E9F

Transmission line lengths and stubs

Explain velocity factor, what shorted and open lines look like at 1/8, 1/4 and 1/2 wavelength, and why open wire beats coax on loss.

12 pool questions1 on the exam

Syllabus: Transmission lines: characteristics of open and shorted feed lines; coax versus open wire; velocity factor; electrical length; coaxial cable dielectrics; microstrip

Waves are slower in a line, so it is electrically longer than it looks

Velocity factor = wave speed in the line ÷ speed of light. The insulating dielectric sets it: air is about 1, plastic slows the wave. A slower wave has a shorter wavelength, so a physical length holds more wavelengths: electrical length exceeds physical length.

Slower wave, shorter wavelength in the line, so the line is physically shorter for the same electrical length.

Velocity factor0.66

Wave speed in line66% of light

Physical half-wave length7.02m

RememberPhysical length = electrical length × VF. Dielectric sets VF.

A shorted or open line looks like a short, an open, or a reactance

What the generator sees depends on the length. Every quarter wavelength the picture flips (short becomes open); every half wavelength it repeats. In between: under a quarter wave, a shorted line is inductive and an open line is capacitive.

Reactance repeats every half wavelength and flips sign (and short to open) every quarter wavelength.

Line length0.125 λ

Generator sees+j1 Z₀

Far end	⅛ λ	¼ λ	½ λ
Shorted	inductive	very high Z	very low Z
Open	capacitive	very low Z	very high Z

RememberShorted: ¼ λ flips it, ½ λ copies it. Open is the mirror image.

Open wire loses least; foam beats solid; microstrip lives on a board

Same job, different trade-offs. Air makes a line faster and lower loss.

Parallel-conductor (open-wire) line has lower loss than plastic-dielectric coax. Foam coax versus solid, all else equal: lower loss, higher velocity factor, lower safe maximum voltage. All three.

RememberMore air in the dielectric: faster, lower loss, less voltage handling.

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Practise the 12 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".

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