Two-Level Stability Analysis of Complex Circuits

Abstract

A new methodology is proposed for the small-and large-signal stability analysis of complex microwave systems, containing multiple active blocks. It is based on a calculation of the system characteristic determinant that ensures that this determinant does not exhibit any poles in the right-hand side of the complex plane (RHS). This is achieved by partitioning the structure into simpler blocks that must be stable under either open-circuit (OC) or shortcircuit (SC) terminations. Thus, the system stability is evaluated by means of a two-level procedure. The first level is the use of pole-zero identification to define the OC-or SC-stable blocks, which, due to the limited block size, can be applied reliably. In large-signal operation, the OC-or SC-stable blocks are described in terms of their outer-tier conversion matrices. The second level is the calculation and analysis of the characteristic determinant of the complete system at the ports defined in the partition. The roots of the characteristic determinant define the stability properties. The Nyquist criterion can be applied since, by construction, the determinant cannot exhibit any poles in the RHS. In addition, one can use pole-zero identification to obtain the values of the determinant zeroes. Because the determinant is calculated at a limited number of ports, the analysis complexity is greatly reduced.

Stability and Oscillation Analysis at Circuit Level and Through Semi-Analytical Formulations

“…The stability analysis proposed in [23] is based on a partition of the structure into N active blocks (containing both active and passive linear elements), connected through a passive linear network (Fig. 1).…”

“…6(a). Again, the results obtained with conventional pole-zero identification depend on the location at which the closed-loop transfer function is calculated [see In [23] the stability analysis in Section A was extended to large-signal operation and applied to a system of three Class-E amplifiers subject to coupling at their output ports, as may happen due to antenna cross talk. The large-signal analysis is carried out through a linearization of the HB equations about the periodic steady-state solution at ω o with NH harmonic terms.…”

“…The implementation on commercial software is more demanding than in the small-signal case. As explained in [23], the verification of the SC/OC stability of the blocks is carried out with the aid of ideal filters, plus conventional pole-zero identification inside the blocks. On the other hand, the user This article has been accepted for inclusion in a future issue of this journal.…”

“…To be physical, the solution obtained with HB must be stable, which can only be ensured with a complementary stability analysis [8]- [21]. This work presents a review of recent methodologies for stability [22], [23], and oscillation analysis [24]- [26] developed at University of Cantabria. As indicated through the text, it includes several new theoretical contributions with respect to previous publications by the group on the two topics.…”

“…Recently a new method has been introduced [23], which is based on a definition of the characteristic determinant that, by construction, cannot exhibit any RHS poles. Unlike [9], [14], the calculation of this determinant does not require access to the intrinsic device terminals.…”