hw7_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 #7 Solutions Due Tuesday, October 16, 2007 EE 105 Fall 2007 Prof. Liu Problem 1. DC Biasing of Cascode Stage a) V b 2 = V T ln parenleftbigg I C I S + 1 parenrightbigg = 792 mV b) To obtain the appropriate current, we need V BE 1 = V BE 2 (assuming I C 1 I C 2 ). We know that V E 1 = V C 2 = V b 2 300 mV, since the base-collector junction is forward biased by 300 mV. Since V b 1 = V C 2 + 792 mV, we have V b 1 = 1 . 284 V . If we want to be more precise, we need: I E 1 = 1 + β β I S parenleftBig e V BE 1 /V T 1 parenrightBig = I C 1 V BE 1 = V T ln parenleftbigg βI C 1 (1 + β ) I S + 1 parenrightbigg = 792 mV As you can see, our approximation that I C 1 = I C 2 is a good approximation, since we obtain the same value for V BE 1 . Problem 2. Short-Circuit Transconductance We know R out from our analysis of a cascode previously (when we short the input to ground, we obtain the same circuit).

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