Power bus resonance characteristics of a gapped power-plane with a slit and a split power-plane with a gap were studied, using a fast algorithm based on a full cavity-mode resonator model and the segmentation method. Inductance and capacitance models were used to account for a field coupling along the slit and across the gap, respectively. Good agreements between the calculated and measured results were found to demonstrate the effectiveness and accuracy of our fast algorithm and the segmentation method, as well as the inductance model for the slit and the capacitance model for the gap. </p

Koga, Ryuji

Wada, Osami

Wang, Zhi Liang

English

Okayama University Digital Information Repository

Modeling of gapped power bus structures for isolation using cavity modes

Okayama University Scientific Achievement Repository

EngineeringElectrical Engineering fieldsOkayama University Year 2003Modeling of gapped power bus structuresfor isolation using cavity modesZhi Liang Wang Osami WadaOkayama University Okayama UniversityRyuji KogaOkayama UniversityThis paper is posted at eScholarship@OUDIR : Okayama University Digital InformationRepository.http://escholarship.lib.okayama-u.ac.jp/electrical engineering/95Modeling of Gapped Power Bus Structures for Isolation Using Cavity Modes Zhi Liang Wang', Osami Wada'.2, and Ryuji Koga'.' Graduate School of Natural Science and Technology, Okayama University Dept. of Communication Network Eng., Okayama University Tsushima-naka 3-1-1, Okayama 700-8530, Japan (Principal contact: zlwang@cne. okayama-u.ac.jp) Abs t rac t  Power bus resonance characteristics of a yapped power-plane with a slit and a split power-plane with a gap were studied, using a fast algorithm based on a f.11 cavity-mode resonator model and the segmen- tation method. Inductance and capacitance models were used to account for a field coupling along the slit and across the gap, respectively. Good agree- ments between the calculated and measured results were found to demonstrate the effectiveness and ac- curacy of our fast algorithm and the segmentation method, as well as the inductance model for the slit and the capacitance model for the gap. Keywords Power bus resonance, isolation, full cavity-mode res- onator model; segmentation method, model for a slit, model for a gap. 1. INTRODUCTION Based on the full cavity-mode resonator model [l], a fast algorithm can be applied for accurately calcu- lating power bus resonance characteristics. The fast algorithm is attributed to  a closed-form expression for the impedance Z-matrix of the power/ground planes, which is in the form of a singly infinite s e  ries [2-41. This is assuming that the pattern of the power/ground planes is rectangular. When the pat- tern is entirely arbitrary, we must rely upon full wave numerical methods such as FDTD and F E M  However, in actual PCBs, an entirely arbitrary pat- tern of the power/ground planes is not very com- mon: in many cases, the pattern consists of several segments, which have simpler shapes, such x rect- angles. In addition, a slight difference in the circum- ference of the pattern does not affect the resonance characteristics very much, so that we may approx- imate its shape with some rectangles. In a previ- ous work [5], the fast algorithm was extented for a pattern consisting of several segments of rectangles, / Power plane DSViCS Port I Part D Part 0 Fig.1: Geometry of rectangular p o y r  bus structure and its planar circuit model. using the segmentation method [6,7] that was pro- posed many years ago for analyzing two-dimensional microwave planar circuits. The accuracy of the seg- mantation method has been demonstrated by good agreements between the calculated and measured results. Board designers and EMC engineers frequently d e  bate the merits of introducing finite sized gaps (slits) into the power and/or gound  planes of multilayer PCBs. In fact, gapped power and/or ground planes are often used in high-speed digi- tal circuit designs for minimizing the propagation of high-frequency noise on dc power buses. The high-frequency performance of gapped power-plane structures up to  gigahertz range has been studed 0-7803-7835-0/03/$17.00 0 2W3 IEEE 10 recently by using a full-wave approach called the CERIPIE.[8] and by using a hybrid FEM/MOM a p  proach [9]. In this presentation, we show that such gapped power-plane structures can also be analyzed by using the fast algorithm derived from the full cavity-mode resonator model, combined with the segmentation method and the coupling models for a slit and a gap. 2. FULL CAVITY-MODE RESONATOR MODEL The full cavity-mode resonator model is an an- alytical description of the impedance matrix (Z- parameters) of an unloaded power/ground plane structure (a bare board). For a rectangular power/ground plane structure with length a and width b (see Fig. l), an expression for quickly calcu- lating the transfer impedance between the two ports on the power/ground planes was developed [3]: m wildah z., = 7c, cos(k,,y.) COS(kynyj) J 26 n=O [cos(a,z-) + cos(a,z+)] x sinc' (kvnw) > (1) a, sin a, where sinc(z) = sin(z)/x; k,, = n x / b ,  n, = a,,/-, z* = 1 - (zi f z j ) / a ,  ( z i , ~ ; )  and (z,, ?I,) are the coordinates of the center of the i th  and j t h  ports in the z- and y-directions, respec- tively, w is much less than the wavelength of interest and represents the port (via) half width, h i s  the di- electric thickness between the power/ground planes, w is the radian frequency, pd is the permeability of the dielectric, and j = a. The constant C, is assigned as C, = 1 if n = 0, and Cn = 2 if n # 0. The complex transverse wavenumber n is obtained as K' = w 2 p d ~ , j  - j 2 w ~ , j & / h ,  where ZS represents the surface impedance of the power/ground conduc- tors. It should be pointed out that the dielectric loss naturally appears in the imaginary part of the dielectric constant, while the conductor loss is incor- porated by the surface impedance of the conductors. When the board is loaded with passive components or active devices (Fig. l), the impedance charac- teristics of the loaded board can be analyzed by considering the loaded board as a multi-port circuit network interconnected by the Z-matrix elements of the corresponding bare board [3; 41. The aforementioned expression for the rectanglar power/ground plane can be easily applied to  those geometries that result from the connection of rect- angles by using the segmentation method [5-71. In the method, the interconnection between segments (4 Fig.2: Geometry of gapped power-plane with a slit and its analytical models. 11 w . =  1 0 m m .  I - 8 0 n m . N u m b c r o f t o t a i  oor trN=I l  Br.q"In'y (MHZ) Fig.3 Comparisons between calculated and measured ~ S I I ~  and lSa11 for the board of Fig. Z(a) with analytical model of Fig. 2(b). is discretized into a finite number of virtual ports; in which continuous voltage and current distribu- tions along the interconnection are approximated by stepped functions. The number of ports used for the interconnection therefore determines the accu- racy of the segmentation method. 3. MODELS FOR A SLIT A N D  A G A P  To prevent noise propagating from its sowce to  susceptible devices, the gapped power plane has been used as a technique to mitigate noise in digi- tal circuit design. EMC engineers have also devel- oped many "split" or "gapped" ground plane de- sign strategies for reducing the common mode ra- diation from cables attached to  the PCBs. The RF performance of such segmented structures up to the gigahertz frequency range requires, in prin- ciple, a full-wave approach like the CEMPIE [8] or the hybrid FEM/MOM approach [9]. In this sec- tion, we show that the resonance characteristics of a gapped power bus can also be analyzed by us- ing the full cavity-mode resonator model combined with the segmentation method. However, directly applying the segmentation method for the problem fails to  give correct results, due to the fact that the field coupling between the adjacent edges of the segments along a slit or across a gap has not been taken into account in the full cavity-mode resonator model, Furthermore, as we show later, the model used to  account for the coupling effect for a slit is different from that for a gap; thus these two cases are discussed separately. 3.1 A Power-Plane wi th  a Slit We at first consider a power-plane with a slit shown in Fig. 2(a). When the slit is wide, we may treat the whole pattern as a combination of three rectan- gular segments. When the slit is narrow, assuming that the slit width s is small enough so that we may ignore the electric length of s, directly applying the segmentation method then leads to the analytical model shown in Fig. 2(b) where the two segments are interconnected by the virtual ports at the part with a conducting bridge and are opened at the part with a slit. The ( M  - 2) virtual ports are uniformly distributed over the conducting bridge with a port width w = ( b  - 1)/(M - 2) and are assigned num- bers ranging from 2 t o m  = ( M -  1). The observing ports B on the left segment and A on the right are assigned numbers 1 and M .  The formulation of the multi-port circuit analysis for the structure can be found in an earlier paper[lO]. With the model in Fig. 2(b), the calculated IS111 at port A and lSz,l from port A to  port B were com- pared with the measured ones in Fig. 3 for a slit length 1 = 80 mm and the location w2 = 70 mm with the widths (a) s = 5.0mm and (b) s = 0.2mm, re- spectively. The dielectric permittivity was assumed to be a constant E, = 4.3 - j 0.086 (material: FR-4 glass epoxy) for all frequencies. As shown in Fig. 3, very good agreements were obtained for a wide slit (Fig. 3(a), s = 5.0mm 3 h ,  h: the dielec- tric thickness) between the calculated and measured results while the obvious differences were observed for a narrow slit (Fig. 3(b), s = 0.2 mm) at lower- order resonances. The reason for this is attributed to the field coupling between the adjacent edges of the segments along the slit when the width is nar- row, because such coupling had not been taken into account in the full cavity-mode resonator model due to  the "open" sidewalls (the perfect magnetic walls) used as the boundaries for the segments. When a slit is cut on the power-plane, it cuts off the path of the electric current for the modes whose currents flow toward a direction perpendicular to  the slit. The current has to  flow around the slit, and its path gets lengthens. When the slit length 1 is less than one fourth of the wavelength ( 1  < X/4), the effect can be described in terms of an equivalent 12 111 .I. ..I a. 1#1. ..I . ' . " " ' '  Frcq"C"CY<M"Z> Fig.4: Comparisons between calculated and measured /SII~ and ISZII for the board of Fig. 2(a) with analytical model of Fig. Z(c). I I,. <,I I . .  I,. ,I.. ~ 8 ,  Frrgu*nry<MHz) Fig.5: Same as Fig. 4 but for slit width s = 0.6 mm. series inductance that is distributed along the slit as a multiport network, as shown in Fig. 2(c). The to- tal partial inductance of the slit can be determined by visualizing it as a shorted coplanar slot-line with half the length of the slit. When the coplanar slot- line is symmetrical, the expression for this induc- tance can then be summarized as [I]] with k' = m, k = s/(s + Z W )  , (3) where w is the width of the two strip lines and is a p  proximated by the smaller of W I  and wp in Fig. 2(a) for our present asymmetrical case. This inductance is then distributed along the slit as part of a multi- port network, and the port inductance increases as the distance from this port to  the shorted conduct- ing bridge increases. Arranging the port numbers for the distributed inductance as M to ( N  - I), as shown in Fig. 2(c), the port inductance is given as (4) L ( N - M ) ( N - M + ~ )  L, = ( N  - P) where p = M ,  M + 1, . . . , N - 2, N - 1. The calcn- lated lSlll at port A and lS2,1 to  port B were again compared with the measured ones in Figs. 4 and 5 ,  for different values of the slit width and length. The effectiveness of the inductance model for the slit was demonstrated by good agreements between the calculated and measured results for all of these four cases. As already described, we accounted for the presence of a slit on the power plane by using an inductance. However, one could argue that capacitive coupling effect across the narrow slit could be present as well. Actually, when the power plane is completely split into two segments by a narrow gap, the coupling between the two segments by a gap capacitance on the order of several picofarads is very important for studying the isolation effect between these two seg- ments provided by the gap, as we will show in the next subsection. With Eq. (5) given below for this gap capacitance, we calculated the IS11l and lSzl1 for our case of having a conducting bridge between the two segments. Both the slit inductance and the gap capacitance were considered. The results plot- ted in Fig. 6 were compared with the ones obtained when the slit is modeled as open or is modeled by only the slit inductance. The overlap found between two curves of only L or both I, and C a t  low frequen- cies below 1 GHz indicates that the gap capacitance 13 w , -  70 n n . i =  80 m n . r - 0  2 m m  P..1".rr). (MHZ, Fig.6 /Sz i j  with different models for slit. Comparisons of calculated lSlll and has little effect when the slit is shorted by a con- ducting bridge, while the slight differences among the three curves at high frequencies above 1 GHz indicate that whichever model is used for the slit is no longer important as the frequency increases. 3.2 A Split Power-Plane with a Gap We consider a split power-plane with a gap shown in Fig. 7(a) next. The effect of split power is- land structures on power bus isolation has been experimentally and theoretically investigated [8, 9, 121. Without any direct connection between the two power segments or islands, the primary cou- pling mechanism is capacitive coupling across the gap. The gap capacitance may be obtained hy con- sidering the two segments = parallel-coupled mi- crostrip lines [MI. It is given as c = -  In [coth (f:)] 71 where s is the gap width, and k' is defined by Eq. (3). With this capacitance and the model of Fig. 7(b), thecalculated (Sll( at port A and (S21)  t o  port -o=16Smm A ( a )  rT7l I N  ( b )  Fig.7: Geometry of split power-plane with a gap and its analytical model. 0 c: -20 ~ - < L -40 YI - - --60 200 400 600 800 1000 -80 Frsqucncy (MHz)  Fig.8: Comparisons between calculated and measured lSlll and lS21l for the board of Fig. ?(a) with analytical model of Fig. 7(b). 14 B were compared with the measured ones in Fig. 8, for gap widths s = 0.2 mm and s = 3.0 mm, respec- tively. The agreement between the calculated r e  sults and the measured ones is good, except for the frequencies where both power islands have degen- erated resonance due to the same width b.  Rather than using the capacitance model, greater accuracy in the numerical simulation can he achieved by us- ing a multiport mutual coupling network [14] repre senting the coupling between the two adjacent seg- ments. However, a great deal of computational ef- fort has to be made due to  the increase in the num- ber of ports and due to the need to calculate the mutual coupling coefficients. 4. CONCLUSION A fast algorithm based on the full cavity-mode resonator model was applied for analyzing power bus resonance characteristics of gapped power- plane structures, combined with the segmentation method. For a power-plane with a slit, an induc- tance model was introduced for representing the coupling effect due to the slit. The value of the in- ductance is obtained by treating the slit as a shorted coplanar slot-line. For a split power-plane with a gap, a capacitance model is used for taking into ac- count the field coupling across the gap. The value of the capacitance is determined by considering two segments of the split power-plane as parallel- coupled microstrip lines. Good agreements between the calculated and measured results demonstrated the effectiveness and accuracy of our fast algorithm and the segmentation method, as well as the induc- tance model for the slit and the capacitance model for the gap. Acknowledgement-This work was supported by the Project for the Reduction of Electromagnetic Noise Levels, Research for the Future Program, Japan Society for the Promotion of Science (JSPS). REFERENCES [l] C.-T. Lei, R. W. Techentin, and B. K. Gilbert, “ High-frequency characterization of power/ground- plane structures;’ IEEE Trans. Microwave Theory Tech.. Vol. 47, pp. 562.569, May 1999. (2) A. Benalla and K. C. Gupta, ”Faster Computation of 2-matrices for Rectangular Segments in Pla- nar Microstrip Circuits,” IEEE %m. Microwave Theory Tech., Vol. MTT-34, pp. 733-736, June 1986. [3] Z. L. Wang, 0. Wada, Y .  Toyota, and R. Koga, “An improved dosed-form expression for accn- rate and rapid calculation of power/ground plane impedance of multilayer PCBs,” Proceedings of Symposium on Electromagnetic Theory, EMT-OO- 68, pp. 17-23, Toyama, Japan, Oct. 2000. (41 J. Trinkle, A. Cantoni, and K. Fynn, “Efficient impedance calculation of loaded power ground planes,” Proceedings of the 15th Zurich Symposium and Technical Exhibitwn on Electromagnetic Com- patibility, 18, pp. 285-290, Zurich, Switzerland, Feb. 18-20, 2003. (51 Z. L. Wang, 0. Wada, Y. Toyota, and R. Koga, “Application of segmentation method to analy- sis of power/ground plane resonance in multilayer PCBs,” Pnxeeding of the 3rd Ink Symposium on Electromagnetic Compatibility, pp. 775-778, Bei- jing, China, May 2002. [6] T. Okoshi, Y. Uehara, and T. Takeuchi, ‘The seg- mentation method-An approach to the analysis of microwave planar circuits,” IEEE Pam. Mi- crowave Theory Tech., Vol. 24, pp. 662-668, Oct. 1976. [7] R Chadha and K. C. Gupta, “Segmentation method using impedance matrices for analysis of planar microwave circuits,” IEEE h m .  Mi- mwave Theory T&., Vol. 29, pp. 71-74, Jan. 1981. [8] J. Fan, J. L. Drewniak, H. Shi, and J. L. Knighten, ‘DC power-bus modeling and desigu with a mixed- potential integral-equation formulation and circuit extraction,” IEEE Darn. Electmmagn. Compat., Vol. 43, pp. 426436, Nov. 2001. [9] Y. Ji and T. H. Hubing, “On the modeling of a Gapped POHRI-BUS tructure using a Hybrid FEM/MOM Approach,” IEEE IIfnm. Electro- magn. Compat., Vol. 44, pp. 566569, Nov. 2002. [lo] Z. L. Wang, 0. Wada, Y. Toyota and R. Koga, “Power Bus Resonance Characteristics in Multilayer Printed Circuit Boards with Slits,’’ Proceedings of the 15th Int. Zurich Symposium and Technical Exhibition on Electromagnetic Corn- patibility, 5A5, pp. 23-28, Zurich, Switzerland, Feb. 2003. (111 R Lee Hill, T. Van Doren, T. H. Hubing, and J. L. Drewniak, “Common mode currents induced on wires attached to multilayer printed wire boards with segmented ground planes,” Proceedings of the 1994 IEEE International Symposium on Electro- magnetic Comptibility, Chicago, pp. 116120, Aug. 1994. 1121 J. Chen, T. H. Huhing, T. P. Van Doren, and R. E. DuBroff, ‘“Power bus isolation using power islands in printed circuit boards,” IEEE %m. Electro- magn. Compat., Vol. 44, pp. 373-380, May 2002. (131 T. C. Edwards and M. B. Steer, Foundations of In- terconnect and Microstrip Design (Third Edition), Chichester, John Wiley &, Sons, Chap. 8, 2WO. [14] J. R James and P. S. Hall (eds.), Handbook of Mi- cmstrip Antennas, United Kingdom, Peter Pere- grinus Ltd., Chap. 9, 1989. 15 

An improved dosed-form expression for accnrate and rapid calculation of power/ground plane impedance of multilayer PCBs,”

Application of segmentation method to analysis of power/ground plane resonance

Bus Resonance Characteristics in Multilayer Printed Circuit Boards with Slits,’’

Common mode currents induced on wires attached to multilayer printed wire boards with segmented ground planes,”

DC power-bus modeling and desigu with a mixedpotential integral-equation formulation and circuit extraction,”

Efficient impedance calculation of loaded power ground planes,”

Faster Computation of 2-matrices for Rectangular Segments

High-frequency characterization of power/groundplane structures;’

On the modeling of a Gapped POHRI-BUS Structure using a Hybrid FEM/MOM Approach,”

Segmentation method using impedance matrices for analysis of planar microwave circuits,”

The segmentation method-An approach to the analysis of microwave planar circuits,”

Modeling of gapped power bus structures for isolation using cavity modes

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