Synthesis of Planar Microwave Circuits Through Aggressive Space Mapping Using Commercially Available Software Packages Jordi Selga, 1 Ana Rodrı´guez, 2 Marta Gil, 1 Jorge Carbonell, 3 Vicente E. Boria, 2 Ferran Martı´n 1 1 GEMMA/CIMITEC, Departament d’Enginyeria Electro ` nica, Universitat Auto ` noma de Barcelona, 08193 Bellaterra, Barcelona, Spain 2 Departamento de Comunicaciones-iTEAM, Universidad Polite ´ cnica de Valencia, 46022 Valencia, Spain 3 Departamento de Ingenierı´a Electro ´ nica, Universidad Polite ´ cnica de Valencia, 46022 Valencia, Spain Received 27 November 2009; accepted 3 May 2010 ABSTRACT: This article is focused on the practical implementation of a software tool for the synthesis of planar microwave circuits based on aggressive space mapping (ASM), which makes use of commercially available software packages as the core program (MATLAB V R ) and as the electromagnetic (EM) fine model simulation space (Agilent Momentum V R ). All technical details related to the control of the cited EM commercial software tool, by means of a general purpose and user-friendly environment (MATLAB in our case), are discussed in detail. The new synthesis tool has been designed to cope with the automatic layout generation of planar metamaterial structures, which is a novel practical application of the ASM algorithm. More specifically, the automated synthesis of microstrip lines loaded with complementary split ring resonators has been considered in this work. However, this synthesis tool can be easily custom- ized to deal with the design of many other planar structures. V C 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE 20:527–534, 2010. Keywords: space mapping; planar microwave circuits; microstrip technology metamaterial trans- mission lines; complementary split ring resonator I. INTRODUCTION Aggressive space mapping (ASM), originally proposed by Bandler et al. in 1995 [1], is a technique for electromag- netic (EM) optimization that uses a Newton-type iteration to find the EM solution of a given problem, provided a set of specifications, or requirements, is known. It is indeed an improved approach to space mapping (SM) (also proposed by Bandler et al. [2] in their pioneering work), where efficiency is enhanced by using each ap- proximate solution to the problem in the iteration process, so that a progressively improved design after each itera- tion is expected. A recent paper on the state-of-the-art and relevant achievements of SM optimization can be found in Ref. [3]. However, to the authors’ knowledge, the prac- tical application of the ASM algorithm to the completely automated design of planar metamaterial transmission lines has not been discussed up to now. In both SM and ASM techniques, two simulation spaces are considered. In one simulation space, X c , the variables are linked to a coarse model, which is simple and computationally efficient, although not accurate, whereas in the other space, X f , the variables are linked to a fine model, typically more complex and CPU intensive but significantly more accurate. Let us consider that the model parameters in the coarse and fine model are repre- sented by the vectors x c and x f , respectively. The goal in ASM is to solve the following set of nonlinear equations: f ðx f Þ¼ Pðx f Þ x  c ¼ 0 (1) where x  c is the vector corresponding to the parameters of the coarse model providing the target response, and P is a mapping function between the coarse and fine model Correspondence to: J. Selga; e-mail: jordi.selga@uab.cat V C 2010 Wiley Periodicals, Inc. DOI 10.1002/mmce.20458 Published online 28 July 2010 in Wiley Online Library (wileyonlinelibrary.com). 527