An amplifier's differential input stage (Chapter 3 style

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Feedback, operational amplifiers and analogue signal processing

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Problem

An amplifier's differential input stage (Chapter 3 style, two matched transistors with common-emitter connection, current gain βF=150\beta_F = 150) is biased by a Wilson current source (Chapter 2) that delivers a precise tail current Itail=200 μAI_{\rm tail} = 200\,\mu\mathrm{A} to the pair, so each input transistor carries IC=100 μAI_C = 100\,\mu\mathrm{A}. Take VT=25.9 mVV_T = 25.9\,\mathrm{mV} at 300 K300\,\mathrm{K}. The amplifier is used as a non-inverting amplifier whose DC loop gain is T0=3×104T_0 = 3\times10^4. ((a)) Find gmg_m and rπr_\pi for one input transistor, then the differential pair's input resistance Rid=2rπR_{\rm id} = 2r_\pi, and use Blackman's formula for the non-inverting input to find the amplifier's closed-loop input resistance Rin=Rid(1+T0)R_{\rm in} = R_{\rm id}(1+T_0). ((b)) The open-loop amplifier has two poles at f1=300 Hzf_1 = 300\,\mathrm{Hz} and f2=1.5 MHzf_2 = 1.5\,\mathrm{MHz}, and the loop's DC value is the same T0=3×104T_0 = 3\times10^4. Find the closed-loop natural frequency fnf_n and damping ratio ζ\zeta, and the approximate step-response overshoot.

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