TITLE:
Nullors, and Nullor Circuits; There Applications in Symbolic Circuit Analysis and Design
AUTHORS:
Reza Hashemian
KEYWORDS:
Admittance Method, Analog Circuits, Nullors, Nullor Circuits, Sum of Tree Products, Transfer Functions
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.1,
January
25,
2024
ABSTRACT: The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.