A rack carries two shielded cables of a different

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electronics, Instrumentation & Communication · Sensors, detectors and experimental instrumentation

Inside the Instrument, Ch Transmission lines, grounding and the bench

Problem

A rack carries two shielded cables of a different, thicker construction from RG-58. Each cable's shield has a lumped resistance

R_s = 0.05\,\Omega

and self-inductance

L_s = 25\,\mathrm{nH}

over its run (illustrative manufacturer figures for this cable type). Each shield is the signal's return. For parts (b) and (c), take the shield bonded to the rack earth at both ends, with the earth path between the two bonds of negligible impedance, as in the chapter's model. ((a)) Find the shield's cutoff frequency

f_c = \omega_c/2\pi

with

\omega_c = R_s/L_s

. ((b)) One cable carries a

20\,\mathrm{kHz}

analogue audio signal; find the fraction of the return current that flows in the shield, using

|I_{\rm shield}/I| = \omega L_s/\sqrt{R_s^2 + (\omega L_s)^2}

. ((c)) The other carries a

5\,\mathrm{MHz}

digital clock; find the same fraction for it. ((d)) State which grounding scheme (single-point or multi-point) is appropriate for each cable, giving the reason, and say what the shield carries once that scheme is in place.

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