hw12_sol - ECE 442 HW12 Solutions 1. We observe that,...

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ECE 442 HW12 Solutions 1. We observe that, because of the diode connection between collector and base of Q2, delivering the constant current to the external circuitry would make the output voltage v o of the current source constant, since: i C = I S e v BE V T v BE 2 = V T ln ( i C 2 I S ) v B 2 = V T ln ( I o I C ) = const v o = v C 2 = v B 2 = const However, a good current source should produce the value of current independent of the voltage at its termi- nals. Observing the output resistance, since collector and base are shorted, it results in a very low value of R o : R o = r π || 1 g m || r o 1 g m However, a good current source should have its output resistance as high as possible (on the order of r o ). 2. a) Using the formulas as derived in class: V BE = V T ln ( I O I S ) = 0 . 025 × ln 0 . 001 10 - 15 = 0 . 691 V I O = I REF × m 1 + m + 1 β ( 1 + V O - V BE V A ) I REF = I O ( 1 + m + 1 β ) m ( 1 + V O - V BE V A ) = 1 . 024 mA R = V CC - V BE I REF = 5 - 0 . 691 1
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hw12_sol - ECE 442 HW12 Solutions 1. We observe that,...

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