A microphone preamplifier 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 microphone preamplifier chain has three stages, treated separately. ((a)) A high-pass RC network has

R = 15\,\mathrm{k\Omega}

in series with

C = 68\,\mathrm{nF}

, output taken across the resistor. Derive

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

as a ratio of polynomials in

s

, and state the pole of the low-pass companion factor

1/(1+sRC)

that appears in the denominator, together with its corner frequency

f_c

. ((b)) A following two-pole filter has

f_0 = 800\,\mathrm{Hz}

and

Q = 0.8

, with denominator

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

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

y[k] = 0.95\,y[k-1] + 0.05\,x[k]

f_s = 20\,\mathrm{kHz}

. Find the pole of

H(z)

and the

-3\,\mathrm{dB}

corner frequency.

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