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A general equivalent-circuit-based method for the de-embedding of scattering parameters is presented. An equivalent circuit representation is used to model the embedding package. The parameters in the models are estimated with a statistical method using measured data from all de-embedding standards jointly together. Hence, it is possible to assess parameter estimates and their variance and covariance due to measurement uncertainties. A general de-embedding equation, which is valid for any five-port with a defined nodal admittance matrix, is derived and used in the subsequent de-embedding of measured device data. Different equivalent circuit models for the embedding network are then studied, and tradeoffs between model complexity and uncertainty are evaluated. Furthermore, the influence of varying number and combinations of de-embedding standards on the parameter estimates is investigated. The method is verified, using both measured and synthetic data, and compared against previously published work. It is found to be more general while keeping or improving accuracy.