How Do Infinitely Long LC Circuits Behave?

[channel1]

Homework Statement

I'm curious about infinitely(?) long LC Circuits. Say you have a circuit (and I am 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 can't 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----

Homework Equations

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

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 don't think that's right...

 

[channel1]

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)

 

[channel1]

actually this is a much better diagram that i found, unfortunately the couldn't figure it out either: http://i.imgur.com/YJDaD.png

 

[gneill]

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.