Impedance Matching & Transformer Ratio Calculator
Enter source and load impedances to get the required transformer turns ratio for maximum power transfer, along with mismatch loss, SWR, and power transfer percentage. Nothing uploaded.
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Learn more: turns ratio, mismatch loss and why audio and RF disagree
The turns ratio is a square root
A transformer matches two impedances when its turns ratio is N = sqrt(source / load). Matching a 600 ohm source to an 8 ohm load needs sqrt(600 / 8) = 8.66 to 1, not 75 to 1, because impedance scales with the square of the turns ratio while voltage scales linearly. The voltage ratio across the transformer is 1 / N, here 0.1155.
What a mismatch costs without a transformer
The calculator also shows what happens with no transformer. The reflection coefficient is (load - source) / (load + source), SWR is (1 + |reflection|) / (1 - |reflection|), and mismatch loss is -10 log10(1 - reflection squared). For 600 ohms into 8 ohms the reflection coefficient is -0.974, the SWR is 75 to 1, the mismatch loss is 12.8 dB and only about 5.2% of the power is delivered.
A mild mismatch is far less costly. Feeding a 50 ohm source into a 75 ohm load gives a reflection of 0.2, an SWR of 1.5 to 1, a loss of 0.18 dB and 96% of the power delivered.
Why audio does not chase a match
Wikipedia's article on the maximum power transfer theorem says efficiency is only 50% when the load resistance equals the source resistance, the condition for maximum power transfer. In audio engineering, it says, a load much larger than the source resistance is called impedance bridging, and efficiency approaches 100% as the source resistance approaches zero.
That is why audio amplifiers have a low output impedance compared with the speaker's, while RF systems match the source, line and load to avoid reflections. The two fields use the same equations to solve different problems.
FAQ
What does SWR measure?
Standing wave ratio measures how much power reflects from a mismatch instead of being absorbed by the load. An SWR of 1 to 1 is a perfect match, and higher ratios mean more power is reflected toward the source.
Why does RF equipment care about a bad SWR?
Reflected power on a mismatched line wastes transmitted power and can stress a transmitter's output stage, so RF gear often has protection that cuts power when SWR is high.
Is matching headphones the same as matching speakers?
The same low output impedance idea applies. High-impedance headphones may need an amplifier that can supply enough voltage, which is a separate issue from impedance matching.