A sensor is read by an amplifier with and

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

20\,\Omega

sensor is read by an amplifier with

e_n = 4\,\mathrm{nV}/\sqrt{\mathrm{Hz}}

and

i_n = 1\,\mathrm{pA}/\sqrt{\mathrm{Hz}}

. Noise figures are referred to

290\,\mathrm{K}

. ((a)) Find the noise figure with the sensor connected directly. ((b)) Find the optimum turns ratio of an ideal step-up transformer, and the noise figure it gives. ((c)) Find the noise figure if ten such amplifiers are instead paralleled on the sensor, their outputs averaged. ((d)) The transformer's magnetising inductance,

L_m = 5\,\mathrm{mH}

, sits in parallel across its primary. Treating the amplifier as drawing no current, find the frequency below which the signal reaching the primary falls by more than

3\,\mathrm{dB}

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