Leakage InductanceEdit
Leakage inductance is a fundamental parasitic in power magnets that governs how efficiently energy can be transferred between windings. In practical devices such as Transformer and other Inductor with multiple windings, not all of the magnetic flux links every winding perfectly. The portion of inductance that does not couple to the other winding shows up as an additional series inductance in the equivalent circuit, and it has real consequences for performance, especially in high-frequency power electronics.
In a two-winding arrangement, leakage inductance appears as a series element on each winding and is driven by imperfect magnetic coupling. It arises from stray flux that follows paths that do not link the companion winding, from physical separation between windings, and from nonuniform current distribution in the windings themselves. While a certain amount of leakage is unavoidable, its magnitude is a key design parameter in many power-converter topologies, including Flyback converters and Forward converters, where it can influence switching transients, peak currents, and EMI.
Physical basis
The magnetic coupling between windings is quantified by a coupling coefficient k, which ranges below 1 for real devices. The mutual inductance M between windings, together with their self-inductances L1 and L2, satisfies M = k√(L1L2). Leakage inductances on the primary and secondary sides are then defined as the portions of L1 and L2 that do not participate in mutual coupling: - Llk1 = L1 − M^2/L2 - Llk2 = L2 − M^2/L1
When the windings are perfectly coupled (k → 1), these leakage terms vanish. In practice, typical values of leakage can be a few percent to a few tens of percent of the winding inductances, depending on geometry, winding techniques, and core design. The geometry that governs leakage includes the distance between windings, the layering pattern, winding direction, and the presence of return paths for the magnetic flux. Frequency effects such as skin and proximity effects can also make the effective leakage inductance appear to shift somewhat at high operating frequencies, as parasitic capacitances and conductor losses interact with the flux path. See also Mutual inductance and Coupling coefficient for related concepts.
Mathematical description
A standard small-signal model of a transformer with leakage uses an ideal transformer in series with leakage inductances. In a simple two-winding picture, the primary and secondary network can be written in terms of self-inductances L1, L2 and mutual inductance M. The leakage inductances are then: - Llk1 = L1 − M^2/L2 - Llk2 = L2 − M^2/L1
Equivalently, if the windings are similar (L1 ≈ L2 ≈ L and M ≈ kL with k ≈ 0.9–0.99 for good coupling), the leakage on each side is approximately L(1 − k^2). This makes leakage highly sensitive to the square of the coupling coefficient when the windings are closely matched. In many designs, the magnetizing inductance Lm (the portion of the inductance that links to the other winding) is conceptually separated from the leakage path in the equivalent circuit, yielding a representation that includes an ideal transformer, a magnetizing branch, and the two leakage inductances in series with their respective windings. See Transformer and Inductor for broader modeling context.
Impacts in power electronics
Leakage inductance plays a dual role depending on the topology: - In many switching power supplies, leakage inductance couples with parasitic capacitances to create voltage spikes when switches turn on or off. This can stress semiconductor devices and generate electromagnetic interference (EMI). Designers combat this with snubbers and clamps (for example, RCD snubber), careful layout, and sometimes active clamp schemes. - In forward and flyback topologies, leakage energy is energy that does not contribute to the intended transfer to the load and is typically lost as heat or radiated EMI unless paths exist to reclaim or limit it. Consequently, engineers strive to minimize leakage through winding techniques and core selection, and to tailor the switching waveform to minimize di/dt and ringing.
The exact role of leakage differs by topology: - In Flyback converter, energy is stored primarily in the windings during the on-time and released to the load during the off-time. Leakage contributes to peak currents and voltage stresses; effective control of leakage is important for reliability and efficiency. - In Forward converter, leakage energy must be managed during the switching transitions to prevent excessive voltage spikes on the primary switch, requiring appropriate clamping and layout strategies.
See also Snubber circuit for common methods of mitigating leakage-related transients, and Power electronics for broader context on how leakage inductance factors into design trade-offs.
Design considerations and mitigation
Because leakage is inherent in real devices, designers adopt strategies to limit its adverse effects: - Winding technique: tightly coupled, interleaved windings reduce leakage paths. Techniques such as bifilar or closely coupled windings on a single core leg help minimize stray flux paths. - Physical layout: placing windings as close together as possible, minimizing the distance between primary and secondary, and reducing return-path loop areas all reduce leakage. - Core and window design: selecting core materials and geometries that support compact, well-coupled windings improves coupling coefficient k and reduces Llk relative to L. - Controlled leakage in some specialized cases: while most designs aim to minimize leakage, there are niche applications and advanced energy-management schemes where leakage is leveraged in a controlled way or mitigated through active circuits.
In all cases, the leakage is described in the manufacturer’s data as part of the transformer’s or inductor’s parasitics, and it is included in simulations with the standard equivalent-circuit models that feature Llk1, Llk2, and the ideal transformer core. For modeling and simulation, see Mutual inductance and Coupled inductors to understand how non-ideal coupling is represented in circuit models.
Modeling and simulation
Accurate models of leakage inductance are essential for predicting switching behavior, EMI, and thermal load in power supplies. Designers use a combination of: - Empirical testing to extract L1, L2, M, and thereby Llk1, Llk2 for a given winding arrangement - Circuit-level models that place leakage inductances in series with the windings and an ideal transformer for the coupling - Electromagnetic field simulations to visualize flux paths and identify leakage paths in complex geometries
These models feed into time-domain simulations of switching transients, enabling optimization of layout and snubbing strategies before fabrication. See Transformer and Inductor for foundational modeling approaches, and Mutual inductance for the relationships among L1, L2, and M.