120 to 220 Volt AC Conversion Equations

Alternating Voltage

• Voltage varies along with the alternating current. Voltages can be described as root mean square (RMS). "TAB Electronics Guide to Understanding Electricity and Electronics" states "AC voltages are always assumed to be V rms values unless otherwise stated." Alternating current voltages are phase shifted by 120 degrees. The phase-shifted voltage can be phase shifted forward or backward from the primary voltage. The line voltage magnitude is equal to the square root of three multiplied by the phase voltage.

Phase Voltage Conversion

• Convert the phase voltage to the line voltage by dividing the phase voltage by the square root of three. A 220 volt line voltage divided by the square root of three yields a phase voltage of 127 volts. A 120 volt line voltage divided by the square root of three, or 1.73205, equals a 69.28 phase voltage.

Efficiency

• When voltage is converted, a fraction of the energy is lost. The energy efficiency of the power conversion equals the power out divided by the power in. The voltage out multiplied by the current out is divided by the voltage in by the current in. For a 120 to 220 volt AC conversion where the current stays at 100 amps, the efficiency is 120 x 100 divided by 220 x 100 or 12,000 divided by 22,000 for an efficiency of 0.545 or 54.5 percent.

Power Loss

• Power lost during conversion equals power out minus power in. Power equals voltage times current. Voltage out times current out minus the voltage in times the current in equals the power lost. For a 120 to 220 volt AC conversion, power lost is 220 multiplied by the current out minus 120 times the outgoing current. For a 220 to 120 volt AC conversion, power lost is 120 multiplied by the current out minus 220 times the outgoing current.

Current

• Primary current equals the voltage divided by the wire resistance. A 220 volt current on a 12 ohm wire arrives at the transformer with 220 divided by 12 for 18.33 amps. For a 120 volt current on a wire with resistance of 10 ohms, the current will be 120 divided by 10 for 12 amps of current. Current in amps also equals the power in watts divided by the voltage and the cosine of the phase angle.