THE INDEFINITE–ADMITTANCE MATRIX

In the preceding chapter, networks were characterized by their port behaviors. Fundamental to the concept of a port is the assumption that the instantaneous current entering one terminal of the port is always equal to the instantaneous current leaving the other terminal of the port. However, we recognize that upon the interconnection of networks, this port constraint may be violated. Thus, it is sometimes desirable and more advantageous to consider n-terminal networks, as depicted in Fig. 2.1.

In this chapter, we discuss a useful description of the external behavior of a multiterminal network in terms of the indefinite-admittance matrix and demonstrate how it can be employed effectively for the computation of network functions. Specifically, we derive formulas expressing the network functions in terms of the first-order and the second-order cofactors of the elements of the indefiniteadmittance matrix. The significance of this approach is that the indefiniteadmittance matrix can usually be written down directly from the network by inspection.

Since in the remainder of this book we deal exclusively with linear, lumped, and time-invariant networks, the adjectives linear, lumped, and time-invariant are omitted in the discussion unless they are used for emphasis.