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 on the right-hand side (RHS) of the complex plane. This is achieved by partitioning the structure into simpler blocks that must be stable under either open-circuit (OC) or short-circuit (SC) terminations. Thus, the system stability is evaluated using 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.
Highlights
DESIGNERS of nonlinear circuits often find qualitative differences between the solution simulated and the solution measured [1]–[5]
To avoid the possible coexistence of right–hand side of the complex plane (RHS) zeroes and RHS poles, OC–stable blocks should be represented in terms of impedances and short– circuit (SC)–stable blocks should be represented in terms of admittances
When analyzing the stability of the third amplifier under a single OC termination at the output port, one obtains the results shown in Fig. 3(b), where the real part of its dominant poles has been represented versus VGS
Summary
DESIGNERS of nonlinear circuits often find qualitative differences between the solution simulated and the solution measured [1]–[5]. Unlike the methods based on the use of the Nyquist criterion, the pole–zero analysis [26]–[32] is applied to a closed–loop transfer function that can contain both RHS poles and RHS. The recent method [32], based on projecting the closed–loop transfer function on an orthogonal basis of stable and unstable functions, prevents artificial quasi–cancellations that can result from the fitting with a rational function. This method can still miss instabilities due to a low observability.
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