The output stage of a two-stage amplifier is a cascode: a transistor ( , , ) with its…

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

Inside the Instrument, Ch Loop gain in real feedback circuits

Problem

The output stage of a two-stage amplifier is a cascode: a transistor

Q_2

(

g_{m2} = 40\,\mathrm{mA/V}

r_{\pi 2} = 8\,\mathrm{k\Omega}

r_{o2} = 80\,\mathrm{k\Omega}

) with its base held at a fixed bias, stacked on a lower stage that presents a small-signal resistance of

3\,\mathrm{k\Omega}

Q_2

's emitter. That resistance acts as an emitter-degeneration resistance

R_E = 3\,\mathrm{k\Omega}

for

Q_2

. ((a)) Using the exact degenerated-transistor result from Blackman's formula, calculate the resistance

R_{\rm out}

looking into the collector of

Q_2

. By how much would the approximation

r_o(1+g_mR_E)

overstate it, and why? ((b)) This cascode forms the output node of an amplifier whose open-loop small-signal model has two poles: a dominant pole at

f_1 = 2\,\mathrm{kHz}

(input stage) and a second pole at

f_2 = 8\,\mathrm{MHz}

. The amplifier is placed in a feedback loop with DC loop gain

T_0 = 8000

. Find the closed-loop natural frequency

f_n

and damping ratio

\zeta

, and state whether the step response overshoots.

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