E9F – Transmission lines: characteristics of open and shorted feed lines; 1/8 wavelength; 1/4 wavelength; 1/2 wavelength; feed lines: coax versus open-wire; velocity factor; electrical length; coaxial cable dielectrics; velocity factor
The physical length of a coaxial cable transmission line is shorter than its electrical length because electrical signals move more slowly in a coaxial cable than in air. (E9F03) The term we use to quantify the difference in how fast a wave travels in air versus how fast it travels in a feedline is velocity factor.
The velocity factor of a transmission line is the velocity of the wave in the transmission line divided by the velocity of light in a vacuum. (E9F01) Put another way, velocity factor is the term for the ratio of the actual speed at which a signal travels through a transmission line to the speed of light in a vacuum. (E9F08) The dielectric materials used in the line determines the velocity factor of a transmission line. (E9F02)
The typical velocity factor for a coaxial cable with solid polyethylene dielectric is 0.66. (E9F04) That makes the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically one-quarter wavelength long at 14.1 MHz about 3.5 meters. (E9F05)The approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically one-quarter wavelength long at 7.2 MHz is 6.9 meters. (E9F09)
The velocity factor of air-insulated, parallel conductor transmission lines is a lot closer to 1 than the velocity factor for coaxial cable. The approximate physical length of an air-insulated, parallel conductor transmission line that is electrically one-half wavelength long at 14.10 MHz is 10 meters. (E9F06)
While having a higher velocity factor is not really such a big advantage, open-wire or ladder line feedlines do have other advantages. For example, ladder line has lower loss than small-diameter coaxial cable such as RG-58 at 50 MHz. (E9F07)
Sometimes we use various lengths of coax to match an antenna system or to filter out frequencies. A 1/8-wavelength transmission line presents an inductive reactance to a generator when the line is shorted at the far end. (E9F10) A 1/8-wavelength transmission line presents a capacitive reactance to a generator when the line is open at the far end. (E9F11)
A 1/4-wavelength transmission line presents a very low impedance to a generator when the line is open at the far end. (E9F12) A 1/4-wavelength transmission line presents a very high impedance to a generator when the line is shorted at the far end. (E9F13)
A 1/2-wavelength transmission line presents a very low impedance to a generator when the line is shorted at the far end. (E9F14) A 1/2-wavelength transmission line presents a very high impedance to a generator when the line is open at the far end. (E9F15)
All of these choices are correct when talking about significant differences between foam-dielectric coaxial cable and solid-dielectric cable, assuming all other parameters are the same (E9F16):
- Foam dielectric has lower safe operating voltage limits
- Foam dielectric has lower loss per unit of length
- Foam dielectric has higher velocity factor
Dave New, N8SBE says
A very practical application of the 1/4 wave short/open rule is how I wired my 6-band 20-6 m quad. A lot of multi-band quad designs that use separate feeds for each driven loop advises to use an antenna switch that grounds the unused loops. Having only an antenna switch available that leaves the unused connections open rather than grounded, I hit on the idea of cutting the individual feed lines (RG-8x) to make them electrically 1/4 wave for the band that each was being used for. Then, when the antenna switch opened all but the chosen band, all the other driven loops were effectively grounded, because the open connections on the switch were transformed into shorts at the antenna end for all the unused feeds.