Ideal Transformer Calculator

An ideal transformer assumes zero core losses, no magnetic flux leakage, and zero winding resistance. Under these theoretical conditions, power input perfectly equals power output. The mathematical foundation relies on the turns ratio, which dictates how voltage and current scale between the primary and secondary coils.

The fundamental equations governing this relationship are:

Vs = Vp * (Ns / Np)

Is = Ip * (Np / Ns)

Where Vp and Vs represent primary and secondary voltages, Ip and Is represent primary and secondary currents, and Np and Ns denote the number of turns in the primary and secondary windings respectively.

Imagine you are designing a step-down power supply transformer. You have a primary voltage (Vp) of 240 volts, a primary current (Ip) of 0.5 amperes, a primary winding count (Np) of 1,200 turns, and a secondary winding count (Ns) of 150 turns. Let us find the secondary voltage (Vs) and secondary current (Is).

Step 1: Calculate Secondary Voltage (Vs)

Using the formula Vs = Vp * (Ns / Np), substitute the known values: Vs = 240 * (150 / 1200). First, find the turns ratio (150 / 1200 = 0.125). Then, multiply by 240 to get a secondary voltage of 30 volts.

Step 2: Calculate Secondary Current (Is)

Using the formula Is = Ip * (Np / Ns), substitute your numbers: Is = 0.5 * (1200 / 150). The inverse turns ratio is 8. Multiplying 0.5 by 8 yields a secondary current of 4 amperes. Thus, stepping down the voltage increases the available current proportionally while maintaining constant total power.

Keep these best practices in mind when working with transformer mathematics and circuit designs:

Account for Real-World Losses: Remember that ideal transformers do not exist in the physical world. Real transformers experience copper losses (windings resistance) and core losses (eddy currents and hysteresis), meaning actual output power will always be slightly lower than input power.

Double-Check Units: Always ensure your current and voltage units are consistent (e.g., amperes and volts) before performing calculations to avoid scaling errors in your final output.