Origin of the deviation of intermodulation distortion in high-Tcthin films from the classical 3:1 scaling

A simple theoretical model for calculating microwave power dependence of IMD products from a given power dependence of the surface impedance Zs = Rs + jXs is presented. The model is based on a polynomial representation of Zs(Hrf) (Hrf is the microwave magnetic field) and the Fourier integral method. Various power dependences of Zs are considered and it is shown that irrespective of the functional form of Zs(Hrf), the low power slope of the third-order IMD versus input power is always 3:1. Claims made in the literature that in some particular cases (such as Zs(Hrf) being a non-analytical function or in the case of unequal amplitudes of the fundamental tones), deviation towards slopes lower than 3:1 is possible are thoroughly re-examined here and are found either unconvincingly substantiated or inapplicable to conventional IMD experiments. Instead we propose that numerous observations of the deviation of IMD scaling from 3:1 reported for HTS thin films are due to extrinsic conditions such as spectral characteristics of the microwave sources or insufficiently low input powers over which the measurements were taken. This conclusion is supported by successful fitting of experimental data on the power dependence of IMD in YBaCuO thin film, which exhibits non-3:1 scaling, using the model presented here. Finally, the relative contributions of Rs(Hrf) and Xs(Hrf) to the IMD power dependence are discussed and shown to be highly sensitive to the underlying mechanism of the nonlinearity.