Flyback turns ratio

Part 21 · Voltage Regulation · page 1 of 3

Key point: \(N=N_p/N_s\) scales voltage and current. On the same core \(L_p/L_s=N^2\), so an LCR meter recovers \(N=\sqrt{L_p/L_s}\), not \(L_p/L_s\). A flyback stores, then dumps.

\(A_L=80\,\mathrm{nH/t}^2\). Orange is the primary. Green is the secondary. They are never on together.

1
Same turns. Store, then dump.
Np 8, Ns 8, VIN 12 V, D 0.40. N is 1.00. Lp and Ls are both 5.12 µH. Lp/Ls is 1.00. VOUT is 8.00 V. Orange charges the core. Then green dumps it. A forward transformer would have both windings on at once. This one does not.
2
The L ratio is the square.
Np 16, Ns 8. N is 2.00. Lp is 20.5 µH. Ls stays 5.12 µH. Lp/Ls is 4.00. √(Lp/Ls) is 2.00, the same number as N. VOUT is 4.00 V. Measure 20 µH and 5 µH and you do not have a 4:1 transformer. You have 2:1.
3
Halve Ns and the trap gets worse.
Ns 4. N is 4.00. Lp stays 20.5 µH. Ls is 1.28 µH. Lp/Ls is 16.00. √(Lp/Ls) is 4.00. VOUT is 2.00 V. Dividing the two meter readings gives 16. That is not the turns ratio. Take the square root.
4
Amp-turns match at the handoff.
Back to 16:8. D 0.50. VOUT is 6.00 V. The sketch peak is 1.20 A primary and 2.40 A secondary. 16×1.20 and 8×2.40 are both 19.2. Pause on the edge and the two bars match. ½Lp ip² equals ½Ls is². The square in L and the square in current cancel.
5
Duty moves VOUT. The meter ratio does not.
D 0.70, still 16:8. VOUT is 14.00 V. N is still 2.00. Lp/Ls is still 4.00. CCM here is VOUT = VIN × (Ns/Np) × D/(1−D). The LCR reading did not change.

Leakage is not in \(A_L\). The clamp and BCM control are not drawn. Page 2 is the parabola.

Store, then dump · N vs N²

Turns are the side of the square. Inductance ratio is the area.

Np turns Ns turns VIN V D —

Q1 on · core charging

Turns N vs inductance N²

0 %

N = N_p/N_s—

L_p—

L_s—

L_p/L_s = N²—

√(L_p/L_s)—

VOUT—

Gold packet: store then dump. Square: the side is turns ratio \(N\); the area is inductance ratio \(N^2\). An LCR meter gives you the area — take the square root.

Same-core solver

Type what you know — measured \(L\), turns, or \(A_L\). Same core: \(L=N^2 A_L\). Green cells are solved.

N_p turns N_s turns N = N_p/N_s L_p µH L_s µH A_L nH/t²

Enter any two of N_p, N_s, N — or L_p and L_s from an LCR meter.