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A novel approach to the simulation of continuous-time ΔΣ modulators is presented. The proposed method uses analytical integration instead of numerical integration commonly used by SPICE-like simulators. First of all, expressions for a single integrator (which can be any integrator described by a second order model) are derived. These expressions allow one to calculate the states of the system at the next sampling event, using the states at the previous sampling event as initial conditions. Starting from these expressions recursive relations are derived for an (n+1)-th order ΔΣ modulator. Since all derived expressions are in the time-domain, different forms of jitter can be implemented easily. To improve the simulator efficiency, all time-independent variables (i.e those that remain constant during a simulation) are calculated beforehand. The simulation method is implemented in C and experimental results show the method to be 20-30 times faster than a SPICE-like simulation of linear macromodels with a complexity comparable to the model used by the proposed method.