Network analysis and synthesis
(ECEg3122)
Contents:
Chapter one – Introduction (analysis)
Chapter two – Network topology (Analysis)
Chapter three – Two-port network (Analysis)
Chapter four - Network function (synthesis)
Chapter five – Elements of realizability theory and
Network synthesis (synthesis)
Chapter six – Introduction Filter Network
(synthesis)
1
Chapter - one
Introduction
Introduction:
• Analysis and Design:—continuous processes for Improvement
of response ---- (Basis of Research and Development
activities)
2
NETWORK ANALYSIS
• Network is a system with interconnected electrical elements. Network and
circuit are the same.
• The only difference being a circuit shall contain at least one closed path.
3
TYPES OF NETWORKS
4
Cont..
5
6
Ohms Law
7
Cont..
8
Chapter - two
Network Topology
• A physical network is an assembly of interconnected
branches.
• Example, a telephone network, a power system, a
transport network, a computer network, constitute
physical networks.
• The geometrical interconnection of the various branches
is called network topology
• The connection of the network, shown by replacing all
physical elements by replacing all physical elements by
lines is called a graph.
9
Cont..
10
Elementary Concepts
11
Graphs ↔ Networks
12
Graphs ↔ Networks
• A branch represents a single element such as a
voltage source or a resistor.
• A node is the point of connection between
two or more branches.
• A loop is any closed path in a circuit.
• A network with b branches, n nodes, and l
independent loops will satisfy the
fundamental theorem of network topology:
b l n 1
13
Loop and cut set Analysis
14
Loop and cut set Analysis
15
Cont..
16
Loop Analysis
17
Cont..
18
Cut set Analysis
19
Cont..
20
Cont..
A fundamental cut set w.r.t. that tree is a cut set that only contains one
branch of the tree.
There may be many fundamental cut sets w.r.t. a given tree.
21
Chapter – Three
Two-port Network
What is a port?
• It is a pair of terminals through which
a current may enter or leave network.
One port or two terminal
circuit
Two port or four terminal circuit
• It is an electrical network with
two separate ports for input
and output.
• No independent sources.
22
Impedance parameters
23
Cont..
24
Cont..
25
Cont..
26
Cont..
27
Admittance parameters[y]
28
Cont..
29
Cont..
30
Cont..
31
Hybrid parameters
32
Cont..
33
Cont..
34
Transmission parameters
35
Cont..
36
Cont..
37
Two Port Parameter Conversions :
38
Interconnection Of Two Port Networks
39
Example
40
Cont..
41
CHAPTER – FOUR
NETWORK FUNCTIONS
INTRODUCTION:
42
Cont..
43
Cont..
44
Network function types
45
Cont..
46
Cont..
(ii) Transfer functions:
• If the excitation and response are measured at
different sets of terminals(see fig. below), then the
corresponding network function is called a transfer
function.
47
poles and zeros of network function :
48
Cont..
Example:
1.
2. For the network shown, write the mesh equation in terms of (a) differential
equations and (b) the complex-frequency variable s.
3. For the network shown, write the node equation in terms of (a) differential
equations and (b) complex-frequency form.
49
Cont..
Assignment: (30%)
1. For the figure given below, the only information we posses about the system
in black box is: (1) it is an initially inert linear system; (2) when Vi(t) =
𝜹 𝒕 , then
With this information, determine what the excitation Vi(t) must be in order to produce a
response V0(t) = t𝒆−𝟐𝒕 u(t).
2. Find the Z and T parameters of the circuit.
3. Find the transmission parameters for the single-element two-port networks.
4. What is the y parameter presentation of the circuit.
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