Transformer turns ratio: voltage, current, impedance and how to size the windings
A transformer is two coils on one iron core. The changing current in the primary makes a changing magnetic flux, the flux threads every turn of both coils, and every turn gets the same voltage. So Vp / Vs = Np / Ns: the voltages are in the ratio of the turns, the currents in the inverse ratio, and a load on the secondary looks a² times bigger from the primary. This calculator gives the secondary voltage from the turns, or the turns for the voltage you want, with the currents, power and reflected impedance for a load, and two helpers: the primary turns a core needs, and the ratio that matches two impedances.
How to use the transformer calculator
- Type the primary voltage and its turns. If you only know the ratio, any pair of turns in that ratio will do (230 V on 23 turns is 10 V per turn).
- Type the secondary turns to find the secondary voltage, or type the secondary voltage you want and leave the turns blank: they are designed and rounded to a whole number, and the voltage the rounded turns really give is shown.
- Add a load (ohms) and an efficiency to get both currents, the power in and out, the losses and the impedance the primary sees.
- The drawing shows the two windings with their turns in proportion, the core, the AC source and the load, with a volts-per-turn panel. Click a winding or the load for its own notes. The Core & matching tab finds the primary turns for a core (N = V / 4.44 f B A) and the ratio that matches a source to a load.
The formulas
Vp / Vs = Np / Ns = a Vs = Vp × Ns / Np Ns = Np × Vs / Vp
a is the turns ratio, written Np : Ns. A 230 V to 12 V transformer is about 19:1, a step-down; a 12 V to 230 V inverter transformer is 1:19, a step-up; an isolation transformer is 1:1. Only the ratio matters for the voltage; the actual number of turns is set by the core (below).
Currents and power
Ip / Is = Ns / Np = 1 / a Vp Ip = Vs Is
An ideal transformer passes power through unchanged, so whatever the voltage is multiplied by, the current is divided by. A 19:1 step-down giving 12 V at 5 A draws only 0.26 A from the 230 V mains. The low-voltage winding carries the big current and is wound with thick wire; the high-voltage winding with many turns of thin wire. Real transformers lose a few percent in the copper resistance and the core (hysteresis and eddy currents), so the primary draws a little more than the ideal: the efficiency field takes that off.
Impedance transformation
Zp = a² × Zs a = √(Zsource / Zload)
Divide the voltage by a and multiply the current by a, and the impedance (voltage over current) changes by a². An 8 Ω speaker on a 25:1 output transformer looks like 5 kΩ to the valve driving it; a 50 Ω aerial on a 1:3 balun looks like 450 Ω. To match a source to a load, pick a = √(Zsource/Zload): the matching helper does the sum and writes the turns.
How many turns a core needs
Np = Vp / (4.44 × f × Bmax × Acore)
The ratio says nothing about the absolute number of turns; the core does. Too few primary turns and the flux needed to oppose the mains voltage exceeds what the iron can carry: it saturates, the magnetising current shoots up and the transformer hums and overheats. For a sine wave the turns needed are V / (4.44 f B A) with B the peak flux density (1.0–1.3 T for silicon steel at 50 Hz, 0.2–0.3 T for ferrite at tens of kHz) and A the core's cross-section in m². A 230 V, 50 Hz primary on a 10 cm² core at 1.2 T needs 864 turns, about 266 mV per turn. Higher frequency means fewer turns, which is why switch-mode transformers are so small.
Real transformers
The no-load secondary voltage is a few percent above the rated one and sags under load (winding resistance and leakage inductance), so a 12 V winding reads 13 V or so unloaded. The voltage a rectifier produces is the peak, √2 times the RMS, less the diode drops: a 12 V secondary gives about 15–16 V DC into a capacitor. Transformers are rated in VA (volts × amps), and a rectifier-capacitor load heats the windings more than its DC watts suggest, so derate by about 1.6. The turns ratio, finally, is why transformers only work on AC: a steady current makes a steady flux, and a steady flux induces nothing.
Your transformer, step by step
- Ratio: 1,150 turns / 60 turns = 19.2:1 (a = 19.167), 200 mV per turn.
- Secondary voltage: 230 V × 60 turns / 1,150 turns = 12 V.
- Currents: Is = 12 V / 10 Ω = 1.2 A; Ip = 1.2 A / 19.2 / 95% = 65.9 mA.
- Power and impedance: 14.4 W out, 15.2 W in; the primary sees 19.2² × 10 Ω = 3.67 kΩ.
Worked example: 230 V to 12 V with a 10 Ω load
A mains transformer has 1150 primary turns and 60 secondary turns: a = 1150 / 60 = 19.167, written 19.2:1, and 230 V / 1150 = 200 mV per turn. The secondary gives 60 × 200 mV = 12 V. A 10 Ω load draws 1.2 A, which is 14.4 W; at 95 % efficiency the primary supplies 15.2 W and draws 65.9 mA from the mains. From the primary side the 10 Ω load looks like 19.2² × 10 Ω = 3.67 kΩ. To get 9 V instead, the secondary needs 9 × 1150 / 230 = 45 turns.
Questions
Can I run a transformer backwards?
Yes: a 230 V to 12 V transformer fed with 12 V AC gives 230 V. The ratings stay the same (the 12 V winding still takes the big current), and it needs AC, not DC.
Why does my 12 V transformer give 13.5 V?
The rating is at full load; unloaded, the winding resistance drops nothing and the voltage is 5–10 % higher. Under the rated load it falls to 12 V.
Does the number of turns matter if the ratio is right?
For the voltage, no; for the core, yes. Too few turns saturate the core (see "How many turns a core needs"); too many waste copper and add resistance.
What does a transformer's VA rating mean?
The product of rated voltage and rated current on the secondary, the power it can pass continuously without overheating. A 12 V, 2 A secondary is 24 VA; with a rectifier and capacitor, plan for about 1.6 times the DC watts.