Unformatted text preview: ECE164 Analog Integrated Circuit Design First Midterm Exam, October 28, 1997
M All of the problems relate to the following ampli er circuit. Each problem may be solved without relying on the solution to the other problems. You may assume that 1 and 2 are identical transistors, that the input signal frequencies are su ciently low that all capacitances can be ignored, and that ds for = 1 2 3. Please be absolutely sure to fully explain your reasoning. Correct answers without justi cation will not receive credit.
M R r
k k VDD M1 R I
BIAS M2 Ii + Vi − Vo M3 1. (30 points) If i is increased from zero to DD , 3 will rst operate in the cuto region, then transition into the saturation region, and nally transition into the triode region. At what values of i do these transitions occur. For simplicity, you may assume that 3 is in strong inversion for gs3 T3 , and that there is no inversion layer for gs3 T3 . 2. For this problem, assume that i is chosen such that 3 in saturation. a) (15 points) Derive an expression for i as a function of only i and the device parameters of the circuit (e.g., 3 T3 BIAS , etc.). a) (15 points) Derive an expression for o as a function of only i and the device parameters of the circuit. c) (15 points) Using the results of parts a) and b), derive the small signal input resistance and small signal gain of the ampli er. For this problem, do not use the small-signal model of the circuit in your derivation. 3. (25 points) Again assume that 3 is in saturation. Draw the small-signal model of the circuit, and use it to derive the small-signal input resistance, small-signal output resistance, and small-signal gain of the ampli er. For simplicity, you may assume ds = 1 for = 2 3.
V V M V M V >V V <V V M I V Rk V I V V M r
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- Integrated Circuit, Small-signal model, Analog Integrated Circuit, input signal frequencies, signal input resistance