Null double injection and the extra element theorem

Abstract

The extra element theorem (EET) states that any transfer function of a linear system can be expressed in terms of its value when a given `extra' element is absent, and a correction factor involving the extra element and two driving-point impedances are seen by the element. In the present work, the EET is derived and applied to several examples in a manner that has been developed and refined in the classroom over a number of years. The concept of null double injection is introduced first, because it is the key to making easy the calculation of the two driving-point impedances needed for the EET correction factor. The EET for series and parallel elements is then considered, and attention is also given to the EET as an analysis tool, to the symmetry of the two forms of the EET, and to return ratios and sensitivity