Microstrip High- and Low-Impedance Short-Line Sections

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

Any help ?



 

The following is the derivation process for expression 4.50

ABCD matrix for transmission line at Figure 4.7(a)



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




Comparing the two ABCD matrices above gives :






Applying trigonometry double angle formula :

 

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

Please see the correction below:




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)

 

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