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This paper demonstrates new systematic approaches to equivalent circuit model extraction for defected ground structure (DGS) directly from full-wave frequency domain simulation. The DGS circuits being modeled may be either lossy or lossless. Adaptive frequency sampling (AFS) is used to minimize the computational effort of electromagnetic (EM) simulation while critically assisting in determining the cutoff frequency and attenuation pole location of the DGS circuits. A simple circuit model for lossy DGS circuits without any optimization of lumped element component values is presented. Furthermore, lossless circuit model relative complex along with a determined starting point of optimization of lumped element values is also presented in detail. The overall results are an efficient and accurate means to produce the complete equivalent models of DGS circuit for the design of various RF and microwave circuits such as oscillators that may require the high accurate nonlinear design procedures.