Extra Class question of the day: Transmission line characteristics

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)