Passive intermodulation mechanism of microstrip lines based on the electrothermal coupling effect

The nonlinear coefficient of the transmission line equations for passive intermodulation (PIM) model of microstrip lines was determined based on electrothermal coupling effect. Considering the fact that the distributed resistance per unit length of the transmission line can be influenced by the Joule heating effect from input microwave power, the nonlinear component of the distributed resistance was calculated through the temperature coefficient effect of metal material resistivity. Thus, a completely physic model of PIM on microstrip lines was developed. The calculation results of the model demonstrate that the PIM level increases with the increasing temperature coefficients of resistivity of metal material while decreases with increasing thermal conductivity of dielectric material. In addition, in a practical roughness condition, the PIM level increases with increasing roughness of the strip. The presented physical model can explain the related published experimental work rationally. The theoretical results can be applied to design and fabricate low PIM microstrip circuits.