Two independent amplifier channels

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

Inside the Instrument, Ch Low-noise front ends and noise measurement

Problem

Two independent amplifier channels, each with input voltage noise density

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

, are cross-correlated to measure the Johnson noise power spectral density of a

100\,\Omega

resistor at

300\,\mathrm{K}

. ((a)) Find the source's Johnson noise power spectral density

S_{\rm source} = 4k_BTR

. ((b)) Using

M \gtrsim (r\,e_n^2/S_{\rm source})^2

, find the number of averages

M

needed to bring the residual a factor

r = 8

below the source. ((c)) If each average corresponds to a frequency resolution of

1\,\mathrm{Hz}

(one average per second), how long does the measurement take, in hours?

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