A resistive bolometer with at is illuminated through a mechanical chopper and read…

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 Noise and the signal-to-noise ratio

Problem

A resistive bolometer with

R_s = 50\,\mathrm{k\Omega}

300\,\mathrm{K}

is illuminated through a mechanical chopper and read out with a lock-in amplifier. Two front-end amplifiers are available: amplifier A (bipolar) with

e_n = 4.0\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

i_n = 10\,\mathrm{pA}/\sqrt{\mathrm{Hz}}

; amplifier B (FET) with

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

i_n = 0.10\,\mathrm{pA}/\sqrt{\mathrm{Hz}}

. The chopper runs at

923\,\mathrm{Hz}

, chosen because the nearest harmonics of

50\,\mathrm{Hz}

mains (

900

and

950\,\mathrm{Hz}

) and of

60\,\mathrm{Hz}

mains (

900

and

960\,\mathrm{Hz}

) are all at least

23\,\mathrm{Hz}

away. The lock-in's output stage is a first-order filter with time constant

\tau = 0.50\,\mathrm{s}

. The bolometer's responsivity, referred to the amplifier's input node, is

5.0\,\mathrm{V\,W^{-1}}

. ((a)) By comparing each amplifier's optimum source resistance

e_n/i_n

with

R_s

, make a first choice of amplifier, then confirm it by computing each amplifier's total input-referred density at

R_s

. ((b)) Using that amplifier, find the total noise voltage density referred to the input, combining the sensor's Johnson noise with the amplifier's

e_n

and

i_nR_s

, and state which term dominates. ((c)) Find the effective noise bandwidth of the lock-in for this time constant. ((d)) Find the rms noise voltage referred to the input and the smallest optical power detectable at a signal-to-noise ratio of one.

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