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:
[latex]\frac{N_{p}}{N_{s}} = \sqrt{\frac{Z_{p}}{Z_{s}}}[/latex]
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
[latex]\frac{N_{p}}{N_{s}} = \sqrt{\frac{600}{4}}[/latex]
…
[latex]\frac{N_{p}}{N_{s}} = \sqrt{150}[/latex]
…
[latex]\frac{N_{p}}{N_{s}} = 12.247….[/latex]
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)