# hw12_soln - UNIVERSITY OF CALIFORNIA AT BERKELEY College of...

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UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences Homework #12 Solutions Due Thursday, December 6, 2007 EE 105 Fall 2007 Prof. Liu Problem 1. BJT Differential Pair a) Assuming R 1 = R 2 (and appropriate transistor matching), the circuit is perfectly symmetric if we know that V in 1 = V in 2 . This means that each branch carries I EE / 2 of current, so that I C 3 = I C 4 and therefore I B 3 = I B 4 . Since R 1 = R 2 , these base currents split evenly through R 1 and R 2 to produce V out + = V out - , or V out = 0. b) Noting that node X is a virtual ground, we have: | A DM | = g m 1 ( r o 1 bardbl r o 3 bardbl R 1 ) = I EE 2 V T parenleftbigg 2 V An I EE bardbl 2 V Ap I EE bardbl R 1 parenrightbigg = 1 2 V T (2 V An bardbl 2 V Ap bardbl R 1 I EE ) = 50 I EE = 1 . 253 mA Problem 2. MOSFET Differential Pair a) I SS = 2 1 2 W L μ n C ox ( V GS 1 V T H ) 2 = W L μ n C ox V 2 ov 1 = 444 μ A A DM = g m 1 R D 1 = 2 I D 1 V GS 1 V T H R D 1 = I SS V ov 1 R D 1 = 22 . 22 Since the sign of A DM

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