Foil Windings in Power Inductors:
Methods of Reducing AC Resistance
Weyman Lundquist
President and CEO
West Coast Magnetics
SMPS Inductor Winding Resistance
Includes AC and DC Resistance
Every successful design requires minimization
of total AC plus DC winding losses.
Comparison of DC Resistance:
Foil, Solid Wire & Litz Wire
FOIL
DCR = 1.9mΩ

SOLID WIRE
DCR = 4.3 mΩ
50/40 awg LITZ WIRE
DCR = 22.9mΩ
Foil windings:


Fast and easy to wind
Do not require bobbins or other supports
Components of Winding Losses
Resistive loss
Ptotal  I Rdc  I
2
dc
2
ac ,rms
Eddy-current loss
Rdc  Pskin  Pproximity
dc loss
Pdc  I dc2 Rdc
ac loss
Pac  I ac2 ,rms Rac
“ac resistance”
Rac 
Source: J. Pollock Thayer School of Engineering at Dartmouth
Pac
I ac2 ,rms
Skin Effect
B-Field
x
J
Current
Density

Induced
Current
Main
Current
Skin Effect

An isolated conductor carrying highfrequency current which generates a field
in itself that forces the current to flow near
the surface of the conductor.
Proximity Effect
B-Field
oo
ooo
ooo
ooo
oo
xx
xxx
xxx
xxx
xx
J
Current
Density
x

Induced
Current
Main
Current
Proximity Effect


An isolated conductor is placed in an uniform
external field
External field results from other wires and windings
near the conductor but mainly from the field present
in the core window.
Magnetic Field Inside Core
Window
Ungapped E-core
Gapped E-core
Magnetic Field Inside Gapped
Inductor Core Window
Legend:
Red: strong field
Blue: weak field
Lines: constant field
magnitude
Gapped E-core
Current Distribution:
Ungapped E-Core and Gapped E-Core
Full Foil:
Ungapped Core
AC current evenly
distributed on surface
of foil across full width
of foil.
Shaped Foil:
Gapped Core
AC current pulled to
small copper cross
section in the vicinity
of the gap.
Shaped Foil is a patented technology developed by
Professor Charles Sullivan and Dr. Jennifer Pollock at Dartmouth College.
Patented Inductor Technology

Very Low DCR, High Window Utilization


Low AC Resistance


Foil winding
AC loss reduction comparable to litz wire
SIGNIFICANTLY LOWER TOTAL WINDING LOSSES
Shaped Foil is a patented technology developed by
Professor Charles Sullivan and Jennifer Pollock at Dartmouth College.
Experiment: Is the New
Technology Really Better?

Objective: A conclusive comparison of the
new technology to conventional windings

Step 1: Define the Inductor






Inductance: 90 uH
Current: 40 Adc
Ripple: Triangle wave at 50 kHz
Core: E70/33/32 Epcos N67 material
Gap: 2.64 mm (1.32 mm each center leg)
Turns: 15
Experiment: Is the New
Technology Really Better?

Step 2: Wind inductors with conventional
windings using best practices



Full window
Single layer
Step 3: Determine winding losses for
each inductor as a function of ripple
magnitude
Winding Cross Sections
Long Cut
Full Foil
20/32 Litz
20/32 Litz
Solid Wire
Solid Wire
Prototype Cut
400/40 Litz
50/40 Litz
Method of Estimating
Losses

DC Resistance


Core Losses


Measure voltage drop under 5 Amp DC load
Derived from Epcos loss curves
AC resistance


Sweep from 10 kHz to 200 kHz with Agilent
4294A network analyzer
Use Fourier decomposition to translate
sinusoidal sweep data to triangular waveform
Total Loss Comparison:
50 kHz
Solid Wire
40 awg litz
Full Foil
32 awg litz
Shaped Foil Tech.
Shaped Foil Tech.
Total Loss Comparison:
200 kHz
Full Foil
Solid Wire
40awg litz
Shaped
Shaped
Shaped
Shaped
Shaped
Foil
Foil
Foil
Foil
Foil
Tech.
Tech.
Tech.
Tech.
Tech.
Experimental Verification
Source: J. Pollock Thayer School of Engineering at Dartmouth
1.4
Inductance = 97 μH
Number of turns, N = 15
Core size: E71/33/32
Ripple ratio = 20%
1.2
Full-width Foil
Rac, Ω
1
0.8
Prototype Notched Foil #3
Prototype Notched Foil #2
Prototype Notched Foil #1
0.6
0.4
Optimization Program Loss
0.2
0
FEA of Notched Foil
0
50
100
150
200
250
Temperature Rise Measurement:
Results at 15% Ripple
Additional Development Work
Completed:

Optimization of Foil Shape (cutout) for minimum loss.

Simulation program to predict copper losses in foil
windings for full foil and shaped foil windings.

Simulation program to plot inductance vs. Idc for gapped
cores.

Optimization of foil shape in distributed gap (powdered
cores).
Foil Shape Optimization in
Distributed Gap, Powdered Cores
Source: Jennifer Pollock. Optimizing Winding Designs for High Frequency
Magnetic Components. PHD thesis, 2008
Thank you for your time
Weyman Lundquist, President
West Coast Magnetics
4848 Frontier Way, Ste 100
Stockton, CA 95215
www.wcmagnetics.com
800-628-1123
The author gratefully acknowledges Professor Charles Sullivan, Thayer
School of Engineering at Dartmouth and Jennifer Pollock, PHD EE for
their work and contributions to this presentation.