A pressure-sensor signal 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 pressure-sensor signal chain has three stages, treated separately. ((a)) An RC anti-alias filter has

R = 4.7\,\mathrm{k\Omega}

in series with

C = 220\,\mathrm{nF}

, with the 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)) The next stage is a two-pole active filter with

f_0 = 2.0\,\mathrm{kHz}

and

Q = 1.5

, whose denominator is

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

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

y[k] = 0.8\,y[k-1] + 0.2\,x[k]

at a sampling rate

f_s = 5.0\,\mathrm{kHz}

. Find the pole of

H(z)

and the

-3\,\mathrm{dB}

corner frequency.

Browse the problem library