SMPS Transformer Calculator
SMPS Transformer Calculator
Size a switch-mode transformer for a forward or flyback converter by the area-product method: the core area product Ap, primary and secondary turns for your core, wire gauges from the current density, the skin depth and, for a flyback, the air gap.
Transformer core and windings
Forward converter, 100 W at 12 V from a 36 V minimum input, 90% efficient, 0.5 V diode, 100 kHz, 45% duty, 0.2 T swing, 400 A/cm², Ku 0.4, a core with Ae = 97 mm²
Area product, turns and wire
- λ
- flux linkage per cycle: volt-seconds on the primary (forward) or inductance × peak current (flyback)
- B
- flux swing (forward) or peak flux density (flyback), in tesla
- Ku
- window utilisation: copper area ÷ window area
- J
- current density in the copper
- ρ
- copper resistivity at 100 °C, 2.27 × 10⁻⁸ Ω·m
Worked example
Forward converter, 100 W at 12 V from a 36 V minimum input, 90% efficient, 0.5 V diode, 100 kHz, 45% duty, 0.2 T swing, 400 A/cm², Ku 0.4, a core with Ae = 97 mm²
Pin = 100 ÷ 0.9 = 111.1 W; primary pulse 6.859 A, RMS 4.601 A; secondary RMS 5.590 A
Ns/Np = 12.5 ÷ (36 × 0.45) = 0.7716; λ = 36 × 0.45 ÷ 100 kHz = 162 µV·s
Ap = 162 µV·s × (4.601 + 0.7716 × 5.590) ÷ (0.2 × 0.4 × 4 × 10⁶ A/m²) = 0.451 cm⁴
Np = 162 µV·s ÷ (0.2 T × 97 mm²) = 8.35 → 9 turns; Ns = 9 × 0.7716 → 7 turns
Wire: primary 1.150 mm² → AWG 16, secondary 1.398 mm² → AWG 15; skin depth 0.240 mm, so use 8 and 9 strands of AWG 25
Choosing a core and windings by area product
A transformer’s core has two jobs. Its cross-section Ae carries the flux, and Faraday’s law sets how many turns it needs to keep the flux density within bounds: N = V·t ÷ (B·Ae). Its window Wa holds the copper, and the turns multiplied by the wire area set by your current density must fit in it with room for the bobbin and insulation. Multiply the two and the turns cancel: the product Ap = Wa·Ae depends only on the power, frequency, flux density, current density and fill factor. That is McLyman’s area-product method: work out Ap, pick the smallest core whose datasheet Ap is larger, then design the turns for that core’s Ae.
Forward or flyback. In a forward converter the transformer passes energy straight through; the flux swings once per cycle by Vin·D/f per turn, so B here is the swing. In a flyback the transformer is a coupled inductor that stores the energy in an air gap, and B is the peak flux at the peak primary current: Np = Lm·Ipk ÷ (B·Ae). For the same power a flyback needs a bigger core, because it must store the energy as well as pass it on (the example becomes 0.613 cm⁴ as a flyback at 0.25 T). The gap shown ignores fringing, which lets a real gap be somewhat longer for the same inductance.
Wire and skin effect. Each winding’s copper area is its RMS current divided by the current density; the page rounds up to the next American Wire Gauge size using ASTM B258’s diameter formula. At high frequency the current crowds into a skin about δ deep (0.240 mm at 100 kHz in copper at 100 °C). A round wire much thicker than 2δ wastes copper, so the page also gives the thickest strand no wider than 2δ and how many of them in parallel, or in litz, carry the same current. Proximity effect between layers can matter more than skin effect in multilayer windings; Dixon’s handbook covers it.
Check the result. Turns are rounded up, which lowers the flux density shown; confirm the core loss at that flux and frequency from the ferrite’s loss curves, and that the windings fit once insulation and, for mains designs, safety margins are included. The converter itself is designed on the forward converter calculator and the flyback converter calculator. Mains voltage can kill. This page does the arithmetic only; for anything connected to the supply, follow your local electrical code and have the work done or checked by a licensed electrician.
Frequently asked questions
What is the area product of a transformer core?
The window area times the effective core area, Wa × Ae, usually in cm⁴. It measures how much power a core can handle at a given frequency, flux density and current density.
How do you calculate the number of primary turns?
From Faraday’s law: Np = Vin × ton ÷ (B × Ae) for a forward, or Lm × Ipk ÷ (Bmax × Ae) for a flyback, rounded up. The forward example gives 8.35, so 9 turns.
What wire gauge do I need for a transformer winding?
Divide the winding’s RMS current by the current density to get the copper area, then take the next AWG size up. 4.601 A at 400 A/cm² needs 1.150 mm², AWG 16.
When does skin effect matter in a transformer?
When the wire is thicker than about twice the skin depth, which is about 7.6/√f cm in copper at 100 °C: 0.240 mm at 100 kHz. Use litz wire or parallel strands.
Related calculators
References
- McLyman CWT. Transformer and Inductor Design Handbook, 4th ed. CRC Press, 2011. The area product Ap = Wa·Ac, window utilisation Ku, current density and core selection.
- Dixon LH. Magnetics Design Handbook. Texas Instruments (Unitrode) SLUP132, 2001. Winding losses and penetration (skin) depth, about 7.6/√f cm in copper at 100 °C.
- ASTM B258-18. Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors. ASTM International.
- Fairchild Semiconductor (now onsemi). Design Guidelines for Off-line Flyback Converters Using Fairchild Power Switch (FPS). Application note AN-4137, 2003. Ripple factor KRF and Lm.
- Choi H-S. Design Guidelines for Off-line Forward Converters Using Fairchild Power Switch (FPS). Fairchild Semiconductor (now onsemi) application note AN-4134, 2003. Reset-winding duty limit Dmax ≤ Np/(Np + Nr), drain stress VDC,max(1 + Np/Nr), turns ratio and output inductor.