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Energy of a wave in a transmission line

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    An ideal transmission line has a characteristic impedance of Z=50 Ohms and
    v=200,000km/s propagation velocity. A sinusoidal signal with frequency f=1GHz and
    A=10mV amplitude is traveling down the line.Its total duration is 10s.What total
    energy is it carrying?

    2. Relevant equations

    P = IV
    w = 2[pi]f
    V(x,t)=Re{A exp[i(wt-kx)]}
    I(x,t)=Re{A/Z exp[i(wt-kx)]}

    3. The attempt at a solution

    I drew a picture of a transmission line that terminated into to a resistor with the same characteristic impedance as the line. The sinusoidal wave was coming in from the left only. The reflection amplitude of this wave is 0, so I think I should be able to say that all the energy in the wave was "burned" off by the resistor.

    A resistor burns energy at the rate of V^2/R J/s, which I said was equal to (A)^2/(Z), the amplitude of the wave squared divided by the characteristic impedance. I then multiplied the power by 10 seconds to get the total energy dissipated by the resistor, which I calculated to be 2*10^-5 J.

    The small answer and the fact that I didn't use all the information given pretty much yells to me that I did something wrong. I imagine that time and position dependence of the voltage and current might have something to do with it, but I'm not exactly sure.
    Last edited: Feb 16, 2010
  2. jcsd
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