2. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Introduction
• Block diagram is a pictorial representation of
the sequence of events in a process
• For complicated systems difficult to reduce
block diagrams
• Signal flow graph – a graphical representation
of the relationship between variables
– Provides relationship between system variables
without the need for reduction
4. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Signal Flow Graph (SFG)
• A signal-flow graph is a diagram consisting of
nodes that are connected by several directed
branches and is a graph representation of a set of
linear relation.
• Only valid for linear system
5. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Basic elements of SFG
• Branch: A unidirectional path segment
• Nodes: The input and output points or
junctions
7. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
• Path: A branch or a continuous sequence of branches
that can be traversed from one node to anther node.
Basic elements of SFG
1. Forward Path
2. Feedback path
8. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
• Loop: A closed path that originates and
terminates on the same node, and along
the path no node is met twice.
Basic elements of SFG
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2. Feedback Path Gain: -G1H1
Basic elements of SFG
In this case there is one loop or Feed back path
14. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Basic elements of SFG
3. Non-touching loop gain:
Two Non-touching loops gain: G2H2H3
G2H2H7G7
G7H7H3
Three Non-touching loops gain: G2H2H3H7G7
15. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Basic elements of SFG
)(sR
)(sG
)(sC )(sG
)(sR )(sC
block diagram: signal flow graph:
In this case at each step block diagram is to
be redrawn. That’s why it is tedious method.
So wastage of time and space.
Only one time SFG is to be drawn and
then Mason’s gain formula is to be
evaluated.
So time and space is saved.
21. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Mason’s gain formula
The linear dependence (Gain) T i j between input
variable x i and output variable x j is given by
the following formula:
k ijkijk
ij
P
T
22. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Mason’s Gain Rule
Mason’s gain rule is as follows: the transfer function of a
system with signal-input, signal-output flow graphs is
332211
)(
ppp
sT
Δ=1-(sum of all loop gains)+(sum of products of gains of all
combinations if 2 non-touching loops)- (sum of products of gains of all
combinations if 3 non-touching loops)+…
A path is any succession of branches, from input to output, in the
direction of the arrows, that does not pass any node more than once.
A loop is any closed succession of branches in the direction of the
arrows that does not pass any node more than once.
25. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Individual
loops
L 1 = G2 H2
L 4 = G7 H7
L 3 = G6 H6
L 2= G3 H3
Pair of Non-touching loops
L 1L 3 L 1L 4
L2 L3 L 2L 4
Ex 1: Signal-Flow Graph Models
26. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
..)21(1( LiLjLkiLjLLL
P
R
Y kk
Y s( )
R s( )
G1 G2 G3 G4 1 L3 L4 G5 G6 G7 G8 1 L1 L2
1 L1 L2 L3 L4 L1 L3 L1 L4 L2 L3 L2 L4
Ex 1: Signal-Flow Graph Models
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L 7 = - G 1G2 G 7G 6 H3
L 6 = - G 1G2 G 3G 4G 8 H3
L 8= - G 1G2 G 3G 4G 5 G 6 H3
Ex 2: SFG
LOOPS
