How to Simplify Backward Impedance Matching Equations?

AI Thread Summary
The discussion revolves around simplifying complex backward impedance matching equations in transmission line theory. The user outlines their steps, including calculating input impedance and equivalent impedance, but finds the resulting equations overly complicated. They express a desire for a simpler method to achieve their goal. A forum member suggests that the user should type their work directly into the forum for clarity, referencing a LaTeX primer for formatting assistance. The conversation emphasizes the need for clearer communication and potentially more efficient problem-solving techniques in impedance matching.
inter060708
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Homework Statement


https://scontent-lax3-1.xx.fbcdn.net/v/t34.0-12/14804959_10155526179417281_80533891_n.png?oh=649ee14155ac558b21c6553f003e418b&oe=5809EAA0

Homework Equations

The Attempt at a Solution


1) I determined the input impedance of the first transmission line (Zin1).
2) I calculated the equivalent impedance (Zeq) of 50 Ohms and Zin1
3) Found corresponding impedance of Gamma_s (Zs)
4) I switched the position of Zs with Zeq
5) Replaced Zs with its complex conjugate (Zs*)
6) Found input impedance of Zeq at length -l2
7) Set it equal to Zs*, solve for real and imaginary coefficients to get l1 and l2

The equation turns out to be very complicated and I am sure there is easier way, please help. Thank you
https://scontent-lax3-1.xx.fbcdn.net/v/t35.0-12/14647238_10155526274642281_613988889_o.jpg?oh=461d284cb7c90bcccfc46c1e3d960cb8&oe=5808D15D
 
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inter060708 said:

Homework Statement


https://scontent-lax3-1.xx.fbcdn.net/v/t34.0-12/14804959_10155526179417281_80533891_n.png?oh=649ee14155ac558b21c6553f003e418b&oe=5809EAA0

Homework Equations

The Attempt at a Solution


1) I determined the input impedance of the first transmission line (Zin1).
2) I calculated the equivalent impedance (Zeq) of 50 Ohms and Zin1
3) Found corresponding impedance of Gamma_s (Zs)
4) I switched the position of Zs with Zeq
5) Replaced Zs with its complex conjugate (Zs*)
6) Found input impedance of Zeq at length -l2
7) Set it equal to Zs*, solve for real and imaginary coefficients to get l1 and l2

The equation turns out to be very complicated and I am sure there is easier way, please help. Thank you
https://scontent-lax3-1.xx.fbcdn.net/v/t35.0-12/14647238_10155526274642281_613988889_o.jpg?oh=461d284cb7c90bcccfc46c1e3d960cb8&oe=5808D15D
Your picture is basically unreadable. Could you type your work into the forum instead? There is a LaTeX primer in the Help/How To section of the forum -- click on INFO at the top of the page.
 

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