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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.9 n.2 México Oct./Dec. 2005




Computing Symbolic Expressions in Analog Circuits Using Nullors


Cálculo de Expresiones Simbólicas en Circuitos Analógicos usando Anuladores


Esteban Tlelo Cuautle1,2, Carlos Sánchez López1 and Federico Sandoval Ibarra3


1 INAOE, Department of Electronics,
Luis Enrique Erro No. 1, Tonantzintla, Puebla. 72000 México.
Tel/Fax: +52–222–2470517,

2 Instituto Tecnológico de Puebla

3 CINVESTAV, Guadalajara Unit,


Article received on July 14, 2003; accepted en July 08, 2005



A novel method is introduced to compute symbolic expressions in analog circuits modeled by nullors. The proposed method is based on the formulation of a compact system of equations (CSEs) by manipulation of data–structures, which highly improves traditional symbolic–methods. It is demonstrated that by modeling all active devices using nullors, the CSEs is easily formulated by manipulation of both the nullor and admittance interconnection–relationships. Several examples leads us to conclude on the suitability of the proposed symbolic–method to be incorporated within a symbolic simulator.

Keywords: Symbolic analysis, Modeling and simulation, Circuit theory, Data structures, Nullor.



Se presenta un nuevo método para calcular expresiones simbólicas en circuitos analógicos modelados con anuladores (nullors). El método propuesto se basa en la formulación de un sistema de ecuaciones compacto (SEC), a través de la manipulación de estructuras de datos, lo cual mejora notablemente los métodos simbólicos tradicionales. Se demuestra que modelando todos los dispositivos activos usando nullors, el SEC se formula fácilmente por manipulación de las relaciones de interconexión del nullor y admitancias. Algunos ejemplos conducen a concluir en la confiabilidad del método simbólico propuesto para incorporarlo dentro de un simulador simbólico.

Palabras Clave: Análisis simbólico, Modelado y simulación, Teoría de circuitos, Estructura de datos, Anulador.





This work was supported in part by CONACyT/MEXICO under project number 40321, and CoSNET/MEXICO under project number 454.03p.



1. Cabeza, R.; and Carlosena, A., "On the use of symbolic analyzers in circuit synthesis," Analog Integrated Circuits and Signal Processing, 25: 67–75 (2000).        [ Links ]

2. Chua, Leon O.; and Lin, Pen–Min, Computer–aided analysis of electronic circuits, (Prentice Hall, 1975).        [ Links ]

3. Fernández, F.V. et al., Symbolic Analysis Techniques: Applications to Analog Design Automation, (IEEE Press, 1998).        [ Links ]

4. Floberg, Henrik, Symbolic analysis in analog integrated circuit design, (Kluwer Academic Publishers, 1997).        [ Links ]

5. Randall, Geiger L.; and Sánchez–Sinencio, E., "Active Filter Design Using Operational Transconductance Amplifiers: A Tutorial," IEEE Circuits and Devices Magazine, pp.20–32 (March, 1985).        [ Links ]

6. Gielen, G.; and Sansen, W., Symbolic analysis for automated design of analog integrated circuits, (Kluwer Academic Publishers, 1991).        [ Links ]

7. Moschytz, George S., Linear integrated networks: Fundamentals, (Van Nostrand Reinhold Company, 1974).        [ Links ]

8. Palumbo, G.; and Pennisi, S., "Current feedback amplifiers versus voltage operational amplifiers," IEEE TCAS–I, 48 (5): 617–622 (May 2001).        [ Links ]

9. Tlelo–Cuautle, E.; and Sánchez–López, C., "Symbolic computation of NF of transistor circuits, IEICE Transactions on Fundamentals of Electronics," Communications and Computer Sciences, E87–A (9): 2420–2425 (September 2004).        [ Links ]

10. Sánchez–Sinencio, E., "Special section on symbolic circuit analysis techniques," IEEE TCAS–II Analog and digital signal processing, 45 (10) (October 1998).        [ Links ]

11. Schmid, H., "Approximating the universal active element," IEEE TCAS–I, 47 (11): 1160–1169 (November 2000).        [ Links ]

12. Silva–Martínez, J.; Steyaert, M.; and Sansen, W., High Performance CMOS Continuous–Time Filters, (Kluwer Academic Publishers, 1993).        [ Links ]

13. Tlelo–Cuautle, E. et al., "SIASCA: Interactive system for the symbolic analysis of analog circuits," IEICE Electronics Express, 1 (1): 19–23 (April, 2004).        [ Links ]

14. Torres–Muñoz, D.; and Tlelo–Cuautle, E., "Síntesis de filtros en modo voltaje y modo corriente usando un dispositivo activo universal," Revista Internacional: Información Tecnológica, 15 (6): 59–62 (Diciembre 2004).        [ Links ]

15. Sánchez–López, Carlos; and Tlelo–Cuautle, Esteban, "Behavioral Model Generation for Symbolic Analysis of Analog Integrated Circuits," IEEE ISSCS, (Iasi, Romania, July 14–15, 2005).        [ Links ]

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