ABSTRACT
Any lumped network obeys three basic laws: Kirchhoff’s voltage law (KVL), Kirchhoff’s current law (KCL), and the elements’ laws (branch characteristics). For filter applications, we write the frequencydomain instead of the time-domain network equations. Three general methods for writing network equations are described in Chapter 19. They are the node equations, loop equations, and hybrid equations. This section outlines another method, the signal flow graph (SFG) method of characterizing a linear network. The basic definitions of terms and theorems related to SFGs are presented in Section 8.4. The concepts of tree, cotree, loop, and cutset, required for the present discussion, are introduced in Chapter 7. Note that the terms loop, tree, and cotree refer to directed circuit, spanning tree, and cospanning tree defined in Chapter 7. Consider first the construction of SFGs for linear networks without controlled sources. For all practical
networks, the independent voltage sources (E) contain no loops, and the independent current sources (J) contain no cutsets. Under these conditions, it is always possible to select a tree T, such that all voltage sources are included in the tree and all current sources are included in the cotree. The network branches are divided into four sets (each set may be empty) indicated by subscripts as follows:
E: independent voltage sources J: independent current sources Z: passive branches in the tree, characterized by impedances Y: passive branches in the cotree, characterized by admittances
A step-by-step procedure for constructing an SFG is given below.
