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Homework Help: Transmission line

  1. Mar 6, 2014 #1
    A 50 ohm transmission line is terminated with 60 ohm and 30 ohm resistors in parallel. The voltage at the input to the line is V(t) = 100 cos (5X10 ^ 9 t) and the line is 3/8 th of a wavelength long. What average power is delivered to each load resistor ?

    My ans is getting 81.6 but actual ans given is 69 . I simply used the formula P = (V^2) (1-L^2) / 2 Z
    where L = reflection coefficient
    Z = characteristic impedance
     
  2. jcsd
  3. Mar 6, 2014 #2
    If I understand this:
    The terminating resistance is 1/((1/60)+(1/30)) = 20 ohms
    The RMS voltage will be 100 * sqrt(2) = 70.71 volts
    The length of the transmission line doesn't make a difference because we have a voltage source at one end.

    So:
    The RMS voltage at the resistor end will be 70.71 * 2(20)/(20+50) = 70.71 * (4/7) = 40.41 V
    So the power that the resistors are dissipating would be V*V/r = 40.41*40.41/20 = 81.63 watts

    Well, that's your answer.

    I think the bad assumption is about the way the input voltage source is connected to the transmission line. It would normally be connected through a 50 ohm resistor. Once you put that 50 ohm resistor in, then you will need to take into consideration the effects of the 3/8 wavelength.
     
  4. Mar 7, 2014 #3

    rude man

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    1. Get the correct formula for the load voltage E2 as a function of source voltage E1, line chas. impedance Z0, load impedance Z2, and length of line expresed as a fraction of wavelength.

    2. Then, power to the two load resistors is P = |E2|2/R
    where R = 30 ohms and 60 ohms.
     
  5. Mar 7, 2014 #4

    rude man

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    Uh-uh.
     
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