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Equating (1) to (3) and (2) to (4) allows formulation of the system of linear equations 2 3 RB Ri RB Ri r R Ri rb re e B 6 7 i v RB RB Ri RB i 6 7 b 7 6 4 RC RL 5 ic 0 re rm 1 rc re RC RL from which, by Cramer s rule, ic 2 = , where R Ri RB Ri RC RL B rb re 1 rc re re re rm RB RB Ri RC RL 2 re rm vi Then Av vL RL kRC ic R L R C re rm vi vi RL RC

[by the quotient rule] [by Theorem 27.2] [by Theorem 26.1]

The CE tee-equivalent circuit of Fig. 6-10(b) is suitable for use in the analysis of an EF ampli er if the collector and emitter branches are interchanged. Use this technique to calculate (a) the voltage-gain ratio Av vL =vB and (b) the input impedance for the ampli er of Fig. 3-26(a).

(a) The appropriate small-signal equivalent circuit is given in Fig. 6-12. By KVL around the B; C loop, with rm rc (from Problem 6.3), vB rb ib rm ib 1 rc ib ie rb rc ib 1 rc ie

[by the power chain rule]

Adjusting Entries: (a) Supplies Expense Supplies (b) Rent Expense Prepaid Rent (c) Depreciation Expense Accumulated Depreciation (d) Salaries Expense Salaries Payable 765 765 900 900 500 500 200 200

B rb ib + iS + LB _ rm ib RB _ (1 _ ) rc C ic RE RL ie re E iL + LL _

Fig. 6-12 Application of KVL around the C; E loop, again with rm rc , gives RE RL RE RL ie rc ib re 1 rc i RE RL RE RL e

By Cramer s rule applied to the system consisting of (1) and (2), ie 2 = , where RE RL RE RL rc re rb re 1 rc RE RL RE RL 2 rc v B

Because csc x = 1/(sin x), it is, along with sin x, periodic, of period 2 , and odd. Therefore, we need only nd the graph for 0 < x < . Now 1 1 = = =1 2 sin ( /2) 1 As x decreases from /2 toward 0, sin x decreases from 1 toward 0. Therefore, csc x increases from 1 to + . Likewise, as x increases from /2 toward , sin x decreases from 1 toward 0, and csc x increases from 1 to + . In fact, since sin (( /2) + u) = sin(( /2) u), the graph will be symmetric about the line x = /2 (see Fig. 28-2). csc

(b) The input impedance can be found as Zin RB k vB =ib . Now, in the system consisting of (1) and (2), by Cramer s rule, ib 1 = , where RE RL v 1 re 1 rc RE RL B RE RL RE RL RB rb re 1 rc R B rc re RE RL RE RL Hence, Zin RB k v RE RL RE RL 1 B RB rb re 1 rc rc re RE RL RE RL

Answer the following questions relating to a CE-connected transistor: (a) How are the input characteristics (iB versus vBE ) a ected if there is negligible feedback of vCE (b) What might be the e ect of a too-small emitter-base junction bias (c) Suppose the transistor has an in nite output impedance; how would that a ect the output characteristics (d) With reference to Fig. 3-9(b), does the current gain of the transistor increase or decrease as the mode of operation approaches saturation from the active region

28.3 Prove the identi ty tan (u v) =

9

(a) The family of input characteristics degenerates to a single curve one that is frequently used to approximate the family. (b) If IBQ were so small that operation occurred near the knee of an input characteristic curve, distortion would result. (c) The slope of the output characteristic curves would be zero in the active region. (d) iC decreases for constant iB ; hence, the current gain decreases.