Chapter 8

Numerical Methods for Simulating Coupled-Oscillator Arrays

Coupled-oscillator arrays present a challenge to the designer due to difficulties both in the accurate simulation of oscillator elements and in the requirement for computationally efficient simulation techniques for large arrays. In addition, coupled-oscillator array design is made more difficult by the presence of multiple operating modes and stability considerations. As a result, a number of approximations need to be used to reduce the simulation time. These are describing function models for nonlinear elements [15, 118, 129, 130], along with perturbation models, infinite array approximations and continuum models shown in Chapter 3 [38, 39] and in Chapter 4 [4244], respectively.

The progress in recent years in nonlinear simulation techniques has led to more accurate analysis and optimization methods for nonlinear circuits such as oscillators and mixers, as well as arrays [120,131]. Furthermore, these nonlinear simulation tools can be combined with electromagnetic simulation in order to analyze radiating structures and nonlinear antennas and arrays.

In this chapter, an introduction to numerical methods for simulating nonlinear circuits is presented [131, 132], focused on the simulation of autonomous circuits such as oscillators, followed by an introduction to convex optimization principles [133]. Nonlinear simulation techniques are demonstrated in order to trace the steady-state solutions of coupled-oscillator ...

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