Signal-flow graph

A signal-flow graph (SFG) is a special type of block diagram, constrained by rigid mathematical rules, that is a graphical means of showing the relations among the variables of a set of linear algebraic relations. Nodes represent variables, and are joined by branches that have assigned directions and gains. A signal can transmit only in the direction of the arrow.

Figure 1: Simple SFG

Example 1 Simple amplifier

$y_{1}=a_{11}x_{1}\,$

becomes the signal flow graph of Figure 1.

Figure 2: Two-port SFG

Although this equation is represented by the SFG of Figure 1, the algebraically equivalent relation

$x_{1}={y_{1}}/{a_{11}}\$

is not considered to be implied by Figure 1. That is, the SFG is unilateral, sometimes emphasized by calling x₁ a "cause" and y₁ an "effect", or by calling x₁ an "input" and y₁ an "output".

Example 2 Two-port network

$y_{1}=a_{11}\ x_{1}+a_{12}\ x_{2}$

$y_{2}=a_{21}\ x_{1}+a_{22}\ x_{2}$

becomes the signal flow graph of Figure 2.