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Radio Frequency Power

  1. Nov 25, 2014 #1
    1. The problem statement, all variables and given/known data
    A coaxial transmission line consists of an inner cylindrical conductor of radius 1mm and a cylindrical outer conductor chosen to make the characteristic impedance 75 ohms. The space between the conductors is filled with a gas that can stand a maximum field of 10^5 Vm^-1 without dielectric breakdown. Estimate the maximum mean radio-frequency power that can be transmitted along this line into a matching load.

    2. Relevant equations
    The impedance of a co axial cable is Z=Zo*ln(b/a)/n*2*pi where b is outer radius, a inner radius and n is sqrt(permittivity).

    3. The attempt at a solution
    So for the empty coaxial cable I had Z=Zo*ln(b/a)/2*pi

    I rearranged this to work out the value of the outer radius which I got as 3.49mm.

    I used the distance between inner and outer radius and the max electric field to work out potential difference. I then tried to the use the standard P=Vi formula to work out power but my answer is about 8 times too big. I assumed all the power is transmitted due to impedance matching.
     
  2. jcsd
  3. Nov 25, 2014 #2

    berkeman

    User Avatar

    Staff: Mentor

    Welcome to the PF.

    The breakdown voltage is based on the peak voltage, while the power is based on the RMS voltage. Still, that should only give you a difference of √2, not 8. Can you post your work so we can check the numbers?
     
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