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.

Highlights

  • Non-Foster circuits [1]-[6] are based on the use of negative capacitors or inductors, implemented through transistorbased negative impedance converters (NICs) [1]-[3], [7]-[8]

  • Using the NIC h-parameter matrix [3], it is shown that any practical two-port NIC is always short-circuit stable (SCS) and open-circuit unstable (OCU) at one port, and open-circuit stable (OCS) and short-circuit unstable (SCU) at the other port

  • The analysis described has been applied to the non-Foster transmission line in Fig. 1, containing N = 3 NICs

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Summary

INTRODUCTION

Non-Foster circuits [1]-[6] are based on the use of negative capacitors or inductors, implemented through transistorbased negative impedance converters (NICs) [1]-[3], [7]-[8]. The analytical formulations and numerical methodologies presented in [25] were restricted to a non-Foster circuit based on a single NIC. The procedures take advantage of the possibility to perform the stability analysis per subintervals of the perturbation frequency, as is usually done in the numerical pole-zero identification [31]-[33]. This will allow distinguishing the mechanism for low frequency instabilities from other instabilities detectable at higher frequencies. Ideal negative elements are considered instead of transistor-based NICs. Here the stability analysis will be carried out in a numerical manner, using complete and realistic models of all the elements in the NICloaded line.

NON-FOSTER TRANSMISSION LINE
LOW-FREQUENCY INSTABILITY
C2 Cdc2 G a2 p Na1 a2 N
GLgm1 3C
HIGH-FREQUENCY INSTABILITY
50 Measurements
CONCLUSION

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