Selected Publications, by Topic
With notes. Topics:
Microprocessor power delivery.
Related links: Chronological list.
Download experimental BibTeX file: dmcper.bib
(read the notes at the top of the file.).
Using a 2D model for numerical modeling (i.e., finite-element analysis)
of a 3D structure (such as an E-core) is not as straightforward as it
sounds, as shown in “An
Improved Two-Dimensional Numerical Modeling Method for E-Core
Transformers .” The straightforward approach can lead to
substantial errors. In the course of developing a better way to do this,
we found that we needed better accuracy from an analytical approximation
to the fringing reluctance around a gap. Although the literature
contains exact formulas for the 2D situation, we needed to develop an
accurate approximation for the actual 3D situation, and this can be
found in the same
paper. For more detail on any of this, you can download Anderson
complete thesis on the same topics.
"Optimal Choice for Number of Strands in a Litz-Wire Transformer
Winding" gives general background and explains how to choose a
strand number and diameter for the absolute minimum loss.
Unfortunately, this minimum loss design is usually very expensive.
Thus, "Cost-Constrained Selection of Strand Wire and Number in a Litz-Wire
Transformer Winding." becomes very important. This second
paper shows how to generate a curve showing the possible trade-offs
between loss and cost. Both of these first two papers address only
simple geometries such as standard transformer windings. With
geometries in which 2- and 3-D fields are important,
the “SFD” method described in "Computationally Efficient Winding Loss Calculation with Multiple
Windings, Arbitrary Waveforms, and Two- or Three-Dimensional Field
Geometry" can calculate loss accurately. Optimization,
considering cost, for such geometries is addressed in "Optimization of a flyback transformer winding considering
two-dimensional field effects, cost and loss." A general purpose
version of this optimization technique has been implemented in a free
CAD tool that is detailed in "Easy-To-Use CAD Tools for Litz-Wire Winding Optimization,"
and is available from our software page.
The optimization software is a great way to reduce the cost of
litz wire. Another approach is to skip the insulation on
individual strands, as analyzed in "Stranded Wire With Uninsulated Strands as a Low-Cost Alternative to
See also inductor design for low AC resistance.
Inductor design for low AC resistance
The effect of an air gap used in an
inductor on the field distribution can sometimes result in disastrous
winding AC resistance. One mitigation strategy is to use a
low-permeability "distributed gap" to avoid the high flux one gets near
a single lumped gap. This requires special materials, but we
discuss a popular alternative using multiple small gaps in conventional
material, in "The
Quasi-Distributed Gap Technique for Planar Inductors--Design
Guidelines". We developed a set of reasonably simple equations
that can be used to predict ac resistance in a wide range of planar
inductors, including ones with single gaps, and set of even simpler
For wire-wound, as opposed to planar, inductors, the
quasi-distributed gap technique can also be used. However, in "Optimization of Shapes for Round Wire, High Frequency Gapped Inductor
Windings" we show that a less expensive alternative has better
performance. The position of the turns in the winding window, as
well as the number of strands (in litz wire) or diameter of wire, can be
optimized to result in lower loss than that in an ideal distributed-gap
inductor. In "Analytical Method for Generalization of Numerically Optimized Inductor
Winding Shapes" we show how to generalize the results to from one
set of numerical optimizations to make them useful in any design with
the same geometry. These first two papers do not explicitly
consider cost; in "Analysis of Minimum Cost in Shape-Optimized Litz-Wire Inductor
Windings," we analyze the effect of cost on the shape optimization.
The use of shape optimized windings is further examined in "Optimal Core Dimensional Ratios for Minimizing Winding Loss in
High-Frequency Gapped-Inductor Windings."
High-Frequency Winding Loss Analysis
For a given winding and current,
losses increase with frequency. The best known cause of this is
skin effect, but proximity effect can cause losses to increase
dramatically even when the wire is small compared to skin
depth. In most cases, optimum designs fall in this
intermediate frequency range. This allows simplifications that
allow relatively easy analysis of complex situations such as 2- or 3-D
field geometries and non-sinusoidal waveforms.
Analysis of winding loss with non-sinusoidal currents in simple
situations can be accomplished using an "effective frequency," as
discussed in the appendix of "Optimal Choice for Number of Strands in a Litz-Wire Transformer
Winding ." This has the advantage of allowing the direct use of
relatively simple optimization techniques that were developed for
sinusoidal waveforms. For situations involving different waveforms in
different windings or 2- or 3-D geometries, the "SFD" method described
in "Computationally Efficient Winding Loss Calculation with Multiple
Windings, Arbitrary Waveforms, and Two- or Three-Dimensional Field
Geometry" is required. Optimization, considering cost, for such
geometries is addressed in "Optimization of a flyback transformer winding considering
two-dimensional field effects, cost and loss ."
When the skin depth become small compared to the wire diameter, loss
analysis becomes more complex. The Dowell method is the most common
method used that covers this higher frequency range. It is an
approximate method. Attempts have been made to use an exact Bessel
function solution for higher accuracy. However, the approximation
involved in the use of Bessel functions leads to even greater error. But
since the Dowell gives 5% error at low frequencies and up to 60% error
at high frequencies, an improvement is needed. We developed a more
accurate equation that gives predictions of proximity-effect loss that
are accurate to within a few percent over a wide range of conditions;
the version of this model presented in "Simplified High-Accuracy Calculation of Eddy-Current Loss in
Round-Wire Windings" is easier to use than the version presented in
the original paper, "An
Improved Calculation of Proximity-Effect Loss in High-Frequency Windings
of Round Conductors", although the original is still useful as it
supplies additional background and evaluation of other methods.
Our method calculates the loss based on the magnetic field.
For simple 1-D geometries, the field is easy to calculate, as described
first paper listed above. For 2-D geometries, a 2-D field
calculation is also needed. This field calculation is complicated
by the effect of eddy currents in the wire on the field. From our
loss model, we have also developed "A
Two-Dimensional Equivalent Complex Permeability Model of Round-Wire
Windings" which simplifies the required field calculations. This
model is applied to litz wire in
"An Equivalent Complex Permeability Model for Litz-Wire Windings".
Core Loss in Ferrites with Arbitrary Flux Waveforms
Core loss in ferrites for power
electronics applications is conventionally predicted using the Steinmetz
equation or manufacturers' datasheet plots. Unfortunately, the
Steinmetz equation and manufacturers' data are based only on tests with
sinusoidal waveforms. But many power electronics circuits use
other waveforms. In "Improved
Calculation of Core Loss With Nonsinusoidal Waveforms" we review
existing methods, discuss their limitations, and introduce a new method
that overcomes some of the limitations. The method is substantially
improved in "Accurate
Prediction of Ferrite Core Loss with Nonsinusoidal Waveforms Using Only
Steinmetz Parameters." The new method is highly practical, requiring
no new characterization of a material beyond the Steinmetz equation
parameters that are often provided by the core manufacturer.
Microprocessor Power Delivery
Microfabricated Magnetics for Microprocessor Power
A brief two-page overview of this work is available in "Thin-Film Inductor Designs and Materials for High-Current Low-Voltage
power requirements are rapidly getting very difficult to meet. Not
only are power levels increasing, but voltages are dropping, driving
currents up even faster than power. Particularly difficult is
maintaining a tightly regulated voltage despite rapid changes in load
current. High switching frequencies and miniaturized components
that can be placed very close to the load can overcome these
challenges. We are developing high-frequency (8 MHz) power
inductors fabricated by thin-film deposition and photolithography.
They are described in "Design of Microfabricated Inductors for Microprocessor Power
Delivery" and "Converter and Inductor Design for Fast-Response Microprocessor Power
Delivery", and in the first and second papers titled "Fabrication of Thin-Film V-Groove Inductors
Using Composite Magnetic Materials." Our first measured results
are described in "Measured Electrical Performance of V-Groove Inductors for
Microprocessor Power Delivery."
One of the new high-frequency magnetic materials for this
application is described in "Evaporatively Deposited Co-MgF2 Granular Materials for
Circuit Design for Microprocessor Power Delivery
In "Coupled-Inductor Design Optimization for Fast-Response Low-Voltage
DC-DC Converters," we show how magnetic coupling can be used to
circumvent the tradeoff between efficiency and fast response that
otherwise constrains circuit designs for the challenging new
requirements of microprocessor power delivery (described in the section
above). Circuits for this application are also discussed in "Converter and Inductor Design for Fast-Response Microprocessor Power
Conventionally, non-idealities in
capacitors are models by adding ESR (effective series resistance) and
ESL (effective series inductance). In "Physically-Based Distributed Models for Multi-Layer Ceramic
Capacitors," we show that ESL is a poor approximation to the
behavior of an actual capacitor and we develop more accurate models. The
poster from this presentation is also available. Earlier papers on
this work address film capacitors as well as ceramic capacitors: "Capacitors with Fast Current Switching Require Distributed Models"
and "Improved Distributed Model for Capacitors in High-Performance
Power Electronics Education
The tools and movies discussed in “Three-Dimensional Animations of Power-Electronics Circuits Visualize
Voltage and Current.” are available on the animation Web