Leakage Inductance Analysis
Theory: magnetic energy stored between windings
Overview
In my flyback supply, the switch sees a big voltage spike at turn-off, right at its voltage rating. Is the transformer to blame?
Probably leakage inductance. Most flux from the primary goes through the core and links the secondary, but some passes through the gap between windings and doesn't. That energy can't transfer to the secondary, so at turn-off it has nowhere to go and becomes a voltage spike. Its value is set mostly by winding arrangement and spacing, so how you wind the transformer changes it a lot.
Calculation from magnetic energy
$\mathcal{F}(x)$ is the magnetomotive force (per ampere) at position $x$ across the winding build, MLT the mean length of turn and $h_w$ the winding height. MMF rises through the primary, peaks between windings and returns to zero through the secondary. The area under its square sets the leakage inductance.
Formula for side-by-side windings
$g$ is the gap between windings and $a_1, a_2$ the primary and secondary build thicknesses. The gap counts in full, the winding thicknesses by a third. It scales with turns squared, so more turns raise it quickly.
Leakage flux isn't always the villain
Leakage inductance is disliked as a source of loss and spikes, yet some designs enlarge it deliberately. Neon-sign and discharge-lamp transformers wind primary and secondary apart so leakage inductance naturally limits current. Arc-welding transformers apply the same idea, some moving part of the core to adjust leakage flux and thus welding current. Modern resonant (LLC) converters absorb leakage inductance into the resonant tank, saving a component.
Worked examples
Example 1: arrangement and gap
Primary 20 turns, mean turn length 60 mm, winding height 20 mm, primary and secondary builds 2 mm each (referred to the primary):
| Inter-winding gap | P | S | P/2 | S | P/2 | Ratio |
|---|---|---|---|
| 0.5 mm | 2.76 μH | 0.88 μH | 0.32 |
| 1.0 mm | 3.52 μH | 1.26 μH | 0.36 |
| 2.0 mm | 5.03 μH | 2.01 μH | 0.40 |
Just splitting the primary around the secondary cuts it to about a third.
Yes. Sandwiching splits the MMF peak into two, each half as tall. Energy goes with the square of height, so the total drops sharply. But there are now two gaps, so wider gaps dilute the benefit (0.40 at 2 mm). In supplies where safety standards demand insulation distance between primary and secondary, the gap can't shrink, and interleaving helps less.
Example 2: loss in a flyback
| Condition (2.76 μH) | Leakage loss |
|---|---|
| 5 A peak, 100 kHz | 3.5 W |
| 5 A peak, 200 kHz | 6.9 W |
| 10 A peak, 100 kHz | 13.8 W |
In a flyback, leakage energy fails to reach the secondary at each turn-off and is dissipated in a snubber (unless recovered). It scales with frequency and current squared, so several watts in a 50 W-class supply is not unusual. Cutting leakage inductance to a third cuts this loss by the same factor.
Analysis and measurement
Analysis approach
- Estimate with the formula above and compare arrangement options.
- Use 2D (axisymmetric) magnetic analysis: short the secondary, drive the primary and compute from stored energy.
- Correct for winding ends and portions outside the core with 3D analysis.
- At high frequency, current crowding in the windings slightly lowers leakage inductance; solve at the operating frequency if needed.
Measurement
Measuring primary inductance with the secondary shorted gives approximately the leakage inductance. Long shorting leads add their own inductance, so short with thick, short connections.
“Prototype and production leakage differ”
A hand-wound prototype had low leakage, but production units had twice as much and burned their snubbers. Changes in the number of insulating tape layers or how neatly winding ends are aligned alter the gap $g$ and winding height $h_w$. As the formula shows, the gap counts in full, so going from 0.5 to 1 mm adds nearly 30%. Specify gap and winding method on production drawings and control it by sample measurements of shorted inductance.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Uncontrolled winding gap | Leakage varies in production | Specify and measure |
| Long shorting leads | Leakage over-measured | Short, thick shorts |
| Snubber without leakage estimate | Snubber overheats | Estimate loss with ½LI²f |
| Ignoring interleaving capacitance | Noise and ringing | Evaluate capacitance too |
| Using 2D values as-is | End effects missed | Correct with 3D |
I'd like to try transformer and flyback calculations myself.
Try the flyback converter tool for flybacks and the transformer design tool and transformer magnetics tool for transformer design. Related topics are covered in transformer equivalent circuits, high-frequency transformers, winding loss and planar transformers.
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