Transformer Turns Ratio

Formula

Description

The transformer turns ratio relates the primary and secondary voltages (and inversely, the currents) of an ideal transformer. A step-down transformer has N > 1, reducing voltage while proportionally increasing current. A step-up transformer has N < 1, increasing voltage while reducing current. The turns ratio is determined by the number of wire turns on each winding, and power is conserved (minus losses): V1 × I1 = V2 × I2. Real transformers have efficiency of 90-99% depending on size, with losses due to copper resistance, core hysteresis, and eddy currents.

Variables

• N — Turns ratio (primary to secondary, dimensionless)
• V1 — Primary (input) voltage (V)
• V2 — Secondary (output) voltage (V)

Practical Notes

Transformer impedance transformation follows the square of the turns ratio: Z_reflected = N² × Z_load. This principle is used in audio output transformers, RF matching networks, and current sensing transformers. For isolation transformers, N = 1 but the galvanic isolation between windings is the key feature. Multiple secondary windings can provide different voltage outputs from a single transformer.