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(a) By KVL, VCC ICQ RC IBQ RC RF VBEQ IEQ RE Substituting (5.5) and (5.6) into (1), rearranging, and then assuming ) 1, we obtain ICQ % VCC VBEQ ICBO RC RF RE VCC VBEQ ICBO RC RF RE % 1 R RF = RC RE RC F RE RC RF RE SV RF RC RE RF = RC RE RF VCC VBEQ ICBO RC RF RE RF RC RE 2 2 1
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(b) Based on the symmetry between (2) and (5.7) we have, from Example 5.6, SI S
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In the CB ampli er of Fig. 5-9, the transistor leakage current is shown explicitly as a current source ICBO . (a) Find ICQ as a function of ICBO ; VBEQ ; and . (b) Determine the stability factors that should be used in (5.13) to express the in uence of ICBO ; VBEQ ; and on ICQ .
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Fig. 5-9 (a) By KVL, VEE VBEQ IEQ RE Substituting (5.5) into (1) and rearranging yield ICQ 1 VEE VBEQ ICBO RE 2 1
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(b) Direct application of (5.10) through (5.12) to (2) gives the desired stability factors as S @ICQ 1 VEE VBEQ 2 @ RE SI @ICQ 1 @ICBO SV @ICQ 1 RE @VBEQ
The CB ampli er of Fig. 5-9 has VCC 15 V; VEE 5 V; RE 3 k; RC 7 k; and 50. At a temperature of 258C, the Si transistor has VBEQ 0:7 V and ICBO 0:5 A. (a) Find an expression for ICQ at any temperature. (b) Evaluate that expression at T 1258C.
(a) Let the subscript 1 denote quantities at T1 258C, and 2 denote them at any other temperature T2 . Then, according to Section 5.2, ICBO2 2 T2 25 =10 ICBO1 VBEQ2 VBEQ1 VBEQ VBEQ1 0:002 T2 25
CHAP. 5]
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Hence, by (2) of Problem 5.15, ICQ2 1 VEE VBEQ1 0:002 T2 25 2 T2 25 =10 ICBO1 RE 1
(b) At T2 1258C, (1) gives us ICQ2 51 5 0:7 0:002 125 25 2 125 25 =10 0:5 10 6 1:53 0:512 2:042 mA 50 3 103
For the Darlington-pair emitter-follower of Fig. 5-10, nd ICQ1 as a function of the six temperature-sensitive variables ICBO1 ; ICBO2 ; VBEQ1 ; VBEQ2 ; 1 ; and 2 .
RF ICQ1 IQB1 ICBO1 Q1 ICBO2 Q2 IEQ1 = IBQ2 ICQ2 + VCC
Fig. 5-10 By KVL, VCC IBQ1 RF VBEQ1 VBEQ2 IEQ2 RE By KCL, IEQ2 IEQ1 ICQ2 1 (2)
Using the result of Problem 3.36 in (2) and then substituting IBQ2 IEQ1 , we obtain IEQ2 IEQ1 2 IBQ2 2 1 ICBO2 2 1 IEQ1 2 1 ICBO2 Assuming 1 ; 2 ) 1 and substituting for IEQ1 according to (5.5), we obtain IEQ2 % 2 1 ICQ1 2 1 ICBO2 ICBO1 Also, from (5.6), IBQ1 % ICB1 ICBO1 1 4 3
Now we substitute (3) and (4) into (1) and rearrange to get ICQ1 VCC VBEQ1 VBEQ2 ICBO1 RF 2 RE ICBO2 2 RE RF = 1 2 RE 5
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[CHAP. 5
(a) Determine a rst-order approximation for the change in ICQ1 in the circuit of Fig. 5-10, in terms of the six variables ICBO1 ; ICBO2 ; VBEQ1 ; VBEQ2 ; 1 ; and 2 . (b) Use ICQ1 as found in Problem 5.17 to evaluate the sensitivity factors (that is, the coe cients) in the expression determined in part a.
(a) Since ICQ1 f ICBO1 ; ICBO2 ; VBEQ1 ; VBEQ2 ; 1 ; 2 , its total di erential is given by @ICQ1 @ICQ1 @ICQ1 dI dI dVBEQ1 @ICBO1 CBO1 @ICBO2 CBO2 @VBEQ1 @ICQ1 @ICQ1 @ICQ1 dVBEQ2 d 1 d 2 @VBEQ2 @ 1 @ 2 1
dICQ1
Using the method of Section 5.3, we may write this as ICQ1 % SI1 ICBO1 SI2 ICBO2 SV1 VBEQ1 SV2 VBEQ2 S 1 1 S 2 2 (b) The sensitivity factors in (1) may be evaluated with the use of (5) of Problem 5.17: @ICQ1 R F 2 R E @ICBO1 RF = 1 2 RE @ICQ1 2 RE @ICBO2 RF = 1 2 RE @ICQ1 @ICQ1 1 SV2 @VBEQ1 RF = 1 2 RE @VBEQ2 @ICQ1 RF VCC VBEQ1 VBEQ2 ICBO1 RF 2 RE ICBO2 2 RE @ 1 RF 1 2 RE 2 @ICQ2 1 RE RF ICBO1 ICBO2 1 VCC VBEQ1 VBEQ2 ICBO1 RF @ 2 RF 1 2 RE 2 2
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