7. A.A. Omar, Design of ultrawideband coplanar waveguide-fed Koch- fractal triangular antenna, Int J RF and Microwave Comput-Aided Eng 23 (2013), 200–207. 8. R. Kumar and K.K. Sawant, Design of CPW-feed inscribed square circular fractal antenna for UWB applications, Microwave Opt Tech- nol Lett 53 (2011), 1079–1083. 9. A.R. Maza, B. Cook, G. Jabbour, and A. Shamim, Paper-based inkjet-printed ultra-wideband fractal antennas, IET Microwave Antenna Propag 6 (2012), 1366–1373. V C 2015 Wiley Periodicals, Inc. A NEW ANALYTICAL TECHNIQUE FOR EXTRACTION OF BIAS-DEPENDENT DRAIN RESISTANCE IN GaAs AND GaN HEMTs A. A. Kokolov and L. I. Babak Department of Computer Systems, Tomsk State University of Control Systems and Radioelectronics, Tomsk 634050, Russia; Corresponding author: Kokolov.Andrey@Kcup.Tusur.Ru Received 14 April 2015 ABSTRACT: To improve the quality of transistor modeling, the nonlin- ear behavior of each element of the equivalent circuit must be known. There are few works devoted to the extraction of bias-dependent drain resistance R d , which strongly affects the transistor modeling. In this work, a new analytical technique for the extraction of bias-dependent drain resistance in HEMT small signal model (SSM) is proposed. The efficiency of the new technique is demonstrated for GaN and GaAs HEMTs. It is shown that the new approach leads to the better SSM accuracy in the range of DC biases as compared to the widespread extraction methods. V C 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2536–2539, 2015; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.29366 Key words: small signal model; HEMT; drain resistance; extraction 1. INTRODUCTION The first-pass design of nonlinear microwave circuits needs accurate transistor models. Nonlinear modeling of FETs is based on the correct extraction of small signal model (SSM) in differ- ent bias points, which is the subject of many works [1–6]. The SSM extraction approaches can be divided into three groups depending on the use of optimization methods: analytical, optimization-based, and combined techniques. Earliest attempts to calculate values of FET SSM were based on the pure optimization methods [1]. In this case, the extraction accuracy depends on starting SSM element values as well as on an optimization method. Analytical techniques [2,3] allow the evaluation of SSM intrinsic elements at a fixed frequency as a solution of some equations if extrinsic ones are known. To cal- culate extrinsic elements, usually the additional “cold” measure- ments are used. The combination of analytical expressions, that give initial element values, with subsequent optimization often provides the best solution of the problem considered [4,5]. In the most of the FET SSM extraction techniques, it is sup- posed that the drain (R d ) and source (R s ) resistances are independent on the voltages V ds and V gs . However, as shown in [6], the resistan- ces R d and R s have as linear part (contact resistance) as nonlinear one (bulk resistance), the latter depends on the voltages applied to transistor. Change of drain resistance value affects a quiescent point of transistor and increases dissipated power, which in turn reduces output power and efficiency of nonlinear device. A nonlinear behavior of the drain resistance is important also for the linear transistor modeling in different quiescent points. In this case, the extrinsic SSM elements are supposed to be independent on DC bias, and only intrinsic elements are changed. An assumption that the R d value is held constant degrades an accuracy of FET linear model in a range of DC biases. In addition, the drain resistance value influences values of other elements in FET intrinsic equivalent circuit. The existing techniques for extraction of bias-dependent par- asitic resistors need inconvenient measurements of FETs with different gate lengths [6] or use partial optimization procedure that can lead to nonphysical element values [7,8]. The analytical solution of the SSM equations regarding the drain and source resistances was attempted in [9], but several assumptions and simplifications result in low accuracy. In this article, we propose a new analytical technique for the extraction of HEMT SSM with accounting the bias-dependent drain resistance R d . To demonstrate an efficiency of the tech- nique presented, the derived analytical expressions are applied to extracting GaN and GaAs HEMT linear models. It is shown that the new approach leads to the better SSM accuracy in the range of DC biases as compared to the widespread extraction methods. The measured and modeled S-parameters show a good correlation for different transistor biases up to 40 GHz. 2. ANALYTICAL EXTRACTION TECHNIQUE In contrast to the ordinary linear model of HEMT [2,3], in SSM used in this article (Fig. 1) the drain resistance R d is supposed to be voltage-dependent and included into the internal model part. The remain parasitic elements L g , R g , L s , R s and L d are independent on voltages V ds and V gs , that is, they are constant. These elements can be extracted with using any of traditional techniques [2,4,5]. Elements of the admittance Y-matrix that describe an internal part of the new SSM can be written as follows: Y 11 ¼ g m0  jxC gd D 1jxC gd 1 jxC gs 11jxR gs C gs (1) Y 12 ¼ jxC gd G ds =D (2) Y 21 ¼ G d g m0 1jxC gd   =D (3) Y 22 ¼ G d G ds 1jx C gd 1C ds   =D (4) where g m0 ¼ g m  e 2jxs = 11jxR gs C gs   , G d ¼ 1=R d , G ds ¼ 1=R ds , D ¼ G ds 1G d 1jx C gd 1C ds   . In (1)–(4), Y ij are supposed to be known values, they can be found by converting measured S-parameters of transistor into Y-parameters and then subtracting extrinsic (parasitic) model elements. To find intrinsic SSM elements, we need to solve the com- plicated system consisting of eight nonlinear equations with Figure 1 Small signal model of HEMT with bias-dependent drain resistor R d 2536 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 57, No. 11, November 2015 DOI 10.1002/mop