Stability Criterion of Complex Polynomials in Markov’s Parameters and its’ Application at Selective System’s Design by the D-fragmentation Methods

Abstract

The simple proof of the stability criterion and roof localization of complex polynomials is given in Markov’s parameters. A proof bases on twice reduction of the Hermite-Hurwitz matrix order at introduction of Markov’s parameters. In contrast to a criterion for complex polynomials, its real analogue – the Markov’s criterion – is known from mathematical publications, but it does not practically use in engineering applications. Meanwhile, at high orders of polynomials (n>6), both criteria are preferable compared to Hurwitz and Hermite-Hurwitz criteria owing to the lower order of its matrices. This criterion is applied for stability areas investigation and for the parameter choice of selective radio-electronic devices by the modified D-fragmentation methods, in particular, multi-stage tuned amplifiers on CMOS structures and the three-stage oscillator with the stabilizing resonator. In addition, the problem of comparing the efficiency of the Hermite-Hurwitz criterion with a Markov-type criterion is being solved, and several new effective methods for constructing D-fragmentation diagrams are proposed.