Sections of transmission line:
When the transmission line is cut down to ¼ wavelength, or to any of the whole number multiple of this, it acts as a resonant circuit. The most common length for the transmission line resonator is the quarter wavelength. This type of piece of transmission line is known as quarter wave section.
When the quarter wave section is short circuited at far end, it behaves like a parallel resonant LC circuit, and has high impedance at resonant frequency fo. When it is open at far end, it behaves as a series resonant LC circuit, and has low impedance at fo. Therefore, a quarter wave section turns a short circuit into the open circuit and vice versa of it, at the specific frequency fo.
The length of the quarter wave section depends on fo. It depends on how fast the electromagnetic energy travels along the line. This speed can be specified in terms of a velocity factor, represented as v. The value of v can be given as the fraction of the speed of light. The transmission lines have velocity factors varying from around 0.66 to 0.95. This factor is provided by manufacturers of prefabricated lines like coaxial cable.
If frequency in megahertz is fo and velocity factor of a line is v, then length Lft of a quarter wave section of the transmission line, in feet, is
Lft = 246v/fo
The length in meters, Lm, is
Lm = 75.0v/fo
Problem:
How many feet long is the quarter wave section of transmission line at the 7.05 MHz, if velocity factor is 0.800?
By using the formula
Lft = 246v/fo
= (246 × 0.800)/7.05
=197/7.05 = 27.9 feet