A battery-powered temperature logger needs a low-pass filter ahead of its…

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 battery-powered temperature logger needs a low-pass filter ahead of its analogue-to-digital converter. An engineer designs an equal-component Sallen-Key section for a

500\,\mathrm{Hz}

corner and

Q = 0.707

(Butterworth damping), using the nearest E12 preferred values

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

for both frequency-setting resistors and

C = 22\,\mathrm{nF}

for both frequency-setting capacitors, with passband gain

K = 1.586

. The op-amp used has an input voltage-noise density

e_n = 8\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

. The noise-equivalent bandwidth of a

Q = 0.707

second-order section 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, taking the two

15\,\mathrm{k}\Omega

resistors as the only thermal-noise source in series with the amplifier's own noise, referred through the passband gain

K

(ignore the feedback resistors' own noise). ((c)) A downstream stage must reject an interferer at five times the passband corner by at least

30\,\mathrm{dB}

. Using the Butterworth magnitude

|H| = 1/\sqrt{1+(f/f_0)^{2n}}

for an

n

th-order Butterworth low-pass with its corner at

f_0

, find the minimum order

n

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