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

[Rib5]

Homework Statement

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.

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...}a...}b

Homework Equations

$$\Gamma_{L} = \frac{Z_L-Z_o}{Z_L+Z_o}$$

The Attempt at a Solution

I am pretty sure the formula I am supposed to use is $$\Gamma_L = \frac{Z_L-Z_o}{Z_L+Z_o}$$. What I am not sure is what value to choose for $$Z_L$$. Do I take $$Z_o$$ in parallel with $$R_A$$?

 

[xcvxcvvc]

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.