V1 0 VV2 0 VI1 0 AI2 0 AB_pk 0 TEfficiency 0 %Copper 0 WCore 0 WFPS 0

Drag to orbit, wheel or pinch to zoom. Blue lines are the magnetic flux in the iron: they brighten and reverse with B(t). Orange dots are the current in the primary (left) and secondary (right) coils. The two oscilloscopes show voltage (amber) and current (cyan) over one cycle, slowed down so you can watch it.

Transformer Bench: Core Flux, Saturation, Copper Loss and Lamination Eddy Loss

The primary coil makes a changing flux in the iron, the flux makes a voltage in the secondary: V2/V1 = N2/N1. Then the real world arrives: wire resistance, leakage, iron that saturates and eddy currents that heat the core.

Supply and turns

Load

Construction

Display

Live readouts

Efficiency against output power

Efficiency peaks where copper loss (grows with I²) equals core loss (almost constant). The dot marks the present load.

Magnetisation curve B(H)

The flux density swings between the two marked dots each cycle. Past the knee a small increase of B needs a big increase of H: the magnetising current becomes peaky.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. The view buttons jump to the front, the coils, a top view and a core close-up.
Supply and turns set the primary voltage, frequency and the number of turns N1, N2. Fewer primary turns mean more flux: watch B_pk and the saturation warning.
Load sets the resistance and power factor of what the secondary feeds. Construction sets lamination thickness, copper cross-section and leakage.
Display speed only changes how fast the picture runs; it does not change the physics (real frequency is shown in Hz).
The coil and core glow is a loss indicator, not to scale. Virtual bench only: real mains transformers are dangerous.

The science

Faraday's law. The emf in a winding is e = N dΦ/dt. For a sine supply the rms voltage and the peak flux density are tied by V = 4.44 f N B_pk A, so a core of area A carries B_pk = V/(4.44 f N A). With the same core flux linking both windings, V2/V1 = N2/N1 and (ampere-turns balance) I1 N1 ≈ I2 N2.

Equivalent circuit. Referred to the primary: winding resistance R1 and leakage reactance X1 in series, then the magnetising branch (R_c for core loss in parallel with X_m), then the secondary R2', X2' and the load. We solve it with complex phasors and iterate, because X_m and R_c depend on the flux.

Saturation. The iron is modelled as B = B_s tanh(μ₀ μ_r H / B_s) (μ_r = 7000, B_s = 2.0 T). The magnetising current is i_m = H l_c / N1, found point by point over a cycle, so near the knee the current waveform becomes peaked and X_m falls (we use the fundamental).

Losses. Copper: I1² R1 + I2² R2, with R = ρ N l_turn / A_w (ρ = 2.1e-8 Ω m, hot copper, 0.30 m per turn). Core: hysteresis k_h f B^1.8 per kg plus classical eddy current loss π² σ t² f² B² / (6 ρ_d) per kg for laminations of thickness t (σ = 2 MS/m, ρ_d = 7650 kg/m³). Halving the lamination thickness cuts the eddy loss by four; that is why cores are stacks of insulated plates.

Simplifications. Single-valued B(H) (the hysteresis loop width enters only through k_h), classical eddy loss (valid only when t is much less than the skin depth, so the slider stops at 1 mm), no temperature feedback, no inrush transient, no capacitance, no harmonics in the load, leakage lumped. Coil turn counts drawn in 3D are fixed (18 and 30) and are not the N1 and N2 you set. The sliders use model values, not a particular product. Models built with Blender, scene by Three.js.