Modeling the capacitive behavior of coplanar striplines and coplanar waveguides using simple functions

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Title: Modeling the capacitive behavior of coplanar striplines and coplanar waveguides using simple functions
Author: Abbott, Jeffrey
Abstract: The coplanar waveguide (CPW) structure has been popular for Monolithic Microwave Integrated Circuit (MMIC) design due to the wide versatility of its designable impedance. Since its introduction in 1969, it has been utilized in a wide range of applications and consequently has been analyzed extensively for its electrical characteristics. Other planar structures with similar geometries have also received much attention, including the conductor-backed coplanar waveguide (CBCPW) and coplanar stripline (CPS). A common approach for analyzing these planar structures, assuming quasi-TEM mode of operation, involves the use of conformal mapping techniques. The traditional conformal mappings realize special functions allowing for problems of convergence, computation efficiency, and accuracy during implementation in CAD software. The focus of this thesis is modeling the capacitive behavior of planar devices including the conductor-backed interdigital coplanar waveguide (CBICPW), CPS, and finite-width conductor-backed coplanar waveguide (FWCBCPW) in an infinite well under a quasi-TEM mode of operation. Continuously differentiable, simple functions are used in place of special functions to improve the performance of models within CAD environments. New conformal mapping techniques are introduced that use only simple functions. Combined with other approximations, one can formulate expressions with arbitrary accuracy. A new iterative expression is presented for evaluation of the elliptic integrals ratio, K/K', commonly used in standard expressions for planar structures. The new expression, based on a continuously differentiable function, exhibits a relative error on the order of 10-11 with reduced computational complexity. Results from the new models are compared to the simulated results of a commercial electromagnetic field solver. Experimental results that were available for the CBICPW structure indicated good correspondence to results calculated from the new model.
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Date: 2011-06

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