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29th July 2019, 09:50 #1
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Microstrip High and LowImpedance ShortLine 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

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29th July 2019, 11:02 #2

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30th July 2019, 04:11 #3
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Re: Microstrip High and LowImpedance ShortLine Sections
I am still trying to derive the ABCD matrix for the following circuit configuration.
Any help ?

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31st July 2019, 08:34 #4
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Re: Microstrip High and LowImpedance ShortLine 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

4th August 2019, 10:22 #5
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Re: Microstrip High and LowImpedance ShortLine Sections
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.

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14th August 2019, 09:08 #6
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Re: Microstrip High and LowImpedance ShortLine Sections
The following is the derivation process for expression 4.50
ABCD matrix for transmission line at Figure 4.7(a)
ABCD matrix for πcircuit network at Figure 4.7(b)
Comparing the two ABCD matrices above gives :
Applying trigonometry double angle formula :

17th August 2019, 16:45 #7
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Re: Microstrip High and LowImpedance ShortLine Sections
There is a typo mistake for ABCD matrix for πcircuit 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} << Z_{0} << Z_{L}
Note: In the post above, I have derived expression (5.2) for inductor, which is equivalent to expression (4.50)
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