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Design >> RF Design >> Smith chart of λ/4 Transmission Line
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Message started by blue111 on Mar 18^th, 2019, 7:33am

Title: Smith chart of λ/4 Transmission Line
Post by blue111 on Mar 18^th, 2019, 7:33am

I came across the following slide on power combiner circuit and I have questions about it.

1. Why traverse across the upper half circle ? In other words, why is Zin located at the right side of Zout ?

2. Why when translating an impedance towards the generator we move clockwise around the chart ?

3. Why "ZT-line is the geometric mean of Zout and Zin." ?

4. Why overlay the Smith chart scaled for ZT on top of the Z0 Smith chart ?

Title: Re: Smith chart of λ/4 Transmission Line
Post by SantoS_Nano on Mar 20^th, 2019, 5:19am

Hi...

1. The location of the Zin and Zout on smith chart will depends on the impedance values. In the attached smith chart, I think, the locations were chosen randomly.
But from figure, you can observe that Zin>Zout and both are real (pure resistances).

3. Yes. In quarter-wave transformer case, ZTline is geometric mean of Zout and Zin.
You can observe this result by simply substituting l=lambda/4 in basic "transmission line impedance equation".

4. Question can be more clear.
but scaling with Zo (50ohm) is for simplicity. it is like, ZTline is normalized with Zo (ZTline/Zo).

Regards...