IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 9, SEPTEMBER 2005 2935

Electromagnetic Bandgap Power/Ground Planes forWideband Suppression of Ground Bounce Noiseand Radiated Emission in High-Speed Circuits

Tzong-Lin Wu, Senior Member, IEEE, Yen-Hui Lin, Ting-Kuang Wang, Chien-Chung Wang, and Sin-Ting Chen

Abstract—A power/ground planes design for efficiently elim-inating the ground bounce noise (GBN) in high-speed digitalcircuits is proposed by using low-period coplanar electromagneticbandgap (LPC-EBG) structure. Keeping solid for the groundplane and designing an LPC-EBG pattern on the power plane, theproposed structure omnidirectionally behaves highly efficiently insuppression of GBN (over 50 dB) within the broad-band frequencyrange (over 4 GHz). In addition, the proposed designs suppressradiated emission (or electromagnetic interference) caused by theGBN within the stopband. These extinctive behaviors of low ra-diation and broad-band suppression of the GBN is demonstratednumerically and experimentally. Good agreements are seen. Theimpact of the LPC-EBG power plane on the signal integrity for thesignals referring to the power plane is investigated. Two possiblesolutions, differential signals and an embedded LPC-EBG powerplane concept, are suggested and discussed to reduce the impact.

Index Terms—Electromagnetic bandgap (EBG), electromag-netic interference (EMI), ground bounce noise (GBN), high-speeddigital circuits, radiation, signal integrity (SI), simultaneouslyswitching noises (SSN).

I. INTRODUCTION

WITH the trends of fast edge rates, high clock frequen-cies, and low voltage levels for the high-speed digital

computer systems, the ground bounce noise (GBN) or simul-taneously switching noise (SSN) on the power/ground planesis becoming one of the major challenges for designing the high-speed circuits. Because of the parallel-plate waveguide structurebetween power and ground planes in the advanced high-speedpackages, the resonance modes of the parallel-plate waveguidecan be excited by the GBN. Research has shown the resonancenoise propagating between the power and ground planes couldcause serious signal integrity (SI) or power integrity (PI) prob-lems for the high-speed circuits [1]–[3]. Moreover, due to thecavity resonance effect between the power/ground planes, theGBN also results in significant radiated emissions or electro-magnetic interference (EMI) issues [3].

Manuscript received November 29, 2004; revised May 18, 2005. This workwas supported by the National Science Council, Taiwan, R.O.C., under GrantNSC 93-2213-E-110-010.

T.-L. Wu is with the Department of Electrical Engineering and Graduate In-stitute of Communication Engineering, National Taiwan University, Taipei 106,Taiwan, R.O.C. (e-mail: [email protected]).

Y.-H. Lin, T.-K. Wang, C.-C. Wang, and S.-T. Chen are with the Departmentof Electrical Engineering, National Sun Yat-sen University, Kaohsiung 80424,Taiwan, R.O.C.

Digital Object Identifier 10.1109/TMTT.2005.854248

Several researchers have contributed to the mitigation of theGBN. Adding decoupling capacitors between power and groundplanes is a typical way to eliminate the GBN and reduce theEMI, but they are not effective above a few hundred megahertzdue to the unavoidable lead inductance. Although using the iso-lation moat [3] on the power or ground plane or selecting thelocation of the via ports to eliminate the excitation of the GBN[4] could suppress the GBN at higher frequencies, these ap-proaches are suitable only to suppress the GBN at specific lo-cations. Recently, a new idea for eliminating the GBN is pro-posed by using a photonic bandgap (PBG) [5] or electromag-netic bandgap (EBG) structure on the ground plane to form ahigh-impedance surface (HIS) [1], [2]. By designing the for-bidden bandgap of the EBG structure within the resonant modefrequencies of the power and ground planes, this structure offersan efficient suppression of the GBN propagating in omnidirec-tion of the planes. However, multilayer substrates with speciallydesigned via are required in the EBG structure for achieving theHIS on the ground plane [2].

This paper proposes a novel power/ground planes designusing a low-period coplanar EBG structure (LPC-EBG). Al-though a similar EBG structure designed on the ground planehas been used in filter or antenna design in the microwave range(above 10 GHz) [6], it has not been applied in the elimination ofthe GBN on the power/ground planes of the high-speed digitalcircuits. The key features of this new concept is keeping solidor continuous for the ground plane and designing the LPC-EBGstructure on the power plane. Due to the periodic inductor andcapacitor (LC) networks realized by the combining effect ofthe solid ground and the LPC-EBG power plane, the bandstopbehavior can be achieved. This design is suitable for applyingin high-speed circuits with GBN dominantly existing in thelow-frequency range below 6 GHz [1]. The advantages of thisdesign are broad-band suppression of the GBN due to the com-bining effect of the LPC-EBG structure on the power plane andthe continuous plane on the ground plane, low EMI caused bythe GBN because of the continuous ground reference, and lowcost due to the compatibility with the conventional printed cir-cuit board (PCB) or package substrate manufacturing process.

This paper is organized as follows. Section II describes thedesign concept and corresponding theoretical model of theproposed LPC-EBG structure. In Section III, the distinctivebehavior of GBN elimination, both in frequency and timedomains, is measured and compared with simulation by thethree-dimensional (3-D)-finite-difference time-domain (FDTD)method. The broad-band EMI suppression performance is also

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2936 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 9, SEPTEMBER 2005

Fig. 1. Schematic diagram of proposed test boards. (a) 9-cell LPC-EBG board.(b) 25-cell LPC-EBG board.

Fig. 2. (a) Two unit cells of the LPC-EBG and its corresponding parameters.(b) Equivalent circuit model for the two connecting unit cells in Fig. 2(a).

presented in this section. The impact of the LPC-EBG struc-ture on the SI is discussed, and corresponding solutions aresuggested in Section IV. Conclusions are drawn in Section V.

II. DESIGN AND MODEL OF THE LPC-EBG POWER PLANE

A. Structure Design

In high-speed digital circuit design, power and ground planesare embedded in multilayer substrate of PCB to provide the re-turn current for the high-speed signals and supply the neces-sary dc voltage. From the SI point of view, keeping the ref-erence planes continuous is important, to have a good signalquality. Therefore, in our design, the ground plane is kept con-tinuous, and the LPC-EBG structure is applied on the powerplane. Fig. 1(a) and (b) show two power/ground plane designswith 9 (3 by 3) and 25 (5 by 5) unit cells on a two-layer FR4PCB substrate. The dimension of the substrate is 90 mm 90mm with 0.4 mm thickness. Fig. 2(a) shows two unit cells ofthe LPC-EBG connected by the bridges. Each unit cell consists

of one square metal pad and four connecting narrow bridges.The corresponding geometrical parameters of the unit cell aredenoted as , where is the unit cell period, isthe bridge length, is the bridge width, is the half-gap be-tween adjacent unit cells, and is the gap between the metalpad and the bridge. The corresponding parameters for the de-signs in Fig. 1(a) and (b) are (30, 5, 1, 1, and 1 mm) and (18,3, 1, 1, and 1 mm), respectively. The main differences of thesetwo designs are the cell period and the bridge length .It is noted that these five geometrical parameters significantlyinfluence the bandstop behavior. The parameters of these twodesigns are obtained through an optimal process for achievingwider stopband bandwidth. As will be shown in the next section,these two examples perform broader stopband than our previousdesign [5].

B. Equivalent Model and Stopband Prediction

Although the proposed structure is constructed under atwo-dimensional (2-D) concept, a simple 1-D wave propaga-tion model is developed to efficiently predict the bandwidthand center frequency of the stopband for the LPC-EBG struc-ture. Fig. 2(b) shows the equivalent circuit model for twoconnecting unit cells shown in Fig. 2(a). Each unit sectionof the equivalent model consists of two parts. The first partdescribes the propagation characteristics between the squaremetal pad on the power plane and the continuous ground plane,using an equivalent inductance and capacitance . Thesecond part describes the connecting characteristics of the twoadjacent unit cells, which include the bridging effect with thebridge inductance , bridge capacitance , and the capacitivegap coupling effect between two adjacent unit cells. It isassumed that infinite unit sections are periodically cascaded, asshown in Fig. 2(b), to represent the EBG structure.

Next, the dispersion behavior for the current on this periodiccircuit is derived. As shown in Fig. 2, the current on the firstpart and the second part (sum of the current on and )of section are denoted as and . The electric chargeson and of section are denoted as and . Therelations between the currents and node charges can be derivedas

(1)

(2)

(3)

(4)

Differentiating (3) and (4) with time, and combining with (1)and (2), yields

(5)

(6)

WU et al.: ELECTROMAGNETIC BANDGAP POWER/GROUND PLANES 2937

TABLE IESTIMATED PAD/BRIDGE/GAP INDUCTANCE AND

CAPACITANCE OF THE LPC-EBG STRUCTURE

Considering the periodic conditions of the EBG, it is assumedthat the wave solutions for and in (5) and (6) have thesame frequency and wave number but different amplitudes, andare expressed as

(7)

(8)

where .Substituting (7) and (8) into (5) and (6), and setting the de-

terminant of the coefficients of and to be zero, we obtainthe dispersion relation between and as

(9)

The values of the parameters , and are easilyobtained by the transmission line theory for the microstripline. The gap-coupling capacitance is calculated as

, where is thewidth of the square corner pad, and is the distance betweenthe centers of the neighboring corner pads [7]. The corre-sponding parameter values for the 9-cell and 25-cell LPC-EBGboards are listed in Table I. Employing (9), Fig. 3(a) and (b)show the dispersion diagrams ( as a function of ) for 9-celland 25-cell LPC-EBG boards, respectively. As shown in Fig. 3,there are two modes solved by (9), and a bandgap is clearlyseen between these two modes. The bandwidth of the stopbandpredicted by the 1-D circuit model for the 9-cell board is 4.2GHz, ranging from 1 to 5.2 GHz, and for the 25-cell board is5.7 GHz, ranging from 2 to 7.7 GHz. Validity of this simplemodel will be checked by the measurement in the next section.

III. NUMERICAL AND EXPERIMENTAL RESULTS

A. GBN Suppression

1) Frequency Domain: We first see the bandstop behaviorfor eliminating the GBN in frequency domain. Fig. 4(a) and(b) show both the measured and simulated for the 9-celland 25-cell LPC-EBG boards, respectively. The behaviors ofthe reference board with both power and ground plane beingsolid (or continuous) are also included in these two figures forcomparison. The 3-D-FDTD approach is used to simulate theGBN behavior for all power/ground plane structures. As shownin Fig. 4(a) and (b), good agreement between the measurement

Fig. 3. Dispersion diagrams (f as a function of k). (a) 9-cell LPC-EBG board.(b) 25-cell LPC-EBG board.

and 3-D-FDTD prediction is obtained. Slight discrepancy be-tween them occurs at resonant peaks and at higher frequencies,where the numerical prediction is higher than the measuredresults. The reasons are that the dispersion property of theFR4 structure and the conductor loss due to skin effect is notconsidered in our FDTD modeling. Comparing both LPC-EBGboards with the reference board, it is clearly seen that the pro-posed LPC-EBG power/ground planes significantly eliminatethe GBN with, on average, an over-50-dB suppression in abroad-band frequency range. Here, the bandwidth is definedas the range of the lower than dB. The simulated andmeasured stopband bandwidth for 9-cell board is 3.9 and 4.1GHz, respectively, and is 5.7 and 6.3 GHz, respectively, for the25-cell board. The simulated and measured center frequency is2.9 and 3.0 GHz, respectively, for the 9-cell board, and is 5.2and 5.3 GHz for the 25-cell board. It is seen that the measuredbandwidth and center frequency of the stopband are slightlyhigher than the simulated one for both boards. The reason could


Fig. 4. Comparison of jS j obtained by 3-D-FDTD and measurement. (a)9-cell LPC-EBG board. (b) 25-cell LPC-EBG board.

TABLE IIBANDWIDTH AND CENTER FREQUENCY COMPARISON FOR

THE PROPOSED LPC-EBG STRUCTURE

also be that the conductor loss and the dielectric dispersionbroaden the stopband at a higher frequency range, i.e., near 5GHz for the 9-cell board and near 8 GHz for the 25-cell board.

Table II compares the bandwidth and center frequencyobtained by the 3-D-FDTD, the measurement, and the 1-Dequivalent circuit model. It is found that the 1-D circuit modelhas good accuracy in predicting the stopband behavior ofthe LPC-EBG structure. As shown in Table II, the differencefrom either the 3-D-FDTD approach or the measurement is allbelow 8%. Fig. 5 shows the measured , and forthe 9-cell board, where the receiving port (port1) is locatedat (15 mm, 76 mm), and the noise is, respectively, excited atdifferent locations, port2 (45 mm, 72 mm), port3 (48 mm, 45

Fig. 5. Measured GBN suppression behavior for the noise excited at differentlocations; ports 2, 3, and 4, respectively.

mm), and port4 (48 mm, 12 mm). The left lower corner of theboard is defined as the zero point of the coordinate. It is seenthat the proposed design provides the similar broad-band GBNsuppression behavior for different positions of the noise. Thisbehavior demonstrates that the proposed power/ground planescan omnidirectionally eliminate the GBN on the power plane.

2) Time Domain: Next, we try to understand the GBN sup-pression capability in the time domain for the proposed powerplane. The power/ground planes of those test boards are excitedby a pulse-pattern generator (Anritsu MP1763C) to emulate theGBN on the power plane, and the coupling noise at the receivingport is measured in the time domain by the a signal analyzer(Tektronix CSA8000). All test boards, including the reference,9-cell, and 25-cell boards are measured. Fig. 6(a) shows thewaveform of the excitation waveform launched from the pat-tern generator. It is a periodic square-like wave with frequency2.25 GHz and amplitude 125 mV. The locations of the ex-citation ports are (45 mm, 45 mm) for all test boards, and re-ceiving ports are (15 mm, 75 mm) for both reference and 9-cellboards and (27 mm, 63 mm) for 25-cell board. Fig. 6(b), (c),and (d) show the measured GBN at the receiving port for thereference, 9-cell, and 25-cell boards, respectively. It is seen thatpeak-to-peak amplitude of the coupling noise is about 44, 7, and11 mV, respectively, for these three boards. Compared with thereference board, the GBN can be reduced about 84% and 75%,respectively. It is clearly seen that the GBN is significantly re-duced by the proposed LPC-EBG power planes.

B. Radiation (or EMI) Elimination

Previous literature showed that the microstrip line on theEBG structure may cause significant leakage radiation onthe stopband, due to an imperfect reference plane [8]. Lowradiation or EMI is important in high-speed circuits for thecompliance of the strict electromagnetic compatibility (EMC)regulations. This subsection numerically and experimentallyinvestigates the EMI performance of the proposed LPC-EBGpower/ground plane structure by comparing with the referenceboard.

Fig. 7 shows the EMI measurement setup in an EMC fullyanechoic chamber. The test board is put on the wooden table,


Fig. 6. Measured GBN suppression behavior in the time domain for the proposed power plane. (a) The waveform of the excitation source launched from a patterngenerator. (b) Coupling GBN at the receiving port for the reference board. (c) Coupling GBN at the receiving port for 9-cell LPC-EBG board. (d) Coupling GBNat the receiving port for 25-cell LPC-EBG board.

Fig. 7. Measurement setup for EMI in 3 m fully anechoic chamber.

and the RF signal of 20 mV generated by the signal source (HP8324) is launched into the power plane of the board throughthe high-frequency connector. The height of the receiving an-tenna and test board is fixed at 1.2 m from the floor of thechamber, and the distance between them is 3 m. The radiatedE-field below 1 GHz is measured by a bi-log antenna (Chase

CBL611 B), and above 1 GHz, the horn antenna (R&S HF906)is employed. The wooden table with test board is rotated in360 at the speed of 4.5 /s for each excited frequency point,and the maximum radiated E-field is recorded by the spectrumanalyzer (R&S FSP) with 100 kHz resolution bandwidth. Thesimulated radiated E-field in 3-D-FDTD modeling is obtainedby the near-field and far-field transformation of Kirchhoff’s sur-face integral [9] and Fourier transforms with source normaliza-tion method [3].

Fig. 8(a) and (b) show the simulated and measured EMI ra-diation at 3 m distance for the 9-cell and 25-cell LPC-EBGboards, respectively. The reference board with both power andground plane being solid is also included in both figures forcomparison. Only the EMI behaviors below 4 GHz are mea-sured, due to the limitation of our signal generator. It is seen thatthe agreement between the measurement and the simulation isreasonably good. For the reference board, there are several radi-ation peaks with strength over 55 dB V/m at 1.6, 2.3, 3.3, and3.7 GHz, which are corresponding to the resonance frequenciesof the cavity modes for the 9 cm board. However, for the 9-celland 25-cell boards, all of the radiation peaks have been sup-pressed with the average radiation strength under 40 dB V/m.It is clearly seen that the proposed power/ground plane designperforms with significantly low EMI behavior at the designedbandgap frequency ranges, although several etched slots are de-signed on the power planes.


Fig. 8. Simulated and measured EMI radiation at 3 m. (a) 9-cell LPC-EBGboard. (b) 25-cell LPC-EBG board.

IV. IMPACT ON THE SI AND POSSIBLE SOLUTIONS

Although the proposed power/ground planes designs showexcellent performance on eliminating the GBN and corre-sponding EMI at broad-band frequency ranges, the powerplanes with etched slots would degrade the signal quality forthe signal traces referring to the imperfect power plane [10].This section will discuss the impact of the proposed LPC-EBGpower plane on the SI, and two possible solutions to improvethe SI are discussed.

A. Single-Ended and Differential Signals

Fig. 9(a) and (b) show the single-ended and differential traces,respectively, of 60 mm passing from the first (top) layer to thefourth (bottom) layer and back to the first layer, with two viatransitions along the signal path. The second and third layers arethe 9-cell power plane and solid ground plane, respectively. It isknown that via transitions and imperfect reference plane are twoof the main factors to influence the signal quality for the high-speed signals. This setup in Fig. 9 tries to evaluate the impact ofthe LPC-EBG power plane on the signal quality for the signals,both referring to the power plane and with via transitions. Thetraces are designed as 50 for the single-ended signal, and 100

for the differential impedance. Eye patterns for evaluating the

Fig. 9. Four-layer structure with transmission line transient between the9-cell LPC-EBG power plane and solid ground plane. (a) Single-ended trace.(b) Differential traces.

signal quality are obtained following three steps. First, the two-port and four-port -parameters for the single-ended and differ-ential cases, respectively, are simulated by the 3-D-FDTD. Thebroad-band SPICE-compatible models are then extracted by thecommercial tool SPEED2000 (the boardband SPICE module)using the solved -parameters. According to the broad-bandSPICE models, the eye patterns at the output side are finallygenerated in the HSPICE environment by launching a patternsource of - pseudorandom bit sequence (PRBS), nonreturnto zero (NRZ), coded at 2.5 GHz. The bit-sequence swing andthe nominal rise/fall time are 500 mV and 120 ps, respectively,for the single-ended case, and 250 mV and 100 ps for the dif-ferential cases.

Fig. 10(a) and (b) show the simulated eye patterns for the ref-erence board with continuous power plane and the 9-cell board,respectively. Two parameters, maximum eye open (MEO) andmaximum eye width (MEW), are used as metrics of the eye pat-tern quality. It is seen that for the reference board, MEOmV and MEW ps, and for the 9-cell board, MEOmV and MEW ps. Compared with the reference board,the degradation of the MEO and MEW for the 9-cell board isabout 17% and 4.6% in the single-ended case. It is believedthat this mild degradation is acceptable in practical high-speedcircuits. Furthermore, through suitable components placementand layout designs, such as routing lower speed signals on thetop layer and keeping high-speed traces on the bottom layer,keeping high-speed traces shorter, or avoiding the high-speedsignals crossing the cells, the overall SI performance will besignificantly better than the previously simulated case.

However, if long and high-speed signals are still necessary onthe first layer, the differential signaling approach is a good so-lution in the LPC-EBG power/ground planes design. Fig. 10(c)shows the eye patterns of the differential signals at the outside ofthe configuration in Fig. 9(b). The MEO and MEW are 471 mVand 389 ps, respectively. Compared with the single-ended caseon the 9-cell LPC-EBG board, the improvement of the MEO andMEW is about 30% and 5% in the differential-signal case. It isseen that theSIperformanceof thedifferentialapproach is signifi-cantlybetter thanthesingle-endedcases,both in the9-cellboards.


Fig. 10. Simulated eye patterns. (a) Reference board (continuous power plane)with single-end trace. (b) 9-cell LPC-EBG board with single-end trace. (c) 9-cellLPC-EBG board with differential traces.

B. Embedded LPC-EBG Power Planes

Another idea to solve the SI issues for the EBG-power planeis adding one more ground plane above the EBG power plane.As shown in Fig. 11, the LPC-EBG power plane is embeddedbetween two solid ground planes with the vias electricallyconnecting these two planes. To keep the performance of thebroad-band GBN suppression, a suitable design for the viasdistribution and the substrate thickness between the addedground plane and the power plane is needed.

Fig. 11. Schematic of embedded 9-cell LPC-EBG power plane with groundvia stitching structure.

Fig. 12. Comparison of jS j between embedded 9-cell LPC-EBG powerplane and embedded solid power-plane structure obtained by 3-D-FDTD andHFSS.

As shown in Fig. 11, an embedded 9-cell LPC-EBG boardis designed with the added substrate thickness being 0.4 mm.There are 16 vias on each unit cell; each corner pad has four viauniformly distributed with distance 7.5 mm. Fig. 12 shows thefrequency-domain response of the embedded LPC-EBG powerplane. The reference board with the continuous embeddedpower plane is also presented for comparison. The results aresimulated both by the 3-D-FDTD method and the HFSS, basedon the finite-element method. The agreement between these twoapproaches shows the validity of the simulated GBN-suppres-sion behavior. It is seen that the designed embedded LPC-EBGpower plane still maintains broad-band GBN suppression in thefrequency range from 900 MHz to 4.8 GHz. Compared withthe performance using a two-layer design (one EBG powerand one ground plane) shown in Fig. 5, the embedded powerplane using three layers still keep excellent GBN eliminationcapability. The main advantage of this design is that the signalquality will be better than the previous design, because bothreference planes are now continuous, but the design cost willbe increased because one more layer is needed.

V. CONCLUSION

A novel power/ground planes design using an LPC-EBGstructure is proposed to eliminate the GBN or SSN in high-speedcircuits. Two example designs, 9-unit cell and 25-unit cellLPC-EBG boards, are implemented, and their extinctiveperformance of efficient and wideband GBN suppression istheoretically and experimentally demonstrated both in timeand frequency domains. It has been shown the LPC-EBGpower plane behaves over a 4-GHz stopband with an average


of over 50-dB reduction of the GBN. A simple 1-D equivalentcircuit model with the periodic boundary conditions is alsodeveloped to predict their stopband characteristics. In addition,the proposed design suppresses low radiated emission (or EMI)resulting from the GBN at the designed stopband, althoughthere are several etched slots on the power plane. The impactof the LPC-EBG power plane on the SI for the signal tracesreferring to the power plane is investigated. Two possiblesolutions, differential signals and embedded LPC-EBG powerplanes, are proposed to decrease the influence on the SI.

REFERENCES

[1] R. Abhari and G. V. Eleftheriades, “Metallo-dielectric electromagneticbandgap structures for suppression and isolation of the parallel-platenoise in high-speed circuits,” IEEE Trans. Microw. Theory Tech., vol.51, no. 6, pp. 1629–1639, Jun. 2003.

[2] T. Kamgaing and O. M. Ramahi, “A novel power plane with inte-grated simultaneous switching noise mitigation capability using highimpedance surface,” IEEE Microw. Compon. Lett., vol. 13, no. 1, pp.21–23, Jan. 2003.

[3] T. L. Wu, S. T. Chen, J. N. Huang, and Y. H. Lin, “Numerical and exper-imental investigation of radiation caused by the switching noise on thepartitioned dc reference planes of high-speed digital PCB,” IEEE Trans.Electromagn. Compat., vol. 46, no. 1, pp. 33–45, Feb. 2004.

[4] G.-T. Lei, R. W. Techentin, and B. K. Gilbert, “High frequency char-acterization of power/ground-plane structures,” IEEE Trans. Microw.Theory Tech., vol. 47, no. 5, pp. 562–569, May 1999.

[5] T. L. Wu, Y. H. Lin, and S. T. Chen, “A novel power planes with lowradiation and broadband suppression of ground bounce noise using pho-tonic bandgap structures,” IEEE Microw. Compon. Lett., vol. 14, no. 7,pp. 337–339, Jul. 2004.

[6] R. Coccioli, F. R. Yang, K. P. Ma, and T. Itoh, “Aperture-coupled patchantenna on UC-PBG substrate,” IEEE Trans. Microw. Theory Tech., vol.47, no. 11, pp. 2123–2130, Nov. 1999.

[7] D. F. Sievenpiper, “High-impedance electromagnetic surfaces,” Ph.D.dissertation, Dept. Elect. Eng., Univ. California at Los Angeles, Los An-geles, CA, 1999.

[8] N. Shino and Z. Popovic, “Radiation from ground-plane photonicbandgap microstrip waveguide,” in Dig. IEEE MTT-S Int. Microw.Symp., Jun. 2002, pp. 1079–1082.

[9] O. M. Ramahi, “Near-field and far-field calculation in FDTD simula-tions using Kirchhoff surface integral representation,” IEEE Trans. An-tennas Propag., vol. 45, no. 5, pp. 753–759, May 1997.

[10] Y. H. Lin and T. L. Wu, “Investigation of signal quality and radiatedemission of microstrip line on imperfect ground plane: FDTD analysisand measurement,” in Proc. IEEE Int. Symp. Electromagn. Compat.,Montreal, QC, Canada, Aug. 2001, pp. 319–324.

Tzong-Lin Wu (S’93–M’98–SM’04) received theB.S.E.E. and Ph.D. degrees from National TaiwanUniversity, Taipei, Taiwan, R.O.C., in 1991 and1995, respectively.

From 1995 to 1996, he was a Senior Engineer withMicroelectronics Technology, Inc., Hsinchu, Taiwan,R.O.C. From 1996 to 1998, he was with the CentralResearch Institute, Tatung Company, Taipei, Taiwan,R.O.C., where he was involved with the analysis andmeasurement of EMC/EMI problems of high-speeddigital systems. From 1998 to 2005, he was with the

Electrical Engineering Department, National Sun Yat-Sen University (NSYSU),Kaohsiung, Taiwan, R.O.C. He is currently an Associate Professor with theDepartment of Electrical Engineering amd Graduate Institute of Communica-tion Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. His re-search interests include design and analysis of fiber-optic components, EMCand signal-integrity design, and measurement for high-speed digital/optical sys-tems.

Dr. Wu received the Excellent Research Award and Excellent Advisor Awardfrom NSYSU in 2000 and 2003, respectively, the Outstanding Young EngineersAward from the Chinese Institute of Electrical Engineers in 2002, and the WuTa-You Memorial Award from the National Science Council (NSC) in 2005. Hewas also listed in Marquis Who’s Who in the World in 2001. He is a member ofthe Chinese Institute of Electrical Engineers.

Yen-Hui Lin was born in Chiayi, Taiwan, R.O.C., onFebruary 8, 1977. He received the B.S.E.E. degree in1999, and the Ph.D. degree in 2005, both from Na-tional Sun Yat-Sen University, Kaohsiung, Taiwan,R.O.C.

His research interests include the signal integrity(SI) and EMI designs in high-speed digital circuitsand numerical EM field analysis for EMC problems.

Dr. Lin received the Best Paper Award from theTaiwan Print Circuit Association (TPCA) in 2004.

Ting-Kuang Wang was born in Tainan, Taiwan,R.O.C., on December 27, 1980. He received theB.S.E.E. degree from National Sun Yat-Sen Uni-versity, Kaohsiung, Taiwan, R.O.C., in 2003, andis currently working toward the Ph.D. degree at thesame university.

His current research interest is the power-integritydesign in high-speed circuits.

Chien-Chung Wang was born in Tainan, Taiwan,R.O.C., in 1979. He received the B.S.E.E. degreefrom National Sun Yat-Sen University, Kaohsiung,Taiwan, R.O.C., in 2003, and is currently workingtoward the Ph.D. degree in electrical engineering atthe same university.

His research interests include the EMI/SI measure-ment for high-speed digital circuits and numericalEM field analysis for EMC problems.

Sin-Ting Chen was born in Pingtung, Taiwan,R.O.C., in 1980. He received the B.S.E.E. degreefrom National Sun Yat-Sen University, Kaohsiung,Taiwan, R.O.C., in 2002. He is currently workingtoward the Ph.D. degree in electrical engineering atthe same university.

His research interests are modeling and measure-ment for the power integrity of high-speed packageand printed circuit boards.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53

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