A 50 m signal run must be installed between a fast pulse source and a coincidence…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic waves and their propagation · Electromagnetic waves and their propagation

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

Problem

A 50 m signal run must be installed between a fast pulse source and a coincidence unit; both ends are matched to

50\,\Omega

, so reflections are not an issue here. The run must carry a

100\,\mathrm{MHz}

calibration burst with no more than

4\,\mathrm{dB}

of insertion loss, and isolated logic edges, each arriving after the line has settled from the one before, which must reach at least

90\,\%

of their final value within

20\,\mathrm{ns}

of arriving. Two cables are available: Belden 8240 (RG-58), specified at

3.8\,\mathrm{dB}

per

100\,\mathrm{ft}

100\,\mathrm{MHz}

, for which the chapter's matched-line model of a

30\,\mathrm{m}

length reaches

90\,\%

of its step height about

19\,\mathrm{ns}

after the step arrives. Belden 9913, specified at

1.5\,\mathrm{dB}

per

100\,\mathrm{ft}

100\,\mathrm{MHz}

. Use

1\,\mathrm{ft} = 0.3048\,\mathrm{m}

. Assume both cables follow the chapter's pure

\sqrt f

loss model, each fixed by its own

100\,\mathrm{MHz}

figure. ((a)) Find the total insertion loss, in decibels, of a

50\,\mathrm{m}

run of each cable at

100\,\mathrm{MHz}

, and state which (if either) meets the

4\,\mathrm{dB}

budget. ((b)) From the model's matched step response, find how the

90\,\%

settling time depends on a cable's

100\,\mathrm{MHz}

loss over the run. Use it with the

30\,\mathrm{m}

figure for Belden 8240 to estimate the

90\,\%

settling time of a

50\,\mathrm{m}

run of each cable, and state whether each meets the

20\,\mathrm{ns}

requirement. ((c)) Recommend a cable for the run, giving the physical reason, in terms of

R'

, why a lower-loss cable is also expected to settle faster for the same length.

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