Question

Can someone help me derive the general equation for the Acm (when it is a single-ended common-mode gain) for Q1,Q2 and Q4? I know the general formula for Q1 and Q2 are going to be the same but Q4 is going to be different because you have to take into account ro.

In this assignment, you will design a differential amplifier satisfying the required differential gain, input impedance, and single-ended common-mode gain; when fed by a small-signal. Then you will simulate your circuit on LTSpice to compare the simulation results with hand calculations. +VDD +VpD - VO2 Viike OzXV.2 -Vss -Vss A. Hand design: Design the bipolar differential amplifier and the current source and bias network (R1,Q3, and Q4) above such that: (i) Differential gain: Ad > 200 (ü) Input differential resistance: Ria 50 k., and (iii) Acm < 0.05 where Acm is the single-ended common-mode gain (the gain to a common- mode input signal when the output is measured not differentially but from one of the outputs with respect to ground). Design the circuit with BJTs having B= 200, VA = 100 V, and VBE = ~0.7 V in Forward Active. Use +Vpp = 9 V and -Vss = -9 V. Clearly show your steps. Design Suggestion for Part A. 1. Derive Ad, Rid, and Acm expressions. (When deriving Acm and Rid you can ignore r, of Q1 and Q2. Needless to say, you cannot ignore ro of Q4 when deriving Acm. Do not ignorer, of Q1 or 02 when deriving Aa). 2. Plug the "dc currents", "resistors", "Vih", "B", "VA", etc. into Ad, Rid, and Acm expressions and simplify the expressions to the extent possible (e.g., manipulate the expressions and then replace VA = 100 V, B = 200, etc.) 3. Consider the three design constraints. You basically have each constraint represented in terms of the dc currents, and resistors. 4. Start with dc current selection satisfying your constraint(s) => Find R1, and other parameters associated with the dc current selected. 5. Then based on the constraint(s) => Find R2.

Answer 1

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