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A novel analytical Gaussian approximation is developed for the evaluation of the distortion spectrum introduced by a nonlinear amplifier. This method allows to consider high-order distortion contributions when the device is driven by a broadband signal with Gaussian amplitude distribution. The results are applied to a ninth-order power series model based on well known single-tone and two-tone analysis parameters. The cascade of two or more amplifiers is investigated as well providing a complete set of tools for the early system specification of broadband transceivers. Simulations shows excellent agreement even for high input power levels, when former third-order and fifth-order approximations fail to yield accurate predictions.