A sensor interface uses a non-inverting amplifier built from a single operational…

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

A sensor interface uses a non-inverting amplifier built from a single operational amplifier modelled by a controlled source

Av_d

with open-loop DC gain

A_0 = 2\times10^5

, input (differential) resistance

R_{\rm id} = 2\,\mathrm{M}\Omega

, output resistance

R_o = 75\,\Omega

, and one dominant open-loop pole at

f_p = 5\,\mathrm{Hz}

. The feedback network is

R_1 = 1\,\mathrm{k}\Omega

(from the inverting input to ground) and

R_2 = 4\,\mathrm{k}\Omega

(from the output to the inverting input); the output drives a load

R_L = 1\,\mathrm{k}\Omega

. The input signal is applied to the non-inverting terminal from an ideal voltage source. ((a)) Find the return ratio

T

of the controlled source

Av_d

, including the loading that

R_{\rm id}

R_2

and

R_L

place on the divider. ((b)) Using the asymptotic-gain formula, find the closed-loop DC gain

A_{\rm CL}

. (

R_{\rm id}

does carry a tiny signal from the input round the controlled source, but

d

is of order

10^{-5}

here; take

d = 0

.) ((c)) Treating the open-loop response as a single pole, find the frequency of the closed-loop pole.

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