On Size and Magnetics: Why Small Efficient Power Inductors are Rare

Of the three main component types needed in power converters—switches, capacitors and inductors—the most difficult to integrate on a semiconductor chip or in a planar package is the inductors. This difficulty arises partly from process compatibility challenges with magnetic materials, and is exacerbated by the fact that, because most types of electronics don’t need inductors, there has been relatively little development effort. But a more fundamental challenge is the way magnetics performance scales with size.

Capacitors and semiconductor devices can be made from thousands of small cells connected in parallel, but that approach would severely undercut the performance of magnetic components.

In this work, we examine the scaling relationships for magnetics to demonstrate the inherent difficulty of small size and low profile magnetics. Cases considered include those with winding designs limited by skin and proximity effect and those constrained by efficiency and thermal dissipation. Small-scale magnetic components are typically limited by efficiency rather than heat dissipation. With efficiency constrained, and considering high frequency winding loss effects, it is shown that power density typically scales as the linear dimension scaling factor to the fifth power.

For the full analysis, see the attached paper, Sullivan, C.R., Reese, B.A., Stein, A.L. and Kyaw, P.A.,. “On size and magnetics: Why small efficient power inductors are rare.” IEEE International Symposium on 3D Power Electronics Integration and Manufacturing (3D-PEIM), 2016.

Core loss: What we know and what we don’t know.

There’s a lot we know about magnetic core loss, and at lot we don’t know.  The situation is summarized in presentation slides from my presentation at the PSMA/IEEE Magnetics Workshop.  The slides have the references added at the end with reference numbers sprinkled through.

People were intrigued by the three simple flux crowding simulations shown here.  These aren’t intended to be highly accurate–they are based on constant permeability, and as pointed out by Bruce Carsten, the real behavior is nonlinear.  But the results are still interesting and somewhat surprising.  Based on loss proportional the flux density raised to the 2.5 power, the second picture–the circular hoop–doesn’t reduce loss as you might expect.  Rather, it raises loss by about 3%, compared to the simple square corners at the top.  But the bottom design does reduce loss, by about 8%, compared to the simple square corners.


TPEL – Fundamental Performance Limits of High-Frequency Passive Components

Our new paper accepted for publication in IEEE Transactions on Power Electronics (pdf) explores the potential for new types of passive components and shows that there are exciting opportunities.

  • Analysis of volumetric energy densities of various storage mechanisms shows that mechanical storage may offer order-of-magnitude improvement over conventional electromagnetic passive components.
  • Considering only the limitations imposed by material properties and not by available fabrication methods, both piezoelectric and LC resonators have fundamental performance limits that are much higher than the capabilities of commercial passive components in use today.
  • A prototype 1 cmintegrated LC resonator optimized for low loss is capable of handling 7.42 kW with only 0.06% loss attributable to the resonator when used in a resonant switched-capacitor circuit.

APEC 2018 – Thin Self-Resonant Structures for Wireless Power Transfer

The high-Q achievable by self-resonant structures increases the range and efficiency of wireless power transfer (WPT). However, to date implementations of this structure have been thick, which limits their practical implementations. In the attached paper, we explore the design of thin self-resonant structures.

We describe:
1) a computationally efficient 2-D optimization algorithm is proposed to design thin
resonant structures and illustrate the trade-offs in the design, and
2)a new magnetic core shape is proposed which shapes the magnetic field lines to be parallel to the conductive layers and reduces current crowding.

These advances results in a prototype 3.5 mm thick self-resonant structure, which has a measured quality factor of 560 despite having a diameter of only 6.6 cm; this provides a 3.03× improvement over the state-of-the-art WPT coils in the literature.

See a full description of the thin structure in the attached paper

COMPEL 2017 – Matching Networks with Volume Constraint

Matching networks have useful applications in transforming voltages and impedances in resonant inverters and dc-dc converters. Stacking multiple stages of matching networks can, in some cases, increase the efficiency because each stage is responsible for smaller transformation, but it also reduces the available inductor volume for each stage which can increase the loss.

At COMPEL 2017, we presented a paper (link for pdf) on optimization of matching networks with volume constraints to determine the optimum number of stages and other design choices for various transformation ratios, volumes and impedances. Adding the volume constraint to the typical matching network design process helps provide a better perspective on the number of stages that should be used. Simple design rules for designing matching networks, with a constraint on the available volume, are presented for voltage transformation ratios lower than 20.

COMPEL 2017 – Power Density Optimization of Resonant Tanks Using Commercial Capacitrs

High-frequency power conversion is useful for miniaturization of power electronics, but requires low loss passive components to achieve high power densities without thermal issues.

At COMPEL 2017, we presented a paper (link for pdf) investigating the lowest achievable ESR and the highest achievable power capability of a resonant tank using an air-core inductor with a single-layer foil winding and commercially available capacitors. A loss model is presented and online catalogs of multilayer ceramic capacitors are searched for components that can provide a low ESR when combined with an optimally designed inductor for various resonance frequencies.

The resulting resonator has a measured sub-mΩ ESR and high efficiency with 250 V dc rating in a 1 cm3 volume. The resonant tank, when used in a resonant switched-capacitor converter, has kilowatt-range power capability. A power converter, using this resonant tank, will be limited by the power density of switches and interconnects rather than by passive components.

APEC 2017 High-Q Self-Resonant Structure for Wireless Power Transfer

At APEC 2017 we presented a resonant structure that improves the range and efficiency of wireless power transfer.  High quality factor in resonant coils is essential for both goals, so developed a new technology that achieves Q values that weren’t previously possible. The new structure integrates inductive and capacitive effects to behave as an LC resonator.  It’s made by stacking alternating layers of thin foil and dielectric material in a magnetic core.  The high-Q is achieved through these effects:

  • Thin foil layers mitigate proximity effect.
  • Inductive coupling of sections and integration of capacitance eliminates terminations in high-current paths.
  • Capacitive ballasting forces equal current sharing between all layers.

We experimentally validated this structure and measured a Q of 1173 at 7 MHz despite a coil diameter of only 6.6 cm.    Next, we integrated 2 of the structures into a wireless power transfer system.  We were able to improve the range over which we could maintain efficiency above 94% by a factor of two when compared to the current state-of-the art.  For more details see our presentation slides linked here, or our paper linked here.

A Step-by-Step Guide to Extracting Winding Resistance from an Impedance Measurment

At APEC 2017, Benedict Foo presented a method for extracting winding resistance from an impedance measurement.  For details on this method see the paper.

Impedance analyzer measurements can be helpful in assessing inductor a  transformer winding resistance and predicting winding loss, but the measured ESR does not directly correspond to winding resistance. Neglecting the effects of core loss and winding capacitance can yield significant errors in the prediction. A step-by-step method to account for such effects and extract winding resistance from an impedance measurement is described. The proposed methodology is applicable to both inductors and multi-winding transformers. Several measurements are needed in this method; one is to determine the effects of core loss and the others yield the impedance from which winding resistance is extracted to form a resistance matrix. The winding resistance of a transformer was determined experimentally and the interactions between the winding resistance, effects of core loss, winding capacitance and inductance and their contributions to the measured impedance are demonstrated.

2017 PSMA/PELS Magnetics Workshop Presentations

I gave two presentations at the PSMA 2017 Magnetics Workshop.  Brief summaries and slides are below.

Two-winding electrical core loss test setup.

The first was an introduction to core loss testing, and a survey of basic and advanced methods.  Here are the slides: Survey of Core Loss Test Methods

It includes brief discussions of calorimetric methods and resonant methods.  Calorimetric methods can be tedious, but are valuable as an independent check on other measurements.  Resonant methods can improve accuracy at high-frequencies.

A simple 2:2 foil-winding transformer with current density and flux lines shown. In the top half, these are shown with the two windings excited with the same current, in phase. In the bottom half, they are 180 degrees out of phase. The losses are different by a factor of 4.

The second was a brief overview of magnetics modelling methods, including core and winding losses.  The slides include a list of key references at the end.

As one example of what’s in the presentation, there’s an explanation of why it’s not adequate to model transformer winding loss with two frequency-dependent ac resistance values.  As shown in this figure, the losses depend on the phase between the currents in the two windings, not just on their individual amplitudes.  A model that correctly includes all the interactions between the windings is a resistance matrix.

Methods of finding the resistance matrix are discussed in the presentation and detailed in the references listed at the end.



Simplified litz wire design

125-strand litz wire (5x25)

125-strand litz wire (5×25)

We’ve published a lot of papers on litz wire. Their emphasis has been academic, reporting new optimization results and calculation techniques.  But they are are often too complex for design work, for an engineer who has many different issues to deal with.  With that in mind, we took a different approach in a paper presented at APEC 2014, focusing on making the simplest possible design method that would still provide good practical guidance of litz wire design.  We found a way to incorporate the results of some of our more sophisticated analysis into simple formulas that can be quickly and easily calculated in a spreadsheet or the like, so that you can get good recommendation for litz designs very easily.

Illustration of the main page of the spreadsheet you can download.

Spreadsheet main page

The full paper is available on our web site.  The first two pages are all you need to read to get complete instructions on the method.  To demonstrate how easy it is to use in a spreadsheet, here is the method implemented in a spreadsheet.  You only need to put in four numbers–frequency, number of turns, core window breadth and turn length–and you get a range of options with the performance of each listed.

The simplest calculation is for a transformer winding, but the paper and the spreadsheet also include calculations for gapped inductors, accounting for the field in the region of the gap.  Similarly the base method is for sinusoidal currents, but both include an easy adjustment to deal with nonsinusoidal waveforms.

There are some situations that this method can’t deal with–for example, if you have an unusual geometry, or multiple windings with different current waveforms in each winding.  In those cases, our online LitzOpt calculator (which has recently been updated to be a little more robust and user friendly) can address most situations directly, or pretty much any situation in combination with an external field simulation.

In addition to being easier to use, the new method also features a calculation that helps you choose some of the details of the wire construction–how many strands are twisted together in each step.  Typically one might combine somewhere between 7 and 50 strands in the first step, and then twist several of those bunches together in the second step, etc.  The details of this sequence affect how well the wire eliminates skin effect. The later twisting steps should never combine more than 5 bundles together, but it’s often OK combine many 10s of strands in the first step.  The new calculations tell you how many it’s OK to combine in that first step.

Another choice in the construction is the pitch of twisting at each step.  This paper and spreadsheet don’t provide any guidance on that, but we are publishing a new paper on that topic at COMPEL 2014.  That paper will appear here soon after the conference.