Nullators and norators in circuits education: A benefit or an obstacle?

Abstract

The study of circuits and systems requires some basic reasoning with various equivalent interconnections of components like resistors, sources, ideal opamps, ideal transistors, short and open circuits…. Students should be able to handle a rich variety of such interconnections correctly and appropriately. Special components like nullators and norators bring in some valuable insights, flexibility and design methods based thereupon. From the practical experience of teaching nullators and norators in basic circuits courses for electrical engineering students, the authors stress a number of didactical goals and experiences. First, it is crucial that the students understand the notions of nullator and norator and are able to distinguish these from other components, such as short circuits, open circuits, resistors, and sources. Second, they should be able to reason correctly with interconnections that involve nullators and norators. Third, they should be able to find equivalents for circuits having nullators and norators. Analysis and design of circuits with nullators and norators will be presented. A particular case study of the use of nullators and norators for the implicit inversion of a 2 × 2 matrix will be used as an illustration of some unexpected results, which we will hardly find without nullators and norators. This will lead to an evaluation of the didactical processes of using nullators and norators.