A type-K thermocouple

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

Electronics for Measurement, Ch Noise and the signal-to-noise ratio

Problem

A type-K thermocouple, whose junction and lead resistance together give a source resistance

R_s = 10\,\Omega

290\,\mathrm{K}

and whose sensitivity is

41\,\mathrm{\mu V\,K^{-1}}

, feeds a chopper amplifier (one that modulates its input internally, to move it above its own

1/f

corner) with

e_n = 6.0\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

and

i_n = 1.0\,\mathrm{pA}/\sqrt{\mathrm{Hz}}

. Its output passes through a first-order

RC

low-pass filter with

R = 100\,\mathrm{k\Omega}

and

C = 1.0\,\mathrm{nF}

. The three noise sources, the thermocouple's Johnson noise, the amplifier's voltage noise, and the voltage the amplifier's current noise produces across

R_s

, are independent and are all referred to the amplifier's input. ((a)) Find the three noise voltage densities, their quadrature sum, and the dominant term with its share of the noise power. ((b)) Find the noise-equivalent bandwidth of the

RC

low-pass filter. ((c)) Find the rms noise voltage referred to the input. ((d)) Find the smallest temperature difference detectable at a signal-to-noise ratio of one.

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