased and current gain remains unaffected, the power gain A p ( A A i will decrease. Howeer, the drawback of reduced power gain is offset by the adantage of increased bandwidth.

4 338 Principles of Electronics 13.3 Gain of Negatie Voltage Feedback Amplifier Consider the negatie oltage feedback amplifier shown in Fig The gain of the amplifier without feedback is A. Negatie feedback is then applied by feeding a fraction m of the output oltage e 0 back to amplifier input. Therefore, the actual input to the amplifier is the signal oltage e g minus feedback oltage m e 0 i.e., Actual input to amplifier e g m e 0 The output e 0 must be equal to the input oltage e g m e 0 multiplied by gain A of the amplifier i.e., (e g m e 0 A e 0 or A e g A m e 0 e 0 or e 0 (1 + A m A e g or e A 0 e 1 + A m g Fig But e 0 /e g is the oltage gain of the amplifier with feedback. Voltage gain with negatie feedback is A A f 1 + A m It may be seen that the gain of the amplifier without feedback is A. Howeer, when negatie oltage feedback is applied, the gain is reduced by a factor 1 + A m. It may be noted that negatie oltage feedback does not affect the current gain of the circuit. Example The oltage gain of an amplifier without feedback is Calculate the oltage gain of the amplifier if negatie oltage feedback is introduced in the circuit. Gien that feedback fraction m Solution. A 3000, m 0.01 Voltage gain with negatie feedback is A A f 1 A m

5 Amplifiers with Negatie Feedback 339 Example The oerall gain of a multistage amplifier is 140. When negatie oltage feedback is applied, the gain is reduced to Find the fraction of the output that is fedback to the input. Solution. A 140, A νf 17.5 Let m be the feedback fraction. Voltage gain with negatie feedback is A νf A 1 + A m ν or m ν or m ν 140 m ν Example When negatie oltage feedback is applied to an amplifier of gain 100, the oerall gain falls to 50. (i Calculate the fraction of the output oltage fedback. (ii If this fraction is maintained, calculate the alue of the amplifier gain required if the oerall stage gain is to be 75. Solution. (i Gain without feedback, A ν 100 Gain with feedback, A νf 50 Let m be the fraction of the output oltage fedback. A Now A νf ν 1 + Aν mν or m ν or m ν or m ν (ii A νf 75 ; m ν 0.01 ; A ν? Aν A νf 1 + Aν mν or Aν Aν or A ν A ν A ν Example With a negatie oltage feedback, an amplifier gies an output of 10 V with an input of 0.5 V. When feedback is remoed, it requires 0.25 V input for the same output. Calculate (i gain without feedback (ii feedback fraction m. Solution. (i Gain without feedback, A ν 10/ (ii Gain with feedback, A νf 10/0.5 20

6 340 Principles of Electronics Aν Now A νf 1 + Aν mν or m ν or m ν 40 or m ν Example The gain of an amplifier without feedback is 50 whereas with negatie oltage feedback, it falls to 25. If due to ageing, the amplifier gain falls to 40, find the percentage reduction in stage gain (i without feedback and (ii with negatie feedback. Solution. A νf A 1 + Aν mν or m ν or m ν 1/50 (i Without feedback. The gain of the amplifier without feedback is 50. Howeer, due to ageing, it falls to 40. %age reduction in stage gain % 50 (ii With negatie feedback. When the gain without feedback was 50, the gain with negatie feedback was 25. Now the gain without feedback falls to 40. New gain with negatie feedback Aν Aν mν 1 + ( %age reduction in stage gain % 25 Example An amplifier has a oltage amplification A and a fraction m of its output is fedback in opposition to the input. If m 0.1 and A ν 100, calculate the percentage change in the gain of the system if A ν falls 6 db due to ageing. Solution. A ν 100, m ν 0.1, A νf? A νf Aν Aν mν Fall in gain 6db Let A 1 be the new absolute oltage gain without feedback. Then, 20 log 10 A ν /A ν1 6 or log 10 A ν /A ν1 6/ or Aν Aν 1 Antilog or A ν1 A ν /2 100/2 50 New A νf Aν A m % age change in system gain % 9.09 ν1 ν

7 Amplifiers with Negatie Feedback 341 Example An amplifier has a oltage gain of 500 without feedback. If a negatie feedback is applied, the gain is reduced to 100. Calculate the fraction of the output fed back. If, due to ageing of components, the gain without feedback falls by 20%, calculate the percentage fall in gain with feedback. Solution. A 500 ; A f 100 ; m? A A f 1 + A m 500 or m m Now A ; m ; A f? A A f A m % age fall in A f % 100 Note that without negatie feedback, the change in gain is 20%. Howeer, when negatie feedback is applied, the change in gain (4.7% is much less. This shows that negatie feedback proides oltage gain stability. Example An amplifier has an open-loop gain A 100,000. A negatie feedback of 10 db is applied. Find (i oltage gain with feedback (ii alue of feedback fraction m. Sodlution. (i db oltage gain without feedback 20 log , log db Voltage gain with feedback db Now 20 log 10 (A f 90 or log 10 (A f 90/ A f Antilog (ii A f A 1 + A m 100,000 or , 000 m m Example An amplifier with an open-circuit oltage gain of 1000 has an output resistance of 100 Ω and feeds a resistie load of 900 Ω. Negatie oltage feedback is proided by connecting a resistie oltage diider across the output and one-fiftieth of the output oltage is fedback in series with the input signal. Determine the oltage gain with negatie feedback. Solution. Fig shows the equialent circuit of an amplifier along with the feedback circuit. Voltage gain of the amplifier without feedback is A0 RL A ν...see Art R + R out L

8 342 Principles of Electronics A f Aν A m (1 50 ν ν 47.4 Fig Example An amplifier is required with a oltage gain of 100 which does not ary by more than 1%. If it is to use negatie feedback with a basic amplifier the oltage gain of which can ary by 20%, determine the minimum oltage gain required and the feedback factor. Solution. A A m or A m A... (i 0.8 A Also A m or A m 0.8 A...(ii Multiplying eq (i by 0.792, we hae, A m A... (iii Subtracting [(ii (iii], we hae, A A Putting the alue of A ( 2475 in eq. (i, we hae, m 2475 m Adantages of Negatie Voltage Feedback The following are the adantages of negatie oltage feedback in amplifiers : (i Gain stability. An important adantage of negatie oltage feedback is that the resultant gain of the amplifier can be made independent of transistor parameters or the supply oltage ariations. Aν A f 1 + A m ν ν

9 Amplifiers with Negatie Feedback 343 For negatie oltage feedback in an amplifier to be effectie, the designer deliberately makes the product A m much greater than unity. Therefore, in the aboe relation, 1 can be neglected as compared to A m and the expression becomes : Aν 1 A f Aν mν mν It may be seen that the gain now depends only upon feedback fraction m i.e., on the characteristics of feedback circuit. As feedback circuit is usually a oltage diider (a resistie network, therefore, it is unaffected by changes in temperature, ariations in transistor parameters and frequency. Hence, the gain of the amplifier is extremely stable. (ii Reduces non-linear distortion. A large signal stage has non-linear distortion because its oltage gain changes at arious points in the cycle. The negatie oltage feedback reduces the nonlinear distortion in large signal amplifiers. It can be proed mathematically that : D D f 1 + Aν mν where D distortion in amplifier without feedback D f distortion in amplifier with negatie feedback It is clear that by applying negatie oltage feedback to an amplifier, distortion is reduced by a factor 1 + A m. (iii Improes frequency response. As feedback is usually obtained through a resistie network, therefore, oltage gain of the amplifier is *independent of signal frequency. The result is that oltage gain of the amplifier will be substantially constant oer a wide range of signal frequency. The negatie oltage feedback, therefore, improes the frequency response of the amplifier. (i Increases circuit stability. The output of an ordinary amplifier is easily changed due to ariations in ambient temperature, frequency and signal amplitude. This changes the gain of the amplifier, resulting in distortion. Howeer, by applying negatie oltage feedback, oltage gain of the amplifier is stabilised or accurately fixed in alue. This can be easily explained. Suppose the output of a negatie oltage feedback amplifier has increased because of temperature change or due to some other reason. This means more negatie feedback since feedback is being gien from the output. This tends to oppose the increase in amplification and maintains it stable. The same is true should the output oltage decrease. Consequently, the circuit stability is considerably increased. ( Increases input impedance and decreases output impedance. The negatie oltage feedback increases the input impedance and decreases the output impedance of amplifier. Such a change is profitable in practice as the amplifier can then sere the purpose of impedance matching. (a Input impedance. The increase in input impedance with negatie oltage feedback can be explained by referring to Fig Suppose the input impedance of the amplifier is Z in without feedback and Z in with negatie feedback. Let us further assume that input current is i 1. Referring to Fig. 13.6, we hae, e g m e 0 i 1 Z in Now e g (e g m ν e 0 + m e 0 (e g m e 0 + A ν m ν (e g m e 0 [ä e 0 A ν (e g m e 0 ] (e g m e 0 (1 + A ν m ν i 1 Z in (1 + A ν m ν [ä e g m e 0 i 1 Z in ] * A f 1/m. Now m depends upon feedback circuit. As feedback circuit consists of resistie network, therefore, alue of m is unaffected by change in signal frequency.

10 344 Principles of Electronics or e g i 1 Z in (1 + A m But e g /i 1 Z in, the input impedance of the amplifier with negatie oltage feedback. Z in Z in (1 + A ν m ν Fig It is clear that by applying negatie oltage feedback, the input impedance of the amplifier is increased by a factor 1 + A ν m. As A ν m is much greater than unity, therefore, input impedance is increased considerably. This is an adantage, since the amplifier will now present less of a load to its source circuit. (b Output impedance. Following similar line, we can show that output impedance with negatie oltage feedback is gien by : Z Z out out 1 + Aν mν where Z out output impedance with negatie oltage feedback Z out output impedance without feedback It is clear that by applying negatie feedback, the output impedance of the amplifier is decreased by a factor 1 + A ν m ν. This is an added benefit of using negatie oltage feedback. With lower alue of output impedance, the amplifier is much better suited to drie low impedance loads Feedback Circuit The function of the feedback circuit is to return a fraction of the output oltage to the input of the amplifier. Fig shows the feedback circuit of negatie oltage feedback amplifier. It is essentially a potential diider consisting of resistances R 1 and R 2. The output oltage of the amplifier is fed to this potential diider which gies the feedback oltage to the input. Referring to Fig. 13.7, it is clear that : R1 Voltage across R 1 e0 R1 R + 2 Voltage across R1 R1 Feedback fraction, m e R + R 0 1 2

11 Amplifiers with Negatie Feedback 345 Fig Example Fig shows the negatie oltage feedback amplifier. If the gain of the amplifier without feedback is 10,000, find : (i feedback fraction (ii oerall oltage gain (iii output oltage if input oltage is 1 mv. Solution. A ν 10,000, R 1 2 kω, R 2 18 kω R1 2 (i Feedback fraction, m ν R1 R (ii Voltage gain with negatie feedback is Aν 10, 000 A f Aν mν , (iii Output oltage A f input oltage 10 1 mv 10 mv Fig Fig Example Fig shows the circuit of a negatie oltage feedback amplifier. If without feedback, A 10,000, Z in 10 kω, Z out 100 Ω, find :

12 346 Principles of Electronics (i feedback fraction (ii gain with feedback (iii input impedance with feedback (i output impedance with feedback. Solution. (i Feedback fraction, m R1 10 R1 + R (ii Gain with negatie feedback is A νf Aν 10, Aν mν , (iii With negatie oltage feedback, input impedance is increased and is gien by : Z (1 + A ν m ν Z in in ( feedback (1 + 10, kω kω 10 MΩ (i With negatie oltage feedback, output impedance is decreased and is gien by ; Z Z out 100 Ω Ω out 1 + A m 1 10, ( feedback ν + Example The gain and distortion of an amplifier are 150 and 5% respectiely without feedback. If the stage has 10% of its output oltage applied as negatie feedback, find the distortion of the amplifier with feedback. Solution. Gain without feedback, A ν 150 Distortion without feedback, D 5% 0.05 Feedback fraction, m 10% 0.1 If D f is the distortion with negatie feedback, then, D 0.05 D νf % 1 + A m ν It may be seen that by the application of negatie oltage feedback, the amplifier distortion is reduced from 5% to 0.313%. Example An amplifier has a gain of 1000 without feedback and cut-off frequencies are f khz and f khz. If 1% of output oltage of the amplifier is applied as negatie feedback, what are the new cut-off frequencies? Solution. A ν 1000 ; m ν 0.01 The new lower cut-off frequency with feedback is f1 1.5 khz f 1( f Hz 1 + A m The new upper cut-off frequency with feedback is ν ν f 2( f f 2 (1 + m ν A ν (501.5 khz ( MHz Note the effect of negatie oltage feedback on the bandwidth of the amplifier. The lower cut-off frequency is decreased by a factor (1 + m ν A ν while upper cut-off frequency is increased by a factor (1 + m ν A ν. In other words, the bandwidth of the amplifier is increased approximately by a factor (1 + m ν A ν. BW ( f j BW (1 + m ν A ν

13 where Amplifiers with Negatie Feedback 347 BW Bandwidth of the amplifier without feedback Bandwidth of the amplifier with negatie feedback BW ( f 13.6 Principles of Negatie Current Feedback In this method, a fraction of output current is fedback to the input of the amplifier. In other words, the feedback current (I f is proportional to the output current (I out of the amplifier. Fig shows the principles of negatie current feedback. This circuit is called current-shunt feedback circuit. A feedback resistor R f is connected between input and output of the amplifier. This amplifier has a current gain of A i without feedback. It means that a current I 1 at the input terminals of the amplifier will appear as A i I 1 in the output circuit i.e., I out A i I 1. Now a fraction m i of this output current is fedback to the input through R f. The fact that arrowhead shows the feed current being fed forward is because it is negatie feedback. Fig Feedback current, I f m i I out Feedback fraction, m i I I f out Feedback current Output current Note that negatie current feedback reduces the input current to the amplifier and hence its current gain Current Gain with Negatie Current Feedback Referring to Fig , we hae, I in I 1 + I f I 1 + m i I out But I out A i I 1, where A i is the current gain of the amplifier without feedback. I in I 1 + m i A i I 1 (ä I out A i I 1 Current gain with negatie current feedback is A if Iout Ai I1 Iin I1 + mi Ai I1 or A if Ai 1 + mi Ai This equation looks ery much like that for the oltage gain of negatie oltage feedback amplifier. The only difference is that we are dealing with current gain rather than the oltage gain. The following points may be noted carefully : (i The current gain of the amplifier without feedback is A i. Howeer, when negatie current feedback is applied, the current gain is reduced by a factor (1 + m i A i. (ii The feedback fraction (or current attenuation m i has a alue between 0 and 1. (iii The negatie current feedback does not affect the oltage gain of the amplifier.

14 348 Principles of Electronics Example The current gain of an amplifier is 200 without feedback. When negatie current feedback is applied, determine the effectie current gain of the amplifier. Gien that current attenuation m i Ai Solution. A if 1 + m A Here A i 200 ; m i A if i (0.012 (200 i Effects of Negatie Current Feedback The negatie current feedback has the following effects on the performance of amplifiers : (i Decreases the input impedance. The negatie current feedback decreases the input impedance of most amplifiers. Let Z in Input impedance of the amplifier without feedback Z in Input impedance of the amplifier with negatie current feedback Referring to Fig , we hae, Z in V in I1 Fig and Z Vin in Iin But V in I 1 Z in and I in I 1 + I f I 1 + m i I out I 1 + m i A i I 1 I Z 1 Zin Zin in I + m A I + m A or Z Zin in 1 + m A 1 i i 1 1 i i i i Thus the input impedance of the amplifier is decreased by the factor (1 + m i A i. Note the primary difference between negatie current feedback and negatie oltage feedback. Negatie current feedback decreases the input impedance of the amplifier while negatie oltage feedback increases the input impedance of the amplifier. (ii Increases the output impedance. It can be proed that with negatie current feedback, the output impedance of the amplifier is increased by a factor (1 + m i A i. Z out Z out (1 + m i A i where Z out output impedance of the amplifier without feedback Z out output impedance of the amplifier with negatie current feedback

15 Amplifiers with Negatie Feedback 349 The reader may recall that with negatie oltage feedback, the output impedance of the amplifier is decreased. (iii Increases bandwidth. It can be shown that with negatie current feedback, the bandwidth of the amplifier is increased by the factor (1 + m i A i. BW BW (1 + m i A i where BW Bandwidth of the amplifier without feedback BW Bandwidth of the amplifier with negatie current feedback Example An amplifier has a current gain of 240 and input impedance of 15 kω without feedback. If negatie current feedback (m i is applied, what will be the input impedance of the amplifier? Solution. Z in Zin 1 + ma i i Here Z in 15 kω ; A i 240 ; m i Z in (0.015 ( kω Example An amplifier has a current gain of 200 and output impedance of 3 kω without feedback. If negatie current feedback (m i 0.01 is applied; what is the output impedance of the amplifier? Solution. Z out Z out (1 + m i A i Here Z out 3 kω ; A i 200 ; m i 0.01 Z out 3[1 + (0.01 (200] 9 kω Example An amplifier has a current gain of 250 and a bandwidth of 400 khz without feedback. If negatie current feedback (m i 0.01 is applied, what is the bandwidth of the amplifier? Solution. BW BW (1 + m i A i Here BW 400 khz ; m i 0.01 ; A i 250 BW 400[1 + ( ] 1400 khz 13.9 Emitter Follower It is a negatie current feedback circuit. The emitter follower is a current amplifier that has no oltage gain. Its most important characteristic is that it has high input impedance and low output impedance. This makes it an ideal circuit for impedance matching. Circuit details. Fig shows the circuit of an emitter follower. As you can see, it differs from the circuitry of a conentional CE amplifier by the absence of collector load and emitter bypass capacitor. The emitter resistance R E itself acts as the load and a.c. output oltage (V out is taken across R E. The biasing is generally proided by oltage-diider method or by base resistor method. The following points are worth noting about the emitter follower : Fig

16 350 Principles of Electronics (i There is neither collector resistor in the circuit nor there is emitter bypass capacitor. These are the two circuit recognition features of the emitter follower. (ii Since the collector is at ac ground, this circuit is also known as common collector (CC amplifier. Operation. The input oltage is applied between base and emitter and the resulting a.c. emitter current produces an output oltage i e R E across the emitter resistance. This oltage opposes the input oltage, thus proiding negatie feedback. Clearly, it is a negatie current feedback circuit since the oltage fedback is proportional to the emitter current i.e., output current. It is called emitter follower because the output oltage follows the input oltage. Characteristics. The major characteristics of the emitter follower are : (i No oltage gain. In fact, the oltage gain of an emitter follower is close to 1. (ii Relatiely high current gain and power gain. (iii High input impedance and low output impedance. (i Input and output ac oltages are in phase D.C. Analysis of Emitter Follower The d.c. analysis of an emitter follower is made in the same way as the oltage diider bias circuit of a CE amplifier. Thus referring to Fig aboe, we hae, V CC Voltage across R 2, V 2 R2 R + R 1 2 VE V2 V Emitter current, I E R R E BE E Collector-emitter oltage, V CE V CC V E D.C. Load Line. The d.c. load line of emitter follower can be constructed by locating the two end points iz., I C(sat and V CE(off. (i When the transistor is saturated, V CE 0. Fig I C(sat V R CC E This locates the point A (OA V CC R E of the d.c. load line as shown in Fig (ii When the transistor is cut off, I C 0. Therefore, V CE(off V CC. This locates the point B (OB V CC of the d.c. load line. By joining points A and B, d.c. load line AB is constructed. Example For the emitter follower circuit shown in Fig (i, find V E and I E. Also draw the dc load line for this circuit. Solution. Voltage across R 2, V 2 V CC R R1 + R V Voltage across R E, V E V 2 V BE V Emitter current, I E VE 9.72 V R 910 Ω ma E

17 Amplifiers with Negatie Feedback 351 Fig VCC 18 V D.C. load line I C (sat ma RE 910 Ω This locates the point A (OA ma of the d.c. load line. V CE(off V CC 18 V This locates point B (OB 18 V of the d.c. load line. By joining points A and B, d.c. load line AB is constructed [See Fig (ii] Voltage Gain of Emitter Follower Fig shows the emitter follower circuit. Since the emitter resistor is not bypassed by a capacitor, the a.c. equialent circuit of emitter follower will be as shown in Fig The ac resistance r E of the emitter circuit is gien by : 25 mv r E r e + R E where r e I E Fig Fig In order to find the oltage gain of the emitter follower, let us replace the transistor in Fig by its equialent circuit. The circuit then becomes as shown in Fig Note that input oltage is applied across the ac resistance of the emitter circuit i.e., (r e + R E. Assuming the emitter diode to be ideal,

18 352 Principles of Electronics Output oltage, V out i e R E Input oltage, V in i e (r e + R E Voltage gain of emitter follower is A ν Vout ie RE RE V in ie ( r e + RE r e + RE or A ν RE r + R e E In most practical applications, R E >> r e so that A ν j 1. In practice, the oltage gain of an emitter follower is between 0.8 and Example Determine the oltage gain of the emitter follower circuit shown in Fig Solution. RE Voltage gain, A ν r + R Now r e 25 mv I E Voltage across R 2, V 2 V CC R R + R e 1 2 E 5 V Fig Fig Voltage across R E, V E V 2 V BE V VE 4.3 V Emitter current, I E R 0.86 ma 5kΩ E 25 mv 25 mv r e 29.1 Ω I E 0.86 ma R Voltage gain, A ν E 5000 re R E Example If in the aboe example, a load of 5 kω is added to the emitter follower, what will be the oltage gain of the circuit? Solution. When a load of 5 kω is added to the emitter follower, the circuit becomes as shown in

19 Amplifiers with Negatie Feedback 353 Fig The coupling capacitor acts as a short for a.c. signal so that R E and R L are in parallel. Therefore, the external emitter resistance R E changes to R E where Fig R E R E R L 5 kω 5 kω 2.5 kω R E 2500 Voltage gain, A ν r e + R E Comments. This is the same example as example except that load is added. Note the loading effect on the oltage gain of an emitter follower. When load is added to the emitter follower, the oltage gain drops from to This is really a small change. On the other hand, when a CE amplifier is loaded, there is drastic change in oltage gain. This is yet another difference between the emitter follower and CE amplifier Input Impedance of Emitter Follower Fig (i shows the circuit of a loaded emitter follower. The a.c. equialent circuit with T model is shown in Fig (ii. Fig As for CE amplifier, the input impedance of emitter follower is the combined effect of biasing resistors (R 1 and R 2 and the input impedance of transistor base [Z in (base]. Since these resistances

20 354 Principles of Electronics are in parallel to the ac signal, the input impedance Z in of the emitter follower is gien by : Z in R 1 R 2 Z in(base where Z in (base β (r e + R E 25 mv Now r e and R I E R E R L E Note. In an emitter follower, impedance of base [i.e., Z in (base] is generally ery large as compared to R 1 R 2. Consequently, Z in (base can be ignored. As a result, approximate input impedance of the emitter follower is gien by : Z in R 1 R 2 Example For the emitter follower circuit shown in Fig , find the input impedance. Solution. V CC Voltage across R 2, V 2 R R1 + R Voltage across R E, V E V 2 V BE V VE 4.3 V Emitter current, I E R 4.3 kω 1 ma A.C. emitter resistance, r e E 25 mv 25 mv 25 Ω 1mA I E 5 V Fig Effectie external emitter resistance is R E R E R L 4.3 kω 10 kω 3 kω Z in (base β (r e + R E 200 ( kω Input impedance of the emitter follower is Z in R 1 R 2 Z in (base 10 kω 10 kω 605 kω 5 kω 605 kω 4.96 kω Note. Since 605 kω is much larger than R 1 R 2 ( 5kΩ, the former can be ignored. Therefore, approximate input impedance of emitter follower is gien by : R 1 R 2 10 kω 10 kω 5 kω Z in Output Impedance of Emitter Follower The output impedance of a circuit is the impedance that the circuit offers to the load. When load is

21 connected to the circuit, the output impedance acts as the source impedance for the load. Fig shows the circuit of emitter follower. Here R s is the output resistance of amplifier oltage source. It can be proed that the output impedance Z out of the emitter follower is gien by : Amplifiers with Negatie Feedback 355 Z out R E r e + R in β where R in R 1 R 2 R s In practical circuits, the alue of R E is large enough to be ignored. For this reason, the output impedance of emitter follower is approximately gien by : R Z out in r e + β Fig Example Determine the output impedance of the emitter follower shown in Fig Gien that r e 20 Ω. Fig R Solution. Z out in r e + β Now R in R 1 y R 2 y R s 3 kω y 4.7 kω y 600 Ω 452 Ω Z out Ω 200 Note that output impedance of the emitter follower is ery low. On the other hand, it has high input impedance. This property makes the emitter follower a perfect circuit for connecting a low impedance load to a high-impedance source Applications of Emitter Follower The emitter follower has the following principal applications :

22 356 Principles of Electronics (i To proide current amplification with no oltage gain. (ii Impedance matching. (i Current amplification without oltage gain. We know that an emitter follower is a current amplifier that has no oltage gain (A ν j 1. There are many instances (especially in digital electronics where an increase in current is required but no increase in oltage is needed. In such a situation, an emitter follower can be used. For example, consider the two stage amplifier circuit as shown in Fig Suppose this 2-stage amplifier has the desired oltage gain but current gain of this multistage amplifier is insufficient. In that case, we can use an emitter follower to increase the current gain without increasing the oltage gain. Fig (ii Impedance matching. We know that an emitter follower has high input impedance and low output impedance. This makes the emitter follower an ideal circuit for impedance matching. Fig shows the impedance matching by an emitter follower. Here the output impedance of the source is 120 kω while that of load is 20 Ω. The emitter follower has an input impedance of 120 kω and output impedance of 22 Ω. It is connected between high-impedance source and low impedance load. The net result of this arrangement is that maximum power is transferred from the original source to the original load. When an emitter follower is used for this purpose, it is called a buffer amplifier. Fig It may be noted that the job of impedance matching can also be accomplished by a transformer. Howeer, emitter follower is preferred for this purpose. It is because emitter follower is not only more conenient than a transformer but it also has much better frequency response i.e., it works well oer a large frequency range Darlington Amplifier Sometimes, the current gain and input impedance of an emitter follower are insufficient to meet the requirement. In order to increase the oerall alues of circuit current gain (A i and input impedance, two transistors are connected in series in emitter follower configuration as shown in Fig Such a circuit is called Darlington amplifier. Note that emitter of first transistor is connected to the

23 Amplifiers with Negatie Feedback 357 base of the second transistor and the collector terminals of the two transistors are connected together. The result is that emitter current of the first transistor is the base current of the second transistor. Therefore, the current gain of the pair is equal to product of indiidual current gains i.e. *β β 1 β 2 Note that high current gain is achieed with a minimum use of components. The biasing analysis is similar to that for one transistor except that two V BE drops are to be considered. Thus referring to Fig , V CC Voltage across R 2, V 2 R2 R + R 1 2 Voltage across R E, V E V 2 2V BE V2 2V Current through R E, I E2 BE R Since the transistors are directly coupled, I E1 I B2. Now I B2 I E2 /β 2. IE2 I E1 β Input impedance of the darlington amplifier is Z in β 1 β 2 R E... neglecting r e 2 E Fig In practice, the two transistors are put inside a single transistor housing and three terminals E, B and C are brought out as shown in Fig This three terminal deice is known as a Darlington transistor. The Darlington transistor acts like a single transistor that has high current gain and high input impedance. * I E1 β 1 I B1 ( I E1 j I C1 Now I E1 is the base current of Q 2 i.e. I E1 I B2. Now I E2 β 2 I B2 β 2 I E1 β 2 β 1 I B1 IE2 ββ 1 2 IB 1 Oerall current gain, β ββ 1 2 IB 1 IB 1

24 358 Principles of Electronics Characteristics. The following are the important characteristics of Darlington amplifier : (i Extremely high input impedance (MΩ. (ii Extremely high current gain (seeral thousands. (iii Extremely low output impedance (a few Ω. Since the characteristics of the Darlington amplifier are basically the same as those of the emitter follower, the two circuits are used for similar applications. When you need higher input impedance and current gain and/or lower output impedance than the standard emitter follower can proide, you use a Darlington amplifier. Darlington transistors are commonly aailable. Like standard transistors, they hae only three terminals but they hae much higher alues of current gain and input Fig impedance. Example Determine (i d.c. alue of current in R E (ii input impedance of the Darlington amplifier shown in Fig Fig Solution. (i Voltage across R 2, V 2 V CC 10V kω 5V R1 + R R kω kω D.C. current in R E, I E2 V2 2 VBE 5V 2 0.7V 3.6V 1.09 ma RE 3.3 kω 3.3 kω (ii Input impedance, Z in β 1 β 2 R E (70 (70 (3.3 kω MΩ This example illustrates that the input impedance of Darlington amplifier is much higher than that of an ordinary transistor. Example For the Darlington amplifier in Fig , find (i the d.c. leels of both the transistors and (ii a.c. emitter resistances of both transistors.

25 Amplifiers with Negatie Feedback 359 Solution. (i D.C. Bias Leels Fig V CC Base oltage of Q 1, V B1 R 12V 2 10 kω R + R 20 kω +10kΩ 1 2 Emitter oltage of Q 1, V E1 V B1 V BE 4V 0.7V 3.3V Base oltage of Q 2, V B2 V E1 3.3V Emitter oltage of Q 2, V E2 V B2 V BE 3.3V 0.7V 2.6V Emitter current of Q 2, I E2 VE2 2.6V R 1.3 ma 2kΩ ma Emitter current of Q 1, I E ma β 100 (ii A.C. Analysis A.C. emitter resistance of Q 1, r e1 A.C. emitter resistance of Q 2, r e2 I E E 25 mv 25 mv 1923Ω ma I E 1 25 mv 25 mv 1.3 ma 19.23Ω I E 2 MULTIPLE-CHOICE QUESTIONS 4V 1. When negatie oltage feedback is applied to an amplifier, its oltage gain... (i is increased (ii is reduced (iii remains the same (i none of the aboe 2. The alue of negatie feedback fraction is always... (i less than 1 (ii more than 1 (iii equal to 1 (i none of the aboe 3. If the output of an amplifier is 10 V and

26 360 Principles of Electronics 100 mv from the output is fed back to the input, then feedback fraction is... (i 10 (ii 0.1 (iii 0.01 (i The gain of an amplifier without feedback is 100 db. If a negatie feedback of 3 db is applied, the gain of the amplifier will become... (i db (ii 300 db (iii 103 db (i 97 db 5. If the feedback fraction of an amplifier is 0.01, then oltage gain with negatie oltage feedback is approximately... (i 500 (ii 100 (iii 1000 (i A feedback circuit usually employs... network. (i resistie (ii capacitie (iii inductie (i none of the aboe 7. The gain of an amplifier with feedback is known as... gain. (i resonant (ii open loop (iii closed loop (i none of the aboe 8. When oltage feedback (negatie is applied to an amplifier, its input impedance... (i is decreased (ii is increased (iii remains the same (i none of the aboe 9. When current feedback (negatie is applied to an amplifier, its input impedance... (i is decreased (ii is increased (iii remains the same (i none of the aboe 10. Negatie feedback is employed in... (i oscillators (ii rectifiers (iii amplifiers (i none of the aboe 11. Emitter follower is used for... (i current gain (ii impedance matching (iii oltage gain (i none of the aboe 12. The oltage gain of an emitter follower is... (i much less than 1 (ii approximately equal to 1 (iii greater than 1 (i none of the aboe 13. When current feedback (negatie is applied to an amplifier, its output impedance... (i is increased (ii is decreased (iii remains the same (i none of the aboe 14. Emitter follower is a... circuit. (i oltage feedback (ii current feedback (iii both oltage and current feedback (i none of the aboe 15. If oltage feedback (negatie is applied to an amplifier, its output impedance... (i remains the same (ii is increased (iii is decreased (i none of the aboe 16. When negatie oltage feedback is applied to an amplifier, its bandwidth... (i is increased (ii is decreased (iii remains the same (i insufficient data 17. An emitter follower has... input impedance. (i zero (ii low (iii high (i none of the aboe 18. If oltage gain without feedback and feedback fraction are A and m respectiely, then gain with negatie oltage feedback is... A (i (ii A 1 Am 1 + Am (iii 1 + Am (i (1 + A m A A 19. The output impedance of an emitter follower is... (i high (ii ery high (iii almost zero (i low 20. The approximate oltage gain of an amplifier with negatie oltage feedback (feedback fraction being m is... (i 1/m (ii m (iii 1 (i 1 m 1 + m 21. If A and A fb are the oltage gains of an amplifier without feedback and with negatie feedback respectiely, then feedback frac-

27 tion is... (i 1 1 (ii A A f b A A f b (iii A + 1 A A (i 1 1 A A fb 22. In the expression for oltage gain with negatie oltage feedback, the term 1 + A m m is known as... (i gain factor (ii feedback factor (iii sacrifice factor (i none of the aboe 23. If the output impedance of an amplifier is Z out without feedback, then with negatie oltage feedback, its alue will be... (i (iii Z out 1 + Am 1 + Am Z out fb (ii Z out (1 + A m (i Z out (1 A m 24. If the input impedance of an amplifier is Z in without feedback, then with negatie oltage feedback, its alue will be... (i (iii Z in 1 + Am 1 + Am Z in (ii Z in (1 + A m (i Z in (1 A m 25. Feedback circuit... frequency. (i is independent of (ii is strongly dependent on (iii is moderately dependent on (i none of the aboe 26. The basic purpose of applying negatie oltage feedback is to... (i increase oltage gain (ii reduce distortion (iii keep the temperature within limits (i none of the aboe 27. If the oltage gain of an amplifier without feedback is 20 and with negatie oltage feedback it is 12, then feedback fraction is... (i 5/3 (ii 3/5 (iii 1/5 (i In an emitter follower, we employ... negatie current feedback. Amplifiers with Negatie Feedback 361 (i 50% (ii 25% (iii 100% (i 75% 29. An amplifier has an open loop oltage gain of 1,00,000. With negatie oltage feedback, the oltage gain is reduced to 100. What is the sacrifice factor? (i 1000 (ii 100 (iii 5000 (i none of the aboe 30. In the aboe question, what will happen to circuit performance? (i distortion is increased 1000 times (ii input impedance is increased 1000 times (iii output impedance is increased 1000 times (i none of the aboe 31. The non-linear distortion of an amplifier is D without feedback. The amplifier has an open-loop oltage gain of A and feedback fraction is m. With negatie oltage feedback, the non-linear distortion will be... (i D (1 + A m (ii D (1 A m 1 + Am D (iii (i D 1 + Am 32. The output and input oltages of an emitter follower hae a phase difference of... (i 180º (ii 90º (iii 0º (i 270º 33. It is most necessary to control signal-to-noise ratio at... (i initial stage (ii drier stage (iii output stage (i detector stage 34. In order to obtain good gain stability in a negatie oltage feedback amplifier (A oltage gain without feedback ; m feedback fraction,... (i A m 1 (ii A m >> 1 (iii A m < 1 (i none of the aboe 35. Emitter follower is also known as... (i grounded emitter circuit (ii grounded base circuit (iii grounded collector circuit (i none of the aboe

28 362 Principles of Electronics Answers to Multiple-Choice Questions 1. (ii 2. (i 3. (iii 4. (i 5. (ii 6. (i 7. (iii 8. (ii 9. (i 10. (iii 11. (ii 12. (ii 13. (i 14. (ii 15. (iii 16. (i 17. (iii 18. (ii 19. (i 20. (i 21. (i 22. (iii 23. (i 24. (ii 25. (i 26. (ii 27. (i 28. (iii 29. (i 30. (ii 31. (i 32. (iii 33. (i 34. (ii 35. (iii Chapter Reiew Topics 1. What do you understand by feedback? Why is negatie feedback applied in high gain amplifiers? 2. Discuss the principles of negatie oltage feedback in amplifiers with a neat diagram. 3. Derie an expression for the gain of negatie oltage feedback amplifier. 4. What is a feedback circuit? Explain how it proides feedback in amplifiers. 5. Describe the action of emitter follower with a neat diagram. 6. Derie the expressions for (i oltage gain (ii input impedance and (iii output impedance of an emitter follower. Problems 1. An amplifier has a gain of without feedback. Determine the gain if negatie oltage feedback is applied. Take feedback fraction m ν [50] 2. An amplifier has a gain of 10,000 without feedback. With negatie oltage feedback, the gain is reduced to 50. Find the feedback fraction. [m 0.02] ν 3. A feedback amplifier has an internal gain A ν 40db and feedback fraction m ν If the input impedance of this circuit is 12 kω, what would hae been the input impedance if feedback were not present? [2kΩ] 4. Calculate the gain of a negatie oltage feedback amplifier with an internal gain A ν 75 and feedback fraction m ν 1/15. What will be the gain if A ν doubles? [12.5 ; 13.64] 5. An amplifier with negatie feedback has a oltage gain of 100. It is found that without feedback, an input signal of 50 mv is required to produce a gien output, whereas with feedback, the input signal must be 0.6 V for the same output. Calculate (i gain without feedback (ii feedback fraction. [(i 1200 (ii 0.009] Fig Fig Fig shows the negatie feedback amplifier. If the gain of the amplifier without feedback is 10 5 and R Ω, R kω, find (i feedback fraction (ii gain with feedback. [(i 0.001(ii 1000]

29 Amplifiers with Negatie Feedback In Fig , if input and output impedances without feedback are 2 MΩ and 500 Ω respectiely, find their alues after negatie oltage feedback. [302MΩ; 1.6Ω] 8. An amplifier has a current gain of 240 without feedback. When negatie current feedback is applied, determine the effectie current gain of the amplifier. Gien that current attenuation m i [52.7] 9. An amplifier has an open-loop gain and input impedance of 200 and 15 kω respectiely. If negatie current feedback is applied, what is the effectie input impedance of the amplifier? Gien that current attenuation m i [4.41 kω] 10. An amplifier has A i 200 and m i The open-loop output impedance of the amplifier is 2kΩ. If negatie current feedback is applied, what is the effectie output impedance of the amplifier? [6.8 kω] Discussion Questions 1. Why is negatie oltage feedback employed in high gain amplifiers? 2. How does negatie oltage feedback increase bandwidth of an amplifier? 3. Feedback for more than three stages is seldom employed. Explain why? 4. Why is emitter follower preferred to transformer for impedance matching? 5. Where is emitter follower employed practically and why? 6. What are the practical applications of emitter follower?