Transformer Turns / Voltage / Current / Impedance Ratio

The transformer turns ratio a = Np/Ns, which equals the voltage ratio Vp/Vs, the inverse current ratio Is/Ip, and the square root of the impedance ratio, so a secondary load Zs reflects to the primary as a^2 x Zs. A 480-to-120 V unit is 4:1; 50 A on the secondary is 12.5 A on the primary, and an 8 ohm load looks like 128 ohm to the source. That a^2 impedance transformation is exactly how a 70 V speaker line or an audio output stage matches a load. Ideal lossless ratio; the winding resistance and leakage reactance that sag real voltage under load are the separate voltage-regulation check. A design aid; the nameplate governs.

a = Np/Ns = Vp/Vs = Is/Ip; Ip = Is/a; Zp = a^2 x Zs.

The ideal (lossless) transformer turns / voltage / current / impedance relations, first-principles; the nameplate and the manufacturer's data govern.

The ideal-transformer ratios are standard first-principles circuit relations; the voltages come from the nameplate.

Estimate. AHJ and licensed professional govern.

Field names used by the API: primary_voltage_v, secondary_voltage_v, secondary_current_a, load_impedance_ohm, turns_ratio, primary_current_a, reflected_impedance_ohm

• Ideal transformer lossless, unity coupling; a = Np/Ns = Vp/Vs = Is/Ipcircuit theory
• Impedance ratio a load reflects to the primary as a^2 times its valuecircuit theory
• Nameplate ratio no winding resistance or leakage reactance; those are the voltage-regulation tilescope of this tile