Advanced: Transformer Theory
Faraday's law
Induced voltage is proportional to turns and the rate of change of magnetic flux.
Sinusoidal design equation
For fixed voltage, turns, and core area, lowering frequency raises required flux density and risks saturation.
Equivalent circuit
A practical model includes winding resistances, leakage inductances, magnetizing inductance, core-loss resistance, ideal turns ratio, and parasitic capacitances.
Reflected impedance
Copper loss
At high frequency, skin and proximity effects raise AC winding resistance above DCR.
Voltage regulation
Percent impedance
Power transformers often state percent impedance, closely related to the voltage required to circulate rated current with the secondary shorted under test conditions.
Three-phase power
Wye and delta connections change phase and line relationships and can introduce phase displacement described by transformer vector groups.
Inrush
Flux is related to the time integral of applied voltage. An unfavorable switching instant combined with residual flux can temporarily drive the core deep into saturation and cause very high magnetizing current.
High-frequency design
Switch-mode transformers use high frequency to reduce core and winding size, but leakage inductance, interwinding capacitance, skin depth, proximity effect, insulation geometry, and EMI become more important.
Thermal design
Transformer rating is ultimately a temperature problem as well as a magnetic one. Core loss and copper loss must keep the hottest winding and insulation within their permitted temperature at the specified ambient and cooling conditions.