Signal Flow Graph

Prof. D. Kannadassan,

School of Electronics Engineering

ECE102 - Microwave Engineering Fall 2012_13 1

Problems with Port parameter analysis

• Port parameters like [Z], [Y] and [S], the fundamental definition on the

confirmation is “current/incident components at all ports will flow inside”

• So, they all can be useful for single network analysis, but they fails or

become complex when series/parallel connection of networks are made. To

solve this issue, ABCD parameter and Signal Flow graph were introduced.

• Signal flow graph is a graphical, easy, more effective and flexible method

to solve

Signal Flow Graph

• A signal flow graph (SFG) is a graphical representation of signals that are

flowing from one port to another, or ratio of signals. Here in our

Microwave Engineering, we are going to use S parameters as key element

in Signal Flow graph.

• Primary components:

– Nodes: To represent the system variables. The each port has two nodes, 1.

incident/entering ( ai ) and 2. reflected/leaving ( bi ) components

– Braches: Directed path between nodes, representing the flow of signal from

one node to other. Every branch will be associated with S parameters

(reflection or Transmission coefficients)

≡

• Signals (branches) should travel in only one direction

– If a braches “m” is traveling from Node 2 to 1. The reverse path, 1 to 2,

should be defined by another branch, may be “n”

1 2

m

n

Note carefully..

Two Port N/W

Load

Source

Cascading of three diff n/w

Solving SFG and Rules

• Using SFG, we can solve a network problem for a particular parameter

calculation, signals. It’s also useful to reduce the unwanted components by

reducing with balance in network.

• The solvation can be done by “Decomposition”, they have rules

• Decomposition Rules

– Rule-1 (Series Rule): Two braches, whose common node has one incoming and one

outgoing braches, may be combined to form a single branch. The resultant branch will

have the product of confidents of original two branched.

– Rule-2: (Parallel Rule) Two branches, are traveling from one common node to another

common node, shall be combined to a single branch. The new branch will be addition on

both the coefficients of original two branches

– Rule-3: (Self-loop Rule) A node with one self loop (the branch which starts and ends in

same node) of coefficient Sij can be eliminated by multiplying 1/(1- Sij ) with coefficients

the feeding branches

– Rule-4: (Splitting Rule) A node may be split into two (in different variable name), as

long as the resulting SFG contains each combination of separate branches (input/output)

that connected to original node

Only for outgoing branch

Problem – 1.7

Construct a Signal Flow graph for the following network

Determine Input reflection coefficient Γin using Signal flow graph

• Solution:

• Step -1: Construction of Signal Flow Graph. Check the incoming/outgoing

signal of network carefully

• Starting the solution need some logical idea, it will come by solving many

problems.

• Step-2: Use splitting rule for the node a2

• Step-3: Series Rule at node a2’

Original common Node

Remember:

While duplication

of nodes, there

should not be any

change in

operation of

network

• Step-4: Apply Self-loop rule at b2

• Step-5: Use series rule at b2

• Step-6: Use parallel rule at a1 and b1

Γin

Problem – 1.8

• Find the input reflection coefficient Γin at port-1 and P2/P1

P1

P2

P3

Γ2

Γ3

00

0

00

23

2312

12

S

SS

S

SΓin