Nullors, and Nullor Circuits; There Applications in Symbolic Circuit Analysis and Design
- 1 Reza Hashemian, Northern Illinois University, Dekalb, USA
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.
- Tlelo-Cuautle, E. (2002) An Efficient Biasing Technique Suitable for any Kind of the Four Basic Amplifiers Designed at Nullor Level. 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), Phoenix-Scottsdale, 26-29 May 2002, III-535-III-538. https://doi.org/10.1109/ISCAS.2002.1010279
- Haigh, D.G. and Radmore, P.M. (2006) Conductance Matrix Models for the Nullor Using Limit Variables and Their Application to Circuit Design. IEEE Transactions on Circuits and Systems I: Regular Papers, 53, 2214-2223. https://doi.org/10.1109/TCSI.2006.882809
- Hashemian, R. (2010) Local Biasing and the Use of Nullator-Norator Pairs in Analog Circuits Designs. VLSI Design, 2010, Article ID 297083. https://doi.org/10.1155/2010/297083 http://www.hindawi.com/journals/vlsi/2010/297083.html
- Wang, H., Huang, W. and Chiang, N. (2010) Symbolic Nodal Analysis of Circuits Using Pathological Elements. IEEE Transactions on Circuits and Systems II: Express Briefs, 57, 874-877. https://doi.org/10.1109/TCSII.2010.2082930
- Lin, W.C., Wang, H.Y., Liu, C.Y. and Lee, T.F. (2003) Symbolic Analysis of Active Device Containing Differencing Voltage or Current Characteristics. Elsevier, Amsterdam.
- Filaretov, V. and Korotkov, A. (2004) Generalized Parameter Extraction Method in Case of Multiple Excitation. ResearchGate, Berlin.
- Filaretov, V. and Gorshkov, K. (2020) Efficient Generation of Compact Symbolic Network Functions in a Nested Rational Form. International Journal of Circuit Theory and Applications, 48, 1032-1056. https://doi.org/10.1002/cta.2789
- Hashemian, R. (2022) A Comprehensive and Unified Procedure for Symbolic Analysis of Analog Circuits. IEEE Transactions on Circuits and Systems I: Regular Papers, 69, 2819-2831. https://doi.org/10.1109/TCSI.2022.3165152
- Pierzchala, M. and Fakhfakh, M. (2014) Symbolic Analysis of Nullor-Based Circuits with the Twograph Technique. Springer, Circuits, Systems, and Signal Processing, 33, 1053-1066. https://doi.org/10.1007/s00034-013-9696-y
- Hashemian, R. (2021) Application of Nullors in Symbolic Single Port Transfer Functions using Admittance Method. 2021 IEEE International Symposium on Circuits and Systems (ISCAS), Daegu, 22-28 May 2021, 1-5. https://doi.org/10.1109/ISCAS51556.2021.9401272
- Lin, P.M. (1991) Symbolic Network Analysis. Elsevier Publishers, New York.
- Shi, G., Tan, S.X.-D. and Tlelo-Cuautle, E. (2014) Advanced Symbolic Analysis for VLSI Systems. Springer, New York. https://doi.org/10.1007/978-1-4939-1103-5