This document discusses signal flow graphs (SFG), which are a graphical technique used to analyze microwave networks in terms of reflected and transmitted waves. It introduces the basic components of SFGs, including nodes and branches, and how sources and loads are represented. The document outlines four rules for constructing and manipulating SFGs: the series rule, parallel rule, recursive rule, and node splitting rule. It provides examples of applying each rule. The document concludes by stating that SFGs can be used to derive expressions for input and output reflection coefficients Γin and Γout of microwave networks.

1. SIGNAL FLOW GRAPH
Name: Sudhakar Shastri
Register Number:14MCE1009
Submitted to :Prof. Niraj Kumar

2. Contents
 Introduction
 Basic components
 Representation of source and load
 Rules of SFG
 Construction of SFG
 Applications

3. Introduction
 SFG is a useful technique for analysis of
microwave networks in terms of reflected
and transmitted waves.
 Signal and Scattering parameters can be
described using a graphical technique called
Signal Flow Graphs (SFG).

4. BASIC COMPONETNS
 Nodes
 Branches

5. REPRESENTATION OF SOURCE AND
LOAD
 Source representation
 Load representation

6. RULES OF SFG
 Series rule
 Parallel rule
 Recursive rule (self loop)
 Node splitting rule

7. RULE 1:Series Rule
 S-parameters for paths in series can be
combined into one path by multiplying the s-
parameters.
V3=S32S21V1

8. RULE 2:Parallel Rule
 S-parameters for multiple paths connecting
the same two nodes can be combined into a
single path by adding the s-parameters.
V2=SaV1 + SbV2=V1(Sa + Sb)

9. RULE 3:Recursion Rule
When a node has a self loop of co-efficient S,
the self loop Can be eliminated by multiplying
coefficients of the branches feeding that node
by 1/(1-S)
V2=S21V1 + S22V2
V3=S32V2
Eliminating V2
V3=S32S21V1/1-S22

10. RULE 4:Node Splitting Rule
A node may be a split into two separate nodes
as long as the resulting flow graph contains,
once and only once, each combination of
separate input and output branches that
connect to the original node
V4=S42V2 =S21S42V1

11. APPLICATIONS
 Use signal flow graph to derive expressions
for Γin and Γout
For the two port network given below:

12. CONTD…

13. CONTD…