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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
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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
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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.