What is the reflection coefficient on a transmission line at a resistor halfway?

  1. 1. The problem statement, all variables and given/known data
    If I have a coaxial transmission line, with a resistor halfway through, and another resistor at the end, how do I calculate the reflection coefficient for the spot where the resistor is halfway?

    Here is a diagram of what I mean. Dashes and dots are are the lines, and } are resistors.

    ----------
    ....}a....}b



    2. Relevant equations
    [tex]\Gamma_{L} = \frac{Z_L-Z_o}{Z_L+Z_o}[/tex]


    3. The attempt at a solution
    I am pretty sure the formula I am supposed to use is [tex]\Gamma_L = \frac{Z_L-Z_o}{Z_L+Z_o}[/tex]. What I am not sure is what value to choose for [tex]Z_L[/tex]. Do I take [tex]Z_o[/tex] in parallel with [tex]R_A[/tex]?
     
    Last edited: Aug 31, 2010
  2. jcsd
  3. you know how you can take any length of transmission line plus an impedance at the end, and transform it into a single impedance that the source sees?

    Well, put your finger over resistor a and the rest of the circuit, and apply that formula to transform your circuit from
    L/2 of wire-> impedance a -> L/2 of wire -> impedance b
    into
    L/2 of wire -> impedance a -> equivalent impedance B

    you need to use the length L/2, not L, when you calculate the equivalent impedance for resistor b, because you're calculating the equivalent impedance that resistor a sees. Next, now that resistor behaves just like they do in your circuits class. Take equiv b in parallel with a (assuming a branches across and connects the wires) to find a single impedance at the "end of the wire" (which represents what impedance is seen at the halfway point). Then apply your reflection equation.
     
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