文档介绍：0912 S1-S8 Page 605 Saturday, October 5, 2002 10:06 PM
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Signal Flow Graphs
in Filter Analysis
and Synthesis
Formulation of Signal Flow Graphs for Linear
Networks
Synthesis of Active Filters Based on Signal Flow
Graph Associated with a Passive Filter Circuit
Pen-Min Lin Synthesis of Active Filters Based on Signal Flow
Purdue University Graph Associated with a Filter Transfer Function
Formulation of Signal Flow Graphs for works
Any work 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 frequency-
domain instead of the time-work equations. Three general methods for work
equations are described in Chapter . They are the node equations, the loop equations, and the hybrid
equations. This section outlines another method, the signal flow graph (SFG) method of characterizing
a work. The basic definitions of terms and theorems related to signal flow graphs are presented
in Chapter . The concepts of tree, co-tree, loop, and cutset, required for the present discussion, are
introduced in Chapter 7. Note that the terms loop, tree, and co-tree refer to directed circuit, spanning
tree, and co-spanning tree defined in Chapter 7.
Consider first the construction of signal flow graphs for works without controlled sources.
For all works, 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 co-tree.
work 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 co