A Novel Neural Smith Chart for Use in Microwave Circuitry Filiz Gu ¨ nes  , 1 M. Fatih C ¸ ag ˘ lar 2 1 Department of Electronics and Communication Engineering, Yıldız Technical University, _ Istanbul, Turkey 2 Department of Electronics and Communication Engineering, Su ¨ leyman Demirel University, Isparta, Turkey Received 8 February 2008; accepted 22 May 2008 ABSTRACT: In this article, briefly the Smith chart is mapped with an artificial neural network (ANN) covering its whole details to be exploited CAD of the microwave circuitry. Thus, relative to the similar works in the existing literature, this article provides the continuous Smith chart domain to facilitate the ‘‘Smith chart’’ methodology in solving the highly nonlinear transforma- tion equations between the rectangular impedance and polar reflection planes for an infinite number of passive impedance to be used in design tasks of the microwave circuits. Data ensem- bles for the training and testing processes are obtained from the systematically selected loca- tions on the Smith chart with the adaptive radius sampling algorithm. The ANN architecture is also simple, which consists of the two simple multilayer perceptron (MLP) modules with the common inputs which are the termination Z S 5 R S 1 jX S , line {‘, Z 0 } operation bandwidth B between the defined f min , f max and the dielectric e. Briefly, the outputs of these ANN modules are the standing waves and the impedance transformation, which are the characteristic fea- tures of the transmission line circuits. Activation of the hidden layers of the modules are per- formed by the tangential-sigmoid type of function while the output layers are activated linearly. Furthermore, the neural unit element (NUE) is defined by the two independent neural net- works as problems in the forward and reverse directions to be incorporated into the analysis and design algorithms of the unit element (UE). This can also be considered as solving the si- multaneous nonlinear equation set for (‘, Z 0 ) parameters of the required impedance transfor- mations Z OUT (x) 5 R OUT (x) 1 X OUT (x) from the given complex termination Z S 5 R S 1 jX S . Applications of the Neural Smith chart are given by the numerous examples with the proved accuracy. Thus it has been verified that this neural Smith chart can be exploited for the whole classical transmission line theory including impedance matching. V V C 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE 19: 218–229, 2009. Keywords: transmission line; single stub impedance matching; double stub impedance matching; data generation; artificial neural network; multilayer perceptron; Smith chart; unit element I. INTRODUCTION Analysis and design of microwave circuits are gener- ally tedious with their highly nonlinear equations and lack in the insight to their related problems. The Smith chart provides a very useful graphical tool to these types of problems with its numerous applica- tions. However, the manual interpretation of the Smith chart can be error prone. In the literature, works on the computerized Smith chart took place between 1992 and 1995 by Prasad and her group in [1–3]. In their work, the Smith chart is represented Correspondence to: F. Gu ¨nes  ; e-mail: gunes@yildiz.edu.tr DOI 10.1002/mmce.20343 Published online 20 August 2008 in Wiley InterScience (www. interscience.wiley.com). V V C 2008 Wiley Periodicals, Inc. 218