REFERENCES 1. J. Tao, C.H. Cheng, and H.B. Zhu, Compact dual-band slot-antenna for WLAN applications, Microwave Opt Technol Lett 49 (2007), 1203– 1204. 2. J.H. Yoon, G.H. Han, D.H. Kim, J.C. Lee, S.M. Woo, and H.H. Kim, Design of triangular slot antenna for triple-band(2.4/5.2/5.8 GHz) an- tenna with fork-like tuning stub, Microwave Opt Technol Lett 49 (2007), 1561–1565. 3. H.M. Hsiao, J.W. Wu, Y.D. Wang, J.H. Lu, and S.H. Chang, Novel dual-broadband rectangular-slot antenna for 2.4/5-GHz wireless com- munication, Microwave Opt Technol Lett 46 (2005), 197–201. 4. J.W. Wu, 2.4/5-GHz dual-band triangular slot antenna with compact operation, Microwave Opt Technol Lett 45 (2005), 81– 84. 5. W. Ren, Z. Shi, H. Liu, and K. Chen, Novel compact 2.4/5-GHz dual-band T-slot antenna for WLAN operations, Microwave Opt Tech- nol Lett 49 (2007), 1236 –1238. 6. J.Y. Sze, C.G. Hsu, and S.C. Hsu, Design of a compact dual-band annular-ring slot antenna, IEEE Trans Antennas Wireless Propag Lett 6 (2007), 423– 426. © 2008 Wiley Periodicals, Inc. ANALYSIS OF CONDUCTOR-BACKED COPLANAR WAVEGUIDES USING ADAPTIVE-NETWORK-BASED FUZZY INFERENCE SYSTEM MODELS Celal Yildiz, Kerim Guney, Mustafa Turkmen, and Sabri Kaya Department of Electrical and Electronics Engineering, Faculty of Engineering, Erciyes University, Kayseri 38039, Turkey; Corresponding author: yildizc@erciyes.edu.tr Received 6 June 2008 ABSTRACT: A method based on adaptive-network-based fuzzy infer- ence system (ANFIS) is presented for the quasi-static analysis of con- ductor-backed coplanar waveguides. The ANFIS is a class of adaptive networks which are functionally equivalent to fuzzy inference systems. Four optimization algorithms, hybrid learning, genetic, simulated an- nealing, and least-squares, are used to determine optimally the design parameters of the ANFIS. The results of ANFIS are compared with the results of experimental works, quasi-static and full-wave spectral do- main approaches, conformal mapping technique, and a commercial elec- tromagnetic simulator IE3D. The results of ANFIS models are in very good agreement with the results of other methods and experimental works. When the performances of ANFIS models are compared with each other, the best result is obtained from the ANFIS model trained by the hybrid learning algorithm. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 439 – 445, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop. 24059 Key words: conductor-backed coplanar waveguides; effective permittiv- ity; characteristic impedance; adaptive-network-based fuzzy inference system; quasi-static analysis 1. INTRODUCTION Coplanar waveguides (CPWs) are used extensively in microwave devices. They offer several advantages over conventional micro- strip lines in designing and manufacturing microwave integrated circuits (MICs). These are low dispersion, high flexibility in the design of characteristic impedance, and easy connection to the shunt lumped elements, or devices without using via holes [1, 2]. In addition to these advantages, a conductor-backed CPW provides superior mechanical strength and heat sinking capabilities in com- parison with conventional CPWs. It also allows easy implementa- tion of mixed coplanar/microstrip circuits. These and several other advantages make conductor-backed CPWs ideally suited for MIC as well as monolithic MIC (MMIC) applications [2–9]. In the literature, various methods [4 – 6] based on quasi-static approximations have been presented for the calculation of charac- teristic parameters of conductor-backed CPWs. The characteristic parameters of conductor-backed CPWs have been obtained by using conformal mapping technique (CMT) [4, 5]. The numerical formulas based on spectral domain approach (SDA) were pre- sented for the analysis of the quasi-TEM parameters of conductor- backed CPWs [6]. The dispersion characteristics of conductor- backed CPWs based on full-wave analysis have been reported in [2, 7, 8]. Shih and Itoh [2] have analyzed conductor-backed CPWs by using the full-wave SDA. The dispersion characteristics of conductor-backed CPWs were also obtained by using an alterna- tive formulation of the transverse resonance technique [7] and two-dimensional finite-difference time-domain method [8]. As aforementioned, conductor-backed CPWs have been ana- lyzed with the use of quasi-static or full-wave methods. Although full-wave methods are the most accurate tools for obtaining the transmission line characteristics but analytically extensive, quasi- static methods are quite simple but do not threaten the dispersive nature of generic transmission lines. Consequently, approximation of the quasi-static methods becomes worse as the transmission line becomes dispersive. However, the quasi-static methods provide accuracies comparable with the full-wave methods for frequency up to 20 GHz [6]. Advances in MMIC technology and progress in computer- aided design (CAD) tools have led the researchers to develop CAD models for the analysis of microwave transmission lines. In this work, an alternative method for the quasi-static analysis of con- ductor-backed CPWs, based on the adaptive-network-based fuzzy inference system (ANFIS) [10, 11], is presented. Four different optimization algorithms, hybrid learning (HL) algorithm [10, 11], least-squares (LSQ) algorithm [12, 13], genetic algorithm (GA) [14 –15], and simulated annealing (SA) algorithm [16], are used to train the ANFIS. These optimization algorithms are employed to obtain better performance and faster convergence with simpler structure. The ANFIS is a class of adaptive networks which are function- ally equivalent to fuzzy inference systems (FISs). The FIS is a popular computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. The ANFIS can simulate and analyze the mapping relation between the input and output data through a learning algorithm to determine optimal parameters of a given FIS. It can be trained with no need for the expert knowledge usually required for the standard fuzzy logic design. The ANFIS has the advantages of modeling the uncertainty ability of FISs and learning capability of neural networks. The ANFIS architecture requirements are fewer and simpler compared to neural networks. Both numerical and linguistic knowledge can be combined into a fuzzy rule base by employing fuzzy methods. A prominent advantage of the ANFIS is that, after proper training, ANFIS completely bypasses the repeated use of complex iterative processes for new cases presented to it. Because of these attractive features, ANFIS has been applied to many areas in the literature [17–28]. In this article, the next section briefly describes the determina- tion of the characteristic parameters of conductor-backed CPWs. ANFIS and learning algorithms are explained in the third section. The application of the ANFIS to the quasi-static analysis of con- ductor-backed CPWs is given in the fourth section. The results are then presented and conclusion is made. DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 2, February 2009 439