Comparative Study of Passive Intermodulation Distortion in Wilkinson Power Dividers/Combiners and Branch Line Couplers Eslam N. Mohamed Ayman G. Sobih Ayman M. El-Tager Electronic Eng. Dpt., Electronic Eng. Dpt., Electronic Eng. Dpt., MTC, Cairo, Egypt. MTC, Cairo, Egypt. MTC, Cairo, Egypt. Eslamnasr388@gmail.com Ayman_sobih@yahoo.co.uk prof.ayman.eltager@ieee.org Abstract—Passive intermodulation distortion manifests itself as a nonlinear mixing product in passive devices. The nonlinearity in microstrip lines (MSL) has a distributed nature and can be associated with the dielectric substrate and/or the printed conductor. In this paper, the nonlinearity modeling of uniform microstrip line is discussed. It is partitioned into short segments; each described by its equivalent RLCG circuit, and has been analysed using Harmonic Balance nonlinear simulation to evaluate PIM (passive intermodulation) effect of the microstrip line for different lengths and widths. The proposed PIM MSL model is compared to Shitvov's model and recent reported measurements, and verified using X-parameter simulation. The generalized PIM MSL model is applied in device level such as Wilkinson power divider (WPD) and branch line coupler to predict the PIM effect of each. Finally, a comparison between conventional WPD, inductive loaded WPD and branch line coupler, is conducted based on the introduced MSL model. Keywords- nonlinear distortion, passive intermodulation distrotion, nonlinear model of microstrip line, power divider, coupler, PIM3, X-parameter simulation. I. INTRODUCTION PIM is known for its drawback effect on the performance of base stations used in the space, military and civil telecommunications [1-2]. The major disadvantages of PIM are: raising the noise floor, increasing the bit error rate, reducing the coverage area and blocking the receiver. PIM products resulting from nonlinear frequency mixing in passive devices usually occur in the reception band of the system. PIM is initially discovered as a product of nonlinear mixing on rusty metallic contacts [3-4]. A PIM phenomenon is further observed in ferrite circulators [5], waveguide and cable joints [6], duplexers [7], attenuators [8] and antennas [9]. PIM is usually confined in contact phenomena such as tunneling, thermionic emission and fritting, and non-contact phenomena such as ferromagnetic, thermal ionization and field emission. Recently, the electro-thermal theory of PIM in antennas is studied in [10]. On the other hand, the PIM effect in printed MSL is studied in [11]. Furthermore, the telegraph equation is solved to build a PIM theoretical model in [12]. In this paper, a unit cell of nonlinear microstrip line (NLMSL) model of 50-Ω MSL has been verified with the theoretical model in [12]. Then a generalized model for different widths and lengths has been produced and applied in different devices such as Wilkinson power dividers/combiners and branch line couplers to predict their PIM performance. Moreover, X-parameter simulation is used to verify the proposed NLMSL model which is utilized in Wilkinson power dividers and branch line couplers. II. THEORTICAL BACKGROUND The origin of PIM nonlinearity could be from one of two sources; namely, microstrip conductor line and substrate dielectric material [13]. Therefore, one or more of the model elements shown in Fig. 1 should be nonlinear. Figure 1. Nonlinear model of an infinitesimal length of a MSL [14]. Moreover, the nonlinearity in microstrip line is modelled by adding nonlinear parameter R 2 to the linear resistance, and the nonlinear resistance can be expressed as: 2 0 2 () RI R RI   (1) Where R 0 is the linear resistance and R 2 is the nonlinear coefficient. The linear resistance in telegraph equation is replaced by R (I) in equation (1). Assuming complete matching at input and output ports, the telegraph equations can be solved to obtain the third order intermodulation distortion current as follows [12]:   2, 1 1,0 0, 1 2, 1 ( X) ( (2 )X) 2, 1,1 ( (2 x) 2 ) I X (1 )e e e l l J J J J D [ Q [ [Q               (2) 57 2018 International Conference on High Performance Computing & Simulation 978-1-5386-7879-4/18/$31.00 ©2018 IEEE DOI 10.1109/HPCS.2018.00024