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hwset8solution - ECE 453 Homework Assignment 8 Solution 7-4...

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ECE 453: Homework Assignment 8 Solution 7-4 Solution [ Z ] = Z 1 + Z 3 Z 3 Z 3 Z 2 + Z 3 7-10 Solution a. [ Y ] = 1 R e + r π + g m R e r π + 1 R f 1 R f g m r π R e + r π + g m R e r π 1 R f 1 R f b. Z IN = ( R L + R f )( R e + r π + g m R e r π ) R L + R f + R e + r π + g m r π ( R e + R L ) Z OUT = ( R S + R f )( R e + r π + g m R e r π ) + R S R f R S + R e + r π + g m r π ( R e + R S ) A v = g m R L R f R L + R f 1 1 + R e ( g m + 1 r π ) + R L R L + R f c. We want Z IN | R L = R = R : R = ( R + R f )( R e + r π + g m R e r π ) R + R f + R e + r π + g m r π ( R e + R ) which yields R 2 (1 + g m r π ) R f ( R e + r π + g m r π R e R ) = 0 (1) We also want Z OUT | R S = R = R : R = ( R + R f )( R e + r π + g m R e r π ) + RR f R + R e + r π + g m r π ( R e + R ) which yields R 2 (1 + g m r π ) R f ( R e + r π + g m r π R e + R ) = 0 (2) Equations (1) and (2) di ff er in the second term and they cannot be satisfied simultaneously unless R r π + (1 + g m r π ) R e , in which case the equations become essentially identical. Noting that g m r π = β , and assuming that R r π + (1 + β ) R e
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