LC Circuit Input Admittance

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Discussion in 'Homework Help' started by jegues, Feb 6, 2012.

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  1. Feb 6, 2012 #1
    jegues

    Thread Starter Well-Known Member

    Sep 13, 2010
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    I'm confused as to how I'm supposed to solve for an LC circuit having the following admittance in the s domain,

    Y_{in}(s) = \frac{0.5s}{s^{2}+1} + \frac{2s}{s^{2}+2}

    Can anyone explain how?
     
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  2. Feb 6, 2012 #2
    t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    789
    Consider a series LC branch which has an impedance


    Z(s)=Ls+\frac{1}{Cs}=\frac{L(s^2+\frac{1}{LC})}{s}

    The admittance of such a branch is

    Y(s)=\frac{s}{L(s^2+\frac{1}{LC})}

    Now consider two such series LC branches with different L,C values connected in parallel.

    Remember: parallel branch admittances are additive
     
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  3. Feb 6, 2012 #3
    jegues

    Thread Starter Well-Known Member

    Sep 13, 2010
    735
    45

    So I can start the design with 2 different C values and 2 different L values, (i.e. two L and C series branches in parallel with one another) which I can then reduce to one L and one C?
     
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  4. Feb 6, 2012 #4
    t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    The resulting 4 element network may be reducible but presumably not to a simple series LC equivalent.
     
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