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 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. 0885–8993/00$10.00 © 2000 IEEE 1276 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000 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 be- tween 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 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 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 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- (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 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. 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 sec- ondary 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.