A platinum resistance thermometer (RTD) of resistance sits at and is read by a…

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 platinum resistance thermometer (RTD) of resistance

R_s = 500\,\Omega

sits at

350\,\mathrm{K}

and is read by a voltage amplifier with input voltage noise density

e_n = 5.0\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

and input current noise density

i_n = 2.0\,\mathrm{pA}/\sqrt{\mathrm{Hz}}

. The amplifier's output passes through a first-order low-pass filter of corner frequency

f_c = 200\,\mathrm{Hz}

. A constant bias current

I = 1.0\,\mathrm{mA}

is forced through the RTD, whose resistance varies with temperature as

\mathrm{d}R/\mathrm{d}T = 0.40\,\Omega\,\mathrm{K}^{-1}

near this operating point. The RTD'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 referred to the input, combine them by a quadrature sum, and state which one dominates the noise power and by what percentage. ((b)) Find the noise-equivalent bandwidth of the first-order low-pass filter. ((c)) Find the rms noise voltage referred to the input. ((d)) Find the smallest temperature change this instrument can detect at a signal-to-noise ratio of one.

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