A Guide to Designing CopperFoil Inductors
The 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 foilwound component has greater mechanical strength than a wirewound component, which makes the copperfoil 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 oxygenfree highconductivity copper (CDA 10100), oxygenfree highconductivity copper (CDA 10200) or Electrolytic ToughPitch (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, which determines the copper's hardness. Copper has three general types of standard tempers: hard, halfhard 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 square mils to circular mils, simply multiply the numerical portion of the square mils figure by 1.2732.
Design Example
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.
Table 1. Copperfoil inductor parameters for design example.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 ThroughholeThis 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 E71/33/323F3 (from Ferroxcube).^{[4]} The 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:
where L is the inductance (Henries), N is the number of turns, A_{E} is the effective core area (in.^{2}), l_{GP} is the core gap (in.), l_{CORE} is the magnetic path length (in.), and INITIAL is the initial relative permiability of the core.
Rearranging the formula enables the length of the gap to be calculated:
In this example, N = 10 is used as a firstpass starting point for calculating l_{GP}. Based on the selected core, the other parameters are A_{E} = 1.058 in.^{2}, l_{CORE} = 5.866 in., µ_{INITIAL} = 2000, and L = 100 µH.
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 (B_{DC}) in gauss can be calculated using the following equation, where I_{L(DC)} is the inductor's maximum dc current (A):
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:
The dc flux density then becomes:
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]}
where V_{L} is the voltage developed across the inductor (V), L is the inductance (H) and dI_{L}/dt is the rate of current change in the indutor (in units of A/s, and will be 20 A/3.33 ms in this example), making V_{L} = 600 V.
The ac flux density for a square wave is found with the Faraday equation, where B_{AC} is the ac flux density (gauss), V_{PK} is the peak voltage (V), ƒ is the frequency (Hz), A_{E} is the effective core area (cm^{2}), and N is the number of turns in the inductor. Here, V_{PK} = V_{L}, so:
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.
Bobbin Fabrication
Fig. 3 outlines a custom bobbin for the E71/33/32 core. There are many papertube companies that will fabricate a bobbin for prototypes. Two wellknown tubebobbin vendors are Dorco and Precision Paper Tube Co.
The size and thickness of the copper foil are chosen based on the data in the fabricatedbobbin 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:
A good rule of thumb is to operate the inductor at no less than 500 CM of conductor crosssectional 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 foil will satisfy this requirement:
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 meanlength turn (MLT) for each of the bobbin's 12 turns is 6290 mils:
This will result in power dissipation from copper losses, P_{COPPER}, as follows:
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
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 hightemperature 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 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.
Table 2. Bill of materials for design example copperfoil inductor. Note that for copper, 6.5 ft includes ~3% additional mrgin.Item Description Ferroxcube core E71/33/323F3, gapped to 0.045 inches (center leg) Bobbin Custom Copper 1.50 in. × 0.008 in. ETP (6.5 ft) Leads #10 heavy (MW80C) Adhesive Manufacturer's choice Dolph varnish CC1105 3M tape 1205 Kapton Solder Sn10 and Sn63Designing 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.
References

Electrotube, http://www.electrocube.com/products/pdf/FoilTransformersSpecificationsPI.pdf

MWS Wire Industries, http//www.mwswire.com/pdf_files/mws_tech_book/MWS_Tech_Book.pdf, p. 28.

Lowden, Eric, Practical Transformer Design Handbook, 2^{nd} Edition, Tab Books, pp. 9 and 290.

Ferroxcube Soft Ferrites and Accessories Data Book, 2005.

Ridsdale, R.E., Electric Circuits, 2^{nd} Edition, McGraw Hill Inc., 1984, p. 88.

Precision Paper Tube Co., Catalog No. P197, p. 4.

DORCO Electronics Inc., http://www.dorco.com/.