A transformer is two coils sharing a magnetic field. AC in one winding, the primary, induces AC in the other, the secondary, with no electrical connection between them. It can step voltage up or down, and it can make one impedance look like another.
How it works
Illustrative, ideal transformer; coil drawings are schematic. Voltage goes with the turns ratio, current goes the opposite way, and power in equals power out.
Secondary voltage12 V
Impedance the source sees400 Ω
Alternating current in the primary makes an alternating magnetic field in the core. That field links the secondary, where, as in any inductor, a changing field induces a voltage. Each turn of wire sees the same changing field and so gets the same voltage, which means the voltage is proportional to the number of turns. Twice the turns, twice the volts.
This needs a changing field, so a transformer works on AC only. DC through the primary makes a steady field and no output. Worse, a mains transformer has little resistance in its primary, so DC on it can burn it out.
Voltage, current and impedance
An ideal transformer loses nothing, so power in equals power out. If the voltage goes down by some ratio, the current goes up by the same ratio.
Worked example: 120 V on 100 turns, 10 turns on the secondary, with a 4 Ω load.
Secondary voltage: 120 × 10 ÷ 100 = 12 V
Secondary current: 12 ÷ 4 = 3 A, power 36 W
Primary current: 36 ÷ 120 = 0.3 A
The source sees 120 ÷ 0.3 = 400 Ω, which is 4 Ω × 10²
Impedance goes with the square of the turns ratio because voltage is scaled by the ratio and current by its inverse, so their quotient is scaled twice.
Impedance ratio = turns ratio squared. 600 Ω to 50 Ω needs √12 = 3.46 : 1.
Presets
Impedance ratio (n²)12×
That is how a transformer matches an antenna to a feed line:
Impedance ratio
Turns ratio
Maps 50 Ω to
Typical use
4 : 1
2 : 1
200 Ω
4:1 balun or unun
9 : 1
3 : 1
450 Ω
9:1 unun, often used with random wires
49 : 1
7 : 1
2450 Ω
end-fed half-wave transformer
Real transformers
Core. Mains transformers use laminated steel; RF transformers use ferrite or powdered-iron cores, or no core at all at VHF. Neither works well in the other's job.
Losses. Winding resistance, core losses and leakage flux (field that does not link both windings) all waste power as heat.
Saturation. Too much flux and the core cannot carry more, the inductance collapses and the current soars.
Frequency. The lower the frequency, the more core a given power needs, which is why a 60 Hz supply transformer is heavy and a switch-mode supply running at tens of kHz or more is small; see Power supplies and regulators.
Broadband RF. Wide-range baluns and ununs use transmission-line transformer techniques, covered in Baluns and ununs.