The amplified output of a resistor (gain ) is displayed on a spectrum analyser

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

The amplified output of a

10\,\mathrm{k\Omega}

resistor (gain

\times 1000

) is displayed on a spectrum analyser. A sharp line at

50\,\mathrm{Hz}

sits above a flat floor. Breaking a ground loop removes the

50\,\mathrm{Hz}

line entirely, but the floor is unchanged, and referred back to the resistor's own terminals it measures

12.7\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

. Encouraged by the success of breaking the ground loop, a technician wraps the whole box in two extra layers of copper screening, hoping to push the floor down further. Someone argues: "Screening removed the mains line, so more screening should reduce the remaining floor too, since it is also an unwanted signal." ((a)) Calculate the Johnson-noise density predicted for this resistor at

T = 290\,\mathrm{K}

and confirm it matches the measured floor. ((b)) Explain, from the physical origin of the two features, why no amount of extra screening will move the floor. ((c)) By what factor would the resistor's absolute temperature have to fall to halve the floor's density?

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