Automated Circuit Modeling Tool for Arbitrary Passive Microwave and RF Components Tom Dhaene, Jan De Geest * , Daniël De Zutter * Agilent EEsof Comms EDA, Lammerstraat 20, B9000 Gent, Belgium, tom_dhaene@agilent.com * INTEC, Ghent University, Sint Pietersnieuwstraat 41, B9000 Gent, Belgium, daniel.dezutter@intec.rug.ac.be An automated circuit-modeling tool is developed for arbitrary passive components. The tool builds compact, parameterized, analytical models based on full-wave EM simulations. The scattering parameters (or the transmission line parameters) of the components are stored as a multidimensional function of frequency and geometrical parameters. The modeling algorithm combines adaptive data selecting and modeling techniques. The circuit models guarantee EM-accuracy and generality, and circuit simulation speed and flexibility. I. INTRODUCTION Accurate parameterized circuit models for arbitrary microwave and RF components are required for the design and optimization of high-speed electronic circuits. Several numerical EM techniques (such as the method of moments) can be used to accurately model passive components. However, most numerical EM techniques require a significant amount of expertise and computer resources, so that they are often only used for verification purposes. On the other hand circuit simulators are very fast, and offer a lot of different analysis possibilities. However, the number of available analytical models is limited, and the accuracy is not always guaranteed up to RF or microwave frequencies. Numerous efforts (e.g. lookup tables [1], curve fitting techniques [2] and neural networks [3]) have been made to build models for general interconnection structures based on EM simulations. A common drawback of the previous efforts is the lack of knowledge about the accuracy of the resulting models. We developed an automated tool for building parameterized circuit models of general passive microwave and RF components with user-defined accuracy [4]-[5]. The analytical models represent the scattering parameters (or transmission line parameters) as a multidimensional function of frequency and geometrical parameters. The models are based on full-wave EM simulations, and can easily be incorporated in circuit simulators. This brings EM-accuracy and generality in the circuit simulator, without sacrificing speed. The model generation process is fully automated. Data points are selected efficiently and model complexity is automatically adapted. The algorithm consists of an adaptive modeling loop (section II) and an adaptive sample selection loop (section III). An example is given to illustrate the technique (section IV). II. ADAPTIVE MODEL BUILDING ALGORITHM The scattering parameters S (or transmission line parameters R, L, G and C) are approximated by a weighted sum of multidimensional orthonormal polynomials (multinomials) P m . The multinomials only depend on the coordinate x ¯ in the multidimensional parameter space R, while the weights C m only depend on the frequency f: The weights C m are calculated by fitting equation (1) on a set of D data points {x ¯ d , S(f,x ¯ d )} (with d = 1, …, D). The number of multinomials M is adaptively increased until the error function E(f,x ¯) = | S(f,x ¯) - A(f,x ¯)| is lower than a user-defined accuracy level in all the data points. For numerical stability and efficiency reasons orthonormal multinomials are used. ) x ( (f)P C ) x A(f, ) x S(f, M m m m ∑ = = ≈ 1 ) 1 (