hw4_midterm_1_1998

hw4_midterm_1_1998 - ECE164 Analog Integrated Circuit...

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Unformatted text preview: ECE164 Analog Integrated Circuit Design First Midterm Exam, November 3, 1998 All of the problems relate to the following circuit. Each problem may be solved without relying on the solution to the other problems. You may assume that M1 , M3 are identical transistors, and that the input signal frequencies are su ciently low that all capacitances can be ignored. Please be absolutely sure to fully explain your reasoning. Correct answers without justi cation will not receive credit. VDD VDD M1 R Vi + − M3 M2 Vo 1. 20 points Derive an expression for Vo as a function of Vi ; ID3 ; k, and VT that is valid when Vi is large enough that M2 is always in saturation and small enough that M1 is always in saturation. You may neglect the channel modulation e ect in this problem. 2. 20 points Derive an expression for the value of Vi that puts M2 on the nominal boundary between the saturation and triode regions in terms of ID3 ; k, and VT . You may neglect the channel modulation e ect in this problem. 3. 20 points Derive an expression for ID3 in terms of R; VDD ; k; and VT . 4. 20 points Derive the small-signal gain Av = vo =vi. Is your answer consistent with that of Problem 1? Explain. If you were not able to answer Problem 1, explain what your answer to this problem implies about the form of the large signal relationship between Vi and Vo  5. 20 points Derive the small-signal output impedance of the circuit. 2 ...
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