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1. Topic: Signal Flow Graph and Mason’s Gain
Formula
Synchros (Unit-1)
Subject: Control Systems
Electrical and Electronics Engineering
2nd Year 2nd Semester
Presented By
Ms. Challagulla K T S R Kowstubha M.Tech.,
Assistant Professor

2. Objective
 What is meant by SFG
 Terms used in SFG
 How to draw SFG from Block Diagram
 How to draw SFG from Linear Equations
 Masson’s Gain Formula
 Transfer function of SFG using Masson’s Gain formula

3. Signal Flow Graph
• SFG is an alternative to block diagrams for graphically
describing systems
• SFG is used to model signal flow in a system
• SFG can be used to derive the transfer function of the system
by Mason’s Rule / Mason’s Gain Formula.

4. • Node
• Branch
• Gain
• Input / Sources
• Output / Sinks
• Path
• Path gain
• Forward path
• Forward path gain
• Loop
• Self loop
• Loop Gain
• Non-touching loop
Terms used in SFG

5. Terms used in SFG
Node: variables.
Branch: Directed branches.
Gain: transmission of that branch
Input/Sources: nodes with out-going branches only
Output/Sinks: nodes with incoming branches only
Path: successive branches without repeated nodes

6. Path gain: the gain of the path
Forward path: path from input to output
Forward path gain: gain of forward path
Loop / Feedback path: a closed path which originates and
terminates on the same node
Self loop: loop with only one branch
Loop gain: gain along the loop
Non-touching loop: two loops are non-touching if they do not
share any nodes nor branches

8. Two forward paths: G1G2G3G4G5G7 & G1G2G3G4G6G7
Four loops: G2H1, G4H2, G4G5H3, G4G6H3
Non-touching loops: G2H1 & G4H2, G2H1 &
G4G5H3, G2H1 & G4G6H3
Example-1

9. Example-2
Three forward path:
A32A43A54A65A76
A72
A42A54A65A74

10.  A32A33, A43A34, A54A45, A65A56, A76A67, A77
 A42A34A23, A65A76A57
•A65A76A67A56 is not a loop since X6 is repeated on the
path!
A72A57A45 A34A23
A72A67A56A45 A34A23

11. Transfer Function of Signal Flow Graph
• Mason’s Gain Formula:
Δ = Determinant of the system
 This formula states the overall gain of the system
 The Transfer function of signal flow graph will be find out by
using Mason’s Gain formula
The overall gain of the system is given by

12. Δ = 1 - (sum of all individual loop gains)
+ (sum of products of gains of all 2 loops that do not touch each other)
– (sum of products of gains of all possible three loops that do not touch
each other) + …
Δi = Δ for part of SFG that does not touch i-th forward path
Δi = 1 if no non-touching loops to the i-th path, or if taking out i-th path breaks all
the loops

13. Example:1
Determine the Transfer Function of given signal flow graph By using Mason’s Gain
Formula
Sol:

14. Conti…

16. Possibilities of Signal Flow Graphs
• Direct Signal Flow Graph Model
• Block Diagram to Signal Flow Graph
• Linear Equation to Signal Flow Graph
Model-1 Model-2
Model-3

17. Converting Block Diagram to Signal Flow Graph
Consider a node at each junction point of signals

19. Conversion of Linear Equations to
Signal Flow Graph

21. Sychros
Transmitter:
The constructional features, electrical circuit and a schematic symbol of
synchro transmitter are shown in figure-2.
The two major parts of synchro transmitters are stator and rotor .The
stators identical to the stator of three phase alternator.
It is made of laminated silicon steel and slotted on the inner periphery to
accommodate a balance three phase winding.
The stator winding is concentric type with the axis of the three coil 120
degree apart. The stator winding is star connected

22. Synchro Transmitter
Operational Diag-1
Operational Diagram-2

23. Synchro Pair

24. Outcome
 What is meant by SFG
 Terms used in SFG
 How to draw SFG from Block Diagram
 How to draw SFG from Linear Equations
 Masson’s Gain Formula
 Transfer function of SFG using Masson’s Gain formula