A Novel Dispersive Numerical Approach for Fast Analysis of Asymmetric Coplanar Waveguide A. Khodja, R. Touhami FEI, U.S.T.H.B, Algiers, Algeria M.C.E. Yagoub EECS, Ottawa U., Ottawa, Canada H. Baudrand ENSEEIHT, Toulouse, France Abstract— In this paper, an efficient full-wave numerical modal method is proposed for fast modeling of asymmetric coplanar structures. For this purpose, trial functions of C and  modes were obtained from a quasi-symmetric model. Keywords- dispersion; trial functions; quasi-symmetric model I. INTRODUCTION CPW are widely used in MMIC's [1-2]. Compared to symmetric structures, asymmetric coplanar ones (Fig. 1) are very attractive because of their easy matching and circuit design flexibility. To efficiently design them, an efficient quasi-symmetric CPW approach is proposed. It uses a modal technique in conjunction with an adequate choice of trial functions to determine the propagation characteristics. x a b1 b2 b3 z y C1 d1 W d2 C2 o o r o Figure 1. Cross sectional view of general asymmetric CPW II. METHODOLOGY By properly selecting the trial functions for C and  modes, an efficient quasi-symmetric approach was developed. It took the magnitudes of trial functions of the asymmetric case expressed on the second half of the considered asymmetric CPW in terms of that expressed on the first half [3]. This quasi-symmetric approach leads, via the Galerkin's technique, to a smaller-size dispersion matrix and thus, reduces the CPU effort required to fully characterizing asymmetric coplanar structures. A comparative study of the propagation characteristics demonstrated the efficiency of the proposed quasi-symmetric model. III. NUMERICAL RESULTS Let us represent the evolution of effective permittivity by using sinusoidal trial functions taking into account the metallic edge effects (where the convergence was achieved without exceeding six trial functions per component). Figure 2 shows clearly that for identical widths of slots (d 1 =d 2 ), the asymmetric CPW behaves as quasi-symmetric one. In addition, for any C-mode width ratio (d 2 /d 1 ), the asymmetric structure has the same propagation properties as quasi- symmetric one, contrarily to the  mode where the quasi- symmetric model is less valid [2], because the  mode is affected by the shielding or slots. 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 C (mm) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Effective permittivity (b =b =3.4935mm) C mode mode  Symmetric case Asymmetric case Quasi-symmetric case 1 1 3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 Width of the central conductor strip w (mm) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 Effective permittivity C mode mode  (b =b =3.4935mm) Asymmetric case Quasi-symmetric case Symmetric case 1 3 (w=0.2mm, d1=d2=0.1mm) (C1=0.5mm, d1=d2=0.1mm) (a=3.556mm, b2=0.125mm, f=33GHz, r=2.2) 0 1 2 3 4 5 6 d /d 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Effective permittivity (b =b =3.4935mm) Asymmetric case Quasi-symmetric case mode  C mode 2 1 1 3 26 28 30 32 34 36 38 40 Frequences [Ghz] 0.80 0.85 0.90 0.95 1.00 1.05 1.10  mode C mode  Asymmetric case [2] Quasi-symmetric case (a=3.556mm, b2=0.125mm, C1=0.1mm, w=0.2mm, d1=0.1mm, f=33GHz, r=2.2) (a=3.556mm, b1=3.556mm, b2=0.127mm, b3=3.429mm, d1=0.1mm, d2=0.3mm,w=0.2mm, C1=1.578mm, r=2.22) Figure 2. Dispersion parameters versus physical and electrical parameters REFERENCES [1] T. Kitazawa and T. Itoh, "asymmetrical coplanar waveguide with finite metallization thickness containing anisotropic media", IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1427-1432, 1991. [2] A. Biswas and V.K. Tripathi, "Analysis and design of asymmetric and multiple coupled finline couplers and filters", IEEE MTT-S Symp., pp. 403-406, 1990. [3] A. Khodja, R. Touhami, M.C.E. Yagoub and H. Baudrand, "Full-wave modal analysis of asymmetric coupled lines using the quasi-symmetric approach", Mediterranean Microwave Symp., Hammamet, Tunisia, 2011. 160