What is the difference between a flyback and a forward transformer?

A flyback transformer stores energy in its gapped core during the switch on-time and releases it to the output during the off-time, acting as coupled inductors. A forward transformer transfers energy directly while the switch is on and needs no air gap, but requires a reset mechanism and an output inductor.

Why does the flyback design include an air gap?

A flyback must store magnetic energy each cycle, and an ungapped ferrite core would saturate at very little current. Introducing an air gap lowers the inductance and dramatically raises the energy the core can store before saturating, which is essential to flyback operation.

What is skin depth and why does it affect wire choice?

At high switching frequencies current crowds toward the surface of a conductor, leaving the center unused; skin depth is the effective penetration distance. If a wire is much thicker than twice the skin depth the extra copper is wasted, so litz wire or paralleled thin strands are often used instead.

What does the Steinmetz equation estimate?

The Steinmetz equation estimates volumetric core loss from the switching frequency and the peak flux swing using empirical material coefficients (k, α, β). Multiplied by the core volume it gives the hysteresis and eddy-current loss in watts, a major part of total transformer loss at high frequency.

SMPS Transformer Calculator

Topology

Vin Min

Vin Max

Vout

Iout

Switching Frequency

kHz

Max Flux Density (Bmax)0.30 T

Ferrite Core

Output Power48.0 W

Efficiency98.8%

Turns Ratio (Np:Ns)14:3

Transformer Design

Primary Turns (Np)14

Secondary Turns (Ns)3

Core Loss0.582 W

Copper Loss0.006 W

Wire Gauge (Primary)AWG 10

Skin Depth0.209 mm

Air Gap0.14 mm

Window Utilization94.5%

Primary RMS Current1.08 A

Core: ETD34

Ae: 97 mm²Aw: 123 mm²Ve: 7,640 mm³le: 78.6 mmAL: 3,100 nH/N²Weight: 40 g

The transformer is the heart of a switch-mode power supply, setting the turns ratio, storing or transferring energy, and contributing the bulk of the losses. This calculator designs a flyback or forward converter transformer on a chosen ferrite core: it derives the turns from Faraday's law, estimates core loss with the Steinmetz equation, sizes wire against skin depth, computes the flyback air gap, and reports an efficiency estimate.

Formula

Np = (Vin_min × Dmax) / (fsw × Bmax × Ae); Pv = k · f^α · Bpeak^β

Vin_min: Minimum input voltage (V)
Dmax: Maximum duty cycle (0.45 in this tool)
fsw: Switching frequency (Hz)
Ae: Core effective cross-sectional area (m²)
Pv: Steinmetz volumetric core loss; k=16.9, α=1.46, β=2.75 for N87 ferrite, Bpeak = ΔB/2

How it works

Enter the topology, the minimum and maximum input voltage, output voltage and current, switching frequency, peak flux density Bmax, and select a ferrite core from the built-in library (with its Ae, Aw, and Ve).
The engine fixes a maximum duty cycle of 0.45, derives the turns ratio and primary turns from Faraday's law (Np = Vin·D / (fsw·Bmax·Ae)), and computes the secondary turns to realize that ratio.
It then finds the primary RMS current, picks a wire gauge at 4 A/mm² limited by skin depth, applies the Steinmetz equation for core loss and I²R for copper loss, sizes the air gap for flyback energy storage, and returns window utilization and efficiency.

Worked example

A flyback transformer: 36–72 V input, 12 V / 5 A output (60 W), 100 kHz switching, Bmax 0.2 T, on an ETD34 core (Ae = 97 mm²).

Turns ratio at Dmax 0.45: (36 × 0.45) / (12.5 × 0.55) ≈ 2.36; with integer turns it settles at 9:4 = 2.25.
Primary turns: ceil((36 × 0.45) / (100000 × 0.2 × 97e-6)) = ceil(8.35) = 9; secondary = 4.
Skin depth at 100 kHz: 66.2 / √100000 ≈ 0.209 mm. Primary RMS current ≈ 3.19 A.
Steinmetz core loss ≈ 0.19 W, copper loss ≈ 0.02 W, giving an efficiency estimate near 99.6% for the transformer alone.

Turns 9:4 (ratio 2.25), core loss ≈ 0.19 W, copper loss ≈ 0.02 W, air gap ≈ 0.41 mm, window utilization ≈ 0.72, transformer efficiency ≈ 99.6%.

Frequently asked questions

What is the difference between a flyback and a forward transformer?: A flyback transformer stores energy in its gapped core during the switch on-time and releases it to the output during the off-time, acting as coupled inductors. A forward transformer transfers energy directly while the switch is on and needs no air gap, but requires a reset mechanism and an output inductor.
Why does the flyback design include an air gap?: A flyback must store magnetic energy each cycle, and an ungapped ferrite core would saturate at very little current. Introducing an air gap lowers the inductance and dramatically raises the energy the core can store before saturating, which is essential to flyback operation.
What is skin depth and why does it affect wire choice?: At high switching frequencies current crowds toward the surface of a conductor, leaving the center unused; skin depth is the effective penetration distance. If a wire is much thicker than twice the skin depth the extra copper is wasted, so litz wire or paralleled thin strands are often used instead.
What does the Steinmetz equation estimate?: The Steinmetz equation estimates volumetric core loss from the switching frequency and the peak flux swing using empirical material coefficients (k, α, β). Multiplied by the core volume it gives the hysteresis and eddy-current loss in watts, a major part of total transformer loss at high frequency.

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