Symbolic Analysis of an Active Linear Circuit Using Nullors

The Symbolic Toolbox can be used to produce the s-domain transfer function of linear active circuits. This example is a Sallen-Key filter.

Nullor analysis is not as well known as it should be. This technique can be used to build the matrix that describes an active linear circuit. Starting with the matrix describing the passive circuit components, the size of the matrix is the reduced as each active component (which is represented by a nullator and a norator) is added.
This example is for a Sallen-Key filter built using an ideal op-amp. It is easily extended to use non-ideal linear models such as dominant pole and can be applied to much larger circuits.