This article presents simple methodologies, fully compatible with commercial harmonic-balance (HB) simulators, to deal with the nonlinear behavior found in wireless power-transfer circuits, oscillator-based sensors, subharmonic injection-locked oscillators, and nonreciprocal isolators. The proposed methods allow the calculation of all the coexistent periodic solutions, including disconnected branches and closed loops that are not detected with conventional time-domain simulations or with standard HB continuation. Two main procedures are used, depending on how the circuit operates. For circuits driven at the fundamental frequency, we make use of a Norton/Thevenin equivalent and define a driven control function obtained from a single HB simulation. Constant-magnitude contours of this function give all disconnected solution curves versus the selected parameter and show how they evolve with input power. When the circuit is driven at a frequency different from the oscillation frequency, or a Norton/Thevenin description is not convenient, we define an equilibrium control function instead. In this case, all coexisting solutions are obtained by finding the roots of an equilibrium equation through a straightforward contour-intersection procedure. We also introduce hybrid methods in which the oscillator core is replaced by a nonlinear admittance function extracted from HB and connected to an external resonator or network. This enables an efficient and realistic analysis and optimization of near-field wireless power transfer, self-injection-locked radar, and tag-to-reader links without changing the oscillator design.
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