Micromachined tunable filter using fractal electromagnetic bandgap (EBG) structures

Transcription

1 Sensors and Actuators A 133 (2007) Micromachined tunable filter using fractal electromagnetic bandgap (EBG) structures Muhammad Faeyz Karim, Ai-Qun Liu, Aibin Yu, Arokiaswami Alphones School of Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore , Singapore Received 8 July 2005; received in revised form 21 March 2006; accepted 22 May 2006 Available online 27 July 2006 Abstract A tunable bandstop filter using fractal electromagnetic bandgap (EBG) structure is designed, simulated and fabricated. The uniform fractal EBG (U-FEBG) structure is realized by replacing the etched rectangular holes with a Minkowski loop generator. A new technique of doubly tapered fractal EBG (DT-FEBG) structure is designed by non-uniform Kaiser distribution on the fractal structures. The Kaiser distribution improves the pass band performance and generates two distant bandgaps. The tunable bandstop filter is tuned by micromachined capacitive bridges. The propagation characteristic of the periodic microelectromechanical system (MEMS) bridges is determined by the dispersion behavior. Different types of parametric analysis are applied to investigate the performance of the MEMS bridges. Surface micromachining fabrication process is employed on the high resistivity silicon substrate to fabricate the filter. The measurement results for the DT-FEBG structure show insertion loss of 1.2 db and the stop-band rejection of 44 db. The tuning range of the U-FEBG structure is 1.1 GHz with insertion loss of db Elsevier B.V. All rights reserved. Keywords: RF MEMS; Capacitive switch; Coplanar waveguide (CPW); Fractal EBG; Bandstop filter 1. Introduction Tunable filters are commonly used as tracking filters for multi-band telecommunication systems, radiometers and wideband radar systems. The conventional tunable filters typically utilize YIG resonators, active resonators or varactors as the tuning element. However, these varactor based tuning filters have low Q values due to high series resistance of diodes. The development in microelectromechanical system (MEMS) technology allows new and innovative design of the tunable bandpass filters [1,2]. Electromagnetic bandgap (EBG) structures are periodic structures that exhibit a bandgap within which a certain band of electromagnetic propagation is prohibited [3]. EBG structures have potential applications in antennas, amplifiers, filters, power combiners, etc. [4,5]. In general 1D and 2D EBG structures in planar microstrip form can be easily realized by printing the patterns on the top of the substrate and are compatible for integration with the existing monolithic millimeters Corresponding author. Tel.: ; fax: address: eaqliu@ntu.edu.sg (A.-Q. Liu). wave integrated circuits (MMIC) fabrication process. In order to achieve an extra degree of freedom, wide stop-band design for coplanar waveguide (CPW) have been investigated. This CPW offers greater design flexibility which requires only single metal level as compared to the microstrip structures. The CPW EBG structures with slots of radial shapes on the ground plane have been employed in the low-pass and bandpass filters [6,7]. In some applications, a multi-band frequency response of the EBG is required, even though EBG structures have a wide stop-band. Usually fractal geometries are used to realize an EBG structure, which shows multi-band and wide stop-band properties. Fractals were first introduced by Mandelbrot [8] and after that wide variety of applications have been found in many branches of science and engineering [9]. Fractals geometrical shapes are generated by iterative process. In practice, an original shape is generated and the shape is modified over a number of iterations. Fractal geometries have been employed in microstrip EBG structures etched in the ground plane, showing dual band characteristics with high insertion loss [10]. The fractal CPW EBG structure has shown low insertion loss but with degradation in the stop-band rejection of the bandstop filter [11]. However, in the literature a MEMS tunable filter using fractal EBG structure /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.sna

2 356 M.F. Karim et al. / Sensors and Actuators A 133 (2007) with less insertion loss, dual frequency band and high rejection level has not been reported. This paper presents a double tapered fractal electromagnetic bandgap (DT-FEBG) technique in CPW configuration. The fractal shapes will be realized by Minkowski loop generator to obtain a dual stop-band frequency response. The fractal EBG structures will be etched on the ground plane as well as on the signal line. The stop-band rejection and the insertion loss performance of these fractal EBG is improved by non uniform Kaiser distribution [12]. A tunable bandstop filter is realized by introducing MEMS capacitive switches. The structures are fabricated on high resistivity silicon substrate where MEMS surface micromachining process are employed. Finally, the discussion on the measurement results in terms of flat responses for the tunable range, stop-band and pass-band of the filter are analyzed. 2. Design of the fractal EBG structure The EBG structure is basically a periodic structure that satisfies the following periodic condition: β = π (1) d where d is the period of the unit cell and β is the wave number in dielectric slab. The cell distance between a half guide wavelength, λ g if β equals to 2π/λ g. The wave number in dielectric is defined as, β = 2πf 0 εeff (2) c where f 0 is the centre frequency of the stop-band, ε eff the effective permittivity of the material, and c is the velocity of light in free space. Using Eqs. (1) and (2), the period d can be calculated for a given stop-band frequency. The aspect ratio used in the design is 0.25 in order to obtain better ripples in the pass-band and good rejection level. The fractal geometrical shapes are generated using the Minkowski loop generator [8]. The starting shape is the square hole of side a (zeroth iteration). In the first iteration, each side is replaced with new scaled generator (a 1 = a/3) with an indentation width of a 2, as shown in Fig. 1. This process continues infinitely until the final fractal geometry is achieved. In this design, the investigation is restricted to the first iteration only. The reason is that the geometry becomes complex after a large Fig. 1. Single cell of the fractal EBG structure. number of iterations which increases bends and turns in the surface profile. This surface profile may deteriorate the performance in certain microwave applications. The structure investigated in this present work has the dimensions of a 1 = a/3 and a 2 = 0.83a 1. The substrate used is high resistivity silicon (ρ = 4000 cm) with dielectric permittivity of ε r = 11.9 and thickness of 675 m. The fractal EBG structure with uniform distribution is etched in the ground plane as shown in Fig. 2. There are a total of eight EBG cells with a period of d = 3564 m. The uniform fractal EBG structure shows two distinct bandgaps with ripples in the pass-band. In the previous work [11], non-uniform distribution is found to reduce the side lobe level of the pass-band and increase the bandwidth of the stop-band, but degrade the stop-band rejection. These problems can be alleviated by introducing double tapered fractal electromagnetic bandgap structures as shown in Fig. 3. The DT-FEBG technique with additional EBG structure in the signal line not only reserves the advantage of the single tapered, but also improves the stop-band rejection and the upper passband loss. The characteristics given by the additional transverse slot at the central signal conductor introduces a series LC circuit in the forward current path with original series LC circuit in the backward current path. This equivalently increases the order of the bandstop filter. The amplitude pattern of the DT-FEBG is designed according to the Kaiser distribution polynomials, and Fig. 2. Schematic of the U-FEBG structure.

3 M.F. Karim et al. / Sensors and Actuators A 133 (2007) Fig. 3. Schematic of the DT-FEBG structure. Table 1 Parameters of the DT-FEBG filter Polynomial values Amplitude ( m) x x x x it can be expressed as, ( z ) T = l ) I 0 (α 1 (2z/l) 2 I 0 (α) (3) where I 0 is the modified Bessel function of the first kind, z/l the normalized longitudinal position in the circuit, l the device length and α = 4. The amplitude of the fractal are made proportional to the Kaiser polynomial x 0, x 1, x 2 and x 3, as shown in Fig. 3. The parameters values are listed in Table 1. The slow-wave factor is extracted from the simulated transmission phase in conjunction with the Bragg s condition and normalized with respect to CPW line as shown in Fig. 4. DT-FEBG has higher rate of phase change with frequency or higher slow-wave factor than the uniform fractal EBG structure. There is a reduction in phase velocity without occupying an extra surface area, the indentation width equals to 0.83 times of the generator length in uniform fractal EBG. Fig. 4. Simulation results of the slow-wave enhancement factor for two types of fractal EBG. 3. Design of the micromachined tunable filter using fractal EBG In the tunable EBG bandstop filter design, the CPW transmission line has a signal strip width of 70 m and the gap width of 115 m as shown in Fig. 5. The transmission line is of high impedance, i.e. 65, because the dimensions of the CPW have been designed by taking into account of periodical loading effects of MEMS capacitive bridges. The uniform fractal EBG structure is selected as compared to DT-FEBG for the tunable filter design as the signal width of DT-FEBG is 2000 m. The Fig. 5. Schematic of the MEMS tunable filter using fractal EBG structure.

4 358 M.F. Karim et al. / Sensors and Actuators A 133 (2007) maximum length of MEMS bridges from ground signal ground cannot exceed 350 m. There are a total of 12 MEMS bridges as each transmission line between the EBG structures contains 4 bridges. The width and length of the bridges are 50 and 300 m [13], respectively. The periodic spacing between bridges is s = 400 m. The MEMS bridges acts as a tuning element due to the change in the height of the bridges, i.e. varying the capacitance, when the dc bias voltage is applied between the signal line and the ground plane. Hence, the frequency of the band rejection can be tuned with different bias levels. When a dc bias voltage is applied on the MEMS bridges, i.e. between the fixed electrode and the beam, it acts like a parallel plate capacitor and its capacitance can be calculated as, C = Wl 1ε 0 (4) g where W =50 m is the width of the of the bridge, l 1 =70 m is the overlapping length of the fixed electrode, g =2 m isthe distance between the two plates and ε 0 = F/m is the permittivity of the vacuum. The capacitance caused by the side walls and even the back side play an important role and is referred as fringe effects. The fringe effects, as result give rise to the capacitance of a mechanical structure which is larger than that calculated by Eq. (4). Therefore, the parallel plate capacitance can be calculated as, Fig. 6. Simulation results of the frequency and capacitance dependence on the height of the bridge. C 0 = 2al 1ε 0 g (5) where l 1 is the length of the plate and a is the width of the plate. For the small distance between the plate (g a) the capacitance can be approximated by, C 1 = C g 2πa ln2πa g + g 2πa ln 1 + 2h g + 2 h g + h2 g 2 where C 1 is the capacitance due to fringe effects, h =1 misthe thickness of the bridge, a =50 m is the width of the bridge, and z =2 m is the height of the bridge. Fig. 6 shows the relationship between the capacitance and fringing effects of the tunable filter. It clearly shows that the capacitance due to fringing effect is greater than the normal capacitance. At 2 m the fringing (6) Fig. 7. Simulation result shows the relationship between the tuning range and insertion loss. because of the increase in the electromagnetic current interaction with the signal line and the ground plane. The propagation characteristics or slow-wave factor is a very important phenomenon for observation in the design of the MEMS bridges. The slow-wave factor of the MEMS bridges can be calculated by Floquet s theorem [14], which is given by, γ = 1 Λ cosh 1 [ (1 + S11 )(1 S 22 ) + S 12 S 21 + (Z 01 /Z 02 )(1 S 11 )(1 + S 22 ) + S 12 S 21 4S 21 ] (7) capacitance is 19.5 ff compared to ff of the normal capacitance, which is around 26% more. Fig. 6 also shows the effects of the height of the bridge on the frequency. The frequency is shifted from 17.6 to 15.2 GHz when the height is varied from 2 to 1.3 m. The total number of bridges per resonators is four and the bridges inter-distances are 400 m. The relationship between the tuning range and the insertion loss plays also an important role in the design of the tunable filter. Fig. 7 shows that the insertion loss is higher with the increase in tuning range. This is where γ is the complex propagation constant, Z 01 the characteristics impedance of port 1, Z 02 the characteristics impedance of port 2 and Λ = 400 m is the period of MEMS bridges. EM simulation results to the method proposed by [14] can be used to obtain the dispersion diagram of the MEMS bridges. The propagation factor in this case is e γλ, and γ = α +jβ is the complex propagation constant in the direction of propagation. The scattering matrix of the mth mode propagating in the z direction is calculated using commercial full wave simulator Zeland

5 M.F. Karim et al. / Sensors and Actuators A 133 (2007) Fig. 8. Dispersion diagram of the CPW line bridges: (a) at a period of 100 m and (b) at a period of 400 m. IE-3D. A high impedance CPW transmission line without any perturbation or fractal EBG is loaded with the MEMS bridges. A comparison has been carried out to find out the slow-wave factor when the number of bridges is varied as well as the distance between each bridge. In Fig. 8(a), the distance between the two bridges remains constant at 100 m while the numbers of bridges are varied. When β/k 0 is approaching the Bragg condition (βλ = π), the signal is highly attenuating and the bandgap for the 8 bridges starts at 15 GHz while for the 6 and 4 bridges it starts at 16 and 16.5 GHz, respectively. Although the bandstop behavior starts early, but there is not much variation in the dispersion at higher frequencies. The results for the switches with a inter-distance gap of 400 m is shown in Fig. 8(b). At higher frequencies of 30 GHz there is a distinct difference between all the two curves. Therefore, the CPW transmission line with the interdistance gap of 400 m has a distinct bandgap which increases with the number of switches. 4. Experimental results and discussions The fabrication process flow is shown in Fig. 9. It begins with the growth of a 1 m thick SiO 2 layer on a 675 m thick Fig. 9. (a g) Fabrication process flow. silicon substrate that serves as a buffer layer. A 1.5 m thick aluminum layer is then evaporated on the buffer layer to layout the CPW structure. After CPW is patterned, 0.1 m TaN with 2k /square sheet resistance is deposited and patterned as pull down electrodes and are connected by 15 m wide TaN bias line to the outside electrode. The SiN of 1.5 m is deposited and patterned as dielectric layer on the CPW grounds and it is also used to isolate the pull down electrodes. The photoresist is used as a sacrificial layer and 2 m of thick layer is coated and patterned. Finally, the metal bridge is dry released using RIE with O 2. Fig. 10 shows the optical photo of the tunable filter using fractal EBG structure. Full wave electromagnetic simulation and the current distribution for the structure is obtained by commercial software, Zeland IE-3D as shown in Fig. 11. It clearly shows that the transmission power cannot pass through the circuit and is maximally attenuated at the bandstop frequency of 17.6 GHz. The comparison of the measured and simulated results is shown in Fig. 12. For two distinct stop-bands at 17.6 and 21 GHz, the

6 360 M.F. Karim et al. / Sensors and Actuators A 133 (2007) Fig. 10. Optical photo of the tunable U-FEBG filter. insertion loss of the uniform fractal EBG structures is around 1.7 db with stop-band rejection of less than 33 db. The DT- FEBG structure is etched on the signal line as well as on ground plane. The dimensions are tapered proportional to the Kaiser distribution polynomial. The measurement result for the DT-FEBG is shown in Fig. 13. The insertion loss is 1.2 db and stop-band rejection is greater than 44 db. The 20 db rejection bandwidth Fig. 12. Comparison of the measured and simulated results of the U-FEBG EBG filter. is at 6.5 GHz. The performance of DT-FEBG is better in terms of insertion loss and stop-band rejection. The simulation and measurement results show close agreement with each other. The measurement results of the fabricated uniform tunable filter using fractal EBG are shown in Fig. 14. There are four Fig. 11. Simulation results of the current distribution of the DT-FEBG bandstop filter: (a) overview and (b) zoom view.

7 M.F. Karim et al. / Sensors and Actuators A 133 (2007) bridges on each section and the initial height of the bridges is 2 m. The bias voltage is applied by 0 35 V and the frequency is tuned over the range from 17.6 to 16.5 GHz. The insertion loss is increased as the bias voltage is raised due to the lowering down of the bridges. The lower pass-band insertion loss varies from 1.7 to 2.5 db. 5. Conclusions Fig. 13. Comparison of the measured and simulated results of the DT-FEBG filter. In this paper, a tunable bandstop filter using fractal EBG structure is designed, fabricated and measured. The fractal structure is constructed using Minkowski loop generator for generating a dual frequency band. The DT-FEBG structure designed with a non-uniform Kaiser distribution has demonstrated its ability to reduce the pass band ripples and increase the stop-band rejection. The tunable fractal bandstop filter is then realized by incorporating MEMS bridges on the signal line. The propagation characteristics and different types of parametric analysis for the MEMS bridges are studied. The measurement results show that insertion loss is 1.2 db and the stop-band rejection greater than 44 db. The tunable fractal structures show the tuning range of 1.1 GHz. The fractal DT-FEBG and tunable fractal EBG filters have high potential applications in microwave integrated circuits and antennas in future. References Fig. 14. Measurement result of the tunable U-FEBG filter: (a) S11 and (b) S21. [1] Y. Liu, A. Borgioli, A.S. Nagra, Robert A. York, Distributed MEMS transmission lines for tunable filter applications, Int. J. RF Microwave Comput. Aided Eng., Special Issue 11 (2001) [2] A. Tamijani, L. Dussopt, G.M. Rebeiz, Miniature and tunable filters using MEMS capacitors, IEEE Trans. Microwave Theory Tech. 51 (2003) [3] E.J. Yablonovitch, Photonic bandgap structures, J. Opt. Soc. Am. B 10 (1993) [4] V. Radisic, Y. Qian, R. Coccioli, T. Itoh, A novel 2-D photonic bandgap structures for microstrip lines, IEEE Microwave Guide Wave Lett. 8 (1998) [5] N.C. Karmakar, M.N. Mollah, Investigations into nonuniform photonicbandgap microstripline low-pass filters, IEEE Trans. Microwave Theory Tech. 51 (2003) [6] B.M. Karyamapudi, J.S. Hong, Coplanar waveguide periodic structures with resonant elements and their application in microwave filters, in: IEEE MTT-S Int. Microwave Symp. Dig., 2003, pp [7] M.L. Her, Y.Z. Wang, C.M. Chang, K.Y. Lin, Coplanar waveguide (CPW) defected ground structure (DGS) for bandpass filter application, Microwave Opt. Technol. Lett. 42 (2004) [8] B.B. Mandelbrout, The Fractal Geometry of Nature, W.H. Freeman, New York, [9] J.L. Vehel, E. Lutton, C. Tricot, Fractals in Engineering, Springer-Verlag, New York, [10] Y.Q. Fu, N.C. Yuan, G.H. Zhang, A novel fractal microstrip PBG structure, Microwave Opt. Technol. Lett. 32 (2002) [11] S.K. Padhi, N.C. Karmakar, Fractal PBG assisted co-planar waveguide, Microwave Opt. Technol. Lett. 45 (2005) [12] M.F. Karim, A.Q. Liu, A. Alphones, X.J. Zhang, Low pass filter using a hybrid EBG structure, Microwave Opt. Technol. Lett. 45 (2005) [13] A.B. Yu, A.Q. Liu, Q.X. Zhang, A. Alphones, L. Zhu, S.A. Peter, Improvement of isolation for RF MEMS capacitive shunt switch via membrane planarization, Sens. Actuators: A Phys. 119 (2005)

8 362 M.F. Karim et al. / Sensors and Actuators A 133 (2007) [14] S.G. Mao, M.Y. Chen, Propagation characteristics of finite-width conductor-backed coplanar waveguides with periodic electromagnetic bandgap cells, IEEE Trans. Microwave Theory Tech. 50 (2002) Biographies Muhammad Faeyz Karim received his BEng degree in electrical engineering in 2000 from National University of Science & Technology, Pakistan, and masters of science degree from Nanyang Technological University, Singapore, in He is currently pursuing his PhD from School of Electrical & Electronic Engineering, Nanyang Technological University. His research interests include RF MEMS, antennas and electromagnetic bandgap structures. Ai-Qun Liu received his PhD in applied mechanics from National University of Singapore in His MSc was in applied physics and BEng was in mechanical engineering from Xi an Jiaotong University in 1989 and 1982, respectively. Currently, he is an associate professor at the Division of Microelectronics, School of Electrical & Electronic Engineering, Nanyang Technological University. He is also an associate editor of the IEEE Sensor Journal. His research interests are MEMS design, simulation and fabrication processes. Aibin Yu received BEng degree in materials science in 1993 from Shanghai Jiaotong University and MEng degree in electronic material and device in 1996 from Shanghai Jiaotong University. Currently, he is a research associate in the Division of Microelectronics, School of Electrical & Electronic Engineering, Nanyang Technological University. He is currently pursuing his PhD in the school. His research interests include microfabrication process and RF MEMS design. Arokiaswami Alphones received PhD degree in optically controlled millimeter wave circuits from Kyoto Institute of Technology (Japan) in Currently, he is an associate professor at the School of Electrical and Electronic Engineering, Nanyang Technological University. He is in the Editorial Review Board of IEEE Microwave Theory and Techniques and Microwave and Wireless Components Letters. He has published and presented over 100 technical papers in international journals/conferences. His current interests are electro-magnetic analysis on planar RF circuits and integrated optics, EMC testing, microwave photonics and hybrid fiber-radio systems. He received IEEE AES/Comm Chapter award 1986 in the area of communications. He had written a chapter on Microwave Measurements and Instrumentation in Wiley Encyclopedia of Electrical and Electronic Engineering He is a senior member of IEEE.