Envelope tracking integral equation based hybrid electromagnetic circuit simulators
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This dissertation presents envelope-tracking hybrid field-circuit simulator for efficiently analyzing narrowband scattering from distributed structures loaded with nonlinear devices. The simulator models the interactions of fields with distributed structures and lumped elements by coupling and simultaneously solving the electric field integral equation and Kirchhoff’s equations, respectively. The coupled nonlinear system of equations is iteratively solved by a time marching scheme that represents the fields, voltages, and currents of interest (signals) as a truncated series of harmonic sinusoids (carriers) multiplied with complex-valued time-varying coefficients (envelopes). Unlike time-domain simulators, which sample the signals at a rate proportional to their maximum frequency content, the proposed envelope-tracking simulator samples the envelopes at a rate proportional to their maximum bandwidth; thus, it requires significantly fewer time steps when solving narrowband problems. Moreover, the envelope-tracking simulator is generally more accurate than its time-domain counterpart because of smaller integration and interpolation errors. Numerical results demonstrate that the proposed simulator improves the tradeoff between accuracy and computational cost, especially when analyzing distributed structures excited by narrowband signals or/and loaded with weakly nonlinear devices. Although the Fourier envelope simulator uses smaller number of time steps, there are other issues relating to the Fourier envelope simulator which are addressed in this thesis: (i) lumped element models that relate voltage envelopes and current envelopes for nonlinear elements are generally unavailable and the approximations used in the simulator to find them are inaccurate for broader band excitations. Higher order interpolation schemes were used in this dissertation to improve the accuracy of these approximations. Numerical results that demonstrate the ability to solve for problems with broader bandwidth of excitation are presented. (ii) As in its timedomain counterpart, adaptive integral method is used to reduce the computational cost of the simulator thus enabling the simulation of larger problems and (iii) Sparse preconditioners are used to improve the convergence of the solution algorithms. Finally, the Fourier envelope method is extended to the analysis of infinitely periodic arrays containing lumped nonlinear loads. Numerical results are presented to highlight the .features of this algorithm.