A Guide to Designing
Copper-Foil Inductors
By Patrick Scoggins, Senior Design Applications Engineer,
Datatronics, Romoland, Calif.
Building magnetic components with copper foil
windings rather than round magnet wire offers
thermal, electrical, and mechanical advantages,
but requires special design considerations.
T
he basic principles of magnetic design and the
techniques used to build magnetic components
have not changed for many years. The general
approach combines standard round magnet wire
with various types of core materials and shapes.
There have been breakthroughs with different core materials
that operate at higher frequencies and extended temperature
ranges. Nevertheless, magnet wire has remained relatively
unchanged with only minor variations to accommodate
different operating temperatures.
Currently, the majority of inductors are designed with
standard round magnet wire. However, in some designs, an
alternative to round magnet wire — copper foil — may be
the better option for the winding.
Copper foil offers several advantages. One is size reduction since components wound with copper foil tend to use
the winding space more efficiently. Better heat dissipation is
another benefit because the mass of the solid conductor can
withdraw heat from the center of the coil more effectively
than magnet wire. Yet another advantage is the reduction
in voltage stresses between turns of a foil winding.[1] In
addition, a foil-wound component has greater mechanical
strength than a wire-wound component, which makes the
copper-foil component far more robust.
Different types of copper foil are available for use in
magnetic designs. Depending on the application, the choice
of copper can be certified oxygen-free high-conductivity
copper (CDA 10100), oxygen-free high-conductivity copper (CDA 10200) or Electrolytic Tough-Pitch (ETP) copper
(CDA 11000).
The CDA 10100 and CDA 10200 are the best choices for
optimized applications where cost may not be an issue. These
types of copper alloys have the highest purity compared to
the ETP type.[2] For commercial applications where cost is
an issue, the ETP is the best choice.
One important characteristic of copper foil is the temper,
Power Electronics Technology July 2007
������
���������������
�����������
�����������������
�������
���
������
������������������
��������
���
�������
�������
�������
Fig. 1. Cross-sectional area in conventional wire-wound magnetics is
usually expressed in circuilar mils, a unit that is easily converted to
square mils, which is a more convenient unit for copper-foil magnetics.
�
�
���
�
Fig. 2. A magnetic component using copper foil as the conductor is
characterized by the same parameters — such as dc resistance (DCR)
and series inductance (L) — as a component implemented with copper
wire.
which determines the copper’s hardness. Copper has three
general types of standard tempers: hard, half-hard and soft.
The application will determine what type of temper to use.
In most commercial applications, soft copper is the best type.
Soft copper is more popular than the other types because it is
easier to wind in manufacturing and it is easier to solder.
The same guidelines in designing with conventional
magnet wire also apply when designing with copper foil,
the only difference is that copper foil involves working with
square mils. The circular mil area (CM) compared to the
square mil (1 CM = 0.7854 sq. mil) is illustrated in Fig. 1.[3]
Square mils are easily converted to circular mils. To convert
30
www.powerelectronics.com
CONVENTIONAL MAGNETICS
Parameter
Value
Inductance
100 µH (min)
DC current
20 A
Power rating
200 W
Duty cycle
50%
DCR
5.0 mΩ (max)
Operating frequency
300 kHz (square wave)
Package type
Through-hole
core will need to be gapped to avoid saturation.
The following formula is used to determine the gap, where
the magnetic permeability of free space is accounted for as
a numerical constant:
 H
3.19   × N 2 × A E × 10 −8
 in. 
L=
,
 GAP + ( CORE µ INITIAL )
Eq. 1
where L is the inductance (Henries), N is the number of
turns, AE is the effective core area (in.2),  GAP is the core gap
(in.),  CORE is the magnetic path length (in.), and µINITIAL is
the initial relative permiability of the core.
Rearranging the formula enables the length of the gap
to be calculated:
Table 1. Copper-foil inductor parameters for design example.
square mils to circular mils, simply multiply the numerical
portion of the square mils figure by 1.2732.
Design Example
 GAP
In the following example, a dc inductor is designed that
will use copper foil for the conductor. Table 1 shows the
parameters for the inductor corresponding to information
that a customer would present to satisfy the requirements
for a given application. Note that in this example, core loss
and temperature rise are considered negligible.
This design will begin with choosing a core. With the
power level at 200 W and the frequency at 300 kHz, the choice
will be to use a ferrite material. A core that will work in this
application is an E71/33/32-3F3 (from Ferroxcube).[4] The
 H
3.19   × N 2 × A E × 10 −8
 in. 

=
− CORE .
L
µ INITIAL
Eq.2a
In this example, N = 10 is used as a first-pass starting point
for calculating  GAP . Based on the selected core, the other
parameters are AE = 1.058 in.2,  CORE = 5.866 in., µINITIAL =
2000, and L = 100 µH.
 H
3.19   × 102 × 1.058 in.2 × 10 −8
 in. 
5.866 in.
−
=
100 µH
2000
Eq. 2b
0.031 in. = 31 mils.
Kooler Inductors
Inductors made from Magnetics’® Kool Mµ® E cores run
cooler than those made with gapped ferrite cores. Eddy
currents, caused by the fringing flux across the discrete
air gaps of a gapped ferrite, can lead to excessive heat
due to heavy copper losses. The distributed air gaps
inherent in Kool Mµ can provide a much cooler inductor.
Kool Mµ E cores are available in many industry standard
sizes. Magnetics now offers cores in 14 sizes (from 12
mm to 80 mm) and four permeabilities (26µ, 40µ, 60µ,
and 90µ). New sizes are being added. Standard bobbins
are also available.
If you are using gapped ferrite E cores for inductor
applications, see what Kool Mµ E cores can do for you.
You may even be able to reduce core size in addition to
having a cooler unit. For more information, contact
Magnetics.
www.mag-inc.com
NAFTA SALES AND SERVICE
P.O. Box 11422 • Pittsburgh, PA 15238-0422
Phone 412.696.1333 • Fax 412.696.0333
1-800-245-3984 • email: magnetics@spang.com
ASIA SALES & SERVICE
+852.3102.9337 • email: asiasales@spang.com
New Kool Mu Segments Available
Power Electronics Technology July 2007
32
EUROPE SALES & SERVICE
+31.40.255.2319 • email: eusales@spang.com
www.powerelectronics.com
CONVENTIONAL MAGNETICS
����
�������������������������
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
�����
Fig. 3. Bobbins for copper-foil conductors can be fabricated as either phenolic fiberglass or paper. [6,7] (All dimensions in inches.)
The next step is to verify that dc flux density does not
encroach the upper bound supported by the selected core.
The dc flux density (BDC) in gauss can be calculated using the
following equation, where IL(DC) is the inductor’s maximum
dc current (A):
BDC =
0.6 × N × IL(DC )
 GAP
=
VPK is the peak voltage (V), f is the frequency (Hz), AE is the
effective core area (cm2), and N is the number of turns in
the inductor. Here, VPK = VL, so:
VPK × 108
B AC =
=
4.0 × A E × N × f
0.6 × 10 × 20 A
= 3870 gauss.
0.031 in.
600 V × 108
= 610 gauss.
4.0 × 6.83 cm 2 × 12 × 300 kHz
Eq. 5
A value of 610 gauss for ac flux density is acceptable for
the core in this example. With the number of turns and the
length of the core gap established, the next step of the design
process is to fabricate a bobbin for the E71/33/32 core.
Eq. 3
The value of 3870 gauss is very close to the upper limit of
the core. The flux density will need to be reduced to about
3000 gauss. Changing the number of loop turns to 12 will
increase the length needed for the core gap, thereby reducing
the dc flux density:
Bobbin Fabrication
 H
3.19   × 122 × 1.058 in.2 × 10 −8
 in. 
5.866 in.
 GAP =
−
=
100 µH
2000
0.045 in. = 45 mils.
The dc flux density then becomes:
0.6 × 12 × 20 A
BDC =
= 3200 gauss.
0.045 in.
Operating the core at a flux density of 3200 gauss is acceptable. So the decision to use 12 turns for the inductor is
finalized. Even though this is a dc inductor, there is an ac
component that needs to be examined. The induced voltage
is calculated with a formula that is a form of Ohm’s law for
inductance.[5]
dI
VL = L × L ,
Eq. 4.
dt
where VL is the voltage developed across the inductor
(V), L is the inductance (H) and dIL/dt is the rate of current
change in the indutor (in units of A/s, and will be 20 A/3.33
s in this example), making VL = 600 V.
The ac flux density for a square wave is found with the
Faraday equation, where BAC is the ac flux density (gauss),
www.powerelectronics.com
Fig. 3 outlines a custom bobbin for the E71/33/32 core.
There are many paper-tube companies that will fabricate a
bobbin for prototypes. Two well-known tube-bobbin vendors are Dorco and Precision Paper Tube Co.
The size and thickness of the copper foil are chosen based
on the data in the fabricated-bobbin drawing. A copper width
of 1.50 in. is used in this example to match the bobbin in
Fig. 3. An interactive process that begins with an arbitrary
choice for the initial value determines the copper thickness.
The thickness chosen for the initial value in this exercise is
0.008 in. The effective area in units of circular mils would
then be calculated as follows:
Eq. 6
A good rule of thumb is to operate the inductor at no
less than 500 CM of conductor cross-sectional area per ampere of current. This ensures the copper will not overheat
during operation. Given an anticipated current of 20 A, it
is quickly seen that the selected dimensions for the copper
33
Power Electronics Technology July 2007
CONVENTIONAL MAGNETICS
������
�����
�����������
Fig. 4. Copper foil must be shielded with electrical insulation before
winding. One options is to cuff the foil with Kapton tape, as shown in
this cross section.
������
�����
�����
������
�
�������������
����������
������������
������
�
�
�
�����
�
�����
����
Fig. 6. The copper-foil conductor in this completely assembled inductor
contributes to the electrical and mechanical robustness of the component. (All dimensions in inches.)
�
������
����
Fig. 5. Lead connections to the opposite ends of the copper-foil conductor must be protected with electrical isolation in the same manner as
the foil itself.
foil will satisfy this requirement:
A E 15, 278 CM
CM
CM
=
= 764
> 500
.
IL
20 A
A
A
Eq. 7.
Despite the reduced danger to overheating, it is still important to examine copper losses. The following formula is
used to calculate the total dc resistance of the copper foil,
where the mean-length turn (MLT) for each of the bobbin’s
12 turns is 6290 mils:
10.371 × N × MLT(in.)
DCR (Ω) =
=
12 × area of copper (CM)
12 × 6.29 × 10.371
= 4.3 mΩ.
12 × 15, 278
Eq. 8.
This will result in power dissipation from copper losses,
PCOPPER, as follows:
PCOPPER = IL 2 × DCR = (20 A)2 × 4.3 mΩ = 1.72 W.
Description
E71/33/32-3F3, gapped to 0.045 inches
(center leg)
Bobbin
Custom
Copper
1.50 in. x 0.008 in. ETP (6.5 ft)
Leads
#10 heavy (MW80C)
Adhesive
Manufacturer’s choice
Dolph varnish
CC-1105
3M tape
1205 Kapton
Solder
Sn10 and Sn63
Table 2. Bill of materials for design example copper-foil inductor. Note
that for copper, 6.5 ft includes ~3% additional mrgin.
completed inductor after the foil has been wrapped around
the bobbin. The bill of materials needed for the complete
manufacture of this component is shown in Table 2.
Designing a dc inductor with copper foil can be achieved
when considering the proper electrical parameters. The
turns, gap, flux density and power loss are all critical in
designing magnetics. Understanding the different types of
copper and their levels of hardness is essential. Even when
these aspects have been considered, any inductor design will
still involve several iterations to verify electrical parameters
and ensure design adequacy. However, the advantages of
inductors wound with copper foil over those wound with
conventional magnet wire make this process worthwhile.
Eq. 9
A copper loss of 1.66 W is acceptable for this example.
With the copper loss, core and number of turns known, the
unit can be prototyped.
Prototype Materials Selection
PETech
References
There are different materials to insulate the copper foil.
If the copper foil is not insulated, the turns would short together. One material is kraft paper. This material is available
in a number of thicknesses and it also impregnates very well.
The second material to insulate copper foil is tape (either
mylar or Kapton). In this example, the copper foil will be
cuffed with 3M, #1205 Kapton tape. Fig. 4 illustrates how the
copper foil appears after it has been cuffed in this manner.
The start and finish lead wires will be attached to the
copper foil with high-temperature solder, as detailed in
Fig. 5. In this application, #10 heavy (MW80C) wire for
the leads will suffice. Fig. 6 shows the appearance of the
Power Electronics Technology July 2007
Item
Ferroxcube core
1. Electrotube, http://www.electrocube.com/products/pdf/
FoilTransformersSpecificationsPI.pdf
2. MWS Wire Industries, http//www.mwswire.com/pdf_files/
mws_tech_book/MWS_Tech_Book.pdf, p. 28.
3. Lowden, Eric, Practical Transformer Design Handbook, 2nd
Edition, Tab Books, pp. 9 and 290.
4. Ferroxcube Soft Ferrites and Accessories Data Book, 2005.
5. Ridsdale, R.E., Electric Circuits, 2nd Edition, McGraw Hill
Inc., 1984, p. 88.
6. Precision Paper Tube Co., Catalog No. P197, p. 4.
7. DORCO Electronics Inc., http://www.dorco.com/.
34
www.powerelectronics.com