Lecture No 7
“MASON's GAIN FORMULA”
Textbook:
Section:
Chapter 3
3.2.3
Instructor: Sqn Ldr M Amir Tahir
Number of Slides: 14
College of Aeronautical Engineering (CAE), NUST
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Objectives
• Purpose of Mason Gain Formula
• Introduction of definitions required for formula
understanding
• To discuss mason’s gain formula
• Examples
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Mason’s
Formula
• Mason’s gain formula is a procedure to find the transfer function of
either a block diagram or a signal flow graph
• Here we only consider rules for signal flow graph, but the same
rules apply to block diagram as well
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Mason’s
Formula
• Definitions

Source Node: A node for which the signals flow only away from the
node

Sink Node: A node for which signals flow only towards the node
(sometimes we need to create a sink node by adding a branch of unity
gain)

Path: A continuous connection of branches from one node to another
with all arrowheads pointing in the same direction
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Mason’s
Formula
• Definitions

Loop: A closed path (with all arrowheads in the same direction) in which
no node is encountered more than once (i.e a node is encountered only
once)

Forward Path: A path that connects a source node to a sink node, in
which no node is encountered more than once (i.e a node is encountered
only once)

Path Gain: Product of the transfer functions of all branches that forms
the path
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Mason’s
Formula
• Definitions

Loop Gain: Product of the transfer functions of all branches that forms
the loop

Non-Touching: Two loops are non-touching if they have no node in
common
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Mason’s
Formula
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Mason’s
Formula
• Example:
Signal Flow Graph
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Mason’s
Formula
• Example:
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Mason’s
Formula
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Mason’s
Formula
p=2
; # of farward paths
M1 = G1G2G3 ; Path gain of farward path M1
M2 = G1G3
; Path gain of farward path M2
# of Loops = 3 Loop gains (1) - G1G2H1 (2) - G2H2 (3) - G3H3
Non-touching loops (1,3) (2,3)
Product of non-touching loops taken two at a time
G1G2G3H1 H3
& G2G3H2 H3
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Mason’s
Formula
• Example:
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Summary
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