To determine Derive the equation ( i B = ( V C C R 2 ) / ( R 1 + R 2 ) − V 0 ( R 1 R 2 ) / ( R 1 + R 2 ) + ( 1 + β ) R E ) . Explanation Calculation: Consider equations from amplifier circuit. i B + i 2 − i 1 = 0 (1) i E − i B − i C = 0 (2) i C = β i B (3) V 0 + i E R E − i 2 R 2 = 0 (4) − i 1 R 1 + V C C − i 2 R 2 = 0 (5) Rearrange Equation (2) to express i E in terms of i B . i E = i B + i C Substitute β i B for i C as follows. i E = i B + β i B = i B ( 1 + β ) Modify equation (1) to express i 2 in terms of i B and i 1 as follows. i 2 = i 1 − i B Substitute i 1 − i B for i 2 in equation (5) and simply the equation as follows. − i 1 R 1 + V C C − ( i 1 − i B ) R 2 = 0 − i 1 R 1 + V C C − i 1 R 2 + i B R 2 = 0 − i 1 ( R 1 + R 2 ) + V C C + i B R 2 = 0 − i 1 ( R 1 + R 2 ) = − ( V C C + i B R 2 ) i 1 = V C C + i B R 2 R 1 + R 2 Substitute i 1 − i B for i 2 in equation (4) as follows. V 0 + i E R E − ( i 1 − i B ) R 2 = 0 V 0 + i E R E − i 1 R 2 + i B R 2 = 0 Substitute V C C + i B R 2 R 1 + R 2 for i 1 and i B ( 1 + β ) for i E as follows

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ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 2, Problem 38P

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Derive the equation (iB=(VCCR2)/(R1+R2)−V0(R1R2)/(R1+R2)+(1+β)RE).

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Electric Circuits. (11th Edition)

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