Transformer Turns Ratio
Secondary voltage, current, and impedance ratio from the turns.
Turns ratio 10.00:1 — voltage scales with the turns, so fewer secondary turns lower it.
Current goes the opposite way to voltage — stepping voltage down multiplies the available current. At 95% efficiency, 115 W in gives 109 W out.
Impedance transforms as the square of the turns ratio, which is why transformers are used to match a speaker to an amplifier or an antenna to a feedline.
Transformers work on changing flux, so they pass AC and block DC entirely — connecting one across a battery shorts the supply through the winding resistance. These relations also assume the core is not saturating; beyond that point the output distorts and current rises sharply.
Voltage follows the turns ratio directly and current follows it inversely. A 1000:100 transformer on 230 V gives 23 V out, with ten times the current available. Impedance transforms as the ratio squared, so 100:1 here.
Three ratios from one number
A transformer is two coils sharing a magnetic core. Alternating current in the primary creates a changing flux, and that flux induces a voltage in the secondary proportional to how many turns it has. Everything else follows from that single relationship.
Voltage scales with the turns ratio: half the turns, half the volts. Current scales inversely, because a transformer cannot create power — stepping voltage down by ten multiplies the available current by ten, minus losses. Impedance scales as the square of the ratio, which is the least intuitive of the three and the most useful in signal work.
Why impedance goes as the square
It falls straight out of Ohm's law. Impedance is V ÷ I; the voltage multiplies by the ratio while the current divides by it, so the quotient changes by the ratio twice over. That is why a 10:1 transformer presents a 100× impedance change — the mechanism behind matching a low-impedance speaker to a high-impedance valve amplifier, or an antenna to its feedline.
An ideal transformer conserves power exactly: Vp × Ip = Vs × Is. Real ones lose a few percent to core hysteresis, eddy currents, and winding resistance.
Worked example: 1000:100 on 230 V
Ratio first, then each quantity in turn:
- 1 Take the turns ratio. 1000 ÷ 100 = 10, so this is a 10:1 step-down transformer.
- 2 Divide the voltage. 230 V ÷ 10 = 23 V on the secondary.
- 3 Multiply the current. 0.5 A drawn on the primary supports about 5 A on the secondary — before losses.
- 4 Apply the efficiency. At 95%, that becomes about 4.75 A.
- 5 Square the ratio for impedance. 10² = 100, so a 8 Ω load on the secondary looks like 800 Ω to the primary.
- 6 Check the power balance. 230 × 0.5 = 115 W in, and 95% of that is 109 W out — the missing 6 W is heat in the core and windings.
Common turns ratios on 230 V
Secondary voltage and the impedance transformation each ratio provides.
| Np : Ns | Type | Secondary V | Impedance ratio |
|---|---|---|---|
| 1 : 1 | Isolation | 230 V | 1 : 1 |
| 2 : 1 | Step-down | 115 V | 4 : 1 |
| 10 : 1 | Step-down | 23 V | 100 : 1 |
| 20 : 1 | Step-down | 11.5 V | 400 : 1 |
| 1 : 2 | Step-up | 460 V | 1 : 4 |
| 1 : 10 | Step-up | 2300 V | 1 : 100 |
What the ideal equations do not tell you
The most important omission is that a transformer only works on AC. Induction depends on a changing magnetic field, so a steady DC voltage induces nothing in the secondary while the primary behaves as a short circuit through its own winding resistance. Connecting a mains transformer to a battery is a reliable way to destroy the battery, the transformer, or both.
Core saturation is the other practical limit. Beyond a certain flux the core cannot magnetise further, the primary inductance collapses, and current rises sharply while the output waveform distorts. This is why a transformer is rated for a specific frequency as well as a voltage — running a 60 Hz transformer at 50 Hz pushes it closer to saturation, since each half-cycle lasts longer.
Finally, an isolation transformer with a 1:1 ratio changes nothing electrically and is still extremely useful: it breaks the galvanic connection between two circuits, so a fault on one side cannot put mains potential on the other. Its whole value is in what it does not transfer.