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A methodology is presented to characterize and model strongly nonlinear behavior of analog circuits with a compact set of nonlinear differential equations. While simulating a circuit in the time domain, the nodal matrix is extracted at each time step, similar to trajectory piecewise sampling (TPW). The circuit snapshots projected on a frequency-state space domain to facilitate the regression problem, based upon the vector fitting algorithm. Strongly nonlinear function approximation of the pole-residue trajectories render analytical models with very high accuracy, even with a limited training sequence. The proposed method proves to scale very well for large circuits with speedups that exceed the TPW implementation. The method is compatible with SPICE3f5 netlisting and commercial CMOS technologies and the models are easily exported as a state space description to behavioral languages such as VHDL-AMS or Verilog-AMS. The method is validated for analog circuits of medium and large size.