Passive Intermodulation Model Based on Conductors Cross-Section for Printed Transmission Line

When the cross section of a transmission line (TL) with a complex shape affects the internal electromagnetic field distribution of the conductor, it is necessary to combine the numerical method and the cross-sectional shape of the conductor to calculate the electrothermal passive intermodulation (ET PIM) current density caused by the uneven current distribution. Therefore, to analyze the influence of TL cross-sectional geometry on ET PIM, an ET PIM model of TL considering conductor cross-sectional geometry and transmission loss is derived. In the model, the modified gradient model is defined to characterize the nonlinear conductivity and conductor loss. Meanwhile, the PIM measurement experiments of the microstrip line, meshed microstrip line and parallel plate waveguide are designed to compare numerical solutions of the ET PIM3 model. Finally, numerical analyses of cross-sectional geometry effects on ET PIM3 generation are made to explain the phenomenon of ET PIM3 measurement. Combined with the measurement results, the numerical solution shows that the ET PIM produced in the high current density region is affected by the cross-sectional geometry, frequency offset, and thermal flux.