IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
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Characterization of Coreless Printed Circuit Board
(PCB) Transformers
S. C. Tang, Member, IEEE, S. Y. (Ron) Hui, Senior Member, IEEE, and Henry Shu-Hung Chung, Member, IEEE
Abstract—In this paper, coreless printed-circuit-board transformers are characterized. A range of coreless printed circuit
board (PCB) transformers with different geometric parameters
have been fabricated and tested. Based on a recently reported
analytic method, the self inductance of these transformers is
calculated. This analytical method is also extended to cover the
prediction of the transformers’ mutual inductance. All calculated
parameters have been confirmed with measurements for the
frequency range from 100 kHz to 30 MHz. These results provide
useful information for the optimal design of coreless PCB transformers.
Index Terms—Coreless PCB transformers, planar transformers
and windings, printed circuit board transformers.
I. INTRODUCTION
T
HE NEED for compactness in power converter has led to
the increase in operation frequency and the use of planar
magnetics. Recent research on planar inductors [1]–[3] and microtransformers [4]–[8] shows that thickness of magnetic material of these devices can be minimized to a few hundred of
micrometer ( m) and the switching frequency can exceed 1
MHz. Although much progress has been made in using printed
transformer windings, the use of magnetic cores in transformers
is still the dominant trend [4]–[9]. Transformers fabricated on
PCB eliminate the manufacturing cost of manual windings [9].
However, space is still required to accommodate the magnetic
cores.
Recently, the use of coreless PCB transformers [10]–[16]
have been reported. These transformers have been successfully
demonstrated in isolated MOSFETs/IGBT’s gate drive circuits.
Coreless PCB transformers do not need space to accommodate
the magnetic core and have no core limitations such as core
losses and saturation. Their sizes can be smaller than those of
core-based transformers. This inherent low-profile property
makes the coreless transformers suitable for applications in
which stringent space and height requirements have to be met.
Moreover, the dielectric breakdown voltage of PCB typically
ranges from 15 kV to 40 kV [17].
In this paper, the inductive characteristics of coreless PCB
transformers with different geometric parameters are studied.
Factors includes: i) outermost radius, ii) number of turns, iii)
conductor width, iv) laminate thickness and v) conductor thickManuscript received October 25, 1999; revised September 8, 2000. The authors are grateful to the Research Grant Council of Hong Kong for their support
of this project under Contract CERG 9040466.
The authors are with the Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong.
Publisher Item Identifier S 0885-8993(00)10578-2.
Fig. 1. Typical structure of a coreless PCB transformer with circular spiral
windings.
ness on the transformer’s characteristics are investigated. The
inductive parameters are calculated using a recently reported analytical method [18]. The calculated results are confirmed with
the measured results for the frequency range from 100 kHz to
30 MHz.
II. INDUCTANCES CALCULATIONS OF CORELESS PCB
TRANSFORMERS
The PCB transformer consists of three parts: the primary
winding, the dielectric laminate, and the secondary winding.
Planar windings of various shapes have been studied [2]. It has
been found that circular spiral windings provide the greatest inductance among various types of winding configuration. Fig. 1
shows the three-dimensional (3-D) structure of a coreless PCB
primary turns and
secondary
transformer. There are
turns, printed on the opposite sides of a double-sided PCB. The
PCB transformer can be built on the same circuit board with
other electronics. It can also be fabricated on another PCB as
a stand-alone device if desired. There is no need to cut hole
on the PCB for accommodating the magnetic cores in coreless
PCB transformers.
The spiral windings in Fig. 1 can be approximated as concentric circular windings connected in series [1] with infinitesimal
connections as shown in Fig. 2. For an -turns spiral coil, the
total self-inductance is the summation of each mutual induc, where
tance pairs between two concentric circular coils,
both and are from 1 to . Fig. 3 shows the -plane cross section of the transformer in Fig. 2. The mutual magnetic flux coupling of primary winding pairs is drawn by thick solid lines and
those of secondary winding pairs appear as thick dotted lines.
0885–8993/00$10.00 © 2000 IEEE
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
where
when
Fig. 2.
Approximation of circular spiral windings as concentric circles.
(6)
when
The self-inductance of the primary and secondary windings are
given by (1) and (2), respectively
(1)
(2)
is number of turns of primary winding and
is
where
number of turns of secondary winding.
Mutual inductance between the primary and the secondary
coils of a planar transformer can also be derived. For an
-turns secondary transformer, the mutual
turns primary and
inductance is the sum of mutual magnetic coupling pairs between primary and secondary coils. The thin arrows in Fig. 3
represent the mutual magnetic flux coupling between the primary and secondary windings. Thus, the mutual inductance between the primary and the secondary windings is given by
(3)
The leakage magnetic flux on the primary side is the difference between the total magnetic flux setup in the primary
winding and that coupled to the secondary. The primary leakage
inductance is given by
(4)
, between two circular
Derivation of mutual inductance,
tracks with rectangular cross section has been reported by
Hurley and Duffy [18]
(5)
permeability of vacuum;
first kind Bessel function of order zero;
inner radius of the th circular track;
outer radius of the th circular track;
height of the th circular track;
inner radius of the th circular track;
outer radius of the th circular track;
height of the th circular track;
separation between the circular tracks.
III. CORELESS PCB TRANSFORMERS WITH VARIOUS
GEOMETRIC PARAMETERS
Equations (1) to (6) indicate that all of the inductive parameters depend on the geometry of the coreless planar transformer.
These inductive parameters vary with
1) outermost radius;
2) number of turns;
3) conductor width;
4) lamination thickness;
5) conductor thickness.
The simulated results obtained from both (5) and the finite element analysis (FEA) [20] are consistent with the measured results. However, computation using the analytic solution in (5)
is more time efficient than that using FEA. The calculations
of self, mutual and leakage inductances of the coreless PCB
transformers using the analytical method are implemented by
MATLAB programs. The laminate used in the coreless PCBbased transformers under test is FR-4 material. The conductor
material is copper with gold plating. The geometry of primary
winding and secondary winding are the same, so they have the
same self-inductance. In this section, the testing frequency is 10
MHz. The effects of the frequency on transformer inductances
will be discussed in Section IV.
A. Different Outermost Radii with the Same Number of Turns
(Transformer Series #1)
A series of coreless PCB transformers with different outermost radii from 3 mm to 33 mm have been tested and simulated. These transformers have different track separation, but
have the same number of turns. The dimensions of this transformer series are tabulated in the second column of Table I. The
TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
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Fig. 3. Diagram showing coupling paths between various turns.
When the diameter,
, is much greater than the laminate
thickness, , the mutual inductance and the leakage inductance
increase linearly. Their asymptotes are given by
(8)
Fig. 4.
#1.
(9)
Dimensions of some coreless PCB transformers in transformer series
The mutual inductance and the leakage inductance can be represented as
(10)
(11)
Fig. 5.
Inductances of transformer series #1.
geometry of primary winding is the same as that of the secondary winding, and they are printed on the opposite side of a
double-sided PCB. Fig. 4 shows the dimensions of coreless PCB
mm to
mm) in this transformer
transformers (from
series. The calculated and measured results are plotted in Fig. 5.
It is found that the self-inductance increases linearly with radius
. The self-inductance of the primary winding is given by
(7)
where is a constant that depends on number of turns and geometry of the primary winding.
are constants that depend on the number
where , , and
of turns, geometry of the transformer windings and the laminate thickness. In general is much greater than . Obviously,
the slope of mutual inductance is much greater than that of the
leakage inductance. It means when radius increases, the increase
of mutual inductance is greater than that of leakage inductance.
Thus, the coupling coefficient of a coreless PCB transformer can
be improved by increasing the transformer area.
B. Different Number of Turns with the Same Radii
(Transformer Series #2)
Coreless PCB transformers with different number of primary
( ) and secondary turns ( ), from one to 20 turns, have
been examined. In this transformer series, the transformer
radius is kept constant so that the track separation decreases
as the number of turns increases. The geometric parameters
are described in the third column of Table I. Fig. 6 shows the
dimensions of some coreless PCB transformers in this series.
Fig. 7 indicates that the self-inductance, mutual inductance and
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Fig. 6.
#2.
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
Dimensions of some coreless PCB transformers in transformer series
Fig. 9. Inductances of transformer series #3.
Fig. 10. Dimensions of coreless PCB transformers of transformer series #4.
Fig. 7.
Fig. 8.
#3.
C. Different Number of Turns with the Same Track Separation
(Transformer Series #3)
Inductances of transformer series #2.
Dimensions of some coreless PCB transformers in transformer series
leakage inductance of the transformers of series #2 follow a
second-order polynomial of as given by
(nH)
(nH)
(12a)
(12b)
(nH)
(12c)
From (12) and Fig. 7, the changes of mutual and leakage inductance are found to be at a similar rate. It implies increasing
the number of turns without increasing the area or decreasing
the laminate thickness cannot improve the transformer coupling
factor significantly.
For traditional core-based transformer, the self-inductance is
proportional to the square of number of turns, i.e., when there
are two windings on the same core but different number of turns,
and
, the inductance ratio is given by
(13)
From (12), it is clear that coreless PCB transformers do not
follow (13). Equation (13) is only valid for coreless transformer
when the number of turn is significantly large so that the
term in (12) is much greater than the term.
This transformer series has different number of turns, from 1
to 40 turns. Their geometric parameters are shown in the fourth
column of Table I. Since the winding separation is fixed, the
transformer radius increases as number of turns increases. Fig. 8
illustrates the configuration of the transformer series.
Fig. 9 shows that as the number of turns increases (the
transformer area also increases), the rates of increase of self-inductance and mutual inductance are much greater than that of
leakage inductance. Similar to the case of transformer series
#1, when radius increases, the increase of mutual inductance
is greater than that of leakage inductance. These results show
that the coupling factor can be increased by increasing the
transformer area with or without increase number of turns.
However, increasing the number of turns has another advantage.
)
The self-inductance increases substantially (in the order of
which can be described as
(nH)
(nH)
(nH)
(14a)
(14b)
(14c)
D. Different Laminate Thickness (Transformer Series #4)
The laminate thickness of PCB’s under test is from 0.4 mm to
1.55 mm. Separation between the primary and secondary windings plays an important role in coreless planar transformer design. The smaller the separation of the printed windings is, the
greater the magnetic flux coupling becomes. As separation increases, the magnetic coupling between the primary and secondary windings decreases. The calculated and the measured
results are shown in Fig. 11. The transformer geometric parameters are given in the fifth column of Table I. The winding configuration of this transformer series is shown in Fig. 10.
TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
1279
TABLE I
DESCRIPTION OF TRANSFORMER SERIES
Fig. 11.
Fig. 12.
Dimensions of coreless PCB transformers of transformer series #4.
Fig. 13.
Inductances of transformer series #5.
Fig. 14.
Dimensions of coreless PCB transformers of transformer series #6.
Inductances of transformer series #4.
E. Different Conductor Width (Transformer Series #5)
The coreless PCB transformers with different track widths
have been examined. The track separation is fixed at 0.5 mm.
The track width for simulation ranges from 0.025 mm to 0.475
mm. In the practical tests, the track width is restricted from 0.1
mm to 0.4 mm. The transformers with different tracks are shown
in Fig. 12. Their dimensions are shown in the sixth column
of Table I. The measured and calculated results are plotted in
Fig. 13. The variations of the inductances can be expressed as
(nH)
(nH)
(nH)
(15a)
(15b)
(15c)
where the track width is in millimeters.
Fig. 13 shows that the self, mutual and leakage inductances
do not vary significantly with the track width. Under the
testing range, the variation of self-inductance is 50 nH which
is about 8% of the self-inductance. By differentiating (15) at
0.25 mm, the tolerance of self-inductance of a 0.25 mm
width winding in series #5 is about 0.183 nH/ m. Similarly,
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
Fig. 15.
Inductances of transformer series #6.
Fig. 16.
Frequency characteristics of a coreless PCB transformer with
z
= 1:55 mm.
N = N = 10 Turns,
the tolerance of mutual and leakage inductances are about
0.006 38 nH/ m and 0.177 nH/ m, respectively.
s
= s = 0:5 mm, w = w = 0:25 mm, h = 0:35 mm and
Differentiating (16) with respect to
yields
(nH/ m)
(17a)
F. Different Conductor Thickness (Transformer Series #6)
(nH/ m)
The conductor thickness for calculation is from 1 m to 100
m. In the test, the PCB conductor thickness is 35 m and 70
m. The pattern of the transformer winding is shown in Fig. 14
and described by the seventh column of Table I. Fig. 15 shows
that the variation of inductances is negligible for the coreless
PCB transformer with different conductor thickness.
The relationship between the inductive parameters and the
conductor thickness, , (in m) of the coreless PCB transformer
series can be expressed as
(nH)
(nH)
(nH)
(16a)
(16b)
(16c)
(nH/ m)
(17b)
(17c)
From (16) and (17), when the conductor thickness is
increased from 35 m to 70 m, the variations of the self-inductance, mutual inductance and leakage inductance are
0.877% 0.005% and 1.768%, respectively. The variation of
conductor thickness does not affect the inductive parameters
significantly.
IV. FREQUENCY CHARACTERISTICS OF CORELESS PCB
TRANSFORMERS
The frequency characteristics of coreless PCB transformer
have been measured. The testing frequency is from 100 kHz to
30 MHz. The configuration of the transformer under examination is shown in Fig. 10. The transformer dimensions are de-
TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
TABLE II
CHANGES OF INDUCTIVE PARAMETERS (FROM 1 MHz TO 30 MHz) OF
THE TRANSFORMER DESCRIBED IN FIG. 10
scribed by the fifth column of Table I but the laminate thickness
is fixed at 1.55 mm. The measured results of inductive parameters are shown in Fig. 16. The inductance variations with frequency are expressed as
(nH)
(18a)
(nH)
(18b)
(nH) (18c)
where is in MHz.
By differentiating (18), the change of inductive parameters of
the coreless PCB transformer can be expressed as
(nH)
(19a)
(nH)
(19b)
(nH)
(19c)
From (19), the variations of self, mutual and leakage inductances of the coreless PCB transformer at 10 MHz are 0.73
nH/MHz, 1.225 nH/MHz and 0.355 nH/MHz, respectively.
When the testing frequency sweeps from 1 MHz to 30 MHz, the
changes of the inductive parameters are tabulated in Table II.
As expected, the inductive parameters do not change much with
frequency because there is no core saturation. Moreover, the
measured results from Fig. 16 and Table II indicate that when
the operating frequency is changing, the coreless transformer
with printed winding structure has smaller inductance deviation than the coreless twist-wire transformers [20]. These results
imply that the analytical method using (1)–(6) is accurate for
predicting the inductive parameters of the coreless PCB transformers in the testing frequency range.
V. CONCLUSION
Self, mutual and leakage inductances of coreless transformers
with various geometric parameters have been analyzed. Based
on an analytical method, the inductive parameters of coreless
PCB transformers are calculated. The calculated results have
been confirmed with the measurements. The inductance of coreless PCB transformers depend on
1281
i)
ii)
iii)
iv)
v)
transformer outermost radius ( );
number of turns ( );
conductor width ( );
laminate thickness ( );and
conductor thickness ( ).
Variations of i) and ii) affect all of the inductive parameters significantly. The self-inductance of coreless PCB transformers is a linear function of the transformers’ outermost radius . The mutual and leakage inductances are also linear functions of provided that is much greater than the laminate
thickness, . The inductive parameters are 2nd order functions
of number of turns, , when is fixed. In the case of fixed
track separation, the inductive parameters are 3rd order functions of number of turns, . The thicker the PCB is, the smaller
the mutual inductance becomes. However, the self-inductance
is not affected by the laminate thickness significantly. The conductor width and thickness do not affect the inductive parameters enormously. The measured frequency characteristics of
coreless PCB transformer with testing frequency ranges from
100 kHz to 30 MHz show that the inductive parameters do not
change with frequency significantly.
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[16] S. Y. R. Hui, S. C. Tang, and H. Chung, “An accurate circuit model for
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S. C. Tang (M’98) was born in Hong Kong in 1972.
He received the B.Eng. (with first class honors) and
Ph.D. degrees in electronic engineering from the
City University of Hong Kong, Kowloon in 1997
and 2000, respectively.
He is a Research Fellow with the City University
of Hong Kong. His research interests include
coreless PCB transformers, high-frequency magnetics, MOSFET/IGBT gate drive circuits, isolation
amplifiers, and low profile converters.
Dr. Tang is the Champion of the Institution of
Electrical Engineers (IEE) Hong Kong Younger Member Section Paper Contest
2000. He received the Li Po Chun Scholarships and Intertek Testing Services
(ITS) Scholarships, in 1996 and 1997, respectively, the First Prize Award from
the IEEE HK Section Student Paper Contest in 1997, was the second winner in
the Hong Kong Institution of Engineers (HKIE) 50th Anniversary Electronics
Engineering Project Competition, and received the Certificates of Merit in the
IEEE Paper Contests (Hong Kong Section), in 1998 and 1999, respectively.
S. Y. (Ron) Hui (M’87–SM’94) was born in Hong
Kong in 1961. He received the B.Sc. degree (with
honors) from the University of Birmingham, Birmingham, U.K. in 1984 and the D.I.C. and Ph.D. degrees from the Imperial College of Science, Technology, and Medicine, London, U.K., in 1987.
He was a Lecturer with the University of Nottingham, U.K., from 1987 to 1990. In 1990, he went
to Australia and joined the University of Technology,
Sydney, where he became a Senior Lecturer in 1991.
He later joined the University of Sydney, where he
became a Reader of Electrical Engineering in January 1996. He is now a Chair
Professor of Electronic Engineering and Associate Dean of the Faculty of
Science and Engineering with the City University of Hong Kong, Kowloon. He
has been appointed an Honorary Professor by the University of Sydney since
2000. He has published over 150 technical papers including about 80 refereed
journal publications.
Dr. Hui received the Teaching Excellence Award from the City University
of Hong Kong, in 1999. He has been an Associate Editor of the IEEE
TRANSACTIONS ON POWER ELECTRONICS since 1997.
Henry Shu-Hung Chung (S’92–M’95) received the
B.Eng. (with first class honors) and Ph.D. degrees
in electrical engineering from The Hong Kong Polytechnic University, Kowloon, in 1991 and 1994, respectively.
Since 1995, he has been with the City University
of Hong Kong. He is currently an Associate Professor
in the Department of Electronic Engineering. His research interests include time- and frequency-domain
analysis of power electronic circuits, switched-capacitor-based converters, random-switching techniques,
digital audio amplifiers, and soft-switching converters. He has authored two
research book chapters, and over 110 technical papers including 50 refereed
journal papers in the current research area.
Dr. Chung received the China Light and Power Prize and was the Scholarship
and Fellowship of the Sir Edward Youde Memorial Fund, in 1991 and 1993,
respectively. He is Chairman of the Council of the Sir Edward Youde Scholar’s
Association and IEEE Student Branch Counselor. He was Track Chair of the
Technical Committee on Power Electronics Circuits and Power Systems of IEEE
Circuits and Systems Society, from 1997 to 1998. He is an Associate Editor of
the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART I: FUNDAMENTAL
THEORY AND APPLICATIONS.