*9.44 In this problem we explore the trade-off between input common-mode range and differential gain in the design of the bipolar BJT. Consider the bipolar differential amplifier in Fig. 9.14 with the input voltages v B1 = VCM +vid/2 v B2 = VCM −vid/2 (a) Bearing in mind that for a BJT to remain in the active mode, vBC should not exceed 0.4 V, show that when v id has a peak vˆid, the maximum input common-mode voltage VCMmax is given by V CMmax = VCC +0.4 − vˆ id 2 −A dVT + vˆ2id (b) For the case VCC = 2.5 V and vˆid = 10 mV, use the relationship above to determine VCMmax for the case Ad = 50 V/V. Also find the peak output signal vˆod and the required value of IRC. Now if the power dissipation in the circuit is to be limited to 1 mW in the quiescent state (i.e., with vid = 0), find I and RC. (Remember to include the power drawn from the negative power supply −V EE = −2.5 V.) (c) If VCMmax is to be +1 V, and all other conditions remain the same, what maximum gain Ad is achievable?