# Microstrip High- and Low-Impedance Short-Line Sections

1. ## Microstrip High- and Low-Impedance Short-Line Sections

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

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

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2. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

Originally Posted by promach
Expression 4.50 can be obtained by equating the ABCD parameters of the two circuits ?
Yes.

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

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3. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

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

Any help ?

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4. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

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

5. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

There is no help since it is too easy.

Can you understand following even a liittle ?

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

6. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

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 :

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7. ## Re: Microstrip High- and Low-Impedance Short-Line Sections

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

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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