Microstrip High- and Low-Impedance Short-Line Sections

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

Yes.

Compare [ABCD] of the followings.
(1) Transmission Line
(2) PI circuit
(3) T circuit

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

Any help ?

The derivation process could be found at page 25 of the pdf attachment

Now the question is how to derive expression 4.50 given the above ABCD matrix ?

Microwave_Network_Parameter.pdf

There is no help since it is too easy.

Can you understand following even a liittle ?
https://www.edaboard.com/showthread....ight=Bode+fano

This is very easy than the above, if you can understand the above even a little.

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 : Z_C << Z₀ << Z_L

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