How to Simplify Backward Impedance Matching Equations?

In summary, the conversation is about finding the input impedance of a transmission line and determining the length of the line using complex conjugates. The equation for this process turns out to be complicated and the person is seeking help for a simpler method.
  • #1
inter060708
24
0

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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  • #2
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.
 

1. What is backward impedance matching?

Backward impedance matching is a technique used to match the output impedance of a source with the input impedance of a load in a circuit. This is done by using a matching network, typically consisting of resistors, capacitors, and inductors, to minimize the reflection of signals and maximize power transfer.

2. Why is backward impedance matching important?

Backward impedance matching is important because it helps to ensure maximum power transfer and minimize signal reflections in a circuit. This can improve the overall performance and efficiency of the circuit, as well as reduce the risk of damage to components.

3. How is backward impedance matching different from forward impedance matching?

The main difference between backward and forward impedance matching is the direction of the signal flow. In backward impedance matching, the signal flows from the source to the load, while in forward impedance matching, the signal flows from the load to the source. This difference affects the design and placement of the matching network in the circuit.

4. What are some common techniques used for backward impedance matching?

Some common techniques used for backward impedance matching include the L-matching network, pi-matching network, and T-matching network. These networks use combinations of resistors, capacitors, and inductors to match the input and output impedances of the source and load. Other techniques such as stub matching, quarter-wave transformers, and transformer matching can also be used.

5. Can backward impedance matching be applied to any circuit?

Yes, backward impedance matching can be applied to any circuit where the output impedance of the source and the input impedance of the load are not equal. It is especially important in high-frequency circuits, such as radio frequency (RF) circuits, where impedance matching is crucial for efficient signal transmission.

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