How do I extract a SPICE model from an EM simulation for use in a circuit simulator?

Extracting a SPICE model from an EM simulation for use in a circuit simulator converts the frequency-domain S-parameter data (generated by the EM solver) into a time-domain compatible equivalent circuit (SPICE model) that can be used in transient, harmonic balance, or SPICE simulations alongside active device models. The extraction methods are: direct S-parameter insertion (the simplest approach: export the S-parameter file (Touchstone .s2p or .snp format) from the EM simulator and import it directly into the circuit simulator as a frequency-domain data block. Most RF circuit simulators (ADS, Microwave Office, SPICE-RF) can use S-parameter data directly. Limitations: only valid within the simulated frequency range, and transient (time-domain) simulation requires conversion to a rational function model), rational function fitting (fit the S-parameter data to a rational function (a ratio of polynomials in the frequency variable) that can be converted to an equivalent circuit of R, L, C, and controlled sources. Tools: Vector Fitting (developed by SINTEF, available as open-source MATLAB code) is the standard algorithm. The rational function is causal, passive, and stable, ensuring that the SPICE simulation is well-behaved), broadband SPICE model (use the rational function fit to generate a netlist of RLCG elements and controlled sources that reproduces the EM-simulated response over the entire frequency range. The generated model has 10-50 elements for a 2-port structure and more for multi-port structures. This model can be used in any SPICE simulator for transient and frequency-domain analysis), and physics-based model extraction (for simple structures like a via or a bond wire: extract the individual parasitic values (L, C, R) by fitting the EM-simulated S-parameters to a physically motivated equivalent circuit. This gives more intuitive models that scale with geometry changes).