Nonlinear circuit analysis using the method of harmonic balance—a review of the art. II. Advanced concepts

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Abstract
The harmonic balance method is a technique for the numerical solution of nonlinear analog circuits operating in a periodic, or quasi‐periodic, steady‐state regime. The method can be used to efficiently derive the continuous‐wave response of numerous nonlinear microwave components including amplifiers, mixers, and oscillators. Its efficiency derives from imposing a predetermined steady‐state form for the circuit response onto the nonlinear equations representing the network, and solving for the set of unknown coefficients in the response equation. Its attractiveness for nonlinear microwave applications results from its speed and ability to simply represent the dispersive, distributed elements that are common at high frequencies.The last decade has seen the development and application of harmonic balance techniques to model analog circuits, particularly microwave circuits. The first part of this article reviewed the fundamental achievements made during this time. In this part, the extension of the method to quasi‐periodic regimes, optimization analysis, oscillator analysis, studies of various convergence strategies, and practical applications are discussed. A critical assessment of the various types of harmonic balance techniques is given. Examples of designs which have been modeled using the harmonic balance technique and built both in hybrid and MMIC form are presented.

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