Transformers & Magnetic Components

A transformer transfers AC energy through mutual flux; an inductor deliberately stores energy in its magnetic field. Both are constrained by Faraday's law,

$$v=N\frac{d\Phi}{dt},$$

so flux change is the applied volt-seconds per turn. This is why frequency, duty ratio, reset interval, and transient asymmetry are core design variables rather than only waveform details.

Ideal relations and real currents #

For tightly coupled ideal windings,

$$\frac{V_1}{V_2}=\frac{N_1}{N_2},\qquad N_1I_1\approx N_2I_2.$$

Real primary current also contains magnetizing current; leakage inductance represents flux not shared by both windings. Winding resistance causes copper loss, core hysteresis and eddy currents cause core loss, and interwinding capacitance transfers common-mode current.

Volt-second balance and saturation #

Periodic steady state requires average winding voltage to be zero over a cycle. A small DC component can walk flux toward saturation, where magnetizing inductance collapses and current rises sharply. Single-ended converters require an explicit reset path; push-pull/bridge drives require symmetry or current-mode mechanisms that prevent flux walking.

For constant winding voltage over interval $t_{on}$,

$$\Delta B=\frac{Vt_{on}}{NA_e},$$

where $A_e$ is effective core area. Worst-case input voltage, maximum duty, minimum frequency, startup, and fault pulses belong in the calculation.

Gap and energy storage #

Adding an air gap raises reluctance, lowers inductance per turn, and moves much of stored energy into the gap where saturation is controllable. This is appropriate for inductors and flyback coupled inductors. A conventional transformer ideally transfers energy instantaneously and minimizes stored leakage energy.

Insulation and parasitics #

Turns ratio does not prove galvanic isolation. Creepage, clearance, wire system, interlayer insulation, hipot test, partial discharge where applicable, temperature class, and construction determine the barrier. Shielding can reduce one coupling path while increasing capacitance elsewhere.

Diagnose saturation using current waveform shape: a late-cycle current knee tracks volt-seconds and core state; an immediate edge spike more often indicates capacitance or leakage ringing. Verify current, flux-balance proxy, temperature rise, regulation, leakage transient, and insulation construction under worst-case steady and transient conditions.