Nullor

A nullor is a theoretical two-port network consisting of a nullator at its input and a norator at its output.^[1] Nullors represent an ideal amplifier, having infinite current, voltage, transconductance and transimpedance gain.^[2] Its transmission parameters are all zero, that is, its input–output behavior is summarized with the matrix equation

{\begin{pmatrix}v_{1}\\i_{1}\end{pmatrix}}={\begin{pmatrix}0&0\\0&0\end{pmatrix}}{\begin{pmatrix}v_{2}\\i_{2}\end{pmatrix}}

In negative-feedback circuits, the circuit surrounding the nullor determines the nullor output in such a way as to force the nullor input to zero.

Inserting a nullor in a circuit schematic imposes mathematical constraints on how that circuit must behave, forcing the circuit itself to adopt whatever arrangements are needed to meet the conditions. For example, an ideal operational amplifier can be modeled using a nullor,^[3] and the textbook analysis of a feedback circuit using an ideal op-amp uses the mathematical conditions imposed by the nullor to analyze the circuit surrounding the op-amp.

^ The name "nullor" was introduced in Carlin. H. J . "Singular network elements", Tech. Doc. Rept. RADC-TDR-63-511, Polytechnic Inst. of Brooklyn, Jan.1964; later published in the March 1964 issue of the IEEE Transactions on Circuit Theory, Volume 11, Issue 1, pp.67-72 https://doi.org/10.1109/TCT.1964.1082264.
^ Verhoeven C. J. M.; van Staveren A.; Monna G. L. E.; Kouwenhoven M. H. L.; Yildiz E. (2003). Structured electronic design: negative feedback amplifiers. Boston/Dordrecht/London: Kluwer Academic. pp. 32–34. ISBN 1-4020-7590-1.
^ Verhoeven C. J. M.; van Staveren A.; Monna G. L. E.; Kouwenhoven M. H. L.; Yildiz E. (31 October 2003). §2.6. Springer. ISBN 1-4020-7590-1.

[1] The name "nullor" was introduced in Carlin. H. J . "Singular network elements", Tech. Doc. Rept. RADC-TDR-63-511, Polytechnic Inst. of Brooklyn, Jan.1964; later published in the March 1964 issue of the IEEE Transactions on Circuit Theory, Volume 11, Issue 1, pp.67-72 https://doi.org/10.1109/TCT.1964.1082264.

[Verhoeven-2] Verhoeven C. J. M.; van Staveren A.; Monna G. L. E.; Kouwenhoven M. H. L.; Yildiz E. (2003). Structured electronic design: negative feedback amplifiers. Boston/Dordrecht/London: Kluwer Academic. pp. 32–34. ISBN 1-4020-7590-1.

[Verhoeven2-3] Verhoeven C. J. M.; van Staveren A.; Monna G. L. E.; Kouwenhoven M. H. L.; Yildiz E. (31 October 2003). §2.6. Springer. ISBN 1-4020-7590-1.

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