A strain-gauge amplifier chain has three stages

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

Electronics for Measurement, Ch Transfer functions, poles and the stability of a loop

Problem

A strain-gauge amplifier chain has three stages, treated separately. ((a)) A low-pass RC filter has

R = 2.2\,\mathrm{k\Omega}

in series with

C = 1.0\,\mathrm{\mu F}

, output taken across the capacitor. Derive

H(s)=V_{\rm out}/V_{\rm in}

as a ratio of polynomials in

s

, and state its pole and its corner frequency

f_c

. ((b)) A two-pole filter that follows it has

f_0 = 5.0\,\mathrm{kHz}

and

Q = 3.0

, with denominator

s^2+(\omega_0/Q)s+\omega_0^2

. Find its pole positions. ((c)) The digitised output is smoothed by

y[k]=0.5\,y[k-1]+0.5\,x[k]

f_s = 8.0\,\mathrm{kHz}

. Find the pole of

H(z)

and the

-3\,\mathrm{dB}

corner frequency.

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