Bay note 03 — Turns, AL and the gap (flyback math that sticks)
From Faraday to AL·N² with a full numerical strip: primary turns, secondary turns, gap intuition and why AL is the number on the core box.
This is the calculation we run before the first turn of wire. It is not software magic — it is Faraday, AL and a gap that stores the energy.
Faraday — primary turns
Np = (Vin(min) × Dmax) / (Ae × ΔB × fsw) (volt-second balance)
Using the 65 W example: Vin(min)=127 V, Dmax=0.45, Ae for EE30 ≈ 60 mm² = 6.0×10⁻⁵ m², ΔB=0.2 T, fsw=65 kHz:
Np = (127 × 0.45) / (6.0e-5 × 0.2 × 65000) ≈ 57.2 / 0.78 ≈ 73 turns
Round to 72–76 turns primary depending on bobbin fills. We re-check flux on the sample with the actual Ae of the core set you approve.
AL and inductance
Ungapped ferrite AL is huge; flybacks need a gap so energy lives in air:
Lp = AL × N²
Target Lp ≈ 320 µH with N=72:
AL = Lp / N² = 320 µH / 5184 ≈ 62 nH/turn²
That AL is what we grind the centre-leg gap to. Quote AL on the print when you already know it — it saves a day of guessing.
Secondary turns
Idealised flyback ratio:
Ns / Np ≈ (Vout + Vf) × (1 − Dmax) / (Vin(min) × Dmax)
24 V out, Vf≈0.7 V, Dmax 0.45:
Ns ≈ 72 × (24.7 × 0.55) / (127 × 0.45) ≈ 72 × 13.6 / 57.2 ≈ 17 turns
Gap intuition (not a substitute for AL)
Rough air-gap: lg ≈ (µ0 × N² × Ae) / Lp (SI). We still verify on an LCR meter at operating bias — not only at 100 kHz and 0 A.
What to put on the print
- Target Lp and Ipk (or energy)
- Ae / core P/N if chosen
- Turns sketch if you have one — we will still check AL
- Probe points for sample test (Lp at Ibias)
Ask for a custom winding via contact with these numbers and we return a gapped core proposal.