Transformer Calculator

A transformer moves energy between windings that share a magnetic core but no electrical connection. Faraday induction gives every turn on that core the same induced voltage, so the winding voltages stand in the same ratio as their turn counts. Because an ideal transformer neither stores nor dissipates energy in steady state, the currents stand in the inverse ratio, and any impedance referred across the transformer scales with the square of the turns ratio. A 240 to 120 volt unit has a 2 to 1 turns ratio, halves the voltage, doubles the available current, and makes a 4 ohm secondary load appear as 16 ohms at the primary. Losses split into two families that behave very differently with load. Core or iron loss, comprising hysteresis and eddy current loss, is set by flux density and frequency and stays essentially constant whenever the transformer is energized. Copper loss is I squared R in the windings and rises with the square of load current. Peak efficiency occurs where the two are equal, usually between 40 and 70 percent of rated load, which is why a distribution transformer rated 98 to 99 percent efficient at full load can be noticeably less efficient carrying a light load. Ratings are given in volt-amperes rather than watts because the windings heat on total current regardless of power factor. A 20 to 25 percent margin above calculated VA is normal practice, covering ambient temperature, harmonic content, and motor inrush of five to eight times running current.

Michael Faraday wound two coils on an iron ring in August 1831 and saw a galvanometer connected to the second coil deflect briefly whenever the first was switched, the founding experiment of electromagnetic induction. Faraday's ring was not a working transformer because it responded only to changes in current; alternating current later supplied that change continuously. Lucien Gaulard and John Dixon Gibbs patented a device they called a secondary generator in 1882 and demonstrated AC distribution in London and at Turin in 1884, but their open magnetic circuit and series-connected arrangement regulated poorly. The modern form came from the Ganz Works in Budapest, where Karoly Zipernowsky, Otto Blathy, and Miksa Deri patented a closed-core, parallel-connected unit in 1885 and gave it the name transformer. William Stanley, working for Westinghouse, built on the same principle for the demonstration lighting system at Great Barrington, Massachusetts, in 1886. Efficiency then improved through materials rather than topology. Robert Hadfield's silicon steel, developed around 1900, cut hysteresis and eddy losses sharply, and Norman Goss patented grain-oriented silicon steel in 1934, which remains the standard core material for power transformers. Amorphous metal cores, introduced commercially in the 1980s, reduce no-load loss by a further 70 percent or so and are used where standing losses dominate lifetime operating cost.