A short length of cable is a good antenna for frequencies th

A short length of cable is a good antenna for frequencies that match the frequency of the fundamental mode of the cable. What should the length of an (air-filled) coaxial cable that terminates in a short circuit circuit at both ends if the cable is to be an antenna for a wave of frequency 88 MHz? What should the length of an (air-filled) coaxial cable that terminates in a short circuit circuit at both ends if the cable is to be an antenna for a wave of frequency 108 MHz? What should the length of an (air-filled) coaxial cable which has one open-circuited end and one close-circuited end if the cable is to be an antenna for a wave of frequency 88 MHz? What should the length of an (air-filled) coaxial cable which has one open-circuited end anti one close-circuited end if the cable is to be an antenna for a wave of frequency 108 MHz? What is the complex reflection coefficient at a load circuit if the load circuit is driven at the resonaut frequency of the circuit and the char

Solution

A) Consider the values of permeability and permittivity has no change in this medium so the velocity of the wave considered to be as \'c\'.

frequency = 88MHz = 88*10⁶ Hz

wavelength = (3*10⁸ )/(88*10⁶ ) = 3.409 m

Length of a closed column for fundamental mode of vibration L = 2 * wavelength   { we know that wavelength = L/2 }

   L = 2 * 3.409 = 6.818 m

B) Similarly for frequency = 108MHz

     Wavelength = c / frequency = 2.778 m

     Length of the coaxial cable = 2 * 2.778 = 5.556 m

C) For one side open cable, fundamental mode wavelength = L / 4

    Length = wavelength * 4

    L = 3.409 * 4 = 13.636 m

D) L = 2.778 * 4 = 11.112 m