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    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








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    Re: Microstrip High- and Low-Impedance Short-Line Sections

    Quote Originally Posted by promach View Post
    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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    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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    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



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    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 ?
    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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    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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    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)

    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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