Closed-form Equation for Passive Intermodulation of Microstrip Line due to Resistivity Nonlinearity

Passive intermodulation (PIM) is one of the harmful interferences in the communication systems. In microstrip circuits, multiple factors can affect the PIM product including the conductor and dielectric materials, the strip dimension and structure et.al. In this paper, the resistive nonlinear effect on the PIM phenomenon for the microstrip line was analyzed. The resistivity nonlinearity coefficient was obtained by solving the heat conduction equation, by which the expression for the distributed PIM signal excitation source was derived, and the closed form PIM equation for uniform microstrip line was obtained eventually. Using the derived equations, the effect of the material properties and the dimension on the PIM product for uniform microstrip line due to conductor resistivity nonlinearity can be quantitatively calculated. The analytical PIM model will contribute to investigation of the PIM phenomenon in more complex microstrip circuits.