Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices

Floquet eigenfunctions and Floquet exponents are encountered in stability and noise analysis of circuits operating at large signal periodic regime. It is analytically verified that the spectrum vectors of the left-hand and right-hand Floquet eigenfunctions and the Floquet exponents (Floquet eigenpairs) are members of the harmonic balance eigenvalues and eigenvectors (HB eigenpairs). The relationships between other HB eigenpairs with the Floquet eigenpairs are discussed. This discussion leads to a practical algorithm for computing the Floquet eigenpairs through HB eigenpairs. Furthermore, it is analytically verified that the main arguments of the study are consistent with the orthogonality/biorthogonality relations between different Floquet eigenfunctions. The new approach has been applied to a P-HEMT oscillator at 10.2 GHz and very good agreement between the Floquet eigenpairs computed through the new approach and the ones computed through the time-domain integration is observed.