λ/8 transmission line

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Think about the input impedance of a lambda/4 line terminated into open or short.
 

A lambda/4 transmission line transforms a short into an open and vice versa!
Also if you have a real impedance, lambda/4 line always transforms into another real impedance. A lambda/8 line can transform a real impedance into a complex impedance which maybe useful sometimes.
 

A lambda/8 line can transform a real impedance into a complex impedance
Click to expand...

@vivekroy Could you show us how ?

By the way, I have math proof for λ/4 transmission line , I am not sure about the derivation proof for the inductor and capacitor using λ/8 transmission line

 

In the expression for Zin, plug in Zo =50 and Zl=25. This is only one example though.
 

vivekroy said:
In the expression for Zin, plug in Zo =50 and Zl=25. This is only one example though.
Click to expand...

Huh ? What ?

If we substitute λ/8 instead of λ/4 into the following Zin equation, then we will have

Zin(L=λ/8) = Zo * (ZL + j*Zo) / (Zo + j*ZL)

Then, what is your purpose of using Zo =50 and ZL=25 ? What do you want to demonstrate or imply ?

 

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