Interleaved Windings: Taming Parasitics in High-Frequency Transformers

In the world of high-frequency power electronics, the transformer is a critical component, but its real-world behavior is far from the ideal models found in textbooks. Unwanted parasitic effects, primarily leakage inductance and interwinding capacitance, introduce significant challenges, leading to voltage spikes, wasted energy, and electromagnetic interference (EMI). This article delves into interleaved windings, a fundamental and elegant geometric technique used by engineers to tame these parasitics. By understanding and mastering this method, designers can dramatically improve transformer performance. The following chapters will first explore the principles and mechanisms of interleaving, dissecting how it alters the magnetic and electric fields within the transformer. We will then shift perspective in the second chapter, Applications and Interdisciplinary Connections, to see how these once-unwanted parasitics are masterfully harnessed as functional components in advanced power converter designs.

In the pristine world of textbook physics, a transformer is a perfect messenger. It takes electrical energy, bundles it into a magnetic field perfectly confined within its iron core, and delivers it to the other side, altering only its voltage and current. But in the real world, as any engineer knows, our components are not so perfectly behaved. The magnetic field, it turns out, is a bit of a wanderer. And in this tendency to stray lies a host of challenges that demand clever solutions. The most elegant of these solutions is a technique known as ​​interleaved windings​​. To understand its genius, we must first appreciate the problem it solves.

Imagine the current flowing through the primary winding of a transformer. It generates a magnetic field, or ​​magnetic flux​​. Most of this flux is well-behaved; it follows the path of least resistance—or more accurately, least reluctance—through the high-permeability material of the transformer core, dutifully linking the secondary winding and enabling energy transfer. This is the ​​magnetizing flux​​, and it is associated with the transformer's ​​magnetizing inductance​​ ($L_m$). This is the inductance you would measure across the primary winding if you left the secondary disconnected—an open circuit. It's a fundamental property related to the core's material and shape, and designers can control it, for instance, by introducing a tiny air gap in the core.

However, some of the flux lines decide not to take the guided tour through the core. They spill out into the surrounding air and insulation, looping from the primary winding back on themselves without ever greeting the secondary. This stray flux is the ​​leakage flux​​. It represents energy that is stored but not transferred. This effect gives rise to an unwanted inductance in series with our ideal transformer, aptly named ​​leakage inductance​​ ($L_{\ell}$). You can feel its presence when you measure the primary inductance with the secondary winding short-circuited; the large magnetizing inductance is effectively bypassed, leaving you with the much smaller leakage inductance.

While small, this leakage inductance is the villain of our story. It stores energy that, when a switch in the circuit abruptly tries to stop the current, has nowhere to go. This trapped energy, $\frac{1}{2}L_{\ell}I^2$, unleashes itself as a damaging voltage spike, generates electromagnetic noise (EMI), and dissipates as wasted heat in protective "snubber" circuits. To build efficient, reliable high-frequency power converters, we must tame this leakage flux.

Leakage inductance is not a property of the core material, but of geometry. It is born in the space between the windings. In a simple transformer, one might wind all the primary turns first, and then wind the secondary turns on top. This creates a distinct separation between the bulk of the primary current and the bulk of the secondary current. It is in this separating space that the leakage flux thrives.

​​Interleaving​​ is the simple, yet profound, technique of breaking up the primary and secondary windings into sections and stacking them in an alternating fashion. Instead of a simple Primary-Secondary (P-S) stack, a designer might use a Primary-Secondary-Primary (P-S-P) arrangement, or even a more complex P-S-P-S structure. The goal is to bring the opposing currents of the primary and secondary into the most intimate proximity possible. The result of this simple geometric rearrangement is remarkable.

To see why interleaving is so effective, we can turn to one of the pillars of electromagnetism: Ampère's Law, which in a simplified form states that the magnetic field ($H$) integrated around a closed loop is proportional to the electric current passing through that loop ($\oint \vec{H} \cdot d\vec{l} = I_{\text{enc}}$).

Imagine looking at a cross-section of the windings. In a non-interleaved (P-S) structure, the total current, or ​​magnetomotive force (MMF)​​, builds up through the entire primary stack and then reverses through the secondary stack. This creates a large region between the P and S blocks where a strong magnetic field exists, representing the stored leakage energy.

Now, consider an interleaved P-S-P structure. The MMF builds up through the first primary section, but it is then almost immediately cancelled by the opposing MMF of the adjacent secondary section. The magnetic field in the window space is dramatically reduced because the opposing currents are constantly cancelling each other's external field.

The energy stored in a magnetic field is proportional to the square of the field strength ($H^2$). Since interleaving drastically reduces $H$, it has an outsized effect on the stored energy. Let's consider a simple thought experiment. Imagine a non-interleaved transformer where the leakage field has strength $H$ in a single gap between the windings. Now, let's split the primary winding in two and sandwich the secondary in between (a P/2-S-P/2 arrangement). As derived from first principles, this arrangement effectively halves the MMF across each of the two new gaps, reducing the field strength in each to $H/2$. The energy density ($\propto H^2$) in each gap drops to one-quarter of its original value. Although we now have two such gaps, the total stored energy—and thus the leakage inductance—is halved! This tighter magnetic coupling between the windings is reflected in a higher ​​coupling coefficient​​ ($k$), a measure of how effectively the flux is shared, pushing it closer to the ideal value of 1.

The reduction of this stray magnetic field has another, less obvious, but equally important benefit. When a conductor is subjected to a time-varying magnetic field, that field induces circulating currents within the conductor itself—​​eddy currents​​. These currents, caused by the field from other nearby windings, are known as the ​​proximity effect​​. They flow uselessly, generating heat ($I^2R$ loss) and dramatically increasing the AC resistance of the windings, which can cripple a transformer's efficiency at high frequencies.

The strong leakage field in a non-interleaved design is a perfect breeding ground for proximity-effect eddy currents. By cancelling this field, interleaving starves the proximity effect at its source. In a beautifully symmetric interleaved arrangement (like P/2-S-P/2), the central secondary layer finds itself in a region where the magnetic fields from the two primary halves almost perfectly cancel. It experiences virtually no external AC field. A simple analysis shows that for a specific idealized case, this arrangement can reduce the total proximity-effect losses by a factor of four compared to its non-interleaved counterpart. Interleaving doesn't just improve the ideal transformer action; it makes the conductors themselves behave more ideally.

It seems too good to be true, and in physics, there is rarely a free lunch. Interleaving vanquishes the leakage inductance, but in doing so, it summons another parasitic foe: ​​capacitance​​.

The primary and secondary windings, being conductive layers separated by an insulator, form a capacitor. The capacitance is described by the familiar formula $C = \varepsilon A/d$, where $\varepsilon$ is the permittivity of the insulation, $A$ is the overlapping surface area of the conductors, and $d$ is the distance between them. Interleaving, by its very nature, increases the face-to-face surface area ($A$) between primary and secondary conductors. For instance, a P-S-P structure effectively creates two capacitors in parallel, roughly doubling the total interwinding capacitance ($C_{pw}$) compared to a simple P-S stack.

This increased capacitance is a serious problem. In a switching converter, the primary winding voltage changes at an enormous rate (high $dv/dt$). This rapidly changing voltage drives a ​​displacement current​​ through the parasitic capacitance, given by $I_{cm} = C_{pw} \frac{dv}{dt}$. This current bypasses the magnetic isolation of the transformer, flowing directly into the secondary side and creating common-mode electromagnetic interference (EMI) that can disrupt other electronic systems. Furthermore, this capacitance must be charged and discharged every switching cycle, which dissipates power ($P \propto f C V^2$), lowering the converter's efficiency.

Here we arrive at the heart of the engineering challenge: a fundamental trade-off. Interleaving reduces leakage inductance ($L_{\ell}$) but increases parasitic capacitance ($C_{pw}$). Which is more important to minimize? The answer, unsatisfyingly but truthfully, is: "It depends."

• In a topology like a ​​flyback converter​​, leakage inductance is an unmitigated disaster. The energy trapped in it must be burned off in a snubber circuit every single cycle. For these designs, minimizing $L_{\ell}$ is paramount, and heavy interleaving is often the right choice.

• In a ​​phase-shifted full-bridge (PSFB) converter​​, the story is far more nuanced. Here, the leakage inductance is cleverly used as part of a resonant circuit to achieve ​​zero-voltage switching (ZVS)​​, a technique that allows the switches to turn on with no voltage across them, eliminating a major source of switching loss. To achieve ZVS, the energy stored in the leakage inductance ($\frac{1}{2} L_{\ell} I^2$) must be sufficient to charge and discharge the parasitic capacitances of the switches. If $L_{\ell}$ is too low (as in a heavily interleaved design), there may not be enough energy, especially at light loads, and ZVS will be lost. If $L_{\ell}$ is too high, the snubber losses become excessive.

This leads to a beautiful illustration of engineering design as an art of compromise. Consider a PSFB design with three constraints: keeping EMI below a limit, maintaining ZVS down to a certain load, and keeping snubber losses below a threshold. A ​​non-interleaved​​ design might have low enough capacitance to pass the EMI test and enough inductance to ensure ZVS, but its high leakage could cause it to fail the snubber loss test. A ​​fully interleaved​​ design would have excellent low snubber loss, but its huge capacitance might make it fail the EMI test, and its tiny inductance might make it fail the ZVS test. The optimal solution is often ​​partial interleaving​​—a carefully tailored compromise that provides just enough inductance reduction to manage losses, while keeping capacitance low enough to control EMI and still having enough inductance to maintain ZVS. It is not a matter of simply minimizing or maximizing a parameter, but of tuning it to the sweet spot where all requirements are met simultaneously.

Is there a way to break the $L_{\ell}$-$C_{pw}$ trade-off? One clever trick is the ​​Faraday shield​​. This is a thin, conductive foil placed in the gap between the primary and secondary windings. By connecting this shield to a stable ground potential, it acts as an interceptor. The displacement current from the primary now flows to the shield and is safely shunted to ground, never reaching the secondary. This dramatically reduces common-mode EMI, giving the designer the freedom to use heavy interleaving to crush leakage inductance without paying the usual EMI penalty.

But this elegant solution hides a deadly trap. The shield must be constructed with a small gap along its length so that it does ​​not​​ form a continuous, closed conductive loop around the magnetic core. If it does—say, through a manufacturing defect or an erroneous connection—it ceases to be an electrostatic shield and becomes a magnetic nightmare.

According to Faraday's Law of Induction, the time-varying magnetic flux from the primary will induce a voltage in this closed loop. Because the loop is a thick piece of copper, its impedance is extremely low. This induced voltage drives an enormous circulating current in the shield. By Lenz's Law, this current creates a powerful magnetic field that opposes the primary's own magnetizing field. To maintain its operation, the power supply must drive a colossal current into the primary just to fight the opposing field from the shorted shield. The transformer's input inductance plummets, the primary current skyrockets, and the massive current flowing in the shield dissipates tremendous power as heat ($P=I^2R$). What was intended as a subtle shield becomes a brute-force heater, and the transformer can quickly self-destruct. It is a stark reminder that in the world of high-frequency magnetics, even the smallest geometric details are governed by the fundamental laws of physics, with consequences that can be both elegantly useful and catastrophically destructive.

In our journey so far, we have dissected the inner workings of a transformer, treating its non-ideal behaviors—leakage inductance and parasitic capacitance—as departures from a perfect model. We viewed them as nuisances to be understood and, if possible, minimized. But now, we pivot. We will discover that in the sophisticated world of modern electronics, these "imperfections" are not merely problems to be solved; they are tools to be wielded. The art of high-frequency magnetics design lies not in fighting the quirks of reality, but in harnessing them, turning apparent bugs into elegant features. This chapter is about that transformation of perspective, where we graduate from being students of parasitics to becoming masters of them.

Leakage inductance, the embodiment of magnetic flux that fails to link both primary and secondary windings, represents energy that seems to get "stuck" in the space around the windings rather than being transferred to the load. In many simple applications, this is precisely the problem it appears to be.

Consider a transformer with multiple output windings. If the primary winding is not well-coupled to a secondary, the voltage delivered to that output will sag more under load than the others. This "poor cross-regulation" is a direct consequence of the energy drop across the leakage inductance. The classic solution is to force better magnetic intimacy between the windings. By interleaving them—for instance, by sandwiching a secondary layer between two halves of the primary winding—we force the opposing currents to flow in close proximity. Their magnetic fields, instead of ballooning out into the window space, largely cancel each other out, dramatically reducing the stored magnetic energy and thus the leakage inductance. This straightforward application of interleaving to improve coupling and regulation is a cornerstone of transformer design.

But what if this trapped energy was not a flaw, but a resource? This is the revolutionary idea behind modern resonant and soft-switching converters. Topologies like the LLC resonant converter or the Phase-Shifted Full-Bridge (PSFB) are designed to switch at incredibly high frequencies, but doing so with brute force would generate immense switching losses. Their secret is Zero-Voltage Switching (ZVS), a graceful maneuver where the power transistors are switched on only when the voltage across them is already zero. To achieve this, the converter needs a precisely valued inductor in the power path to store energy and "ring" the voltage at the switching node down to zero during a small dead time.

Instead of adding a separate, bulky inductor to the circuit, a clever engineer realizes that the transformer's own leakage inductance can be sculpted to perform this exact function. By intentionally designing the transformer with a specific, non-zero leakage inductance, we integrate a critical resonant component directly into the magnetic structure. This is no longer "unwanted" leakage; it is "intentional" leakage, a functional part of the circuit topology. The designer can achieve this by carefully controlling the winding geometry—for example, by adjusting the degree of interleaving or by setting a precise physical gap $g$ between winding layers—to tune the leakage inductance to the exact value needed, perhaps a few microhenries, to resonate with the parasitic capacitances of the transistors. This act of tuning turns the transformer from a simple power transfer element into a multi-functional resonant component, enabling higher efficiency, frequency, and power density.

This concept of harnessing leakage is so fundamental that it transcends the world of power conversion and finds a home in a seemingly unrelated field: electromagnetic interference (EMI) filtering. An EMI filter often requires a common-mode (CM) choke to block noise common to both power lines, and a differential-mode (DM) inductor to filter noise flowing in a loop. A CM choke is built with two windings on a single core, wound such that for common-mode currents, their fluxes add, creating high impedance. For differential-mode currents, their fluxes should ideally cancel, presenting zero impedance. But of course, they don't cancel perfectly. The imperfection is, once again, the leakage inductance. The total inductance seen by a differential-mode current is precisely twice the leakage inductance of a single winding. A designer can exploit this: by building a "leaky" CM choke with intentionally poor interleaving, one can create a component that serves as both a CM filter and a DM filter, a beautiful example of component integration born from a deep understanding of the underlying physics.

If interleaving is such a powerful tool, one might be tempted to think that the solution to every problem is simply "more interleaving." Reality, as always, is more subtle. The act of interleaving is not a simple knob for "goodness"; it is a control that often involves navigating a complex landscape of competing objectives and physical trade-offs. The true art of design lies in finding the optimal compromise.

The most fundamental trade-off is the duality of magnetic and electric fields. When we interleave windings, we push the layers of primary and secondary current closer together. This enhances magnetic coupling and reduces leakage inductance. However, by bringing these large conductive surfaces, often separated by a thin dielectric, closer together, we are also building a very effective capacitor. The more we interleave, the higher the parasitic primary-to-secondary capacitance, $C_{PS}$. In a high-frequency converter with fast-switching voltages, this capacitance provides a direct path for displacement currents ($i_d = C_{PS} \frac{dv}{dt}$), which are a primary source of common-mode noise and EMI. You might design a transformer with wonderfully low leakage, only to find it fails EMI testing spectacularly. The solution often involves a compromise: perhaps reducing the degree of interleaving to lower the capacitance, and accepting a modest, but tolerable, increase in leakage inductance. In many cases, the designer will insert a thin, grounded copper foil—an electrostatic or "Faraday" shield—between the primary and secondary. This shield doesn't stop the magnetic flux, but it intercepts the electric field lines, shunting the noisy displacement current safely to ground before it can pollute the secondary side.

The plot thickens when we have more than two windings. A transformer might have multiple secondaries for different voltage outputs, or auxiliary windings for control power or reset functions. Now, the question is not just whether to interleave, but what to interleave with what. Consider a forward converter that uses a "reset" winding to demagnetize the core when the main switch turns off. For a fast and efficient reset, the energy from the main magnetizing field must transfer quickly to the reset circuit. This requires extremely tight magnetic coupling (minimal leakage) between the primary and the reset winding. One might achieve this by winding them together in a bifilar fashion. At the same time, the reset process induces a sharp voltage swing that you want to isolate from the main secondary output to prevent stress on its rectifier. This requires loose coupling between the reset and secondary windings. The optimal design, therefore, involves selective coupling: create an intimately coupled primary-reset pair, and then physically separate this pair from the secondary winding. A similar logic applies to a planar transformer with multiple outputs. The highest-current secondary, where losses are most critical, is given the prime real estate, tightly interleaved with the primary for minimum leakage inductance and AC resistance. The lower-power, more sensitive secondaries can be placed further away, protected by electrostatic shields to prevent cross-coupling and interference from the high-power channel. It's a game of strategic placement, dictated by the unique role of each winding.

Finally, is there a limit? Can we just keep adding more and more interleaving sections, creating a perfect magnetic "lasagna" of alternating primary and secondary layers? Physics imposes a point of diminishing returns. As we increase the number of interleaving sections, say from a simple P-S-P sandwich to a P-S-P-S-P stack, we do indeed continue to reduce the AC resistance caused by proximity effects. However, each new primary-secondary interface we create adds another parallel-plate capacitor to the total interwinding capacitance. This capacitance can grow very quickly, and at some point, it will either exceed a limit dictated by EMI constraints or the design will run out of available layers in the circuit board stack-up. The optimal design is therefore not the one with the most interleaving, but the one that pushes right up against the most restrictive system constraint—be it capacitance, layer count, or manufacturing cost—to achieve the best possible performance within that boundary.

Our exploration of interleaving has taken us on a remarkable journey. We began with a simple technique to fix a basic flaw in an ideal model. We ended by discovering a sophisticated design parameter that allows an engineer to conduct a veritable symphony of electric and magnetic fields within the tiny volume of a transformer. We have seen how winding geometry can be manipulated to minimize a parasitic, to create a new component, to build a hybrid filter, and to navigate a delicate web of system-level trade-offs. The study of interleaving reveals the true nature of modern engineering: it is a deep and creative application of fundamental physics to create devices that are more efficient, more compact, and more elegant than their "ideal" counterparts could ever be.