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Long LC circuits

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm curious about infinitely(?) long LC Circuits. Say you have a circuit (and im going to describe this sort of like a matrix) with capacitors on the top row, inductors on the bottom row, and one inductor in each column. Assume a current with value "i" is going up through the columns. Can someone please help me understand what is going on in the system? I understand how to solve a basic LC circuit but I cant find any good examples with multiple capacitors and inductors within the same system.

    ----C---------C---------C----
    l l
    L L
    l l
    ----L---------L---------L----

    2. Relevant equations

    C(series) = (1/C + 1/C +...)^-1
    C(parallel) = C+C+...
    L(series) = L+L+...
    L(parallel) = (1/L + 1/L +...)^-1

    3. The attempt at a solution
    I tried looking at this as as 2 repeating series: (a capacitor and inductor in series) + (an inductor in parallel with (a capacitor and inductor in series)) but i dont think thats right...
     
  2. jcsd
  3. Dec 6, 2011 #2
    ugh this website auto "corrected" my diagram -_- the columns go in the spaces between the rows (so not directly under the capacitors but directly under the "-----" gaps)
     
  4. Dec 6, 2011 #3
    actually this is a much better diagram that i found, unfortunately the couldnt figure it out either: http://i.imgur.com/YJDaD.png
     
  5. Dec 6, 2011 #4

    gneill

    User Avatar

    Staff: Mentor

    Usually with these sorts of problems the idea is to identify a 'unit cell' of what comprises the ladder network and then assume that, since it is infinite in length, adding one more cell to the front end ( or back end) won't change the impedance.

    You end up with an equation that goes something like Z = Z + Zcell, or Z = Z || Zcell, or something similar. Of course you might have to deal with series or parallel bits when the cell is added, but you get the idea.
     
    Last edited: Dec 6, 2011
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