Improved harmonic balance implementation of Floquet analysis for nonlinear circuit simulation

Abstract

We present a novel algorithm for the efficient numerical computation of the Floquet quantities (eigenvalues, direct and adjoint eigenvectors) relevant to the assessment of the stability and noise properties of nonlinear forced and autonomous circuits. The approach is entirely developed in the frequency domain by means of the application of the Harmonic Balance technique, thus avoiding lengthy time-frequency transformations which might also impair the accuracy of the calculated quantities. An improvement in the computation time around one order of magnitude is observed.

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

“…The solution is sought in the form of real and imaginary parts (i.e., the sine and cosine components of the actual time function) for each harmonic h of variable w i . This approach is common [11,29,55], although the magnitude and angle of the complex number could also be considered (as in [31] The system of nonlinear equations has the form:…”

Selective Determination of Floquet Quantities for the Efficient Assessment of Limit Cycle Stability and Oscillator Noise

“…Note that, according to the assumption of index-1 DAE, the rank ρ of C(t) is time independent. However, this does not necessarily imply that the entire nullspace of C(t) is time independent, i.e., it may be impossible to find a base for the nullspace whose elements are constant; this is a major limitation for the method presented in [16] that can be applied only to the constant part of the nullspace.…”

“…To this aim, the columns of matrixR need to be reordered by means of the reduced row echelon form (RREF) reduction technique [16]; since for the problem to admit a solution matrixB should be full rank, applying the RREF toB (11) can be cast in the form…”

“…As a matter of fact, HB is the simulation technique of choice for many high frequency or microwave analog circuits. For this reason, the HB determination of the Floquet quantities, although, in general, less efficient than time domain methods for lumped circuits, has drawn attention in the literature [1], [11], [14]- [16].…”

“…A first step in coping with this is the HB matrix manipulation discussed in [16], which can be applied only to eliminate a subset of the n − ρ FEs equal to minus infinity. We propose a novel mixed time-spectral domain numerical approach that removes the limitations of [16] and provides a further added value allowing for the approximate selective determination of the FEs with largest real part only provided that a proper numerical condition is met.…”