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Use a small-signal h-parameter equivalent circuit to analyze the ampli er of Fig. 3-10(a), given RC RL 800 , Ri 0; R1 1:2 k , R2 2:7 k ; hre % 0; hoe 100 S; hfe 90, and hie 200 . Calculate (a) the voltage gain Av and (b) the current gain Ai .

tan (u v) =

(a) The small-signal circuit is shown in Fig. 6-13, where RB R1 R2 = R1 R2 831 . division in the collector circuit, iL RC 1=hoe h i RC 1=hoe RL 1=hoe RL RC fe b By current

LL = Lce _

sin u cos v cos u sin v sin (u v) = [by Theorem 26.6] cos (u v) (cos u cos v) + sin u sin v sin v sin u cos u cos v = [divide numerator and denominator by cos u cos v] sin u sin v 1+ cos u cos v tan u tan v = 1 + tan u tan v

Fig. 6-13

CHAP. 6]

In This :

CHAP. 28]

The voltage gain is then Av hfe RL RC vL RL iL 90 800 2 173:08 vi hie ib hie RC RL hoe RL RC 200 1600 100 10 6 800 2 RB i RB hie i i RB iL RB hie 831 200 173:08 34:87 A Ai L 800 1031 ii RB hie ib RL RB hie v ib 1

(b) By current division,

Fig. 28-2 28.4 Calculate:

Execute the le hEx6_5.CIRi of Example 6.5, then use the Probe feature of PSpice to generate the instantaneous waveforms of input voltage vi and output voltage vL shown by Fig. 6-14. The peak values of vi and vL are marked. Hence, Av vL V 1:1528 4:61 Lm 0:250 vi Vim

Fig. 6-14

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(a) Dx (3 tan2 x); (b) Dx (sec x tan x).

The use of transistor notation in (2.1) gives iB ICBO evBE =vT 1 Then, by (6.5), 1 @i 1 B I evBEQ =vT hie @vBE Q VT CBO 2 1

But, by (1) and Problem 2.1, IBQ ICBO evBEQ =vT 1 % ICBO evBEQ =vT IEQ IBQ 1 VT 1 IEQ 3 (4)

[by the power chain rule]

By (6.13),

(a) The Q point was established in Problem 3.12 and is indicated in Fig. 3-16. i 3:97 2:0 10 3 0:985 hfb % C iE vCBQ 6:1 V 4 2 10 3 (b) By (6.14), hob % iC 3:05 2:95 10 3 12:5 S vCB IEQ 3 mA 10 2

(b) Dx (sec x tan x) = (sec x)Dx (tan x) + (tan x)Dx (sec x) = (sec x)(sec2 x) + (tan x)(tan x sec x) = (sec x)(sec2 x + tan2 x) = (sec x)(tan2 x + 1 + tan2 x) = (sec x)(2 tan2 x + 1)

Find the input impedance Zin of the circuit of Fig. 3-10(a) in terms of the h parameters, all of which are nonzero.

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The small-signal circuit of Fig. 6-13, with RB R1 R2 = R1 R2 , is applicable if a dependent source hre vce is added in series with hie , as in Fig. 6-1(a). The admittance of the collector circuit is given by G hoe and, by Ohm s law, vce By KVL applied to the input circuit, ib vi hre vce hie 2 hfe ib G 1 1 1 RL RC

[by the product rule] [by Theorem 28.2] [by Theorem 28.3]

In terms of the CB h parameters for the ampli er of Fig. 6-15(a), nd (a) the input impedance Zin , (b) the voltage gain Av , and (c) the current gain Ai .

(a) The h-parameter equivalent circuit is given in Fig. 6-15(b). By Ohm s law, vcb hfb ie hfb ie hob 1=RC 1=RL G vS hrb vcb hib ie 1