Synthesis of lossless electric circuits based on prescribed Jordan forms

Abstract

We advance here an algorithm of the synthesis of lossless electric circuits such that their evolution matrices have the prescribed Jordan canonical forms subject to natural constraints. Every synthesized circuit consists of a chain-like sequence of LC-loops coupled by gyrators. All involved capacitances, inductances and gyrator resistances are either positive or negative with values determined by explicit formulas. A circuit must have at least one negative capacitance or inductance for having a nontrivial Jordan block for the relevant matrix.

References in corpus (2)

• Unidirectional Nonlinear PT-symmetric Optical Structures
• Exceptional points of degeneracy and $\mathcal{P}\mathcal{T}$-symmetry in photonic coupled chains of scatterers

Cited by in corpus (5)

• Exceptional points of degeneracy in traveling wave tubes
• Analytic theory of multicavity klystron
• Perturbations of circuit evolution matrices with Jordan blocks
• Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator
• Enhanced Sensitivity of Degenerate System Made of Two Unstable Resonators Coupled by Gyrator Operating at an Exceptional Point