What is the turns ratio of a transformer used to match an audio amplifier having 600 ohm output impedance to a speaker having 4 ohm impedance? [G5C07] A. 12.2 to…

General: Audio Impedance Matching

What is the turns ratio of a transformer used to match an audio amplifier having 600 ohm output impedance to a speaker having 4 ohm impedance? [G5C07]

A. 12.2 to 1
B. 24.4 to 1
C. 150 to 1
D. 300 to 1

This is a simple ratio type equation, almost.  The equation for solving this problem looks like this:

$\frac{N_{p}}{N_{s}} = \sqrt{\frac{Z_{p}}{Z_{s}}}$

Where N is the number of turns, p and s are primary and secondary respectively, and Z is impedance.  If we substitute our numbers, we get

$\frac{N_{p}}{N_{s}} = \sqrt{\frac{600}{4}}$

$\frac{N_{p}}{N_{s}} = \sqrt{150}$

$\frac{N_{p}}{N_{s}} = 12.247....$

So our answer becomes: A. 12.2 to 1.  Note that if we had flipped the values in the equation, we would have wound up with exactly the same value, only inverted, that is, 1 to 12.2.

(image: https://commons.wikimedia.org/wiki/File:Line_level_audio_transformers.jpg)