A vibration-monitoring instrument filters an accelerometer signal with a low-pass…

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

Electronics for Measurement, Ch Active filters, oscillators and timers

Problem

A vibration-monitoring instrument filters an accelerometer signal with a low-pass corner near

10\,\mathrm{Hz}

Q=0.707

. Preferred values

R=160\,\mathrm{k}\Omega

(both frequency-setting resistors) and

C=100\,\mathrm{nF}

(both frequency-setting capacitors) are used, with passband gain

K=1.586

. The amplifier's input voltage-noise density is

e_n = 20\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

, and the filter's noise-equivalent bandwidth is

1.11 f_0

. Room temperature is

290\,\mathrm{K}

. ((a)) Find the realised corner frequency

f_0

. ((b)) Find the rms output noise voltage from the two

160\,\mathrm{k}\Omega

resistors and the amplifier, referred through

K

. ((c)) A mechanical resonance at three times the corner frequency must be attenuated by at least

20\,\mathrm{dB}

. Find the minimum order

n

from the rough

20\,\mathrm{dB}

-per-decade-per-pole rule, and confirm it with the exact Butterworth expression.

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