An operational amplifier has open-loop DC gain and a single dominant pole at (so its…

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

Inside the Instrument, Ch Loop gain in real feedback circuits

Problem

An operational amplifier has open-loop DC gain

A_0 = 1\times10^5

and a single dominant pole at

f_p = 20\,\mathrm{Hz}

(so its gain-bandwidth product is

2\,\mathrm{MHz}

). It is wired as a non-inverting amplifier with ideal closed-loop gain

A_\infty = 20

(feedback fraction

\beta \approx 1/20

) and negligible direct transmission

d

. Take the loop gain as

T(jf) = T_0/(1 + jf/f_p)

with

T_0 = A_0\beta

. ((a)) Without recomputing the whole transfer function, predict whether the distortion-reduction factor

|1+T|

at the third harmonic of a

5\,\mathrm{kHz}

input tone (i.e. at

15\,\mathrm{kHz}

) is close to its DC value or much smaller, then evaluate both numbers. ((b)) Predict whether the closed-loop step response is a single decaying exponential or shows ringing, and find the closed-loop pole frequency.

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