RF CAD-Assisted Nonlinear Transmission Line Model of Distributed Passive Intermodulation

摘要

Characterisation and modelling of distributed passive intermodulation generation in planar microwave components is hampered by a priori unknown physics and location of the sources of microstrip nonlinearities. It has been shown that using even the basic two-tone PIM3 measurements in different frequency bands and in the near-field PIM probing mode on simple microstrip layouts allows identification of the dominant type of the microstrip nonlinearity and PIM generation mechanisms. Using the transmission line formulation and simple static polynomial models of the p.u.l. parameters, the set of general closed-form equations for the forward and reverse PIM products of arbitrary order can be derived from the analysis of the waves propagating on a weakly nonlinear transmission line. It has been shown that an accurate distributed model of PIM generation can be constructed with the aid of Keysight’s X-parameter methodology by cascading equivalent-circuit unit cells representing short sections of the nonlinear TL of the electrical length much smaller than the characteristic wavelength. The CAD implementation of the TLDN model allows efficient characterisation of the nonlinear models based on different polynomial approximations of the distributed nonlinearities. It has been demonstrated that the proposed modulus polynomial model provides fairly accurate approximation with only a few terms, whereas the conventional analytical polynomial model requires much higher order of the describing polynomial. The results of the presented analysis can be used for the modelling of PIM generation by arbitrary modulated signals in complex planar microwave circuits and design of low-PIM microwave circuits.