Definition 4 A Forward Path is a path from the input node to the output node. For example, x, to X2 to X to X4and X, to X2 to x are forward paths Definition 5: A Feedback Path or feedback loop is a path which originates and terminates on the same node. For example, x2 to x, and back to X2 is a feedback path Definition 6: A Self-Loop is a feedback loop consisting of a single branch. For example, A33 is a self-loop 2022-2-3
2022-2-3 21 Definition 4: A Forward Path is a path from the input node to the output node. For example, to to to and to to are forward paths. Definition 5: A Feedback Path or feedback loop is a path which originates and terminates on the same node. For example, to , and back to is a feedback path. Definition 6: A Self-Loop is a feedback loop consisting of a single branch. For example, is a self-loop. X1 X 2 X 3 X 4 X1 X 2 X 4 X 2 X 3 X 2 A33
Definition 7: The Gain of a branch is the transmission function of that branch when the transmission function is a multiplicative operator. For example, 433 is the gain of the self-loop if A3 is a constant or transfer function Definition 8: The Path Gain is the product of the branch gains encountered in traversing a path For example, the path gain of the forward path from X,to x to x, to x, is Definition g: The Loop Gain is the product of the branch gains of the loop. For example, the loop gain of the feedback loop from X2 to X, and back X2 is A32 A23 2022-2-3 22
2022-2-3 22 Definition 7: The Gain of a branch is the transmission function of that branch when the transmission function is a multiplicative operator. For example, is the gain of the self-loop if is a constant or transfer function. Definition 8: The Path Gain is the product of the branch gains encountered in traversing a path. For example, the path gain of the forward path from, to to to is Definition 9: The Loop Gain is the product of the branch gains of the loop. For example, the loop gain of the feedback loop from to and back is A33 A33 X1 X 2 X 3 X 4 . 2 A32 A23 X X 3 X 2
2.4 Construction of signal flow graphs o A signal flow graph is a graphical representation of a set of algebraic relationship and it is a directed graph. The arrow represents the relationship between variables. In general, a variable can be represented by a node Example: A typical feedback system. (In this case, a dummy node and a branch are added because the output node c has all outgoing branch) 2022-2-3 23
2022-2-3 23 2.4 Construction of signal flow graphs ¨ A signal flow graph is a graphical representation of a set of algebraic relationship, and it is a directed graph. The arrow represents the relationship between variables. In general, a variable can be represented by a node. ¨ Example: A typical feedback system. (In this case, a dummy node and a branch are added because the output node C has all outgoing branch)
r+ E H R 2022-2-3 24
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Example: Consider the following resistor network. There are five variablesv, v.v,i,i W SR We can write 4 linear equations R Ri.-R R2 R 2022-2-3 25
2022-2-3 25 Example: Consider the following resistor network. There are five variables, , , , , . 1 2 3 1 2 V V V i i We can write 4 linear equations: 3 4 2 3 2 2 2 2 2 3 3 2 2 1 1 1 1 1 1 1 1 v R i v R v R i v R i R i v R v R i i