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This paper gives closed-form equations for the intermodulation and third harmonic signals generated in a nonlinear transmission line with distributed quadratic nonlinearities in the conductor and dielectric. Although the formulation developed is general, it is intended to be used in planar devices combining high-temperature superconductor (HTS) and oxide ferroelectrics. The analysis in this paper shows that the intermodulation and third harmonic signals produced by an HTS tend to cancel those of a ferroelectric, and that full cancellation is theoretically possible. This opens the way for using HTS/ferroelectric multilayers, not (only) for their tunable or phase-shifting properties, but for highly linear spurious-free planar HTS devices.