# hw11_soln - UNIVERSITY OF CALIFORNIA AT BERKELEY College of...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences Homework #11 Solutions Due Tuesday, November 20, 2007 EE 105 Fall 2007 Prof. Liu Problem 1. Common-Source Stage a) | A v | = 10 = g m 1 ( r o 1 bardbl r o 2 ) = radicalBigg 2 parenleftbigg W L parenrightbigg 1 μ n C ox I D · parenleftbigg 1 λ n I D bardbl 1 λ p I D parenrightbigg parenleftbigg W L parenrightbigg 1 = A 2 v 2 μ n C ox I D ( λ n I D + λ p I D ) 2 = A 2 v I D 2 μ n C ox ( λ n + λ p ) 2 = 7 . 8125 To find the bias voltages, we need to set up a system of equations to solve. I D = 1 2 parenleftbigg W L parenrightbigg 1 μ n C ox ( V GS 1 − V THn ) 2 (1 + λ n ( V DS 1 − V GS 1 + V THn )) = 0 . 5 mA g m 1 = parenleftbigg W L parenrightbigg 1 μ n C ox ( V GS 1 − V THn ) (1 + λ n ( V DS 1 − V GS 1 + V THn )) = A v r o 1 bardbl r o 2 = A v ( λ n + λ p ) I D = 1 . 25 mS Solving these equations simultaneously gives V GS 1 = 1 . 2 V V DS 1 = . 8 V Notice that we’ve assumed M 1 and M 2 were in saturation for this problem. Noting that V DS 1 = V GS 1 − V THn (i.e. M 1 is just on the edge of saturation), we can see our assumption was correct....
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