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Substituting (4) and (5) into (3) gives, nally, vo hfe RC hfe RC hfe av1 bv2 av2 bv1 R v v2 v v2 a b 1 hie C 1 a2 b2
which clearly shows that the circuit ampli es the di erence between signals v1 and v2 .
Supplementary Problems
6.29 For the CB ampli er of Fig. 3-23, nd the voltage-gain ratio Av vL =veb using the tee-equivalent circuit of Fig. 6-3 if rc is large enough that ic % ie . Ans: Av RC RL =f RC RL re 1 rb g For the CB ampli er of Fig. 3-23 and Problem 6.29, RC RL 4 k; re 30 ; rb 300 ; rc 1 M; and 0:99. Determine the percentage error in the approximate voltage gain of Problem 6.29 (in which we assumed ic % ie , relative to the exact gain as determined in Problem 6.1. Ans: Approximate gain is 1.99 percent greater. Use the r-parameter equivalent circuit of Fig. 6-10(b) to nd the current-gain ratio Ai iL =ib for the CE ampli er of Fig. 3-10. Ans: 6.32 Ai RC re rm RC RL 1 rc re RC RL
For the EF ampli er of Fig. 3-26(a), use an appropriate r-parameter model of the transistor to calculate the current-gain ratio Ai iL =is : Ans: Ai R E R B rc RE RL RB rb re 1 rc RE kRL RE RL rc re RE kRL
Apply the de nitions of the h parameters, given by (1.16) through (1.19), to the r-parameter circuit of Fig. 6-3 to nd the CB h parameters in terms of the r parameters. Ans: hib re 1 rb rc = rb rc , hrb rb = rb rc , hfb rb rc = rb rc , hob 1= rb rc
CHAP. 6]
SMALL-SIGNAL MIDFREQUENCY BJT AMPLIFIERS
Apply the de nitions of the z parameters, given by (1.10) through (1.13), to the circuit of Fig. 6-3 to nd values for the z parameters in the equivalent circuit of Fig. 6-29, which contains two dependent voltage sources. Ans: z11 re rb ; z12 rb ; z21 rb rc ; z22 rb rc
ie + z12ic _ B _ +
z21ie
Fig. 6-29
Apply the de nitions of the z parameters, given by (1.10) through (1.13), to the CE h-parameter circuit of Fig. 6-1(a) to nd values for the z parameters in the equivalent circuit of Fig. 6-29 in terms of the CE h parameters. Ans: z11 hie hfe hre =hoe ; z12 hre =hoe ; z21 hfe =hoe ; z22 1=hoe Use the z-parameter model of Fig. 6-29 to calculate (a) the current-gain ratio Ai iL =ii and voltage-gain ratio Av vL =vi for the ampli er of Fig. 3-10(a). Ans: Ai RC RB z21 = RC RL RB z11 z22 RC kRL z12 z21 ; Av z21 RB RL kRC =f z22 RC kRL RB Ri z11 RB Ri g (b) the
For the CE ampli er of Fig. 3-17 with values as given in Problem 6.18, nd (a) the input resistance Ri and (b) the output resistance Ro . Ans: a 24:26 ; b 2:154 k A CE transistor ampli er is operating in the active region, with VCC 12 V and Rdc 2 k. If the collector characteristics are given by Fig. 3-9(b) and the quiescent base current is 30 A, determine (a) hfe and (b) hoe . Ans: a 190; b 83:33 S In the circuit of Fig. 6-30, hre 10 4 ; hie 200 ; hfe 100, and hoe 100 S. (a) Find the power gain as Ap jAi Av j, the product of the current and voltage gains. (b) Determine the numerical value of RL that maximizes the power gain. Ans: a h2 =j hoe RL 1 hoe hie hre hfe hie R 1 j; b 14:14 k L fe