Modeling of Elevated Coplanar Waveguides for High Speed Digital Circuits

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1 0 INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY VOL., NO., NOVEMBER 008 Modeling of Elevated Coplanar Waveguides for High Speed Digital Circuits *S. Kanthamani, Dr. (Mrs).S. Raju, Member, IEEE, Dr.V. Abhaikumar, Senior Member, IEEE RF Systems Lab, Department of ECE Thiagarajar College of Engg. Madurai-60, INDIA Tel: 0-80; Fax: 0-87; Abstract - In high speed sampling and timing circuits, a transmission line having characteristics of higher phase velocity, higher impedance, low insertion loss is preferred. Elevated coplanar waveguide (ECPW) has been identified as the transmission line to achieve such characteristics. Mesh less collocation method for analyzing the ECPW structure is proposed. The quasi - static parameters such as characteristic impedance (Z o ) and effective dielectric constant (ε reff ) for various slot widths are obtained and compared with reported data. An equivalent circuit model for ECPW is proposed and the Radio frequency (RF) performance is obtained based on the results from quasi-static analysis. The proposed model reveals that the return loss of ECPW is less compared to the CPW geometries making it a good candidate for high speed switching applications. the insertion loss. Elevated coplanar waveguide structure and its variations have been reported to be candidates for high speed digital circuits [-6]. An ECPW structure shown in figure. offers higher characteristic impedance for a set of specified structural dimensions, due to the insertion of a dielectric layer in between the elevated conducting strip and ground planes. Keywords: Elevated coplanar waveguide, Mesh less, collocation I. INTRODUCTION Coplanar waveguide (CPW) is widely used in monolithic microwave integrated circuits (MMIC). The existence of upper ground planes allows a straightforward integration of external components without need for vias. But CPW lines suffer from high conductor loss at high and low characteristic impedance extremes []. Low impedance lines rely on narrow slot width, resulting in high current density at the edges and subsequently increasing the conductor loss [].On the other hand, narrow center conductor causes high conductor loss. Non-linear transmission lines require high-impedance CPW s with low attenuation for the generation of short pulses with steep edges [, ]. However the increase in characteristic impedance needs wider circuit and that increases Fig. Elevated Coplanar Waveguide Such structures have been analysed using FDTD method [7] and variational Finite element method [8-0]. These methods involve mesh generation, mesh compatibility, re-meshing and interpolation of solutions between the domains for solving the governing partial differential equations of the chosen problem. Mesh generation can be difficult and time consuming for complex geometries especially when such structures act as basic platform for MEMS devices. To overcome the difficulties, an efficient approach such as mesh-less or mesh-free method has been proposed [,] for numerical solution of partial differential equations corresponding to two or three dimensional structures. Meshes less IJMOT ISRAMT

2 06 VOL., NO., NOVEMBER 008 techniques require only a scattered set of nodes representing the domain of interest. No connectivity information among scattered set of nodes is required, unlike finite element, boundary element or classical finite difference techniques. Mesh less technique are also appealing because of their potential in adaptive techniques, where a user can simply can simply add more points in a particular region to obtain to more accurate results. In this paper a point collocation method is applied to perform the quasi-static numerical analysis of the elevated coplanar wave guides. This paper is organized as follows: Collocation approach and mathematical formulation is introduced in section.numerical results are presented in section. II. METHODOLOGY A. Collocation approach Collocation method approximates solution to boundary value problem by finite linear combination of basis functions. For two point boundary value problem u '' f ( t, u, u' ), a < t < b With boundary conditions u ( a) α, u( b) β, we seek approximate solution of form n u( t) v( t, x) x φ t () i i i () where i are basis functions defined on [a,b] and x is n- vector of parameters to be determined. The same method can also be extended to solve the partial differential equation involved for the problem chosen.[] B. Formulation The entire structure is divided into nine regions as shown in fig.. Fig.Shows the geometry of the problem The governing Lap lace s equation in the space plane and the corresponding boundary and the interface conditions are given as + 0 x y where is the potential distribution. The boundary conditions are Region: (i) 0 at x 0 & 0 < y < b (ii) 0 at y 0 & 0 < x < a (iii) 0 at y b & 0 < x < a () Region : (iv) 0 at y 0 & a (v) 0 at y f & a () Region : (vi) 0 at y 0 & a (vii) 7 at y b & a y y () () IJMOT ISRAMT

3 07 VOL., NO., NOVEMBER 008 Region : (viii) 0 at y 0 & a (ix) 0 at y f & a (6) Region : (x) 0 at x 0 & 0 < y < b (xi) 0 at y 0 & a < x < a (xii) 0 at y b & a < x < a (7) Region 6: (xiii) 0 at y b & a < x < a (xiv) 0 at y f & a < x < a (8) Region 7: (xv) at y g & a (xvi) 7 at y b & a y y (9) Region 8: (xvii) 0 at x 0 & b < y < f (xviii) 0 at y 0 & 0 < x < a (xix) 0 at y f & 0 < x < a (0) Region 9: (xx) at y d & a (xxi) 7 9 at y d & a y y () The interface conditions are Region between and at x a Region between and 8 8 at x a Region between and 9 9 at x a Region between and 7 7 at x a Region between and at x a Region between and 9 9 at x a Region between and 7 7 at x a Region between and at x a Region between and 6 6 at x a Region between and at a x () The problem now is to solve the two-dimensional Laplace equation using mesh less method to find the potential distribution and hence the electrostatic capacitance and the characteristic impedance and the effective dielectric constant of the elevated coplanar waveguide. The capacitance found using this method is used in the equivalent circuit model to find the RF performance of the ECPW. C. Collocation formulation The general solution of the problem space is expressed as polynomials in terms of arbitrary constants A + Bx + Cy + Dxy () IJMOT ISRAMT

4 08 VOL., NO., NOVEMBER 008 The resulting solution obtained through the proposed point collocation method after the application of the boundary conditions for the entire structure is given as A xy B x y C xy D x y A xyb C xy b D x y b A ( y yf ) + B ( xy xyf ) + C ( y y f ) + D( xy xy f ) C ( by + y ) + D ( xby + y ) C7 y D7 xy + C ( ) ( y y f + D xy x yf ) 6 A ( b y) + B where A ( y yf ) + B ( y yf ) + B ( xy xyf ) A ( xy xyb) + B ( x y x yb) + C ( xy x yb) ( xb xy) + C 6 ( fy+ gb fb gy) + D ( gxy+ xfy+ xg xfb) + C ( gy+ gb b + D 6 ( gxy + xy + xgb xb 7 + C 7 ( y g ) + D 7 x ( y g ) ) + y ) line is mm long. It is simulated with scattered point distributions of 9077 (66*66) points by using the method described in the previous section. The solution to the governing equation () along with the boundary conditions (-) is obtained in the form of potentials. Once the potential functions are known, it is easy to calculate the capacitance per unit length of the structure. The impedance and effective dielectric constant of the ECPW structure as a function of the slot width (s) can be calculated using the formulas given as C ε reff (6) C o C Capacitance per unit length with all dielectrics present C 0 - Capacitance per unit length with all dielectrics removed (7) Z o c CC o 9 [ x y b)( y f )( A + B x + C y + D )] 8 ( xy (( y f )( /( g f )) + C 9 ( y g) + D 9 x( y g) () where A A6, B B6, C C6, D D6 are the arbitrary constants to be determined through collocation method. III.NUMERICAL RESULTS AND DISCUSSIONS Quasi-static performance The ECPW structure on a GaAs substrate is considered for the analysis at a frequency of 0GHz. The substrate thickness is 00µm (h s ), inserted dielectric substrate thickness is.µm (h b ), centre strip width (w) is 0 µm, slot width (s) is kept varying from 0 to 0um, thickness of the metal line (t) is.9um and total length of the Effective dielectric constant... Collocation method measured data Slot width(s)um Fig :Real part of Elevated CPW impedance : Comparision between the Collocation method and the measured data available in[]. IJMOT ISRAMT

5 09 VOL., NO., NOVEMBER Fig and gives the computed ε reff and Z o for various slot widths(s).the computed values show good agreement with the fabricated results available in[]. proposed equivalent circuit are obtained using the methodology available in [] as shown in fig (a).figure (b) shows that the return loss and the transmission coefficient values are - 6. db and db respectively at 0 GHz. The proposed ECPW equivalent circuit shows better performance compared to the CPW which has a return loss of -.6dB. Line impedance(ohms) 00 0 Collocation method measured data Slot width(s)um Fig. (a): Equivalent model simulated using ADS. Fig :Effective dielectric constant of Elevated CPW Comparision between the Collocation method and the measured data available in[]. RF performance RF performance of the elevated coplanar waveguide is obtained using the transmission line model. Equivalent circuit model in [] for coplanar waveguide is modified so as to obtain the RF performance of ECPW. The presence of inserted dielectric (h b ) contributes an amount of capacitance which is present in the proposed equivalent circuit. The value of the inserted dielectric capacitance (C id ) is found using the collocation approach. The ECPW structure on a GaAs substrate is considered for the analysis at a frequency of 0GHz. The substrate thickness is 00µm (h s ),inserted dielectric substrate thickness is.µm (h b ),centre strip width (w) is 0 µm, slot width (s) is 8um thickness of the metal line(t) is.9um and total length of the line is mm respectively. The component values per unit length of the Fig (b): Simulated magnitude of S and S with w0µm,s8µm over the frequency range to GHz IJMOT ISRAMT

6 0 VOL., NO., NOVEMBER 008 IV.CONCLUSION A mesh-less analysis of ECPW structure is presented. The quasi-static parameters obtained using this method is compared with the reported data. A good agreement is found. The proposed equivalent circuit model method gives a reasonable RF performance. The simulation time using collocation method is also less compared to simulation done ADS by 0 secs. Mesh less method is very attractive for micro electromechanical systems (MEMS) where miniaturization is an important issue. Research work in progress to develop a miniaturized switch using ECPW platform applicable as high speed interconnects for wireless design. ACKNOWLEDGMENT This work was supported by Management and TIFAC CORE in Wireless Technologies, Thiagarajar Advanced Research Centre, Thiagarajar College of Engineering, Madurai, India REFERENCES [] H.-T. Kim, S. Jung, J.-H. Park, C.-W. Baek, Yong- Kim,Y. Kwon, A new micro machined overlap CPW structure with low attention over wide Impedance ranges, IEEE MTT-S. Dig. (000) [] R.W. Jackson, Considerations in the use of coplanar waveguide for millimeter-wave integrated circuits, IEEE Trans. Microwave Theory Techno. () (986) 0 6. [] F. Schneider, R. Doerner, W. Heinrich, High- Impedance Coplanar waveguides with low attenuation, IEEE Microwave Guided Wave Lett. 6 () (996) 7 9. [] Afshari, E., Hajimiri, A. Nonlinear transmission lines for pulse shaping in silicon, IEEE Journal of Solid-State Circuits, Vol. 0, Issue, March 00 pp 7 7 [] H.Kamitsuna., A Very small, low loss MMIC rat race hybrid using elevated coplanar waveguides.ieee Microwave and Guided Wave letters, vol. 6, pp 7-9, 99 [6] U. Bhattacharya, S. T. Allen, and M. J. W. Rodwell DC-7GHz Sampling Circuits and Sub Pico second Nonlinear Transmission Lines using Elevated Coplanar element method, Proce. th ISRMAT, pp -6, 99. [7] S.Hofschen and I. Wolff, Fellow, Journal of IEEE Simulation of an Elevated coplanar waveguide using -D FDTD IEEE Microwave and Guided Wave letters, vol. 6, No., January 996 [8] S.Raju, B.N.Nityanadan Dr.V.Mohan and V. Abhaikumar Modeling of coplanar and elevated coplanar using a modified universal matrices finite element method, Proce. th ISRMAT, pp -6, 99. [9] S.Raju, B.N. Nityanadan and V. Abhaikumar Analysis of a novel Elevated Coupled waveguide with finite metallization thickness Journal of IETE, vol, No., pp. 9. March April 99 [0] S.Raju, B.N. Nityanadan and V. Abhaikumar, Analysis of a shielded Elevated Coupled Coplanar Waveguide using a Modified Finite Element Method, International Journal of Microwave and Millimeter Wave Computer Aided Engineering, Vol 6, No., pp 0-8. [] Monaghan JJ (98) Why particle methods work. SIAM J.Sci. Stat. Comput. (): - [] Aluru NR, White J (997) An efficient numerical technique for electromechanical structures. Sensors and Actuators A, 8: - [] Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (996) Meshless methods: An over-view and recent developments. Comput. Meth. Appl. Mech. Eng. 9: -7 [] Scientific computing, An introductory survey, second edition, by Michael T.Heath,July 00. [] Jin-Su Ko,Bon-Kee Kim and Kwyro Lee, Simple modeling of Coplanar Waveguide on thick dielectric over Lossy substrate,ieee Transactions on Electron Devices,Vol.,No.,May 997. IJMOT ISRAMT