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TRANSISTOR BIAS CONSIDERATIONS
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Using the results of Problem 3.36 and assuming that ) 1, we may write IEQ 1 ICQ ICBO % ICQ ICBO ICQ 1 ICQ ICBO % ICBO 5:5
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(5.6)
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Substituting (5.5) and (5.6) into (5.4) and rearranging then give ICQ VBB VBEQ ICBO RB RE RB = RE 5:7
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From (5.7) it is apparent that leakage current ICBO increases ICQ . However, ICQ is relatively independent of only when RB = ( RE .
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Shunt-Feedback Bias A compromise between constant-base-current bias and constant-emitter-current bias is o ered by the shunt-feedback-bias circuit of Fig. 3-17, as the following example shows.
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Example 5.4. In the shunt-feedback-bias circuit of Fig. 3-17, VCC 15 V, RC 2 k; RF 150 k, and ICBO % 0. The transistor is a Si device. Find ICQ and VCEQ if (a) 50 and (b) 100. (a) By KVL,   ICQ ICQ RC RF VBEQ VCC ICQ IBQ RC IBQ RF VBEQ ICQ VCC VBEQ 50 15 0:7 ICQ 2:84 mA RF 1 RC 150 103 51 2 103   1 1 ICQ RC VCEQ VCC IBQ ICQ RC VCC   1 15 1 2:84 10 3 2 103 9:21 V 50
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so that Now KVL gives
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(b) For 100, ICQ and VCEQ 100 15 0:7 4:06 mA 150 103 101 2 103   1 1 4:06 10 3 2 103 6:80 V 15 100
With shunt-feedback bias the increase in ICQ is appreciable (here, 43 percent); this case lies between the -insensitive case of constant-emitter-current bias and the directly sensitive case of constant-basecurrent bias.
Example 5.5. Neglecting leakage current in the shunt-feedback-bias ampli er of Fig. 3-17, nd a set of conditions that will render the collector current ICQ insensitive to small variations in . Is the condition practical From Example 5.4, if ) 1, ICQ VCC VBEQ VCC VBEQ % RF RF 1 RC RC
The circuit would be insensitive to variations if RF = ( RC . However, since 0:3 VBEQ 0:7, that would lead to ICQ RC ! VCC ; hence, VCEQ would come close to 0 and the transistor would operate near the saturation region.
CHAP. 5]
TRANSISTOR BIAS CONSIDERATIONS
STABILITY-FACTOR ANALYSIS
Stability-factor or sensitivity analysis is based on the assumption that, for small changes, the variable of interest is a linear function of the other variables, and thus its di erential can be replaced by its increment. In a study of BJT Q-point stability, we examine changes in quiescent collector current ICQ due to variations in transistor quantities and/or elements of the surrounding circuit. Speci cally, if ICQ f ; ICBO ; VBEQ ; . . . then, by the chain rule, the total di erential is dICQ @ICQ @ICQ @ICQ d dI dVBEQ @ @ICBO CBO @VBEQ 5:9 5:8
We may de ne a set of stability factors or sensitivity factors as follows: ICQ % @ICQ S Q @ Q ICQ % @ICQ SI ICBO Q @ICBO Q ICQ % @ICQ SV VBEQ Q VBEQ Q
5:10 5:11 5:12
and so on. Then replacing the di erentials with increments in (5.9) yields a rst-order approximation to the total change in ICQ : ICQ % S SI ICBO SV VBEQ 5:13
Example 5.6. For the CE ampli er of Fig. 5-1, use stability-factor analysis to nd an expression for the change in ICQ due to variations in , ICBO , and VBEQ . The quiescent collector current ICQ is expressed as a function of ; ICBO , and VBEQ in (5.7). Thus, by (5.13), ICQ % S SI ICBO SV VBEQ where the stability factors, according to (5.10) through (5.12), are   @ICQ RB VBB VBEQ ICBO RB RE @ VBB VBEQ ICBO RB RE S @ @ RB RE RB RE 2 @ICQ RB RE SI @ICBO RB = RE @ICQ SV @VBEQ RB RE 5:14
5:15 5:16 5:17
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