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The accelerating trend of active metasurfaces -- such as those incorporating non-Foster matching, programmable control, or space-time modulation -- adds complexity to the computational electromagnetic (CEM) simulation landscape. In this work, we present an equivalent circuit model (ECM) for a particular periodic array element -- the dogbone element -- that incorporates an arbitrary sub-cell electronic circuit. The ECM is capable of predicting the overall surface impedance with any changes in the circuit's impedance. Three full-wave CEM simulations fully determine the EC, and the scattering parameters computed from the ECM for an embedded circuit, however complex, should be substantially similar to those produced by the full-wave code. With metasurfaces for which it is possible to obtain an ECM by this method, the reflection or transmission behavior of the surface under varying circuit conditions can be computed quickly without need of any further full-wave solutions. After highlighting the importance of fully characterizing parasitics in embedded components, we apply the method to the design of a varactor-based tunable metasurface, which upon fabrication and focused beam measurement demonstrates excellent model-measure agreement.