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Microstrip High- and Low-Impedance Short-Line Sections

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promach

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Expression 4.50 can be obtained by equating the ABCD parameters of the two circuits ?

Could anyone advise ?

Note: Screenshots below are taken from Microstrip Filters for RF Microwave Applications, 2nd Edition

gc7rR7Q.png


V62220w.png


MLyZwAt.png


I1cgNDK.png
 

I am still trying to derive the ABCD matrix for the following circuit configuration.

Any help ?

0bsMJ8W.png


iUS3rNJ.png
 

The following is the derivation process for expression 4.50

ABCD matrix for transmission line at Figure 4.7(a)

6FXNyjF.png


ABCD matrix for π-circuit network at Figure 4.7(b)

kfY74ws.png



Comparing the two ABCD matrices above gives :

UWBgCZn.png


gLcohOi.png



Applying trigonometry double angle formula :

NhzALpy.png
 

There is a typo mistake for ABCD matrix for π-circuit network at Figure 4.7(b)

Please see the correction below:

IrNmN5r.png



Ok, now to more detailed part:

How to derive expressions (5.3) ?
I suppose that this involves eliminating the assumption : ZC << Z0 << ZL

Note: In the post above, I have derived expression (5.2) for inductor, which is equivalent to expression (4.50)

CGn8XnG.png
 

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