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Self-oscillating power amplifiers (SOPAs) provide an elegant way to power signals which have high crest factors with a high efficiency. Recently, it has been shown that by pushing this concept to its limits, the stringent specifications of digital subscriber line (xDSL) could be met. For the design of these high bandwidth, low distortion amplifiers in a digital CMOS technology, a thorough analysis of the hard nonlinear system is mandatory. This paper describes behavioral models based on the describing function method and Bessel series expansion of nonlinear modulations. Models have been derived for the self-oscillation, the bandwidth, the dominant third-order distortion and all inter-modulation products of a SOPA line driver. All spectral peaks at the output of a single ended SOPA amplifier are qualitatively and quantitatively explained by these models with a very high accuracy. A calculation speed-up with three orders of magnitude could be obtained compared with a dedicated numerical simulator.