A Guide to Designing Copper-Foil Inductors

Jul 1, 2007 12:00 PM
By Patrick Scoggins Senior Design Applications Engineer, Datatronics, Romoland, Calif.

One important characteristic of copper foil is the temper, 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 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. Copper-foil 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	Through-hole

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 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 first-pass 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 (cm²), 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.