Computation of circuit waveform envelopes using an efficient, matrix-decomposed harmonic balance algorithm

In this paper we introduce a novel algorithm for numerically computing the "slow" dynamics (envelope) of circuits in which a "fast" varying carrier signal as also present. The algorithm proceeds at the rate of the slow behavior and its computational cost is fairly insensitive to the rate of the fast signals. The envelope computation problem is formulated as a differential-algebraic system of equations (DAEs) in terms of frequency-domain quantities (e.g. amplitudes and phases) that capture the fast varying behavior of the circuit. The solution of this DAE represents the "slow" variation of these quantities, i.e., the envelope. The efficiency of this method is the result of using the most appropriate method for each of the circuit modes: harmonic balance for the fast behavior and time-domain integration of DAEs for the slow behavior. The paper describes the theoretical foundations of the algorithm and presents several circuit analysis examples.