Symbolic Analysis and Synthesis of Analog Circuits Using Nullors and Pathological Mirror Elements

  • Miguel A. Duarte-Villaseñor
  • Esteban Tlelo-Cuautle
  • Luis Gerardo de la Fraga
  • Carlos Sánchez-López
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 479)


It has been demonstrated that symbolic circuit analysis of analog circuits modeled by nullors and pathological mirror elements leads us to deal with the nodal admittance (NA) matrix that is more compact than by using traditional modified nodal analysis (MNA). This chapter reviews such a theory and details the inclusion of pathological voltage mirrors and current mirrors into the NA formulation. In this manner, from a circuit topology consisting of nullors and mirrors we show how to perform symbolic circuit analysis and then how to synthesize those circuit elements using MOS transistors. It is also highlighted that from such kind of circuit modeling, one can transform a voltage-mode circuit into a current-mode one and vice versa. We show the design of both modes of operation at the transistor level of design, for which we also provide details on the synthesis approach where each nullator, norator, voltage mirror and current mirror can have multiple options to be implemented with MOS transistors. Several examples are provided to appreciate the advantages of the NA formulation from analog circuits modeled by nullors and mirrors, the symbolic circuit analysis, the transformation from voltage-mode to current-mode and vice versa, and the synthesis of pathological circuits by using MOS transistors. The synthesized circuits are unity-gain-cells, a current conveyor, a current-feedback operational amplifier, and an operational transconductance amplifier, which are designed with standard CMOS integrated circuit technology, and they are applied to implement active filters and oscillators.



This work is partially supported by CONACyT-Mexico under grant 237991.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Miguel A. Duarte-Villaseñor
    • 1
  • Esteban Tlelo-Cuautle
    • 2
    • 3
  • Luis Gerardo de la Fraga
    • 3
  • Carlos Sánchez-López
    • 4
  1. 1.CONACyT-Instituto Tecnológico de TijuanaTijuanaMexico
  2. 2.Instituto Nacional de Astrofísica, Óptica y ElectrónicaPueblaMexico
  3. 3.Centro de Investigación y de Estudios Avanzados del IPNCiudad de MéxicoMexico
  4. 4.Universidad Autónoma de TlaxcalaApizacoMexico

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