DEFECTED ground structures (DGSs) yield low-pass performance

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1 2160 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 Quasi-Static Modeling of Defected Ground Structure Nemai Chandra Karmakar, Senior Member, IEEE, Sushim Mukul Roy, and Isaac Balbin Abstract A quasi-static equivalent-circuit model of a dumbbellshaped defected ground structure is developed. The equivalent-circuit model is derived from the equivalent inductance and capacitance developed due to the perturbed return current path on the ground and the narrow gap, respectively. The theory is validated against the commercial full-wave solver CST Microwave Studio. Finally, the calculated results are compared with the measured results. Good agreement between the theory, the commercially available numerical analyses, and the experimental results validates the developed theoretical model. Index Terms Bandstop filter, defected ground structure (DGS), electromagnetic bandgap (EBG), frequency spectrum, high-impedance surface, low-pass filter (LPF), photonic bandgap. Fig. 1. Isometric view of unit cell DGS. I. INTRODUCTION DEFECTED ground structures (DGSs) yield low-pass performance with a very wide stopband. Due to its wide bandstop property, a DGS has been used in many interesting applications. The DGS is realized as a low-pass filter (LPF) in [1]. Garde et al. [2] proposed a nonuniform ring patterned dumbbellshaped DGS to design an LPF similar to the author s proposition of the nonuniform distribution of electromagnetic bandgap structure (EBGS) [3]. Liu et al. [4] reported an LPF with a multilayer fractal EBGS. Significant ripples appear in the passband. Although the LPF performance reported in [2] and [4] is impressive, the designs need to take care of both the bottom and top layouts that may be in contrast to high-level implications. DGSs are designed by connecting two square electromagnetic bandgap (EBG) cells with a thin slot. Fig. 1 shows the isometric view of a dumbbell-shaped DGS. As can be seen in Fig. 1, is the height of the dielectric substrate, is the width of the microstrip line, and are the arm lengths, and is the width of the gap under the microstrip line on the ground plane. The frequency of operation can be changed with the DGS dimensions. Design and analysis are a challenging problem for DGSs. The easy availability of commercial electromagnetic (EM) solvers is the main resource for the design and analysis of DGS. The fullwave analysis [5] is very involving and does not give any physical insight of the operating principle of the DGS. The flowchart in Fig. 2 shows the conventional design and analysis methods of Manuscript received August 10, 2005; revised February 2, This work was supported by the Australian Research Council under Discovery Project Grant DP : Chipless RFID for Barcode Replacement and Monash University under the M.Sc. and Final Year Project Research Programs. The authors are with the Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Vic. 3800, Australia ( nemai. karmakar@eng.monash.edu.au). Digital Object Identifier /TMTT Fig. 2. Conventional design and analysis method of DGS DGSs. It can be seen in Fig. 2 that the design phase of a DGS starts with the design specifications of stopband frequencies. The dielectric material is selected for the design. The full-wave solver is used to find the -parameters versus frequency behavior of the DGS. If the results are satisfactory, only then can the -parameters be converted to and -parameter matrices and the equivalent LC resonant structure derived from the matrices. The physical insight is understood based on the equivalent-circuit model of the DGS. The other disadvantage of this method is that there is not direct correlation between the physical dimensions of the DGS and the equivalent LC parameters. The derived performance of the DGS is fully unpredictable until the optimized solutions are achieved through a trial-and-error iterative process. Hence, the conventional methods as reported in the open literature are time consuming and may not lead to the optimum design. This paper overcomes this limitation by developing the equivalent-circuit model, which is directly derived from the physical dimensions of the DGS. Fig. 3 illustrates the flowchart of the /$ IEEE

2 KARMAKAR et al.: QUASI-STATIC MODELING OF DGS 2161 Fig. 4. (a) Unit cell DGS. (b) Surface current on ground plane. Fig. 3. Proposed design and analysis method of DGS. method. As can be seen from this figure, a generalized equivalent-circuit model of the DGS is developed first. The design resonant frequency, dimensions, and dielectric properties of the microwave laminate are selected. The design parameter is varied in a do loop until the required frequency is achieved. In the development of the equivalent-circuit model, the structure is assumed to be the combination of a pair of u-shaped filaments of ground currents and the gap and cross discontinuities. For the components, quasi-static equivalent capacitances and inductances are calculated and matrix parameters are extracted. Finally, the matrix parameters are transformed to -parameters versus frequency. This approach gives a comprehensive understanding of the physical principle of DGS how the DGS creates bandstop and bandpass responses and which dimensions play the most critical role in creating the distinct performance. This paper is organized as follows. Section II presents the theory of the DGS unit cell followed by the design in Section III. Section IV deals with the analysis of the equivalent model obtained in Section III. Results and discussion are presented in Sections V and VI, respectively, followed by a conclusion in Section VII. II. QUASI-STATIC THEORY OF DGS For a conventional microstrip transmission line, the quasi-tem mode propagates under the microstrip filament and the infinite ground plane. The electric and magnetic fields are mostly confined under the microstrip line. The return current on the ground plane is the negative image of the current on the microstrip line. As can be seen in Fig. 4(a) of the DGS perturbed microstrip transmission line, the return path of the current is fully disturbed and this current is confined to the periphery of the perturbation [see Fig. 4(b)] and returns below the microstrip line once the perturbation is over. Based on this observation, an equivalent-circuit model shown in Fig. 5 is developed. In this compact model in Fig. 5(a), the current distribution, as shown in Fig. 5(b), is observed. This current distribution in Fig. 5(b) is a more regular version of the current distribution, as shown in Fig. 4(b). Based on the observation of the maximum concentration of the return current, the width of the side filament arms, which contribute to the inductance of the DGS, is selected. Fig. 5(c) shows the equivalent filament model of the DGS. Fig. 5(d) shows the current on the DGS perturbed microstrip line. This equivalent-circuit model starts with a cross at the junction of the dumbbell followed by a transmission line with the arm length, the bend, arm length, the bend, arm length, and finishes with the other cross. The gap is represented by the equivalent capacitances and is connected vertically to the arms of the two crosses. The power is impinged at one arm of the cross and power is extracted from the opposite arm of another cross. Now the equivalent-circuit model of the current filament can be extracted with the equivalent inductances and capacitances of the microstrip discontinuities. The inductances and capacitances are derived from the physical dimensions using quasi-static expressions for microstrip crosses, lines, and gaps available in the open literature [6], [10] [12]. The closed-form expressions for various microstrip discontinuities considered here are based on quasi-static analysis of a thin microstrip line (the thick line or thick ground plane does not affect the behavior of this circuit in terms of location of the attenuation pole. Only the bandwidth of the stopband decreases) [8]. The mode of propagation of the wave is considered to be purely TEM. In the high-frequency region, small changes in inductance, characteristic impedance, and effective dielectric constant (hence, to capacitance) take place. We have incorporated those small corrections by curve fitting, as well as with interpolation from the previous works and available data in [6] and [10] [12]. When estimating the capacitance, as charge is supposed to be a scalar quantity, capacitance values are supposedly unchanged [8]. Since the effective dielectric constant changes very little

3 2162 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 Fig. 5. (a) Truncated structure of DGS (inverted figure: the truncated ground plane is shown on the top and the continuous microstrip line is shown at the bottom). (b) Current distribution on ground plane. (c) Schematic equivalent current sheet. (d) Current distribution on microstrip line. with frequency [9], capacitance changes very little with an increase of frequency. On the contrary, the current distribution is supposed to be a vector quantity and a function of frequency. Hence, the inductance decreases to a limited extent with an increase in frequency. Thus, by curve fitting and interpolation from previous studies, we have made the necessary correction to the dc inductances. Thus, a simplified form of calculation is possible without going into full-wave matrix solvers. III. DESIGN OF DGS The DGS unit cell is designed for the application of a global system for mobile communications (GSM) dual-band mobile communications where most RF and microwave circuits are designed at - and -band. Taking the attenuation pole at 2.4 GHz and the cutoff frequency at 1.2 GHz, the length of and is, where is the guide wavelength of the cutoff frequency. This resonant behavior of DGS can be explained by an equivalent LC circuit model. As mentioned above, the circuit model is derived for the quasi-static expressions for microstrip bends, gaps, and crosses [6] [12]. The filament inductances for bends and straight lines are calculated using expressions found in [6] [12]. For the calculations and practical prototyping, the Taconic ceramic laminate of dielectric constant and thickness mm is used for analysis and CST Microwave Studio is used for simulation on the -parameters versus frequency of the DGS for comparison. IV. ANALYSIS If we extend our view to the concentration of the return current on the ground plane in Figs. 4 and 5, we observe an interesting fact. The current is concentrated at all places along the length of the microstrip line, except at the defect on the ground. At the gap on the ground, the current retraces a certain amount of path and goes along the sidelobes (being confined within a limited width only) and a strong capacitance is introduced in the gap along the length of the microstrip line. A small amount of current also goes directly along the sidelobes instead of traveling along the microstrip line. The circuit model of this truncated structure was then derived and its output behavior was calculated with the help of MATLAB 7 and is then compared with those of the actual unit cell DGS. The results, being in good agreement over a wide range of parameter variation, can be rightly concluded as the circuit model of a unit cell DGS. The special feature of this circuit model is that it incorporates the actual physical dimensions and thereby predicts the outcomes and changes of a unit cell DGS with the variation of the physical dimensions. To the best of the authors knowledge, this type of analysis was not carried out before. The previous studies [1], [5] were based on the Butterworth filter approximation of the DGS and there was no relationship between the proposed design parameters and the equivalent-circuit components. Length of the side arm contributes twice to the inductance arising at the sidelobes in comparison to the length of the side

4 KARMAKAR et al.: QUASI-STATIC MODELING OF DGS 2163 for (3) for (4) Fig. 6. (a) Microstrip gap on ground plane. (b) Equivalent-circuit model. for (5) arm. As a result, keeping the length of one arm constant, if the length of the other is varied, the same variance in the location of the attenuation pole is not observed for similar variance of and. In extracting the equivalent-circuit model, closed-form expressions were used for calculating the circuit parameters of certain microstrip discontinuities that comes to play in this truncated figure [see Fig. 5(a)]. The following is a discussion of individual discontinuities and their equivalent-circuit parameters. A. Microstrip Gap The central discontinuity of the microstrip line of Fig. 5(c) can be represented as the microstrip gap. The equivalent circuit of the microstrip discontinuity is shown in Fig. 6. As can be seen, the gap is represented by two parallel capacitances to ground and a series capacitance. The values of these capacitances are extracted from even- and odd-mode capacitances, as given below. Interestingly, it should be noted that all equivalent capacitances are extracted from the physical dimensions of the gap discontinuity and the dielectric constant [7] where pf pf is the gapwidth. B. Microstrip Cross The two ends of the structure shown in Fig. 5(c) are represented by two microstrip crosses. The power is impinged on one end and is extracted through the other end. The equivalent circuit of such a discontinuity is shown in Fig. 7. As can be seen in this figure, two sets of two symmetrical arms of the microstrip cross are represented by equivalent,, and, and the cross arms are inductively coupled by. Each end of the term is terminated by width and. The equivalent capacitances and inductances are calculated using (7) (10), shown at the bottom of this page [7]. for (6) pf pf (1) for (2) C. Inductance Calculations The two U-shaped filaments of the truncated ground plane [as shown in Fig. 5(a) (c)] of lengths are represented as inductances and are discussed as follows. The inductances here have been calculated based on [6] [12]. Since the filaments that we are referring to are actually rectangular cross sections of wire, a correction must be made to account for the effect of the extra conductor. This is done by conpf (7) NH (8) NH (9) NH (10)

5 2164 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 Fig. 7. (a) Microstrip cross on ground plane. (b) Equivalent-circuit model. Fig. 8. Rectangular filament of wire broken into m 2 n segments. sidering the rectangular cross sections of filaments separated by a distance known as the geometric mean distance (GMD). The GMD is found by calculating of the sum of the logarithm of the distance between pairs of points. To start calculating the GMD, initially the wire must be broken up into points (as shown in Fig. 8) of equal volume that are small compared to the width and depth of the wire. The GMD is then calculated by summing the logarithms of the distances between the pairs of points and then taking of it. This method of GMD allowed us to calculate the inductance created by the side arms of the dumbbell. The concept of the GMD can also be used to calculate the self-inductance of a filament. The self-inductance of a single conductor can be computed by assuming that the self-inductance of the conductor is simply the sum of all the partial mutual inductance of each pair of filaments within the single conductor. This gives rise to the GMD of a filament from itself. It can be calculated by [12] above-mentioned formula and usual circuit theory. Thus, we have ensured that all the inductive effects of the side arms are included. At dc, the current is distributed uniformly throughout the conductor. However, as the frequency rises, there will be a tendency for the current to concentrate at the surface of the filament. It is assumed that the current decreases exponentially inside the filament (skin effect), and that the current is the same at the top and bottom of the conductor, i.e., sidelobe of the ground plane, as shown from the surface current distribution diagram in Fig. 5(b). As a result, the outer portions of the conductor contribute less than the inner parts to the overall self inductance (current has more difficulty passing through the inner parts due to skin effect). Thus, if current is concentrating on the surface, the inductance will decrease. Thus, with an increase of frequency, the inductance decreases. Using (7) (15) and by curve fitting [6] [12], we have done our calculations for the inductances. If two conductors meet at an angle, mutual inductance comes to play at the bend, which we represented as in the circuit diagram (Fig. 9). When two strips of lengths and meet at an angle, then the junction gives a mutual inductance given by [6] NH (12) As here, is zero, which implies in Fig. 9 is 0. The self and mutual inductance can be calculated with the magnetic flux method for mutual inductance and the energy method for effective inductance calculation [12] taking into consideration the high frequency of operation (13) NH (11) If two or more very closely placed inductors are considered in parallel and the net inductance is calculated using two-port circuit parameters, we get an incorrect result as the mutual inductances are not taken into consideration. Thus, the following relation is used that includes the mutual inductances: In our calculation, the side arms are purely inductive and the two arms are combined into a single inductance by using the NH (14) (15) In (13), a single turn of the coil is considered and is the skin depth. Taking into consideration the aforementioned closed-form expressions and circuit parameters, we model the equivalent circuit of the truncated figure (Fig. 9) and then carry on the following conversions using two-port circuit parameters, as shown in Fig. 9.

6 KARMAKAR et al.: QUASI-STATIC MODELING OF DGS 2165 Fig. 9. Equivalent-circuit model of unit cell DGS. As can be seen in this figure, the complete equivalent-circuit model in terms of crosses, bent lines, and the gap capacitances is fully characterized by (1) (15). All these expressions take care of the dimensions of the DGS and the dielectric properties of the substrate. Therefore, from the equivalent-circuit model, a direct correlation between the design parameters and the design specification is calculated. Results are followed by discussions in Section VI, in which the basis of selecting the is discussed. V. RESULTS The parametric study of the design parameters of the proposed DGS and the influence of these parameters on the attenuation pole and cutoff frequency is presented here. This parametric study will give rise to the frequency behavior of a DGS assisted 50- transmission lines. The parametric study leads to the design curves for generic DGS circuits. Therefore, this study is very useful for the designer community. This study also gives insight into the physical properties of the DGS in the frequency behavior. Every set of theoretically calculated results is compared with those obtained from the commercially available EM solver CST Microwave Studio. Good agreement between the two theoretical results validate the proposed theory. Finally, the theoretical results are compared with the measured results of the fabricated prototyped DGS circuit on the Taconic substrate. The agreement is, in general, good, showing on-the-spot attenuation pole. The DGS assisted microstrip transmission line is measured on an Agilent 8510C vector network analyzer (VNA). A. Parametric Study of DGS In Figs , the lengths of and are taken to be 5 mm each with a gap dimension of 0.5 mm. The dielectric constant

7 2166 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 Fig. 10. Variation of resonant frequency with arm length a. Fig. 13. Variation of resonant frequency with gap dimension g. Fig. 11. Variation of resonant frequency with arm length b. of sub- Fig. 14. Variation of resonant frequency with dielectric constant " strate. Fig. 12. Variation of resonant frequency with both side arm lengths a and b simultaneously. of the substrate is 2.2 and height is mm. The microstrip transmission line is of 2.4-mm width and 50- characteristic impedance. When any of the above-mentioned parameters are varied, the other parameters are kept as mentioned above. Fig. 10 shows the variation of the attenuation pole or resonant frequency of the DGS unit cell with the arm length.it can be seen in the figure that the frequency decreases with the arm length. The agreement between the CST Microwave Studio simulation and the theory is very good. Fig. 11 shows the variation of the attenuation pole or resonant frequency of the DGS unit cell with the arm length. Fig. 15. Comparison of S-parameters versus frequency of CST Microwave Studio simulation and theory. Fig. 12 shows the variation of the resonant frequency when both and vary together. It can be seen from the figures that the frequency decreases with an increase in arm length. The agreement between the CST Microwave Studio simulation and the theory is very good. Fig. 13 shows the variation of the resonant frequency with the gap distance. With the gap distance, the gap capacitance diminishes. As a result, the resonant frequency increases with the increase of the gap distance.

8 KARMAKAR et al.: QUASI-STATIC MODELING OF DGS 2167 Fig. 16. Comparison of S-parameters versus frequency of Agilent HP 8510C VNA measurement, CST Microwave Studio simulation, and theory for unit cell DGS using taconic alumina as the substrate with " =10and height 0.63 mm. a = b = 5mm and g = 0:3 mm. Characteristic impedance of microstrip line is 50. Finally, in the parametric study, the dielectric constant of the substrate material is varied. It can be seen in Fig. 14 that the resonant frequency decreases with the dielectric constant of the substrate. Here also, the agreement between CST Microwave Studio and the theory is very good. B. Simulation and Measured Results of DGS After the satisfactory agreement of the comprehensive parametric study of the unit cell DGS between CST Microwave Studio and the proposed theory, the complete -parameter versus frequency plots are shown in Fig. 15. As can be seen in Fig. 15, the attenuation poles for CST and the theory are in very good agreement at 7.87 and 7.9 GHz, respectively. There is a deviation in the stop bandwidth of the two calculations. The discrepancy can be attributed to the simple equivalent-circuit model of the proposed theory that yields narrowband responses compared with the full-wave analysis of CST. However, the precise match of center frequency responses validates the proposed theory. Finally, the theoretical calculation of the DGS is compared with the measured results on an Agilent HP 8510C VNA. The DGS was fabricated on a taconic substrate with and a thickness of 0.63 mm. Both the arm lengths mm and gap dimension was mm. Characteristic impedance of the microstrip line was 50. This exercise also validates the proposed theory for a completely different set of parameters of the DGS. Fig. 16 shows the measured, simulated, and calculated -parameters of the unit cell DGS versus frequency. As can be seen from these figures, similar magnitude of agreement, as shown in Fig. 16 for measured results, CST Microwave Studio simulation, and the proposed theory is achieved. Again, reasons for the discrepancies may be attributed to the simplified circuit model where the dimensions are very frequency sensitive and of narrowband design. In additionally to this highly frequency sensitive theoretical responses, the factor of a parallel resonant circuit varies inversely with the resistance and other losses. Hence, in the CST simulated result, we get a bigger bandwidth compared to the calculated result. VI. DISCUSSIONS The width of the microstrip line considered here corresponds to 50- characteristic impedance. The width of the side arms is chosen here to be 0.2 mm. The width of 0.2 mm was chosen as this is the width that corresponds to the maximum concentration of the current distribution on the side arms. This optimum width changes slightly with an abrupt increase or decrease of arm length and dielectric constant of the slab, but 0.2 mm is a very good approximation for which the computed results match with the simulated or measured ones. As the inductance of a planar strip with square cross section is inversely proportional to the length of the sides, decreasing results in an increase in the side-arm inductance. By raising the inductance of the side arms, the attenuation pole is shifted toward the left. The converse is not true for an increase of, i.e., the attenuation pole does not shift significantly toward a higher frequency, as current concentration is much smaller there. In earlier related literature, the unit cell DGS has been described as a one-pole Butterworth filter [1], [5] where the capacitance comes only from the gap and the inductance comes only from the loop. After doing this sort of analysis of the unit cell DGS, we can say that the variance of the inductance and the capacitance does not follow any linear rule and we can also explain why they do not follow. If we observe Figs. 4(b) and 5(b), it can be clearly seen that the density of current is more in the bends. It is because there is no mutual inductance at a right-angle bend and, hence, current flows with much more ease through this region. The cross capacitances are similar in magnitude with the gap capacitance. Although due to different connectivity they are not in parallel or series with the gap capacitance, they still play a big role in the determination of the location of the attenuation pole. Assuming cross capacitance as zero leads to a significant deviation of the computed results from the measured or simulated one. Additionally, like distributed inductance, there is distributed capacitance of the ground plane along the length of the microstrip line. VII. CONCLUSION In this paper, we have presented a novel equivalent-circuit model of a unit cell DGS. The equivalent-circuit model is derived from the equivalent inductance and capacitance developed due to the perturbed returned current path on the ground and narrow gap, respectively. The filament current path is modeled as a current sheet on the ground plane. The current tightly coupled to the periphery of the dumbbell-shaped DGS. Hence, the model is a combination of various microstrip-line discontinues such as crosses, bends, tees, and the gap capacitances. Based on the developed theory, a comprehensive parametric study is performed and compared with the simulated results of CST Microwave Studio. Excellent agreement regarding the location of the attenuation poles between the proposed theory and CST Microwave Studio simulation has been obtained. The theory has been fully validated against the -parameter versus frequency plot for both the commercial full-wave solvers CST Microwave Studio and the theory. Finally, the calculated results have been compared with the measured results. In general, good agreement between the theory, commercially avail-

9 2168 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 able numerical analyses, and experimental results has validated the developed theoretical model. However, there is a discrepancy regarding the bandwidth calculation. This discrepancy can be attributed to the quasi-static equivalent-circuit model itself where the loss tangent of the dielectric material and other losses were not included. ACKNOWLEDGMENT The authors acknowledge the software supported by CST, Darmstadt, Germany. REFERENCES [1] D. Ahn, J. S. Park, C. S. Kim, J. Kim, Y. Qian, and T. Itoh, A design of the low-pass filter using the novel microstrip defected ground structure, IEEE Trans. Microw. Theory Tech., vol. 49, no. 1, pp , Jan [2] L. Garde, M. J. Yabar, and C. D. Rio, Simple modeling of DGS to design 1D-PBG low pass filter, Microw. Opt. Technol. Lett., vol. 37, no. 3, pp , May [3] N. C. Karmakar and M. N. Mollah, Investigations into nonuniform photonic bandgap microstripline low-pass filters, IEEE Trans. Microw. Theory Tech., vol. 51, no. 2, pp , Feb [4] H.-W. Liu, X.-W. Sun, and Z.-F. Li, A low-pass filter of wide stopband with a novel multilayer fractal photonic bandgap structure, Microw. Opt. Technol. Lett., vol. 40, no. 5, pp , Mar [5] J. S. Park, An equivalent circuit and modeling method for defected ground structures and its application to the design of microwave circuits, Microw. J. Nov [Online]. Available: [6] F. W. Grover, Inductance Calculation: Working Formulas and Tables. New York: Dover, [7] R. Garg and I. J. Bahl, Microstrip discontinuities, Int. J. Electron., vol. 45, no. 1, pp , [8] A. Gopinath and P. Silvester, Calculation of inductance of finite Length strips and its variation with frequency, IEEE Trans. Microw. Theory Tech., vol. MTT-21, no. 6, pp , Jun [9] E. J. Denlinger, A frequency dependent solution for microstrip transmission lines, IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 1, pp , Jan [10] A. F. Thomson and A. Gopinath, Calculation of microstrip discontinuity inductances, IEEE Trans. Microw. Theory Tech., vol. MTT-23, no. 8, pp , Aug [11] B. Easter, The equivalent circuit of some microstrip discontinuities, IEEE Trans. Microw. Theory Tech., vol. MTT-23, no. 8, pp , Aug [12] B. L. Ooi, D. X. Xu, and L. H. Guo, Efficient methods for inductance calculation with special emphasis on nonuniform current distributions, Microw. Opt. Technol. Lett., vol. 40, no. 4, pp , Mar. 5, Engineer with Mitec Ltd., Brisbane, Australia, where he contributed to the development of land mobile satellite antennas for the Australian Mobilesat. From 1995 to 1996, he taught final year courses on microwaves and antenna technologies at Queensland University of Technology, Brisbane, Australia. From September 1998 to March 1999, he was a Research Engineer within the Radar Laboratory, Nanyang Technological University, Singapore. From March 1999 to July 2004, he was an Assistant Professor and Graduate Advisor with the Division of Communication Engineering, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. Since July 2004, he has been a Senior Lecturer with the Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Australia. His research interests cover areas such as smart antennas for mobile and satellite communications, EBG-assisted RF devices, planar phased-array antennas, broadband microstrip antennas and arrays, beam-forming networks, near-field/far-field antenna measurements, microwave device modeling, and monostatic and bistatic radars. He has authored or coauthored over 150 referred journal and conference papers and six book chapters. He is listed in the Marquis Who s Who in Science and Technology ( , ) as a pioneer in planar phased arrays. Dr. Karmakar was the recipient of the third Best Student Paper presented at the 1997 Asia Pacific Microwave Conference, Hong Kong for his doctoral work. His doctoral work was one of the most significant findings at the University of Queensland in 1998 and was published in national media such as ABC Radio and the Canberra Times. Sushim Mukul Roy received the Bachelor of Engineering degree in electronics and telecommunication engineering from Deemed University, Kolkata, India, in 2003, and is currently working toward the Ph.D. degree at Monash University, Clayton, Australia. His areas of interest include passive microwave devices. His current research concerns chipless radio frequency identification systems. Isaac Balbin received the B.Sc./B.E. degree in electricla engineering from Monash University, Clayton, Australia, in 2005, and is currently working toward the M.Sc. (Research) degree in electrical and computer systems engineering at Monash University. His research concerns negative refractive index material and passive RF identification (RFID) tag development. Nemai Chandra Karmakar (S 91 M 91 SM 99) received the B.Sc. (EEE) and M.Sc. (EEE) degrees from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 1987 and 1989, respectively, the M.Sc. degree in electrical engineering from the University of Saskatchewan, Saskatoon, SK, Canada, in 1991, and the Ph.D. degree from University of Queensland, Brisbane, Australia, in His doctoral research concerned the area of switched beam and phased-array antennas for mobile satellite communications. From 1989 to 1990, he was an Assistant Engineer with the Electronics Institute, Atomic Energy Research Establishment, Dhaka, Bangladesh. In August 1990, he was a Research Assistant with the Communications Research Group, University of Saskatchewan. From 1992 to 1995, he was a Microwave Design

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11 易迪拓培训 专注于微波 射频 天线设计人才的培养网址 : CST 学习培训课程套装该培训套装由易迪拓培训联合微波 EDA 网共同推出, 是最全面 系统 专业的 CST 微波工作室培训课程套装, 所有课程都由经验丰富的专家授课, 视频教学, 可以帮助您从零开始, 全面系统地学习 CST 微波工作的各项功能及其在微波射频 天线设计等领域的设计应用 且购买该套装, 还可超值赠送 3 个月免费学习答疑 课程网址 : HFSS 天线设计培训课程套装套装包含 6 门视频课程和 1 本图书, 课程从基础讲起, 内容由浅入深, 理论介绍和实际操作讲解相结合, 全面系统的讲解了 HFSS 天线设计的全过程 是国内最全面 最专业的 HFSS 天线设计课程, 可以帮助您快速学习掌握如何使用 HFSS 设计天线, 让天线设计不再难 课程网址 : MHz NFC/RFID 线圈天线设计培训课程套装套装包含 4 门视频培训课程, 培训将 13.56MHz 线圈天线设计原理和仿真设计实践相结合, 全面系统地讲解了 13.56MHz 线圈天线的工作原理 设计方法 设计考量以及使用 HFSS 和 CST 仿真分析线圈天线的具体操作, 同时还介绍了 13.56MHz 线圈天线匹配电路的设计和调试 通过该套课程的学习, 可以帮助您快速学习掌握 13.56MHz 线圈天线及其匹配电路的原理 设计和调试 详情浏览 : 我们的课程优势 : 成立于 2004 年,10 多年丰富的行业经验, 一直致力并专注于微波射频和天线设计工程师的培养, 更了解该行业对人才的要求 经验丰富的一线资深工程师讲授, 结合实际工程案例, 直观 实用 易学 联系我们 : 易迪拓培训官网 : 微波 EDA 网 : 官方淘宝店 : 专注于微波 射频 天线设计人才的培养易迪拓培训官方网址 : 淘宝网店 :

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