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The quarter wave transformer, as I understand, is supposed to allow matching an input impedance to an output impedance. The formula pertaining to a quarter wave transformer transmission line is

$$Z_\mathit{in} = \frac{Z_0^2}{Z_L}$$

I thought that the condition for a line being matched to the load was [itex] Z_L = Z_0 [/itex], so then wouldn't

$$Z_\mathit{in} = \frac{Z_L^2}{Z_L} = Z_L$$

implying that the characteristic impedance has nothing to do with the match?

I don't understand what I'm missing here! I don't see how the matching criteria that is in the book ([itex] Z_L = Z_0 [/itex]) can be met with the quarter wave line.

Thanks.

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# Quarter Wave Transformer: Understanding Formula

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