A transmission line has a velocity factor of 0.88. You desire to create a quarter-wavelength phasing section at an operating frequency of 150 MHz. Calculate the following:

a) wavelength, freespace

b) wavelength, dielectric

c) length of the phasing section in meters

a) λ = 2 meters

b) λ = 1.76 meters

c) In free space: length of phasing section = 0.5 meters and in dielectric medium: length of phasing section = 0.44 meter

Explanation:

Given that:

velocity factor = 0.88

operating frequency = 150 MHz = 150 * 10⁶ Hz

phasing section is a quarter-wavelength = λ/4

a) Wavelength of free space:

λ = c/f

where c is the speed of light = 3*10⁸

λ = (3*10⁸) / 150 * 10⁶

λ = 2 meters.

b) Wavelength of dielectric:

Velocity of dielectric = speed of light (c) * velocity factor

Velocity of dielectric = 3*10⁸ * 0.88 = 2.64 * 10⁸ m/s

wavelength dielectric = Velocity of dielectric / f = (2.64 * 10⁸) / 150 * 10⁶ = 1.76

wavelength dielectric = 1.76 meters

c) length of the phasing section in meters:

l = λ/4

In free space:

l = 2/4 = 0.5 meter

In dielectric

l = 1.76/4 = 0.44 meter