Characterization of Coreless Printed Circuit Board (PCB) Transformers S

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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 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 Fig. 1. Typical structure of a coreless PCB transformer with circular spiral HE NEED for compactness in power converter has led to windings. T 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- ness on the transformer’s characteristics are investigated. The terial of these devices can be minimized to a few hundred of inductive parameters are calculated using a recently reported an- micrometer ( m) and the switching frequency can exceed 1 alytical method [18]. The calculated results are confirmed with MHz. Although much progress has been made in using printed the measured results for the frequency range from 100 kHz to transformer windings, the use of magnetic cores in transformers 30 MHz. is still the dominant trend [4]–[9]. Transformers fabricated on PCB eliminate the manufacturing cost of manual windings [9]. II. INDUCTANCES CALCULATIONS OF CORELESS PCB However, space is still required to accommodate the magnetic TRANSFORMERS cores. The PCB transformer consists of three parts: the primary Recently, the use of coreless PCB transformers [10]–[16] winding, the dielectric laminate, and the secondary winding. have been reported. These transformers have been successfully Planar windings of various shapes have been studied [2]. It has demonstrated in isolated MOSFETs/IGBT’s gate drive circuits. been found that circular spiral windings provide the greatest in- Coreless PCB transformers do not need space to accommodate ductance among various types of winding configuration. Fig. 1 the magnetic core and have no core limitations such as core shows the three-dimensional (3-D) structure of a coreless PCB losses and saturation. Their sizes can be smaller than those of transformer. There are primary turns and secondary core-based transformers. This inherent low-profile property turns, printed on the opposite sides of a double-sided PCB. The makes the coreless transformers suitable for applications in PCB transformer can be built on the same circuit board with which stringent space and height requirements have to be met. other electronics. It can also be fabricated on another PCB as Moreover, the dielectric breakdown voltage of PCB typically a stand-alone device if desired. There is no need to cut hole ranges from 15 kV to 40 kV [17]. on the PCB for accommodating the magnetic cores in coreless In this paper, the inductive characteristics of coreless PCB PCB transformers. transformers with different geometric parameters are studied. The spiral windings in Fig. 1 can be approximated as concen- Factors includes: i) outermost radius, ii) number of turns, iii) tric circular windings connected in series [1] with infinitesimal conductor width, iv) laminate thickness and v) conductor thick- connections as shown in Fig. 2. For an -turns spiral coil, the total self-inductance is the summation of each mutual induc- Manuscript received October 25, 1999; revised September 8, 2000. The au- tance pairs between two concentric circular coils, , where thors are grateful to the Research Grant Council of Hong Kong for their support both and are from 1 to . Fig. 3 shows the -plane cross sec- of this project under Contract CERG 9040466. tion of the transformer in Fig. 2. The mutual magnetic flux cou- The authors are with the Department of Electronic Engineering, City Univer- sity of Hong Kong, Kowloon, Hong Kong. pling of primary winding pairs is drawn by thick solid lines and Publisher Item Identifier S 0885-8993(00)10578-2. those of secondary winding pairs appear as thick dotted lines.

where

when (6)

Fig. 2. Approximation of circular spiral windings as concentric circles. when

The self-inductance of the primary and secondary windings are permeability of vacuum; given by (1) and (2), respectively first kind Bessel function of order zero; inner radius of the th circular track; outer radius of the th circular track; (1) height of the th circular track; inner radius of the th circular track; outer radius of the th circular track; (2) height of the th circular track; separation between the circular tracks. where is number of turns of primary winding and is III. CORELESS PCB TRANSFORMERS WITH VARIOUS number of turns of secondary winding. GEOMETRIC PARAMETERS Mutual inductance between the primary and the secondary Equations (1) to (6) indicate that all of the inductive parame- coils of a planar transformer can also be derived. For an - ters depend on the geometry of the coreless planar transformer. turns primary and -turns secondary transformer, the mutual These inductive parameters vary with inductance is the sum of mutual magnetic coupling pairs between primary and secondary coils. The thin arrows in Fig. 3 1) outermost radius; represent the mutual magnetic flux coupling between the pri- 2) number of turns; mary and secondary windings. Thus, the mutual inductance be- 3) conductor width; tween the primary and the secondary windings is given by 4) lamination thickness; 5) conductor thickness. The simulated results obtained from both (5) and the finite ele- (3) ment 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 The leakage magnetic flux on the primary side is the dif- transformers using the analytical method are implemented by ference between the total magnetic flux setup in the primary MATLAB programs. The laminate used in the coreless PCB- winding and that coupled to the secondary. The primary leakage based transformers under test is FR-4 material. The conductor inductance is given by material is copper with gold plating. The geometry of primary winding and secondary winding are the same, so they have the (4) same self-inductance. In this section, the testing frequency is 10 MHz. The effects of the frequency on transformer inductances Derivation of mutual inductance, , between two circular will be discussed in Section IV. tracks with rectangular cross section has been reported by Hurley and Duffy [18] 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 trans- (5) former series are tabulated in the second column of Table I. The TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS 1277

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)

(9) Fig. 4. Dimensions of some coreless PCB transformers in transformer series #1. The mutual inductance and the leakage inductance can be rep- resented as

(10)

(11)

where , , and are constants that depend on the number 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. Fig. 5. Inductances of transformer series #1. Thus, the coupling coefficient of a coreless PCB transformer can be improved by increasing the transformer area. geometry of primary winding is the same as that of the secondary winding, and they are printed on the opposite side of a B. Different Number of Turns with the Same Radii double-sided PCB. Fig. 4 shows the dimensions of coreless PCB (Transformer Series #2) transformers (from mm to mm) in this transformer series. The calculated and measured results are plotted in Fig. 5. Coreless PCB transformers with different number of primary It is found that the self-inductance increases linearly with radius ( ) and secondary turns ( ), from one to 20 turns, have . The self-inductance of the primary winding is given by been examined. In this transformer series, the transformer radius is kept constant so that the track separation decreases (7) as the number of turns increases. The geometric parameters are described in the third column of Table I. Fig. 6 shows the where is a constant that depends on number of turns and ge- dimensions of some coreless PCB transformers in this series. ometry of the primary winding. Fig. 7 indicates that the self-inductance, mutual inductance and 1278 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.

Fig. 7. Inductances of transformer series #2. 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- Fig. 8. Dimensions of some coreless PCB transformers in transformer series #3. 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 leakage inductance of the transformers of series #2 follow a is greater than that of leakage inductance. These results show second-order polynomial of as given by that the coupling factor can be increased by increasing the transformer area with or without increase number of turns. (nH) (12a) However, increasing the number of turns has another advantage. (nH) (12b) The self-inductance increases substantially (in the order of ) (nH) (12c) which can be described as

From (12) and Fig. 7, the changes of mutual and leakage in- (nH) (14a) ductance are found to be at a similar rate. It implies increasing (nH) (14b) the number of turns without increasing the area or decreasing (nH) (14c) 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 D. Different Laminate Thickness (Transformer Series #4) are two windings on the same core but different number of turns, The laminate thickness of PCB’s under test is from 0.4 mm to and , the inductance ratio is given by 1.55 mm. Separation between the primary and secondary windings plays an important role in coreless planar transformer de- (13) sign. 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 sec- From (12), it is clear that coreless PCB transformers do not ondary windings decreases. The calculated and the measured follow (13). Equation (13) is only valid for coreless transformer results are shown in Fig. 11. The transformer geometric param- when the number of turn is significantly large so that the eters are given in the fifth column of Table I. The winding con- term in (12) is much greater than the term. figuration 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. 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 Fig. 13. Inductances of transformer series #5. of Table I. The measured and calculated results are plotted in Fig. 13. The variations of the inductances can be expressed as

(nH) (15a) (nH) (15b) (nH) (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 is about 8% of the self-inductance. By differentiating (15) at do not vary significantly with the track width. Under the 0.25 mm, the tolerance of self-inductance of a 0.25 mm testing range, the variation of self-inductance is 50 nH which width winding in series #5 is about 0.183 nH/ m. Similarly, 1280 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 x a x a IH Turns, s a s aHXS mm, w a w aHXPS mm, h aHXQS mm and z aIXSS mm. the tolerance of mutual and leakage inductances are about Differentiating (16) with respect to yields 0.006 38 nH/ m and 0.177 nH/ m, respectively. (nH/ m) (17a) F. Different Conductor Thickness (Transformer Series #6) (nH/ m) (17b) The conductor thickness for calculation is from 1 mto100 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 (nH/ m) (17c) and described by the seventh column of Table I. Fig. 15 shows that the variation of inductances is negligible for the coreless From (16) and (17), when the conductor thickness is PCB transformer with different conductor thickness. increased from 35 mto70 m, the variations of the self-in- The relationship between the inductive parameters and the ductance, mutual inductance and leakage inductance are conductor thickness, , (in m) of the coreless PCB transformer 0.877% 0.005% and 1.768%, respectively. The variation of series can be expressed as conductor thickness does not affect the inductive parameters significantly.

(nH) (16a) IV. FREQUENCY CHARACTERISTICS OF CORELESS PCB TRANSFORMERS The frequency characteristics of coreless PCB transformer (nH) (16b) have been measured. The testing frequency is from 100 kHz to 30 MHz. The configuration of the transformer under examina- (nH) (16c) tion is shown in Fig. 10. The transformer dimensions are de- TANG et al.: CORELESS PRINTED CIRCUIT BOARD (PCB) TRANSFORMERS 1281

TABLE II i) transformer outermost radius ( ); CHANGES OF INDUCTIVE PARAMETERS (FROM 1 MHz TO 30 MHz) OF ii) number of turns ( ); THE TRANSFORMER DESCRIBED IN FIG.10 iii) conductor width ( ); iv) laminate thickness ( );and v) 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 func- scribed by the fifth column of Table I but the laminate thickness tions of number of turns, . The thicker the PCB is, the smaller is fixed at 1.55 mm. The measured results of inductive param- the mutual inductance becomes. However, the self-inductance eters are shown in Fig. 16. The inductance variations with fre- is not affected by the laminate thickness significantly. The con- quency are expressed as ductor width and thickness do not affect the inductive parameters enormously. The measured frequency characteristics of (nH) (18a) coreless PCB transformer with testing frequency ranges from 100 kHz to 30 MHz show that the inductive parameters do not (nH) (18b) change with frequency significantly.

(nH) (18c) REFERENCES where is in MHz. [1] R. F. Soohoo, “Magnetic thin film inductors for integrated circuit appli- By differentiating (18), the change of inductive parameters of cations,” IEEE Trans. Magn., vol. Mag-15, pp. 1803–1805, Nov. 1979. the coreless PCB transformer can be expressed as [2] K. Kawabe, H. Koyama, and K. Shirae, “Planar inductor,” IEEE Trans. Magn., vol. MAG-20, pp. 1804–1806, Sept. 1984. [3] W. A. Roshen and D. E. Turcotte, “Planer inductors on magnetic sub- strates,” IEEE Trans. Magn., vol. MAG-24, pp. 3213–3216, Nov. 1988. (nH) (19a) [4] M. Mino, T. Yachi, A. Tago, K. Yanagisawa, and K. Sakakibara, “Planar microtransformer with monolithically-integrated rectifier diodes for (nH) (19b) micro-switching converters,” IEEE Trans. Magn., vol. MAG-32, pp. 291–296, Mar. 1996. [5] K. Yamasawa, K. Maruyama, I. Hirohama, and P. P. Biringer, “High- (nH) (19c) frequency operation of a planar-type microtransformer and its appli- cation to multilayered switching regulators,” IEEE Trans. Magn., vol. MAG-26, pp. 1204–1209, May 1990. From (19), the variations of self, mutual and leakage induc- [6] K. Onda, A. Kanouda, T. Takahashi, S. Hagiwara, and H. Horie, “Thin type DC/DC converter using a coreless wire transformer,” in Proc. IEEE tances of the coreless PCB transformer at 10 MHz are 0.73 PESC’94, 1994, pp. 1330–1334. nH/MHz, 1.225 nH/MHz and 0.355 nH/MHz, respectively. [7] N. Dai, A. W. Lofti, G. Skutt, W. Tabisz, and F.C. Lee, “A comparative When the testing frequency sweeps from 1 MHz to 30 MHz, the study of high-frequency, low-profile planar transformer technologies,” in Proc. IEEE APEC’94, 1994, pp. 226–232. changes of the inductive parameters are tabulated in Table II. [8] K. Yamaguchi, S. Ohnuma, T. Imagawa, J. Toriu, H. Matsuki, and K. As expected, the inductive parameters do not change much with Murakami, “Characteristics of a thin film microtransformer with circular frequency because there is no core saturation. Moreover, the spiral coils,” IEEE Trans. Magn., vol. MAG-29, pp. 2232–2237, Sept. 1993. measured results from Fig. 16 and Table II indicate that when [9] J. M. Bourgeois, “PCB based transformer for power MOSFET drive,” the operating frequency is changing, the coreless transformer in Proc. IEEE APEC’94, 1994, pp. 238–244. with printed winding structure has smaller inductance devia- [10] S. Y. R. Hui, S. C. Tang, and H. Chung, “Coreless printed-circuit board transformers for signal and energy transfer,” Electron Lett., vol. 34, no. tion than the coreless twist-wire transformers [20]. These results 11, pp. 1052–1054, 1998. imply that the analytical method using (1)–(6) is accurate for [11] S. Y. R. Hui, H. Chung, and S. C. Tang, “Coreless PCB-based trans- predicting the inductive parameters of the coreless PCB transformers for power MOSFETs/IGBT’s gate drive circuits,” IEEE Trans. Power Electron., vol. 14, pp. 422–430, May 1999. formers in the testing frequency range. [12] S. C. Tang, S. Y. R. Hui, and H. Chung, “Coreless PCB transformer with multiple secondary windings for complementary gate drive circuits,” V. C ONCLUSION IEEE Trans. Power Electron., vol. 14, pp. 431–437, May 1999. [13] H. Chung, S. Y. R. Hui, and S. C. Tang, “Design and analysis of multi- Self, mutual and leakage inductances of coreless transformers stage switched capacitor based step-down DC–DC converters,” IEEE Trans. Circuits Syst. I, vol. 47, pp. 1017–1025, July 2000. with various geometric parameters have been analyzed. Based [14] S. Y. R. Hui, S. C. Tang, and H. Chung, “Optimal operation of core- on an analytical method, the inductive parameters of coreless less PCB transformer-isolated gate drive circuits with wide switching PCB transformers are calculated. The calculated results have frequency range,” IEEE Trans. Power Electron., vol. 14, pp. 506–514, May 1999. been confirmed with the measurements. The inductance of core- [15] S. Y.R. Hui and S. C. Tang, “Coreless printed-circuit-board (PCB) trans- less PCB transformers depend on formers,” U.S. patent pending, Feb. 1998. 1282 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000

[16] S. Y. R. Hui, S. C. Tang, and H. Chung, “An accurate circuit model for Henry Shu-Hung Chung (S’92–M’95) received the coreless PCB-based transformers,” in Proc. Eur. Power Electron. Conf., B.Eng. (with first class honors) and Ph.D. degrees Trondheim, Norway, Sept. 1997, pp. 4.123–4.128. in electrical engineering from The Hong Kong Poly- [17] C. F. Coombs Jr., Printed Circuits Handbooks 3rd Edition. New York: technic University, Kowloon, in 1991 and 1994, re- McGraw-Hill, 1998, p. 6.32. spectively. [18] W. G. Hurley and M. C. Duffy, “Calculation of self and mutual imped- Since 1995, he has been with the City University ances in planar magnetic structures,” IEEE Trans. Magn., vol. 31, pp. of Hong Kong. He is currently an Associate Professor 2416–2422, July 1995. in the Department of Electronic Engineering. His re- [19] S. Hayano, Y. Nakajima, H. Saotome, and Y. Saito, “A new type high search interests include time- and frequency-domain frequency transformer,” IEEE Trans. Magn., vol. 27, pp. 5205–5207, analysis of power electronic circuits, switched-capac- Nov. 1991. itor-based converters, random-switching techniques, [20] “Getting started: A 2D Parametric Problem,” Ansoft Corporation, digital audio amplifiers, and soft-switching converters. He has authored two Maxwell 2D Field Simulator, (v. 6.4), July 1997. 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, S. C. Tang (M’98) was born in Hong Kong in 1972. respectively. He is Chairman of the Council of the Sir Edward Youde Scholar’s He received the B.Eng. (with first class honors) and Association and IEEE Student Branch Counselor. He was Track Chair of the Ph.D. degrees in electronic engineering from the Technical Committee on Power Electronics Circuits and Power Systems of IEEE City University of Hong Kong, Kowloon in 1997 Circuits and Systems Society, from 1997 to 1998. He is an Associate Editor of and 2000, respectively. the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART I: FUNDAMENTAL He is a Research Fellow with the City University THEORY AND APPLICATIONS. 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, Birm- ingham, U.K. in 1984 and the D.I.C. and Ph.D. degrees 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.