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Power inductors calculation for storage chokes

Switched-mode power supplies are becoming ever more widespread. The semiconductor manufacturers have contributed by offering a wide range of integrated circuits with simplified circuit design. Care must be taken when selecting the appropriate power inductor storage choke to fully utilize the advantages of switching regulators.

This article is split into two chapters:

Calculation of power inductors
Example of high current inductor types

Calculation of power inductors

The selection of cores and windings of storage chokes are optimized for switching converters and DC-DC converters.

Leading manufacturers of storage chokes following recommendations from various switching converter IC manufacturers, e.g., National Semiconductor, Linear Technology, STMicroelectronics, Texas Instruments, Exar, Diodes, MPS, ON Semiconductor, Semtech, Maxim, and unique customized solutions can be found in their reference design guidelines.

Toroidal Core Types

From the EMC perspective, toroidal storage chokes are ideal: The magnetic field lines mainly pass through the core. The stray field and associated coupling in neighboring conductor tracks or components remain small.

In the field of switching converters, storage chokes serve to buffer electrical energy and, at the same time, to smooth the output current. The energy stored in the core in this process is:

energy-stored-in-storage-choke-inductor-eq.-1.

energy stored in storage chokes inductor eq. 1.

Figure 1. Toroidal storage choke (WE-SI and WE-GI)

The toroidal core volume is divided into many electrically isolated regions to enable high energy storage and minimize the resulting core losses. Therefore, the iron powder used in our storage chokes has three-dimensional, uniformly distributed, microscopic air gaps, which prevent eddy-current losses.

The disadvantage of reduced permeability is balanced by greater maximum energy storage and lower losses. Furthermore, these cores are extremely well suited for applications with high DC magnetization.

Data book specifications

Open-circuit inductance L₀:

If the inductor is operated without DC pre-magnetization or with only a small AC current, the open-circuit inductance L₀ results. This value may be measured with sufficiently sensitive inductance measuring equipment for small AC voltages, e.g. 0.1–0.5 V, and a fixed measuring frequency between 1 kHz and 100 kHz, depending on the inductance value.

Inductance rating L_N:

In addition to the small AC voltage amplitude, the specified DC current is superimposed, and the resulting inductance is measured.

Figure 2. Inductance with DC pre magnetization; IN = 1 A; LN = 100 µH

Current rating I_N:

The DC current is for which the inductance and wire thickness are specified and whose specifications are optimized. As shown in the graph in Figure 2., inductance only saturates with a much larger current.

DC resistance DCR:

The windings resistance value is measured with an ohmmeter at an ambient temperature of +25 °C. The test current for resistance measurement is a small DC current, which does not lead to a significant temperature increase in the wire. As values in the milliohm range are measured here, a 4-wire measurement must be made to minimize measurement errors.

Magnetic field energy E:

The energy for which the core data and windings of the coil is optimized. This is specified in microjoules. The following simple and practically proven formulae can be used for dimensioning a storage choke. A brief extract from the extensive core material program and the following table should provide an overview of the choke dimensioning process. Depending on the application, further specifications from the core material data spectrum may be necessary.

Table 1. Materials and their applications (source: Würth Elektronik)

Iron core material data:

Table 1. shows an overview of the most commonly used materials and their applications.

Operating temperature:

The operating temperature of the iron powder core may be from –55 °C to +125 °C. Prolonged core operation above +75 °C, however, results in increased losses.

Insulation voltage:

The protective coating of the toroidal core uniquely identifies the core material, protects against environmental effects, and provides electrical isolation from the windings. Epoxy resin coatings are used, and an insulation dielectric strength of 500 VDC is achieved as standard. Higher insulation voltages can also be offered.

A_L value: An AL value is specified for every size of the core to calculate the winding turns for the required choke; the tolerance is ±10%.
The standard means of measuring the A_L value are B = 1 mT and f = 10 kHz.

Figure 3. Effective permeability with DC premagnetization

Table 2. Specifications of iron powder cores (source: Würth Elektronik)

d_a = outer diameter
d_i = inner diameter
h = height
l = effective magnetic length
A = effective magnetic cross-sectional area
V = effective magnetic volume l
W = winding wire length for 1 turn

Table 3. Wire table (source: Würth Elektronik)

Storage Choke Calculation:

The following demonstrates how a storage choke can be calculated for a switching converter application:
Example: switching converter (step-down controller – storage choke)

Requirements:

Inductance rating L_N = 100 µH Current rating (DC) I_N = 1 A Peak current through the inductance I_max = 1.5 A Ripple current = 20% of I_max = 0.3 A (see Chapter III/Applications) Switching frequency f = 52 kHz

A maximum AC flux density B_AC = 0.05 T is recommended for iron powder cores (to ensure low core losses). Also the inductance should be selected so the ripple current does not exceed 20%–30% of the maximum current.

Step 1 : Choice of the core material and the necessary core volume (V). As the switching frequency is just 50 kHz, we first select the material 3W7538 with µ_r = 75.

inductor core volume calculation eq. [2]

Selected core: 3W7538, as switching frequency < 70 kHz; core no. 13 d_a = 12.7 mm; d_i = 7.7 mm; h = 4.83 mm

Magnetic data: l = 3.19 cm; A = 0.112 cm2; V = 0.358 cm3 A_L value: 33 nH/N²

Step 2: Required winding turns.

inductor winding turns calculation eq. [3]

L in nH
A_L value in nH/N²

The final number of winding turns must be increased as a result of current dependent permeability. The correction factor for the A_L value is determined from the “effective permeability against DC premagnetization” graph (see Figure 3.).

inductor current dependent permeability eq. [4]

At H = 1724 A/m on the graph in Figure 3. → Effective permeability with DC premagnetization = 80% of the initial permeability.

To be certain that the full inductance rating of 100µH exists with a DC current of 1A, the final number of winding turns is calculated as:

compensated inductor winding turns calculation eq. [5]

Step 3: Determination of the DC resistance

The wire diameter can be ascertained from the relevant wire tables for the required current of 1A, e.g. AWG 22 (d = 0.6 mm). This limits the self-heating of the wire to less than +10°C.

The DC resistance of the windings is given by: