Stability and bifurcation analysis of multi-element non-foster networks

Abstract

A stability and bifurcation analysis of multi-element non-Foster networks is presented, illustrated through its application to non-Foster transmission lines. These are obtained by periodically loading a passive transmission line with negative capacitors, implemented with negative-impedance converters (NICs). The methodology takes advantage of the possibility to perform a stability analysis per subintervals of the perturbation frequency. This will allow an independent analytical study of the low-frequency instability, from which simple mathematical criteria will be derived to prevent bias-network instabilities at the design stage. Then, a general numerical method, based on a combination of the Nyquist criterion with a pole-zero identification of the individual NIC, will be presented, which will enable the detection of both low- and high-frequency instabilities. A bifurcation analysis of the multi-element non-Foster structure will also be carried out, deriving the bifurcation condition from a matrix-form formulation of the multi-element structure. The judicious choice of the observation ports will enable a direct calculation of all the coexisting bifurcation loci, with no need for continuation procedures. These bifurcation loci will provide useful insight into the global-stability properties of the whole NIC-loaded structure.