4000 IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005 Distributed (Parallel) Inductor Design for VRM Applications C. Collins and M. Duffy, Member, IEEE Power Electronics Research Center, Department of Electronic Engineering, National University of Ireland, Galway, Ireland The design of planar magnetic components for application in voltage regulator modules (VRMs) is investigated. In particular, the application of distributed magnetic structures that facilitate locating the VRM closer to the processor load is proposed, so that interconnect impedance and its effects can be reduced. It is shown that in addition to facilitating VRM packaging, the utilization of winding and core regions is improved by replacing a single lumped component with parallel and coupled inductor designs. Index Terms—Distributed magnetics, planar magnetics, voltage regulator module (VRM) inductor. I. INTRODUCTION T IS WIDELY accepted that future voltage regulator modules (VRMs) must be located closer to the load so that voltage deviations due to interconnect impedance can be reduced. However, a major limit is the size of magnetic components required; increasing current levels and tighter regulation windows translate to inductor requirements of higher inductance and current, which make miniaturization more difficult. In an effort to reduce output capacitor size, interleaved phases result in a partly distributed magnetic solution, in which total output current is divided between a number of phases. However, it has been found that the overall size of magnetic components can be larger than that of a single buck inductor [1]. Coupled inductors provide smaller solutions [2], [3], but interconnection with the load is not so flexible, as high current interconnects are coupled together. The possibility of replacing a single lumped inductor with equivalent parallel (i.e., distributed) components was investigated in this work, for each inductor in a four-phase interleaved buck circuit. Both cases of noncoupled and coupled inductors are investigated. Results illustrate how, in addition to being more compatible with load interconnects in this application, distributed components offer improved power density by improving the utilization of winding and core regions. Methods for determining optimum levels of distribution are proposed. A design study of VRM inductor structures is presented, in which detailed modeling and analysis of component performance provides an insight into limits to miniaturization. Magnetic component design is based on standard ferrite cores with PCB windings, as this technology is readily available and already widely applied in this application [2], [4]. Admittedly, PCB windings are not optimal for such high current levels, but as PCB substrates are used to connect the VRM to the load, the number of distributed inductors may be arranged to match the number of VRM output connector pins, thereby facilitating their placement closer to the load. Furthermore, it is shown that paralleling of inductors improves the utilization of PCB copper tracks, as high output currents see several paths having same impedance, rather than being limited to one larger path with variable impedance. I TABLE I COMPARISON OF INDUCTOR COMPONENT SPECIFICATIONS The advantages of distribution are illustrated by comparing lumped, paralleled and coupled inductors designed to provide the same steady-state ripple performance in a VRM10.1 circuit. Component design and modeling procedures are described in Section II, and a comparison of all designs is presented in Section III. It is shown that as a consequence of improved winding and core utilization, higher power density is achieved through distribution. Investigation of increasing levels of distribution shows that noncoupled inductors are limited by core saturation, with coupled components being limited by core loss. The highest level of power density is predicted for uncoupled inductors. Work is ongoing to determine effects of increasing switching frequency on VRM solutions, so that requirements of future magnetic technologies, including integrated magnetics on silicon [5] and cofired technologies [6], may be determined. II. VRM INDUCTOR DESIGN Typical inductor specifications for a four-phase interleaved buck circuit designed to VRM10.1 requirements are given in Table I. All components were designed to provide the same steady-state capacitor ripple current at a switching frequency of 500 kHz; i.e., each circuit phase has the same effective inductance. Clearly, for n parallel components, the inductance of each inductor must be n times larger, but individual current levels are reduced by the same factor. Specifications for equivalent coupled inductors are not so easily defined, but are found by analysing steady-state current waveforms. For example, for any two inductors that carry currents 180 out of phase in a phase interleaved buck converter, the equivalent self inductance per phase is given as (1) Digital Object Identifier 10.1109/TMAG.2005.855163 for a current ripple level, I, and a (negative) coupling factor k. In this case, each winding carries the same dc and ac current 0018-9464/$20.00 © 2005 IEEE COLLINS AND DUFFY: DISTRIBUTED (PARALLEL) INDUCTOR DESIGN FOR VRM APPLICATIONS 4001 level as the equivalent single component. It should be noted that voltage drops across switches were factored into the choice of inductance values given; switch losses were determined by circuit simulation in SPICE under full load conditions, with manufacturers models for the switches included. Fig. 1. Reluctance model of coupled inductor structure. A. Uncoupled Inductor Design The procedure described by core manufacturers was applied to design the uncoupled inductors [7]. All designs were based on standard planar ER and EE cores, with PCB capabilities as follows: eight layers, minimum track: gap of 200:200 m, maximum track height of 140 m. The core material was chosen to be 3F3 from Ferroxcube. In summary, the minimum number of turns was calculated as Fig. 2. Coupled inductor current waveforms in phases 1 & 3. (2) for a maximum flux swing so that core loss density Pv TABLE II COMPARISON OF INDUCTOR STRUCTURES (3) does not cause excessive temperature rise for a given core. The accounts for nonsinusoidal voltage waveforms apquantity plied to the core in this case [8]. Assuming a duty cycle of V/12 V, f was applied. The maximum number of turns that can be fit was limited by of winding loss (4) where, due to the presence of lumped gaps in all designs, it was necessary to apply finite element analysis (FEA) simulation to predict values for [9]. The minimum copper area required to carry an equivalent dc current level was deduced from standard graphs for PCB windings, and the maximum number of , then depends turns that can be fit in a given window area, on the limits of the PCB technology available. In this case, the maximum track width that could be fit in the core window was used. Contributions of winding and core loss were calculated , and the minimum loss for each resulting value of design was chosen for the smallest core than can handle applied current and flux levels, while also ensuring that the core material was not saturated. B. Coupled Inductor Design As designs were limited to standard core shapes in this work, only two inductors were coupled together at a time. Initial design was based on the core size determined for the equivalent single inductor solution, since it was known that the windings will fit. For simplicity of construction, a core with the gap distributed evenly on all three core legs was considered. Work is ongoing to consider alternative coupled structures. The reluctance model shown in Fig. 1 was applied to calculate the gap needed to provide the level of self inductance required. Note mmf directions are shown for dc currents in each inductor. Winding loss was found using FEA simulation as before. Core losses were estimated using (3) given above with values of B determined using the reluctance model in Fig. 1, with predicted current waveforms applied for mmf and mmf . A plot of simulated currents flowing in phase 1 and 3 of the test circuit is given for illustration in Fig. 2. It is interesting to note that due to the high level of I/DT in this case, currents flowing in the coupled inductors always act so as to produce flux cancellation in the outer core legs; i.e., di/dt has the same polarity in both windings. Therefore, the value of is lower than that predicted for the uncoupled inductors. Higher flux levels in the center leg are handled by the larger core area there. Calculations of total loss were repeated for the range of turns that could be accommodated within the limits of loss and saturation of a given core, and again the minimum loss design was chosen. III. COMPARISON OF MAGNETIC SOLUTIONS A. Component Structure and Size Following the procedures described in Section II, the structures of the different magnetic solutions compared in Table II were found. Clearly, uncoupled inductors have the smallest footprint area and the smallest height. It is worth noting that footprint includes the area occupied by copper tracks outside the core. It is seen that parallel components offer reduced footprint to a certain level of distribution. The resulting increased power density provided is explained by greater utilization of winding and core regions, and this is illustrated by comparing individual loss components for the different structures in Section B. Larger solutions for the coupled inductors is explained by restricted standard core sizes. Further improvement may be provided with custom cores. Maximum inductor height is 8.2 mm, which is well within specifications for VRM10.1. The height in this case is provided by the standard core needed to handle loss levels, but is not necessary for accommodating the windings. In terms of interconnection with the load, with 3 parallel components, there are 12 tracks available for connection with 19 socket pins. This should 4002 IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005 terms of transient response time. For the uncoupled and coupled solutions, response times are given respectively, as (5) Fig. 3. Predicted winding and core loss for uncoupled inductor designs. Using the values given in Table I, it was found that coupled inductors provide the shortest response time of 5.3 s over a value of 8.5 s for uncoupled inductors. Shorter response time should be provided with higher coupling factor. The advantage of increased flexibility in interconnecting with the load will be verified in design and testing of prototype VRM board layouts. IV. CONCLUSION AND FUTURE WORK Fig. 4. Predicted winding and core loss for coupled inductor designs. Fig. 5. Comparison of power density for inductor designs. facilitate connection with the load when compared with four larger lumped inductor terminals. B. Component Losses Component winding and core losses are compared for uncoupled designs in Fig. 3. Clearly, ac winding losses are improved in the parallel solutions, and this is explained by reduced eddycurrent effects provided by successively smaller gaps and winding widths. When compared with the maximum loss levels allowed in each design, it is seen that copper utilization is improved by distribution. Lower levels of loss than allowed illustrate how designs were limited by saturation of the core rather than by losses in this case. Maximum flux density levels were in the range of 250–290 mT. In results for the coupled designs in Fig. 4, higher utilization of core regions is explained by the cancellation of dc flux levels, so that saturation is less restrictive. Instead, core losses limit designs in this case. As with uncoupled inductors, a consequence is that winding areas are not fully utilized. Again, it is seen that increasing the distribution level improves the ratio of ac to dc loss and therefore copper utilization. Output power density is compared for all designs in Fig. 5. As expected from Table II, parallel solutions offer the highest power density. The limit to increasing power density is explained by the restriction to standard cores available. The design of distributed parallel inductors to replace equivalent lumped components was described. Detailed modeling and analysis of a range of VRM10.1 inductor designs is presented to illustrate the limits to miniaturization imposed for a given winding and core technology. In addition to providing increased flexibility for interconnection with the load, it is shown that increased levels of power density are achieved by distribution. Noncoupled inductors provide the highest level of power density. Limits to distribution were encountered due to the restriction to standard cores, but work is ongoing to investigate the design of suitable custom cores. Future work will verify the results presented by measurement over different load conditions. The effect of increasing coupling factor will be determined for different coupled inductor structures. Similar analysis will be applied to determine the level of improvement provided for different magnetic technologies and for higher switching frequencies. Methods for optimum component design based on technology capabilities rather than on circuit requirements will be developed, so that designs can be easily scaled for future VRM specifications. REFERENCES C. VRM Performance [1] M. Duffy and C. Collins, “Investigation of passive components size in VRM applications,” in Proc. IEEE PESC, 2004, pp. 4340–4346. [2] P. L. Wong et al., “Performance improvements of interleaving VRMs with coupling inductors,” IEEE Trans. Power Electron., pp. 499–507, Jul. 2001. [3] J. Li, C. R. Sullivan, and A. Schultz, “Coupledinductor design optimization for fast-response low-voltage DC-DC converters,” in Proc. IEEE APEC, vol. 2, 2002, pp. 817–823. [4] J. Wei, P. Xu, and F. C. Lee;, “A high efficiency topology for 12 V VRMpush-pull buck and its integrated magnetics implementations,” in Proc. IEEE APEC, 2002, pp. 679–685. [5] M. Brunet et al., “Electrical performance of microtransformers for DC/DC converter applications,” IEEE Trans. Magn., vol. 38, no. 5, Sep. 2002. [6] W. A. Roshen et al., “Embedded magnetics for integrated power,” in Proc. PESC, 2004, pp. 2467–2473. [7] Design of Planar Power Transformers [Online]. Available: www.ferroxcube.com [8] M. Albach, T. Duerbaum, and A. Brockmeyer, “Calculating core losses in transformers for arbitrary magnetizing currents : A comparison of different approaches,” in Proc. IEEE PESC, 1996, pp. 1463–1468. [9] Ansoft, Maxwell, Electromagnetic 2D Field Simulator [Online] As components were designed to provide the same steadystate currents, the main difference in circuit performance is in Manuscript received February 7, 2005.