Active, resistive, nonlinear, uniform, infinite ladder networks

• Published in: 1988 IEEE International Symposium on Circuits and Systems (ISCAS) pp. 1977 - 1979 vol.3
• Main Author: Zemanian, A.H.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1988
• Subjects: Equations; H infinity control; Voltage
• DOI: 10.1109/ISCAS.1988.15327

A strictly passive, resistive, nonlinear, uniform, infinite ladder network has a characteristic immittance (v,i) to W(vi) with exactly one fixed point in the voltage-current plane, that fixed point is a saddle point of the first kind and occurs at the origin. However, if 'strictly passive' is replaced by 'active', the number of fixed points can be many. If the series resistances and shunt conductances are continuous functions whose zeros are all distinct and changes-of-sign as well, then the fixed points of W appear in a rectangular pattern in the (v,i) plane. Moreover, if v/sub 0/ is a zero of g and i/sub 0/ is a zero of r and if G and R are the derivatives of g and r at v/sub 0/ and i/sub 0/, respectively, and are both positive or both negative, then (v/sub 0/,i/sub 0/) is a saddle point of the first kind. On the other hand, if G and R are of opposite sign, then (v/sub 0/,i/sub 0/) is a center when -4<GR<0 and a saddle point of the second kind when GR<-4.< >