*Improving power density is a permanent challenge of R&D in power electronics. A survey of modern power electronic circuits shows that further optimization has to be based on the passives and particularly on the inductive components.*

*By Alexander Stadler and Christof Gulden, STS Spezial-Transformatoren Stockach GmbH & Co. KG, Am Krottenbühl 1, 78333 Stockach, Germany*

State-of-the-art inductors (e.g. in LC, LCL and filters) contribute a lot to space, weight, losses and cost as well. In this paper, a new generation of power inductors is presented. The thermal management of these components has been optimized using FEM and extensive thermal measurements. Thus, much higher electrical current densities have become possible at the same hot-spot temperature, which is finally equivalent to higher energy density and smaller component size.

In recent work (e.g. [1] [2]), the general influence of the power electronics topology on the filter and especially on the inductor size has been investigated. The next step that usually reduces the size of these components is the electromagnetic optimization [3]. Assuming an optimal construction of coil and core, there are only two options left for further downsizing: Firstly, a core material with higher saturation flux density can be used. Secondly, the electrical current density of the winding can be increased.

Due to the fact that there's no theoretical potential for a new (high frequency) core material with considerably higher saturation limit, the choice of higher current densities promises the highest gain in package density. However, higher current densities lead to higher losses and the main limitation then is given by the maximum hot-spot temperature of the component to avoid accelerated aging and insulation breakdowns. Consequently, the main optimization potential is to minimize the thermal resistance of the inductors and to optimize its internal thermal management.

A survey of today's constructions shows, that approximately 50% of the temperature drop between hot-spot and cooling medium occur inside the housing, which is quite far from optimum. The main goal of the optimized construction shown in Figure 1 is that the temperature drop between hot-spot and housing has been minimized. Thereby, the flat wire helical winding technology (Figure 2) is one of the key components to achieve much higher cooling efficiency. Below, the thermal management is investigated using finite element method (FEM) and data drawn from extensive thermal measurements.

### Simulation and Measurement of the Hot-Spot Temperature Investigation of the Forced-Cooled Heat Sink

To begin with, an analytical model is conducted to optimize the forced cooled heat sink [4] [9] and to predict its thermal resistance. Figure 3 shows a comparison between calculated and measured results. It is found that the thermal resistance can be predicted with adequate accuracy (≤ ± 25%). With the cooler area* *, the heat transfer coefficient can be calculated:

Equation (1) can directly brought into FEM to describe the cooler boundary condition.

### Simulation of the Hot-Spot Temperature

Figure 4 depicts the simulated temperature distribution inside the inductor. In Figure 4a the forced-cooled version is shown. It can be seen that the temperature distribution is nearly homogeneous quite close to the optimum. If the inductor is mounted on a cold plate (Figure 4b), the insulation material between coil and aluminum housing remains as the main thermal barrier. However, a considerably high heat flux can be detected due to the inhomogeneous temperature distribution inside the continuous casted aluminum parts.

**Conclusion **

Figure 5 shows the wind tunnel and the cold plate used for verification and for performance measurements. The performance data of the new components are listed in Table 1. For the forced-cooled inductors it is found that the current density can be increased from 3.7A/mm^{2} to 5.6A/mm^{2} (in other words this corresponds with a size reduction by a factor of 1.5). If the inductors are mounted on a cold plate, even a current density of 8.0A/mm^{2} becomes possible - a value that only has been reached in direct water cooled conductors until now.

The performance data in Table 1 were extracted from the thermal measurements using DC winding current only. However, for high permeability core material and (one-layer) flat wire helical windings (Figure 2), the practical inductor energy density can still be estimated. In all cases *N*=438 turns of flat wire 10x1mm were used. The legs were built from circular ferrite disks with radius *R*=20mm and height *h*=7.5mm to realize a distributed air gap. According to the maximum allowed flux density (e.g. *B _{s}*=400mT for ferrite material), the necessary air gap length

*l*can be calculated to avoid saturation:

_{g}Consequently, for the maximum currents 37 A, 56 A and 80 A given in Table 1, 51 mm, 78 mm and 111 mm total air gap length are required. The inductor energy density

*w*is finally given by the relation between stored magnetic energy (primarily within the air gap volume

_{m}*A*) and inductor box volume

_{g}·l_{g}*V*:

_{bus}As depicted in Table 1, we obtain 847 Ws/m

^{3}, 1269 Ws/m

^{3}and 2599 Ws/m

^{3}, which demonstrates, that the inductor energy density is approximately proportional to the winding current density.

**References:**

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[5] S. Lee: Optimum Design and Selection of Heat Sinks, IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 18, no. 4, 1995, pp. 812 817

[6] P. Teertstra, M. M. Yovanovich, J. R. Culham: Analytical Forced Convection Modeling of Plate Fin Heat Sinks, Journal of Electronics Manufacturing, vol. 10, no. 4, 2000, pp. 253 261

[7] U. Drofenik, J. W. Kolar: A Thermal Model of a Forced-Cooled Heat Sink for Transient Temperature Calculations Employing a Circuit Simulator, International Power Electronics Conference IPEC, April 2005

[8] U. Drofenik, G. Laimer, J. W. Kolar: Theoretical Converter Power Density Limits for Forced Convection Cooling, PCIM Europe Conference, June 2005, pp. 608 619

[9] J. Biela, J. W. Kolar: Cooling Concepts for High Power Density Magnetic Devices, 4th Power Conversion Conference PCC, April 2007