Problem 5 20 pts A coaxial cable of characteristic impedance

Problem 5. (20 pts) A coaxial cable of characteristic impedance 50 2 carries a harmonic voltage wave of frequency 2 x 10 Hz and voltage amplitude 100 uV. It is connected to an old style two wire transmission line TV connector of characteristic impedance 1002. Take the speed of the wave to be 2 x 10s m/s. A) Find the average power carried by the (incident) voltage wave in the 50 n cable. B) Find the amplitude of the voltage wave that is reflected at the join between the two cables. C) Find the amplitude of the voltage wave that is transmitted at the join between the two cables. D) Find the amplitude of the incident current wave. E) Find the amplitude of the current wave that is reflected at the join between the two cables. F) Find the amplitude of the current wave that is transmitted at the join between the two cables G) Find the average power carried by the voltage wave that is reflected at the join between the two cables H) Find the average power carried by the voltage wave that is transmitted at the join between the two cables.

Solution

A) INCIDENT AVERAGE POWER = V² /2R = 10^-10

B) REFLECTED VOLTAGE = 100-50/100+50 * 100

= 33 microvoltage

C) TRANSMITTED VOLTAGE = 2*50/150 *100 = 66 microvoltage

D) IL = VL /R = .065 microampere