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Periodic circuits driven by multitone signals are still a challenging simulation problem despite several numerical methods being presented in the literature. In this paper, a mixed time-frequency method for the solution of this problem and suitable for both autonomous and nonautonomous circuits is presented. The method is based on an extension of the envelope following method, which allows us to reduce the number of unknowns involved in the steady-state problem with respect to previous mixed time-frequency approaches, and a suitable reformulation of the periodicity constraint that allows us to obtain a significant acceleration in the determination of the solution by reducing the time interval along which the envelope analysis must be performed. The method is first presented for nonautonomous circuits and then extended to autonomous ones.