DocumentCode :
2411153
Title :
Active, resistive, nonlinear, uniform, infinite ladder networks
Author :
Zemanian, A.H.
Author_Institution :
New York Univ., Stony Brook, NY, USA
fYear :
1988
fDate :
7-9 Jun 1988
Firstpage :
1977
Abstract :
A strictly passive, resistive, nonlinear, uniform, infinite ladder network has a characteristic immittance (v,i)→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 v0 is a zero of g and i0 is a zero of r and if G and R are the derivatives of g and r at v0 and i0, respectively, and are both positive or both negative, then (v 0,i0) is a saddle point of the first kind. On the other hand, if G and R are of opposite sign, then (v0,i0) is a center when -4<GR<0 and a saddle point of the second kind when GR<-4
Keywords :
active networks; electric immittance; ladder networks; nonlinear network analysis; poles and zeros; active resistive nonlinear uniform infinite ladder networks; characteristic immittance; saddle point; series resistances; shunt conductances; voltage-current plane; zeros; Equations; H infinity control; Voltage;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Circuits and Systems, 1988., IEEE International Symposium on
Conference_Location :
Espoo
Type :
conf
DOI :
10.1109/ISCAS.1988.15327
Filename :
15327
Link To Document :
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