Impedance of the infinitely long circuit

Question

Is there a way to find impedance of the infinite circuit like this?

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It will be much simpler if one has either parallel or series combination but here is both.

score 1 · Accepted Answer · answered Jun 17 '15 at 08:10

The standard trick is to split off the circuit after the first link,

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and treat the 'tail' as another copy of the circuit itself. This means that the impedance $Z$ of the whole circuit must satisfy

$$ Z=2Z_1+\frac{1}{\frac{1}{Z_2}+\frac{1}{Z}}. $$

This gives a quadratic equation in $Z$ which is easy enough to solve.

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