A resistor is held at

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Electronics, Instrumentation & Communication · Coupled oscillators, normal modes and Fourier analysis

Modes, Packets and Media, Ch The continuum limit, Fourier series and the spectrum of a measured signal

Problem

4.7\,\mathrm{k\Omega}

resistor is held at

T_{\rm K}=350\,\mathrm{K}

. Use

k_{\rm B}=1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

. ((a)) Compute its Johnson noise power spectral density

S_V = 4k_{\rm B}T_{\rm K}R

, both in

\mathrm{V^2\,Hz^{-1}}

and as an amplitude spectral density in

\mathrm{nV\,Hz^{-1/2}}

. ((b)) A single periodogram estimate of

S_V

scatters with a standard deviation equal to its own mean value, whatever the record length used. How many independent, equal-length segments must be averaged to bring the fractional scatter down to

10\%

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