IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 2, MARCH 2004
531
Comparison of Realization Techniques for
PFC Inductor Operating in Discontinuous
Conduction Mode
Vytenis Leonavičius, Maeve Duffy, Associate Member, IEEE, Ulrich Boeke, and Seán Cian Ó Mathúna
Abstract—Several design techniques are compared for producing a power factor correction (PFC) boost inductor operating
in discontinuous conduction mode. In this application, fringing
fields associated with high frequency current pulses cause problems of winding loss in the vicinity of an air gap, in particular
with planar core shapes. For this reason, a planar inductor in
which a lumped gap is replaced by a distributed air gap material
is described and investigated. The consequences of lumped versus
distributed air gap for the losses of the boost inductor are investigated. A significant reduction in ac winding loss of the planar
structure with the composite core is demonstrated. However, the
trade-off between reduced winding loss and increased core loss
for this technique has to be considered along with the selection of
proper winding technology. Four boost inductor design realizations are built and compared. Presented winding loss models are
verified with measurements on prototypes operating in an 80 W
PFC converter.
have disadvantages in modern power converters, considering
mechanical integration and manufacturability of the magnetic
component. Low profile (planar) magnetic cores may incur
even higher ac winding losses due to the fringing fields in the
vicinity of the air gap. It is important to choose the proper
magnetic core structure, material, air gap strategy and winding
technology to achieve optimum performance of the magnetic
component. However, the design procedure is somewhat complicated where topologies involve variable switching frequency
and variable current amplitude, which is considered in this
application. These issues are addressed in the paper, giving the
comparison of different techniques to achieve the optimum PFC
inductor design. The performance of several boost inductor
realizations is compared in an 80 W PFC converter.
Index Terms—Air gaps, chokes, composite magnetic core, discontinuous conduction mode, inductors, loss measurement, magnetic devices, magnetic materials, planar magnetics, power factor
correction, windings.
II. ISSUES FOR BOOST INDUCTOR IN DCM OPERATION
I. INTRODUCTION
T
HE BOOST inductor in power factor correction (PFC)
circuits operating under discontinuous conduction mode
(DCM) requires careful design. Conventional PFC inductors
operating in continuous conduction mode (CCM) with constant
switching frequency have a straightforward design procedure,
which allows accurate selection of the inductor realization,
core size, and winding type and size. Here, low ac ripple often
has negligible impact on the winding and core design strategy,
which mainly depends on dc current levels in the component.
In DCM operation, significant core losses may be incurred due
to corresponding high levels of magnetic flux swing. Large
current ripple causes problems of ac winding losses, which
requires special attention to the winding design. Conventional
wire-wound component designs with high profile cores using
litz wire can help in reducing ac effects. Such realizations often
Manuscript received November 21, 2002; revised August 21, 2003. This work
was supported in part by PEI Technologies. Recommended by Associate Editor
J. A. Ferreira.
V. Leonavičius and S. C. Ó Mathúna are with the Energy Processing for ICT,
National Microelectronics Research Centre, Cork, Ireland (e-mail: vytenis.leonavicius@nmrc.ie; cian.omathuna@nmrc.ie).
M. Duffy is with the Department of Electronic Engineering, Nun’s
Island, National University of Ireland, Galway, Ireland (e-mail: maeve.
duffy@nuigalway.ie).
U. Boeke is with Philips Research Laboratories, Group Electronic Modules,
Aachen 52066, Germany (e-mail: ulrich.boeke@philips.com).
Digital Object Identifier 10.1109/TPEL.2003.823249
PFC boost converters in DCM operation have several interesting features [1]. A sophisticated control technique is used
in this particular application to minimize conducted differential mode interference [2]. The switching losses in the boost
diode are low because of a reduced reverse recovery current.
The power metal oxide semiconductor field effect transistors
(MOSFET) can operate with zero voltage switching for input
voltages less than 50% of the output voltage. Also, less energy
must be buffered in the boost inductor compared with converter
designs operating in continuous conduction mode (CCM) [3].
However, the resulting complex current waveform in Fig. 1
has three variable parameters: current amplitude, frequency
and duty cycle. High switching frequency and duty cycle are
modulated over a period of 10 ms (half the mains period).
Such operation complicates the conventional design procedure
for the magnetic component [4]–[6], as the evaluation of core
and winding losses is not straightforward due to variability
of electrical parameters over the wide range.
Inductors designed to operate in DCM have lower inductance
values than those operating in CCM, so that a smaller physical
inductor size may therefore be expected. However, due to large
value of ripple current in DCM, ac winding losses may be larger
than in CCM. Similarly, large flux swings have the potential to
incur higher core losses than with CCM.
As the design of high frequency magnetic components is
driven mainly by the thermal performance, the net reduction
in size of a DCM inductor is therefore limited by the need to
reduce the thermal resistance of the structure to allow higher
ac power losses. Existing wire-wound and planar inductor
structures with two different winding technologies—litz wire
and PCB—will be compared. Emphasis will be given to
0885-8993/04$20.00 © 2004 IEEE
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 2, MARCH 2004
Fig. 1. Boost inductor current waveform (a) over rectified mains period and
(b) waveform over 1 ms.
the investigation of planar magnetic structures as they offer
improved manufacturability (integration and packaging of the
converter) and thermal performance (larger surface to volume
ratio). The distributed air gap technique, which involves the
combination of the low permeability and high permeability
magnetic materials, will be presented as a way of reducing ac
effects in inductor winding.
III. PFC INDUCTOR TOPOLOGIES
In general, the most important limiting factors in PFC inductor design are core saturation and temperature rise arising
from winding and core losses. The conventional approach is
a wire wound magnetic component with a high permeability
gapped ferrite core or the toroidal core with low permeability
distributed gap material as shown in Fig. 2. Litz wire is generally used to control ac winding loss due to skin and proximity effects caused by the large ripple current. Gapped core
structures usually have a significant fringing field around the
lumped air gap because of the large flux swing in DCM operation. Winding turns positioned close to these fringing fields
will generate high eddy current losses. High frequency electromagnetic fields in the vicinity of the gap may cause problems of interference with neighboring circuitry [7]. These issues may decrease the performance of the inductor as well as
the overall circuit. Toroidal cores with powdered metal material
(low permeability) have inherently distributed air gaps. Having
the winding distributed uniformly around the entire core will
keep stray magnetic flux and EMI propagation very low. A less
desirable feature of distributed air gap materials is their large
levels of specific core loss compared with high performance ferrites. Most popular distributed air gap materials currently available for power applications—Permalloy powder (MPP), Kool
Fig. 2. Wire-wound magnetic components: (a) gapped ferrite U core,
(b) distributed gap toroidal core.
and powdered iron—have specific core loss 5 to 20 times
greater than ferrites. DCM operation at switching frequencies
above 50 kHz will result in a core size which is not fully utilized. High performance MPP toroidal cores usually are more
expensive than ferrite cores. Considering the additional costs
for manufacturing such components, toroidal cores are not an
attractive solution for this application and will not be discussed
in this paper.
While litz wire can reduce high frequency losses, this
advantage has limited frequency range and is not a universal
solution [8]. The need to remove turns from the vicinity of the
air gap (with large fringing fields) requires additional efforts
during manufacturing. An alternative approach is a planar
design as shown in Fig. 3. Planar cores have a higher surface
area to volume ratio compared with conventional cores, so
that structures with lower thermal resistance and consequently
lower temperature rise may be designed for the same power
losses [9]. Moreover, planar windings with thin tracks offer
a convenient solution for reducing ac winding losses due to
skin and proximity effects. This technology is compatible
with multilayer PCB manufacturing which provides improved
manufacturability of planar magnetic components. One of the
main drawbacks of PCB windings is the reduction in window
copper utilization when compared with wire-wound design
[10]. This also impacts on the issue of fringing fields [11],
where due to limited window space, it is not possible to remove
windings from the vicinity of the gap. The resulting effects
of increased winding losses may therefore inhibit the use of
planar structures in DCM applications.
LEONAVIČIUS et al.: COMPARISON OF REALIZATION TECHNIQUES FOR PFC INDUCTOR
533
Fig. 3. Planar magnetic component, lumped gap.
Fig. 4.
Planar magnetic component, distributed air gap.
By replacing the lumped gap with a low permeability magnetic material which has a distributed air gap, a method for
overcoming the problems described is provided. The use of distributed air gap materials has been described previously both
for wire-wound high profile and planar magnetic structures, including number of examples of quasidistributed gap techniques
[12]–[20]. The resulting improvement in ac winding losses has
been attributed to the redirection of the magnetic leakage fields
parallel to the length of the winding structure in a 1-D field pattern [13]. The planar structure presented in Fig. 4 is proposed
as being compatible with planar windings (PCB or similar technology). Here the I-part of a standard planar ferrite EI core set
is replaced with a distributed air gap material. A similar structure has been described in [21] for application in a combined
inductor-transformer device. Composite core with 2 different
magnetic materials is an attractive solution, which allows exploitation of inherent advantages of the materials while minimizing each material’s shortcomings [22]. Analysis of winding
and core loss is necessary to demonstrate the trade-off between
reduced winding loss and increased core loss in the distributed
air gap solution using composite planar core.
To illustrate the level of improvement in winding loss, 2-D
finite element analysis (FEA) simulation of a planar winding
structure was carried out for 3 different versions of a gapped
E-PLT 22 core set [23]. These included a lumped gap in the central core leg, a lumped gap distributed between central and outer
core legs (spacer gap) and a composite core with distributed air
gap material for I-plate. During simulation, a pure sinusoidal
ac current with frequency of 200 kHz was used to produce the
magnetic excitation. The four-layer PCB winding had 20 turns
with copper track thickness of 0.105 mm (3 oz. copper), which
is less than the skin depth at the operating frequency. The gap
size in the lumped gap designs (centre gap and spacer gap) is
normalized to the core window height. For the distributed air
gap design, the permeability of the I-plate in a composite core
is adjusted so that it produces the same total reluctance as of
the lumped gap design; from here the equivalent air gap size
is calculated assuming high permeability of the ferrite in both
Fig. 5. (a) AC winding resistance versus effective air gap and (b) total winding
resistance versus ripple.
core parts E and I. The factor of increase in ac winding resistance over dc resistance is plotted as a function of the effective
gap length in Fig. 5(a). As expected, ac winding resistance in
the distributed air gap solution is smaller than that in either of
is only 1.5 for the disthe lumped gap approaches;
tributed air gap approach, as compared with factors of 4 and 14
for the lumped gaps. However, in a typical DCM inductor application, the total current includes components of ac (ripple)
and dc current so that the level of improvement in winding loss
provided by the distributed gap approach is generally less than
given in Fig. 5(a). The total winding resistance over dc resistance as a function of percentage ripple current in Fig. 5(b) illustrates the level of improvement in winding loss to be expected
for different planar inductor realizations. For example, 200%
ripple means DCM operation, taking into account ac current
ripple (sinusoidal wave shape for simplified analysis) with a dc
component present. Total winding resistance in the distributed
for I-plate) design increases very little over
air gap (
. Equivalent spacer gap
its dc resistance
(0.25 mm spacer) design results in a doubled value of winding
resistance. However, centre gap (0.5 mm) design yields over five
times higher total winding resistance over its dc resistance.
The improvement of the ac winding effects in the planar structure with the composite core is evident. However, composite
cores with low permeability magnetic part will have higher core
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 2, MARCH 2004
TABLE I
BOOST INDUCTOR SPECIFICATIONS
Design no. 1: wire-wound design, gapped ferrite core, litz
wire winding [Fig. 2(a)].
Design no. 2: planar design with gapped ferrite core, litz
wire winding (Fig. 3).
Design no. 3: planar design with gapped ferrite core, PCB
winding (Fig. 3).
Design no. 4: planar design with distributed air gap, composite core, PCB winding (Fig. 4).
A. Application Specifications
Specifications for the boost inductor were derived from circuit simulation of the PFC converter described in [1], [2]. Both
switching frequency and duty cycle are modulated over a period of 10 ms (half the mains period) producing inductor current
waveform as shown in Fig. 1. Corresponding specifications for
the boost inductor are given in Table I.
B. Inductor Design Procedure
Fig. 6. (a) Core loss and (b) total inductor losses for different plate materials.
losses when compared with cores made of ferrite material only.
and powPopular distributed air gap materials MPP, Kool
dered iron were compared and values of core loss corresponding
to the conditions described above are presented in Fig. 6(a). Results for the planar ferrite gapped core (0.25 mm spacer) are
also included for comparison. Calculations were carried out for
a dc current of 1.5 A and a variable sinusoidal ripple current at
200 kHz.
As shown, 3F3 ferrite material from Ferroxcube [23] has
the lowest level of the specific core loss. MPP and Kool
materials [24] have higher levels, while powdered iron from
Micrometals [25] has the highest core loss. On the other hand,
total inductor losses (winding plus core losses) compared in
Fig. 6(b), show that design realizations with MPP and Kool
material outperform gapped ferrite core design, i.e. the
reduction in ac winding losses provided by presence of the
distributed air gap material is larger than the corresponding
increase in core losses. This illustrates that planar design
realization with composite core is a viable alternative to the
conventional lumped gap design. It also lends itself an attractive
solution with less manufacturing effort when compared with
the quasidistributed gap technique [15].
IV. PFC INDUCTOR DESIGN
Following the discussion in the previous section, four
inductor design structures were selected for further technical
analysis and practical measurements.
The standard procedure in selecting the optimum magnetic
core size is the area product approach [4], which relates electrical
and magnetic parameters with the core size and geometry.
High frequency effects can be included to get a more accurate
method [6]. Due to the continuously varying waveform over
time and high peak current to rms ratio, optimum design of
the boost inductor cannot be achieved in a single attempt.
A procedure that gives the initial design for the maximum
thermal stress of the component is described in Appendix I.
The assumption of the maximum operating frequency, flux
density and corresponding peak current yields a selection of
the core size larger than optimum.
Since the average frequency and flux density values over the
mains period are lower than the chosen maximum boundary
conditions, design optimization is necessary to produce the
smallest inductor size for the maximum allowed thermal stress.
The optimization takes into account component losses in the
core and the selected winding structure.
Estimations of winding and core losses must account for the
time-varying nature of the applied current waveform in Fig. 1.
For the purpose of this work, each half of the mains period was
divided into 10 equal time intervals and one representative pulse
was used to describe the current waveform over each time interval. Each point presented in Table II has fixed current am, frequency and duty .
plitude
Core losses of the magnetic component can be calculated
using modified Steinmetz equation for each representative current pulse, with an equivalent switching frequency to account
for nonsinusoidal waveform [28], [29]
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535
TABLE II
EXTRACTED TIME POINTS FROM THE CURRENT ENVELOPE
(1)
Here,
—core loss density
, f—switching fre—equivalent frequency,
—peak magnetic flux
quency,
, x, y—empirical parameters [36], which can be
density,
obtained from the magnetic core manufacturer. Total core
losses are calculated as the average power loss density of all
ten time intervals from Table II multiplied by the effective core
volume
(2)
The winding design can be optimized using analytical
methods [5], [8], [26] or FEA methods to account for 2-D field
effects [27]. Skin and proximity losses in wire wound designs
with litz wire can be calculated using 2-D analytical calculation
method [30], which accounts for the H-field distribution in the
winding area including fringing effects. FEA simulation tool
[31] will be used to calculate winding losses for the planar
gapped core with multilayer PCB winding. Such a structure
presents a 2-D problem as shown by the H-field distribution
in Fig. 7(a), which is difficult to evaluate accurately with
analytical tools.
For the distributed gap design in Fig. 7(b), magnetic field
in the winding area is almost 1-D and the Dowell’s analytical
approach [33] can be used to estimate ac effects in the PCB
winding as described in [34]
(3)
where
—ac resistance factor, p—number of parallel layers
(=PCB layers), h—copper track thickness, —skin depth at
given frequency, —layer packing factor, —turns per layer,
wc—copper track width, ww—core window length.
The ac effect correction factor in (3) is for one fundamental
harmonic frequency. To account for the nonsinusoidal nature
of the inductor current waveform, the losses can be calculated
using Fourier series expansion for each of the representative
time point i over the mains period
H
Fig. 7.
-field distribution for different air gap techniques: (a) planar EI core
with spacer gap, (b) planar EI core with distributed air gap in the I part.
ac current harmonic,
—ac resistance factor for jth harmonic
and
frequency. For the triangular current waveform
have the following expressions:
(4)
—winding losses for the ith triangular pulse extracted
where
from the inductor current envelope,
—dc winding resistance,
—dc current component,
—amplitude of the jth
(5)
of triangular waveform and duty D are deThe peak value
fined in Table II. Fourier series expansion up to the 7th harmonic
can be taken to give the accurate result. This
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 2, MARCH 2004
TABLE III
COMPARISON OF INDUCTOR DESIGNS, L = 120 H
method proves to be useful to calculate winding losses in combination with FEA simulations tool [31]. Alternative calculation
procedure for arbitrary current waveforms is described in [26],
which presents a straightforward formula to calculate effective
winding resistance without performing Fourier analysis. Having
calculated winding losses for each time interval, the total losses
are equal to the average value
(6)
As the last step temperature rise
of the magnetic compoof the
nent can be evaluated taking the thermal resistance
magnetic component
(7)
Previous work in [9], [35], [36] describes an empirical forof a magmula which relates the value of thermal resistance
netic component directly to the value of the effective magnetic
volume .
As mentioned earlier, the optimization involves the winding
design for the selected core size. A further optimization can be
done for the core size and shape considering the component temperature rise. This complete design procedure is valid for the
boost inductor operating in DCM, where both core and winding
losses must be taken into account.
V. COMPARISON OF DIFFERENT REALIZATIONS
Four different inductor designs mentioned in the beginning
of Section IV are summarized in Table III. Design no. 1, made
with standard U15/11/6 core of 3C94 ferrite [23] was chosen for
the initial wire-wound solution. In order to control eddy current
losses, 63 0.071 mm litz wire was used in the winding. The
air gap was realized inserting spacers between the U-core halves
on each leg. Design no. 2 is a low profile solution with reduced
thermal resistance (almost by 33% if compared with design no.
1). It has the planar E-PLT 22 core of 3F3 ferrite material [23].
The same litz wire 63 0.071 mm was used to construct the
winding. Such a winding is very difficult to manufacture for a
planar core construction. An alternative cost effective solution
with improved manufacturability is the design no. 3.
The winding is made with four layer 3 oz. copper PCB. Each
layer in the winding has 5 turns with track pitch of 1.04 mm
(0.300 mm spacing). Both design no. 2 and no. 3 have the same
air gap size, which is realized with the spacer between the E
part and the I part of the planar core. Design no. 4 represents
distributed gap approach. It has a composite planar E-PLT 22
and I
core, where E part is made of 3F3 ferrite
material with permeplate was cut from the slab of Kool
[24]. As in the design no. 3 the winding is made
ability
with four-layer PCB. The number of turns for this design was
deliberately increased in order to reduce the peak flux density
in the core.
A. Comparison of AC Winding Resistance
All four designs are compared in terms of the winding
resistance under ac current excitation for the frequency range
up to 400 kHz. Calculations for wire wound designs no. 1
and no. 2 (with litz wire) were done using 2-D analytical
model described in [30]. Design no. 3 and no. 4 (with PCB
winding) analysis was done with 2-D FEA [31]. The simulation
procedure is based on the division of the winding of the magnetic
component into two parts, which produce field distribution in
different planes. The planar conductor inside the magnetic core
window is modeled as the first part, and the end-turns outside
core are modeled as the second part. Planes which represent
H-field distribution of these two segments are perpendicular
to each other. In this way it is possible to perform an accurate
studies of a 3-D planar E-PLT structure using 2-D FEA tool.
LEONAVIČIUS et al.: COMPARISON OF REALIZATION TECHNIQUES FOR PFC INDUCTOR
537
TABLE IV
WINDING RESISTANCE
This so-called “Double 2-D” method is described in [32].
Table IV shows calculated values of the winding resistance
for several operating frequencies.
i.e. ac winding resistance
The factor
over dc resistance is calculated to compare all designs. According to the calculations in Fig. 8, ac effects are lowest
for the design with distributed gap approach (design no. 4),
over the
because of the smallest values of the ratio
frequency range. This can be attributed to the 1-D magnetic
field distribution in the winding area (H-field has dominant
horizontal component, minimum eddy currents). On the other
hand, design no. 2 (planar core, litz wire) shows the highest ac
effects. The winding in the planar structure is closer to the air
gap (lower window height) with high fringing field perpendicular to the winding. Litz wire does not help to reduce ac effects.
Design no. 1 has a similar trend to design no. 2, except that
the first has U core with larger window to accommodate the
winding further away from the air gap.
Design no. 3 (planar core, PCB winding) has better performance than design no. 1 and no. 2. PCB winding is shifted
away from the air gap, although 2-D field distribution within
the winding area has larger vertical component than for the design no. 4 and this causes significant ac winding losses.
The 2-D FEA calculation for the planar gapped core with
multilayer PCB winding (design no. 3) gives a reasonably accurate representation of ac effects in the winding, while 1-D
analysis based on Dowell’s approach gives false result as shown
in Fig. 9(a). For the distributed gap design, 1-D analysis shows
comparable results with 2-D FEA simulations as demonstrated
in Fig. 9(b). Therefore, it validates the (3) to estimate ac winding
effects for the design no. 4.
Fig. 8. AC winding resistance versus frequency.
B. Comparison of Inductor Power Losses
In this section high frequency power losses of the inductor
operating in PFC converter are examined. Calculation results
require experimental validation under actual operating conditions. Performance of the inductor design realizations was
input and
studied in a 80 W PFC converter with 85
output. The measurement setup for total inductor
385
power losses is described in Appendix II and the summary of
these results is presented in Table V.
The lowest power losses have been measured for design no.
1 with a U-core [Fig. 10(a)]. The planar design no. 3 has twice
the power losses compared with design no. 1. However, these
higher losses produce only about 30% higher temperature rise
[Fig. 10(b)] since the planar core has a lower thermal resistance
to ambient.
The higher power losses in this case are due to higher
winding losses. PCB winding in the design no. 3 has 3 times
lower copper cross section (see Table III) when compared
Fig. 9. Comparison of ac resistance calculation methods: (a) design no. 3 and
(b) design no. 4.
with litz wire winding in design no. 1, resulting in higher rms
winding losses. Calculations show that this is even worse for
the design no. 4, which has rms losses similar in the magnitude
of the total losses for the designs with litz wire. Gapped
core designs, however, show significant ac winding losses
accounting around 40% for the design no. 1 and no. 3 to 57%
for the design no. 2 of the total winding losses.
A possible solution to reduce eddy currents in PCB windings of a planar magnetic component is illustrated with planar
inductor design no. 4. Skin and proximity winding losses for
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TABLE V
INDUCTOR PERFORMANCE IN PFC CONVERTER; COMPARISON OF CALCULATED (LEFT) AND MEASURED DATA (RIGHT), (N.V=NO VALUE)
plate.
higher core losses due to the properties of the Kool
As a result, design no. 4 has the highest total losses of all inductors investigated. Nonetheless, planar inductor design no. 2
with litz wire shows by how much the winding rms loss of design no. 3 and no. 4 could be reduced for the case of increased
copper fill factor. This design also has the lowest temperature
rise as demonstrated in Fig. 10(b). The higher core loss in this
case is due to lower ferrite core temperature and the temperature
characteristic of 3F3 ferrite material, where the minimum core
loss is observed at 80 [23].
The accuracy of the models applied for predicting winding
and core losses for the complex current waveform associated
with DCM has been verified by measurements for the design
no. 1 (no error) and the design no. 4 (2.5% error). Somewhat
larger errors between calculations and measurements are observed for the design no. 2 (12% error) and the design no. 3
(8.75% error). In design no. 2 the presence of the lumped air
gap and the leakage fields that link with the winding paths outside the core were not accurately evaluated. Possible error may
come from the winding termination [37] in the measurements of
prototypes, which was not addressed in the technical analysis.
VI. CONCLUSION
Fig. 10. Inductor performance in PFC converter: (a) power losses and
(b) measured peak temperature rise.
the current waveform of Fig. 1 are at least half those in designs with litz wire (design no. 1 and no. 2) and more than
5 times smaller than those produced in the design no. 3 with
PCB winding [Fig. 10(a)]. Unfortunately, the improvement in ac
winding losses has been achieved with much higher rms losses
in the winding due to the lowest copper fill factor, and also
The design of planar inductor with a distributed air gap instead of a lumped gap is described for application in a PFC boost
converter operating under DCM. The motivation for removing
the lumped gap in planar core structure is the potential for reducing ac winding losses caused by high ripple current levels in
this application. However, as shown, additional core losses are
incurred in distributed air gap materials. Analysis of winding
and core losses is presented to illustrate the overall performance
and MPP
achieved with different materials available. Kool
materials are predicted to provide improved performance over
an equivalent lumped gap design.
inductor realizations were built to compare
Several 120
the performance of design strategies, involving different
winding technologies (litz wire versus PCB), core shapes (high
profile versus planar) and gapping techniques (lumped air gap
LEONAVIČIUS et al.: COMPARISON OF REALIZATION TECHNIQUES FOR PFC INDUCTOR
versus distributed). The performance was investigated analytically and confirmed with operation in an 80 W PFC converter.
A significant improvement in ac winding losses of planar core
structures was observed with distributed air gap technique.
However, large ac flux density levels in DCM operation result
material. This might have
in high core losses for Kool
been improved by applying materials with lower specific loss
(e.g. MPP), if the required shapes were available. Also, poor
copper utilization in PCB windings resulted in significant rms
winding losses. These are the two major reasons why overall
losses for the distributed gap approach were larger than for
the lumped gap designs. Also, it has been shown that winding
loss for planar structure may be reduced by increased copper
utilization. This may be achieved by reducing the thickness of
dielectric layers e.g. by using FLEX PCB or stamped copper
windings.
From the technical analysis, it appears that 1-D approach is in
a good agreement with 2-D FEA simulations for the distributed
gap design, which simplifies the design procedure for boost inductor with the complex current waveform. From the practical
analysis some discrepancies were observed between the calculations and measurements. This may be due to the fact that
winding termination was not addressed properly in the technical
analysis. However, total power loss measurements show good
agreement with the calculated results.
Although wire wound component with conventional high
profile gapped core outperformed other design realizations,
all structures including the distributed air gap inductor meet
performance specifications. It is worth noting that elimination
of the lumped air gap may provide a solution with reduced
EMI.
APPENDIX I
INITIAL INDUCTOR DESIGN PROCEDURE
The initial design assumes fixed values of the frequency and
the flux density, which produces the maximum thermal stress
of the magnetic component. The standard procedure using area
product approach [4], allows the selection of the core size for
the given specification parameters from Table I. Maximum operating frequency of 220 kHz and maximum ac flux density
(for the ferrite material) can be assumed as a
boundary condition. Further calculation of physical winding and
air gap is governed by the well known inductance expressions
(8)
,
—corresponding peak
where: L—inductance value,
values of the current and flux density, N—number of turns,
—cross section area of the core, —air gap length, —gap
. In calculating the air gap required
area,
to achieve accurate inductance value, the effective area of the
gap is increased by adding the gap length to both the width
and breadth of the core section to correct for fringing fields.
This iterative calculation method is described in [12]. Gap
length can be calculated iterating
(9)
This procedure is common for the design realizations with
gapped cores (design no. 1, 2, and 3). For the design with com-
539
posite core using two different magnetic materials initial design
procedure is based on the reluctance model shown in Fig. 11.
Reluctance of the particular core part is described by
(10)
where:
—relative permeability, —length and —area of
the section .
E part of the core is made of a standard high permeability fer) and I part of low permerite material (typically
ability distributed air gap material. Material MPP has the lowest
specific losses among other distributed gap materials [24]. However, as this material is only available in the form of ring cores,
with similar material properties has been chosen as
Kool
the next best option. E cores (from which I plate can be cut)
with permeability values of 26, 40, 60, and 90 are commercially
available [24].
The dimensions of the magnetic I plate assumed equal to
those of the standard planar EI core set in order to keep the constant flux density across the entire structure. Using the permeof the different Kool
material and the
ability value
, the number of turns
effective plate length in the model for
is calculated
N which provides the total inductance
for each material
(11)
Flux density
culated with
in the corresponding core part can be cal(12)
Core loss for the boundary conditions are calculated separately for the E part and the I plate. Specific loss data for the
and ferrite materials are provided by the manufacKool
turer in [23], [24], and [36]. Suitable composite core design
can be selected based on the minimum total component losses,
adding up winding and core losses for each design. Following
this methodology, it can be shown that the lowest losses in the
composite core are predicted for the plate with the lowest perin this case).
meability value (
APPENDIX II
INDUCTOR POWER LOSS MEASUREMENTS
The direct electrical measurement of inductor power losses
under the large signal operation, illustrated with Fig. 1, is not
possible since the reactive power flow already claims most
of the resolution of measurement equipment. Additionally,
the complex current time function with triangular waveform
modulated in amplitude and frequency with twice of the mains
frequency would require an enormous resolution in time.
Thus a thermal technique [38], [39] has been used to identify
inductor power losses using component temperature rise as an
intermediate result.
During the measurements, the inductor has been mounted in a
plastic test box filled with quartz sand illustrated with Fig. 12(a).
Due to the quartz sand, the heat transportation is limited to conduction and both convection and radiation inside the box are not
present. The absolute thermal resistance of this test box is less
K/W . However, it is very important that
important
540
Fig. 11. Reluctance model of planar design no. 4 with composite core.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 19, NO. 2, MARCH 2004
measured with 3 PT100 resistors mounted on component surface positions illustrated in Fig. 12(b).
In the third test the inductor has been mounted on its own
100 mm size. Other heat
printed circuit board of 160 mm
generating power components were removed from the board. In
this test the inductor has been stressed again with the boost converter current like in the first test. The measured temperature
rise of the winding and the core is given separately in Table V.
Finally, the last row of Table V gives the ratio of peak temperature rise divided by the measured power losses as an indication for thermal resistance of such a component mounted on a
printed circuit board. The range of measured thermal resistances
for E-PLT 22 core set is 24 K/W 29 K/W. These values are
somewhat lower than the values (31 K/W 42 K/W) presented
in [39] for the same E-PLT 22 core set. This mainly resulted
from different test conditions. In [39], heat transportation was
mainly due to convection, while in our test additional heat conduction was present from the planar core to the ambient via the
PCB. Errors of the power loss measurements have the following
sources:
2% accuracy of the boost converter current;
—
2% accuracy of the dc power load;
—
2 to 6% accuracy of each temperature rise measure—
ment for a constant absolute error of 1 ;
slightly different heat distribution around the inductor
—
for the operation with boost converter and dc current.
ACKNOWLEDGMENT
The authors wish to thank Dr. P. Luerkens, Philips Research
Laboratory Aachen, for discussions of the boost converter design, and G. Kowalin, Philips Research Laboratory Aachen, for
the preparation of magnetic material plates.
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Fig. 12. Thermal measurement setup: (a) test box and (b) position of
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first test. We assume that the dc power losses of the second test
are equal to the unknown power losses of the first test since both
tests generate the same temperature rise for the same thermal
resistance. The temperatures during these two tests have been
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Vytenis Leonavičius was born in Kalvarija, Lithuania, in 1974. He received
the M.Sc. degree in electrical engineering from Kaunas University of Technology, Lithuania, in 1998 and is currently pursuing the Ph.D. degree in microelectronics at the Energy Processing for ICT Team, National Microelectronics
Research Centre, University College, Cork, Ireland.
His main research area is in the design of planar magnetics for switch mode
power supplies, with the focus on functional integration and packaging.
Maeve Duffy (S’95–A’96) was born in Monaghan, Ireland. She received the
B.E. degree (with honors) in electronic engineering and the Ph.D. degree in
planar magnetics from the National University of Ireland, Galway (NUIG), Ireland, in 1992 and 1997, respectively.
She was a Research Officer with PEI Technologies, National Microelectronics Research Centre, Cork, Ireland, from 1997 to 2001. She is currently
a Lecturer with the Department of Electronic Engineering, NUIG. Her main
research interests are in modeling and design of magnetic components,
including planar magnetics and magnetic sensors.
Ulrich Boeke received the M.Sc. degree from the Darmstadt University of Technology, Germany, in 1991.
He has joined the Electronic Modules Group, Philips Research Laboratories,
Aachen, Germany. He is a Senior Scientist in the field of power electronics for
consumer electronics such as displays and lighting systems.
Seán Cian Ó Mathúna received the B.E., M.Eng.Sc., and Ph.D. degrees from
the National University of Ireland, Cork, in 1981, 1984, and 1994, respectively.
From 1982 to 1993, he was instrumental in establishing the Interconnection
and Packaging Group, National Microelectronics Research Centre (NMRC),
University College Cork, Ireland, where he held the position of Senior Research
Scientist. In 1993, he joined PEI Technologies, NMRC, as Technical/Commercial Director, where he was responsible for power packaging, planar/integrated
magnetics, and product qualification. In 1997, he rejoined NMRC as Group
Director with responsibility for Microsystems. In 1999, he was appointed as
Assistant Director for NMRC with responsibility for microelectronics integration with research themes in ambient electronics, biomedical microsystems, and
energy processing for ICT.