Transforming impedances: Question G5C07

In the last two weeks, I’ve received e-mails from two readers of The No-Nonsense General-Class License Study Guide.┬áBoth questioned my explanation of how transformers transform impedance. I wrote:

Transformers are also used to transform impedances. The impedance ratio is also related to the turns ratio, but the transformation is equal to the square of the turns ratio. The turns ratio of a transformer used to match an audio amplifier having a 600-ohm output impedance to a speaker having a 4-ohm impedance is 12.2 to 1. (G5C07)

Doug wrote, “The only way I can reproduce the calculation is by taking the square root of the turns ratio.” His comment made me see where my explanation could be a bit misleading. I wrote back:

Think about it this way. An impedance transformation can go either way. When transforming from a higher impedance to a lower impedance, you divide by the square root of the turns ratio. When transforming a lower impedance to a higher impedance, you multiply by the square of the turns ratio. In either case, the impedance ratio is “related” to the square of the turns ratio.

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