# Processed Power Inductors Shine at High Frequencies

As electronics equipment becomes smaller, especially in computer and telecom applications, lower-voltage dc-dc power supplies are becoming more popular. This has increased the demand for higher-frequency, higher-current magnetic components including inductors. Unfortunately, traditional inductor technology has been unable to match these advances in frequency and current-handling performance.

To fill this void, a new technology known as processed power inductors has emerged. Offering better high-current and high-frequency performance than conventional wound inductors, processed power inductors are finding use in a wide range of applications. They are being designed into voltage regulator modules (VRMs), as well as automotive and industrial power applications. When compared with traditional wound inductors, processed power inductors can offer lower cost and smaller size, which result from improvements in electrical and thermal parameters such as ac resistance, DCR tolerance, core losses and heat dissipation.

### Higher Switching Frequencies

The demand for higher performance in switch-mode power supplies has led to an increase in typical switching frequencies by a factor of 10 over the last decade of product development. The current generation of power-supply design is now focused on increasing switching frequency by another factor of 10 to reach several megahertz.

One of the primary benefits of increasing switching frequency is the overall size reduction that is possible in the design of a high-frequency dc-dc converter, particularly in the magnetic components used in such a power supply, as expressed by the equation:

where L is the inductance (H) of the magnetic component, V_{OUT} is the output voltage (V), D_{MAX} is the maximum duty cycle, V_{INMIN} is the minimum input voltage (V), V_{OUTMIN} is the minimum output voltage (V), F_{SW} is the switching frequency (Hz) and I_{OUTMIN} is the minimum output current (A).

In addition to smaller inductor size, increasing the switching frequency enables faster dynamic response from the power supply. Despite the benefits, higher switching frequencies also result in higher losses for the magnetic components. Many research papers have been dedicated to the optimum design of power inductors with minimum power losses, including the use of planar technology to save pc-board space and to decrease losses. However, planar-wound magnetic components have remained high in cost and, although they have succeeded in reducing component height, have not reduced the pc-board footprints of these devices.

To select the optimum high-frequency magnetic inductors, a designer must consider several factors including winding geometries, magnetic core materials and packaging design to achieve the lowest losses.

### Soft Magnetic Material

At the heart of the processed inductor technology is the use of an air coil and a special soft magnetic composite (SMC) material. The development of SMC has provided inductor cores with normally conflicting magnetic properties — good relative permeability and magnetic saturation. In addition, an SMC offers high electrical resistivity. SMCs use precisely formulated high-purity iron powder bonded with a coating of an organic material to produce a high-density core (approximately 7.4 g/cm^{3}) that also delivers high electrical resistivity when compacted. This high resistivity is a major factor in making these materials attractive in low-loss applications, particularly at high frequencies.

The key to high resistivity is the formation of a uniform insulation film on the grain surfaces of the magnetic powder, which is accomplished through the addition of an interfacial activator along with the water-soluble insulation liquid. This is followed with a process of mixing and drying steps. A rust-preventive solution is also added to the insulation-powder material.

Another factor in creating high-resistivity core material is the use of polyimide thermosetting resin. There is a strong relationship between the high-frequency core loss of a powdered core and its specific resistivity. When the material is ready for processing, it is injected into air-coil molds prepared using a computer-numerical-control winding machine. The magnetic powder is then compressed into an integrated and compact inductor core.

### Benefits of Pre-Tooled Coils

In conventional magnetic-component construction, the inductor windings are usually made of solid round or litz wire. Processed inductors employ pre-tooled parts made of thin copper-foil or helical-coil windings (**Fig. 1**). With precisely defined winding positions, these parts make it possible to accurately predict the geometry of the processed inductors and their electrical specifications.

Another major difference between the conventional and processed inductors is the ratio of the SMC core to copper volumes. Processed devices are typically comprised of a core with a large cross-sectional area, but the winding has a smaller number of turns, as expressed in the formula:

where B is the magnetic flux density (Gauss), n is the number of turns, A_{EFFECTIVE} is the effective core cross section (cm^{2}), e is the excitation (V-s for transformers and A-H for inductors), and K is the dimensional constant (Gauss × cm^{2})/(V × s).

Thus, an increase in cross section will lead to a decrease in the number of turns required. Furthermore, in a processed inductor, the ratio of the effective core cross-sectional area to the winding-window area (A_{EFFECTIVE} : A_{WINDING}) is greater than that of conventional core structures. This geometry allows a smaller number of turns, which is preferable with foil winding, making this technology suitable for low-voltage, high-current, high-frequency inductors. It also can be used for both single- or multiple-layer windings.

Processed inductor technology provides several advantages over traditional inductor design. This includes fully shielded construction, the lowest DCR per microhertz, the ability to handle high-transient current spikes without saturation, ultralow buzz noise (due to composite construction), low board-mounted profiles (**Fig. 2**) and ultralow winding power losses.

Other advantages include an operating temperature to 155°C; a high-current capability (**Fig. 3**); a stable inductance over current, temperature and frequency; high Q values; a smaller size for higher inductance or higher current ratings; the support of surface-mount technology; and an economical device construction.

Factors contributing to the economical device construction of processed inductors are the elimination of the epoxy-bonding process, the elimination of the coating process and support of vertical-integration processes. All of these process steps are required in the manufacturing of conventional wound inductors. Processed inductor technology also enables machine feeding of the coil into the mold to automate the assembly process.

The cost reduction in the device production is realized through more efficient manufacturing methods, including a more highly automated assembly process, thus reducing labor costs while eliminating the need for a separate magnetic core component.

However, the manufacturing processes for traditional inductor designs are proven and mature, with established formulas for winding geometries. Retooling manufacturing lines to produce processed inductors will require significant investment and experience to establish new material formulas and manufacturing processes.

### Traditional Versus Processed Technology

**Table 1** compares the performance of traditional inductor technology, represented by BI Technologies' HM53-001R1LF wound toroidal inductor, with that of the processed inductor technology, represented by BI Technologies' HM72A-101R0LFTR and HM72A-061R0LFTR.

As applied in processed inductors, the technology of foil conductors has many advantages, especially in high switching-frequency applications. A major source of loss at high switching frequencies is due to the uneven current distribution in current-carrying conductors. Consequently, ac resistance can be appreciably higher than dc resistance. Traditional winding technology using round-diameter copper wire produces large ac resistance at high frequencies, due to the proximity effect and skin effect of the wire. Both are caused by the magnetic fields associated with the conductor.

The skin effect reflects the influence of the magnetic field of a current-carrying conductor on itself. The proximity effect is caused by electromagnetic interaction between two neighboring conductors. Both effects push the current toward the outer surface of the conductor, reducing the effective cross section in round inductors. The foil inductors applied in processed technology reduce this effect.

Optimum winding geometry is a significant factor in determining the copper loss (P_{COPPER}), thus minimizing power loss. P_{COPPER} is determined by the following equation:

where I_{RMS} is the root-mean-square current (A), R_{DC} is the dc resistance (Ω) and R_{AC} is the ac resistance (Ω).

Because processed power-inductor cores are constructed using a helicoidally flat wire, these windings produce significantly lower ac resistance. Therefore, a ratio of R_{AC}:R_{DC} at 1 MHz is only 6.5 compared to that of the traditional technology, which can reach 16. **Table 2** shows the relationship between frequency and the R_{AC}:R_{DC} ratio for the processed inductor.

Another advantage in terms of winding power loss for processed inductors is their tolerance for the DCR value. Because there is no open space inside the processed power inductor, the tolerance on the DCR is just ±5%, and for temperature increase, there is only a 3.2°C difference between the DCR_{MAX} and the DCR_{MIN}. For inductors that use traditional technology, the tolerance for the DCR value is ±20% and the temperature increase between DCR_{MAX} and DCR_{MIN} is 15°C.

### Core Losses

Core losses in SMC material are due mainly to eddy currents and hysteresis losses. Power-core losses in processed inductors have been measured as a function of switching frequency and peak flux density, thus core loss can be approximated by the following formula:

where P_{LOSS} is the SMC material power loss (W), V_{CORE}EFFECTIVE is the effective core volume (cm^{3}), F_{SW} is the switching frequency (kHz), B_{MAX} is the maximum flux density (Gauss), and A = 4.3 × 10^{9}, B = 2.86 × 10^{8}, C = -4.95 × 10^{1} and D = 2.99 × 10^{-14}. The formula, together with the device parameters, can be inserted into a computer program, making it possible to calculate the power losses for arbitrary waveforms.

The interpretation of this relationship is that as the frequency is increased, the ac B_{MAX} must be reduced to keep the same loss level. The reduction of B_{MAX} calls for an increased cross section (A_{EFFECTIVE}) if the same number of turns is to be maintained. On the other hand, an increase of A_{EFFECTIVE} implies a larger core volume (V_{CORE}EFFECTIVE), which will increase P_{LOSS}. Cores that exhibit a large cross section but a relatively small volume are preferred. In processed inductance, the ratio of effective cross-sectional area to core volume (A_{EFFECTIVE}:V_{EFFECTIVE}) is the largest — as compared to most conventional cores — thus making it advantageous in high switching-frequency applications.

A high core surface-to-volume ratio helps dissipate heat, as the surface area is related to cooling capacity and total volume is related to heating capacity. A compact coil with good heat conduction and geometry has short thermal paths that help reduce the hot-spot temperature. This improved thermal management allows for up to twice the power loss of a conventional design with the same magnetic volume. Therefore, processed designs are more economical because they allow a relatively higher power handling, as compared to conventional magnetics.

### Future Capabilities

While inductance values for processed inductors are now limited to 33 µH, this is expected to change when core materials switch from metallic powder to ferrite materials. In addition, development work is ongoing for an inductor array using processed technology for multiphase power applications.

The integral, self-leaded, surface-mount construction of a processed inductor eliminates the uncertainties of additional solder connections from the winding to terminating devices, and its intrinsic shielding makes it an ideal choice for space-constrained portable communication such as laptops. High-temperature stability even enables placement in the engine compartment for automotive applications.

Table 1. Comparison between the processed and traditional technology.Part number HM53-001R1LF HM72A-101R0LF HM72A-061R0LF Dimension (mm) 23 × 14 × 23 10.5 × 11.5 × 4 7.23 × 6.8 × 3 Inductance at 0 A (µH) 1.44 1.2 1.2 Inductance at 14 A (µH) 1.1 1 1 Maximum DCR (mΩ) 3 2.75 10 Operating temperature range (°C) -40 to 85 -40 to 155 -40 to 155 Table 2. R_{AC}:R

_{DC}versus frequency for processed inductors for power applications.Frequency (kHz) R

_{AC}:R

_{DC}100 1 300 2.33 400 2.8475 500 3.38 600 3.9 700 4.32 1000 6.44