A Nonlinear Frequency-Domain Model of Passive Intermodulation in Microstrip Lines Supporting 3-D Topology

Traditional modeling of passive intermodulation (PIM) for microstrip transmission lines is limited by the form of nonlinear source, the topology of the microstrip transmission line, and the computational complexity of the model. In this work, we propose a nonlinear coupled-wave model based on typical PIM modeling frameworks, in which the distributed nonlinear sources are rigorously derived using nonlinear mixing theory and formulated in the frequency domain to facilitate structural extension. Moreover, a self-consistent solution to the nonlinear model is proposed to efficiently capture complex nonlinear mixing and interaction in the microstrip transmission lines. The validity of the developed model is confirmed by the near-field measurements of PIM distribution along the microstrip transmission line, and the reverse and forward PIMs are also measured on various samples to further validate the accuracy of the proposed model. Finally, the nonlinear coupled-wave model is extended to a more general form with the aid of full-wave simulation in multiphysics software COMSOL, and the consistency between the nonlinear coupled-wave model and the full-wave version demonstrates the feasibility of structural extension. The PIM distribution and variation at the different bending positions in bent microstrip transmission lines are also analyzed.