A resistor held at is joined to a resistor held at by a lossless transmission line of…

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

Inside the Instrument, Ch Noise sources and amplifier noise

Problem

A resistor R1=75 ΩR_1 = 75\,\Omega held at T1=400 KT_1 = 400\,\mathrm{K} is joined to a resistor R2=75 ΩR_2 = 75\,\Omega held at T2=300 KT_2 = 300\,\mathrm{K} by a lossless transmission line of characteristic impedance Z0=75 ΩZ_0 = 75\,\Omega, so both resistors are matched to the line and neither reflects any power arriving at it. ((a)) Using Nyquist's argument that a resistor matched to a line launches an available noise power kBTΔfk_BT\Delta f into the line in a bandwidth Δf\Delta f, and that a matched termination absorbs whatever arrives without reflecting any of it, explain why the power travelling from R1R_1 towards R2R_2 and the power travelling from R2R_2 towards R1R_1 can be treated as two independent one-way flows. ((b)) Find the net power delivered from the hot resistor to the cold one in a bandwidth Δf=1 kHz\Delta f = 1\,\mathrm{kHz}. ((c)) Check that your expression gives zero net transfer when T1=T2T_1 = T_2.

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