Notes on the Stability of Linear Networks

An extension of Nyquist´s criterion of stability is made by imposing on the transfer factor a less stringent condition, - ∞ < limω→+∞AJ(iω) = limω→-∞AJ(iω) < + 1, instead of the condition, limω→∞|AJ(iω)| = 0(1/ω). With this extension, the criterion will be found more convenient for investigating those networks, such as those with lumped constants, which very often do not satisfy the original condition. A rule, which was given intuitively by Llewellyn for extending Nyquist´s criterion to more general cases, is verified. It is applicable to both unilateral and bilateral systems. In this rule, the impedance or admittance function of the circuit plays the same role as the function of 1 - AJ(iω) in Nyquist´s criterion. Application of the rule to impulsive networks is also considered.