The physical length of a coaxial cable transmission line 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.
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)
Richard Kesler says
Why does the 1/4 wavelength line show a very low impedance?
K9BTU
Dan KB6NU says
Z (impedance) = E/I. Now, envision the voltage and current distribution along the transmission line. At the open end, there won’t be much current (it’s an open circuit!), and the voltage will be high. At the generator end, however, the current is high and the voltage low, so the impedance will be low.
Mary VE3INE says
The last 2 paragraphs are inversely related but why?
Where can I find the illustrations E9F12, 13, 14, and 15?
The Canadian advanced exam has the same questions.
Dan KB6NU says
I know this isn’t the greatest answer, but it has to do with how voltage and current change along a transmission line. I’ll research this a bit more and come up with a better answer.