IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
`
`1275
`
`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 trans-
`formers 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 trans-
`formers.
`
`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 mi-
`crotransformers [4]–[8] shows that thickness of magnetic ma-
`terial 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 thick-
`
`Manuscript received October 25, 1999; revised September 8, 2000. The au-
`thors 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 Univer-
`sity 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 an-
`alytical 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 in-
`ductance among various types of winding configuration. Fig. 1
`shows the three-dimensional (3-D) structure of a coreless PCB
`transformer. There are
`primary turns and
`secondary
`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 concen-
`tric 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-
`tance pairs between two concentric circular coils,
`, where
`both and are from 1 to
`. Fig. 3 shows the
`-plane cross sec-
`tion of the transformer in Fig. 2. The mutual magnetic flux cou-
`pling 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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`SAMSUNG EXHIBIT 1016
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`1276
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`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
`
`where
`
`Fig. 2. Approximation of circular spiral windings as concentric circles.
`
`The self-inductance of the primary and secondary windings are
`given by (1) and (2), respectively
`
`(1)
`
`(2)
`
`is
`
`is number of turns of primary winding and
`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 primary and
`-turns secondary transformer, the mutual
`inductance is the sum of mutual magnetic coupling pairs be-
`tween primary and secondary coils. The thin arrows in Fig. 3
`represent the mutual magnetic flux coupling between the pri-
`mary and secondary windings. Thus, the mutual inductance be-
`tween the primary and the secondary windings is given by
`
`(3)
`
`The leakage magnetic flux on the primary side is the dif-
`ference between the total magnetic flux setup in the primary
`winding and that coupled to the secondary. The primary leakage
`inductance is given by
`
`Derivation of mutual inductance,
`, between two circular
`tracks with rectangular cross section has been reported by
`Hurley and Duffy [18]
`
`(4)
`
`(5)
`
`when
`
`when
`
`(6)
`
`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 parame-
`ters 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 ele-
`ment analysis (FEA) [20] are consistent with the measured re-
`sults. 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 PCB-
`based 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 outer-
`most radii
`from 3 mm to 33 mm have been tested and sim-
`ulated. These transformers have different track separation, but
`have the same number of turns. The dimensions of this trans-
`former series are tabulated in the second column of Table I. The
`
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`TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
`
`1277
`
`Fig. 3. Diagram showing coupling paths between various turns.
`
`Fig. 4. Dimensions of some coreless PCB transformers in transformer series
`#1.
`
`Fig. 5.
`
`Inductances of transformer series #1.
`
`geometry of primary winding is the same as that of the sec-
`ondary winding, and they are printed on the opposite side of a
`double-sided PCB. Fig. 4 shows the dimensions of coreless PCB
`transformers (from
`mm to
`mm) in this transformer
`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
`
`where
`is a constant that depends on number of turns and ge-
`ometry of the primary winding.
`
`(7)
`
`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)
`
`(9)
`
`The mutual inductance and the leakage inductance can be rep-
`resented as
`
`(10)
`
`(11)
`
`are constants that depend on the number
`, and
`where ,
`of turns, geometry of the transformer windings and the lami-
`nate 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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`1278
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`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
`
`Fig. 6. Dimensions of some coreless PCB transformers in transformer series
`#2.
`
`Fig. 9.
`
`Inductances of transformer series #3.
`
`Fig. 10. Dimensions of coreless PCB transformers of transformer series #4.
`
`C. Different Number of Turns with the Same Track Separation
`(Transformer Series #3)
`
`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-in-
`ductance 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 wind-
`ings plays an important role in coreless planar transformer de-
`sign. The smaller the separation of the printed windings is, the
`greater the magnetic flux coupling becomes. As separation in-
`creases, the magnetic coupling between the primary and sec-
`ondary windings decreases. The calculated and the measured
`results are shown in Fig. 11. The transformer geometric param-
`eters are given in the fifth column of Table I. The winding con-
`figuration of this transformer series is shown in Fig. 10.
`
`Fig. 7.
`
`Inductances of transformer series #2.
`
`Fig. 8. Dimensions of some coreless PCB transformers in transformer series
`#3.
`
`leakage inductance of the transformers of series #2 follow a
`second-order polynomial of
`as given by
`
`(nH)
`(nH)
`(nH)
`
`(12a)
`(12b)
`(12c)
`
`From (12) and Fig. 7, the changes of mutual and leakage in-
`ductance 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.
`
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`TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
`
`1279
`
`TABLE I
`DESCRIPTION OF TRANSFORMER SERIES
`
`Fig. 12. Dimensions of coreless PCB transformers of transformer series #4.
`
`Fig. 11.
`
`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
`
`Fig. 13.
`
`Inductances of transformer series #5.
`
`(nH)
`(nH)
`(nH)
`
`(15a)
`(15b)
`(15c)
`
`Fig. 14. Dimensions of coreless PCB transformers of transformer series #6.
`
`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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`1280
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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 N = N = 10 Turns, s = s = 0:5 mm, w = w = 0:25 mm, h = 0:35 mm and
`z = 1:55 mm.
`
`the tolerance of mutual and leakage inductances are about
`0.006 38 nH/ m and
`0.177 nH/ m, respectively.
`
`Differentiating (16) with respect to
`
`yields
`
`F. Different Conductor Thickness (Transformer Series #6)
`
`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/ m)
`
`(nH/ m)
`
`(nH/ m)
`
`(17a)
`
`(17b)
`
`(17c)
`
`From (16) and (17), when the conductor thickness is
`increased from 35 m to 70 m, the variations of the self-in-
`ductance, 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.
`
`(nH)
`
`(nH)
`
`(nH)
`
`(16a)
`
`(16b)
`
`(16c)
`
`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 examina-
`tion is shown in Fig. 10. The transformer dimensions are de-
`
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`TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS
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`1281
`
`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 param-
`eters are shown in Fig. 16. The inductance variations with fre-
`quency 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 induc-
`0.73
`tances of the coreless PCB transformer at 10 MHz are
`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 devia-
`tion 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 trans-
`formers 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 core-
`less PCB transformers depend on
`
`i) transformer outermost radius ( );
`ii) number of turns (
`);
`iii) conductor width (
`);
`iv) laminate thickness ( );and
`v) conductor thickness ( ).
`Variations of i) and ii) affect all of the inductive parame-
`ters significantly. The self-inductance of coreless PCB trans-
`formers is a linear function of the transformers’ outermost ra-
`dius . The mutual and leakage inductances are also linear func-
`tions 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 func-
`tions 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 con-
`ductor width and thickness do not affect the inductive param-
`eters 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.
`
`REFERENCES
`
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`Authorized licensed use limited to: BOSTON UNIVERSITY. Downloaded on March 18,2022 at 13:34:12 UTC from IEEE Xplore. Restrictions apply.
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`IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000
`
`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 Poly-
`technic University, Kowloon, in 1991 and 1994, re-
`spectively.
`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 re-
`search interests include time- and frequency-domain
`analysis of power electronic circuits, switched-capac-
`itor-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.
`
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`coreless PCB-based transformers,” in Proc. Eur. Power Electron. Conf.,
`Trondheim, Norway, Sept. 1997, pp. 4.123–4.128.
`[17] C. F. Coombs Jr., Printed Circuits Handbooks 3rd Edition. New York:
`McGraw-Hill, 1998, p. 6.32.
`[18] W. G. Hurley and M. C. Duffy, “Calculation of self and mutual imped-
`ances in planar magnetic structures,” IEEE Trans. Magn., vol. 31, pp.
`2416–2422, July 1995.
`[19] S. Hayano, Y. Nakajima, H. Saotome, and Y. Saito, “A new type high
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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 mag-
`netics, 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, Birm-
`ingham, U.K. in 1984 and the D.I.C. and Ph.D. de-
`grees from the Imperial College of Science, Tech-
`nology, and Medicine, London, U.K., in 1987.
`He was a Lecturer with the University of Not-
`tingham, 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.
`
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