Introduction to Network Analysis & Synthesis
Electrical network VS Electrical circuit
Examples of Networks
Network theory
Lumped Circuit elements
Classification of Networks
Linear and non-linear Network
Time-invariant and Time-variant Ntw
Passive and Active Network
Network is a combination of electrical
elements connected in any manner
(conductively, inductively or capacitively) to
perform a certain task governed by a certain
laws.
Excitation Response
Network
Electrical network is an interconnection of
electrical elements such as
Resistors
Inductors
Capacitors
Transmission lines
Voltage sources
Current sources and switches
Electrical circuit is a network which has a
closed path that gives the return path for the
flow of current.
Electrical Circuit Electrical Network
current has pass through all current hasn't pass through all
the elements the elements
electronic system electronic system
completely closed path not have a condition of closed
condition path
helpful in transporting the
electrical power to make
"electric lighting", and to
"recharge the storage batteries"
and "run electric motors".
Ex Power transmission system Communication system
(Internet)
Therfore,all the electric circuit
are networks, while a network
is not necessarily a electric
circui
Electrical network Electrical circuit
Filters electrical networks which pass
selective frequency signals.
Amplifiers/ Attenuators electrical networks
which are used to magnify or reduce signal
power level from input to output.
Equalizers electrical networks used to
respond frequency or phase distortions.
Matching networks electrical networks that
match source and load impedances
Network theory can be categorized into three
classes
i. Mathematical modeling of electromagnetic
phenomena
ii. Mathematical analysis of models of
individual elements and systems
iii. Synthesis and design of systems & devices
Electrical system analysis depends on
two fundamental theoretical concepts:
1. The lumped parameter circuit theory
based on laws: KVL and KCL, ohms laws,
etc…
2. Field theory based on Maxwell’s
equations for networks composed of
distributed elements
A circuit element is said to be lumped if the
instantaneous current entering one terminal
is equal to the instantaneous current leaving
at the other terminals otherwise it is
distributed elements
Eg. A television antenna is not a lumped
element as the current at the foot of the
antenna is not the same as that at the tip of
the antenna.
A large part of network theory deals with the
study of lumped circuits.
Lumped circuit is a result of interconnection
of lumped elements. Typical lumped
elements are:
1) Resistors
2) Capacitors
3) Inductors and
4) Voltage and current sources.
1) Resistors: An element which can be
characterized by a curve in the V–I plane
There are two types linear and non-linear
resistors.
a. Linear resistors: I = GV or V=RI
I
I = GV or
slope=G=1/R
Another characterization of linear network is that the
excitation and response of the network are related by a
linear differential equation
b. Non linear resistors: i-v curve is not straight
line, two non- linear resistors are tunnel diode
and SCR(silicon controlled rectifier).
-V BD
0.7V
2) Capacitors: characterized by a curve in the
v-q plane is called a capacitor .
a. linear capacitor :- its characteristic is a straight line
passing through the origin of the v-q plane.
q CV
The current charge relation being
i dq dt iC
dv (t )
dt
The energy in the linear capacitor
b. Non linear capacitor:- is characterized by a
v-q curve other than a straight line through the
origin
A nonlinear capacitor is (metal oxide
semiconductor capacitor)characterized by
(for a voltage-controlled capacitor) 𝑞 = 𝑓(𝑣)
(for a charge-controlled capacitor) 𝑣 = ψ(𝑞).
For a voltage controlled capacitor the current through the
capacitor is
dq (t ) df (v) dv (t )
i (t )
dt dv dt
dv(t )
Or i (t ) C (v)
dt
where C (v) df (v) / dv
3) Inductors: An inductor is called a linear inductor,
if its characteristic is a straight line passing through
the origin in the 𝒊 − Øplane.
Li
The voltage
relation being
flux linkage
v d / dt
di (t )
vL
dt
A nonlinear inductor is characterized by 𝒊 −
Ø curveother than a straight line through the origin
A nonlinear inductor is characterized by
For a current controlled inductor ∅ = 𝑓(𝑖)
for a flux-controlled inductor 𝑖 = ψ(Ø)
Nonlinear inductors can be used in a frequency conversion,
memory and storage.
current-controlled inductor the voltage
across the inductor is
4) Voltage and current sources
a) Independent source
b) Dependent source
Independent current source:
It is a 2-terminal sources that maintains a specific current through it
regardless of the voltage across it terminals. The circuit symbol of
independent current sources is given below,
Independent voltage source:
It is a 2-terminal sources that maintains a specific voltage across its
terminals regardless of the current through it. The circuit symbol of
independent voltage sources is given below,
b) Dependent
It is a 2-terminal sources that generates a voltage
or a current that is determined by a voltage or
current at a specified location in the circuit .
A dependent or controlled source is said to be
voltage or current controlled if its terminal
behavior is controlled by another voltage or
current. This leads to four different controlled
sources which are:
1.Voltage-controlled voltage source(VCVS)
2. Voltage-controlled current source(VCCS)
3. Current-controlled voltage source(CCVS)
4. Current-controlled current source(CCCS)
1. Classification of Networks
a) Linear
b) Non-linear
The relationship between the voltage and current is
described by a linear equation. Consider two
networks N1, and N2
Linear and Non-linear networks
A system (network) is linear if
(i) the principle of superposition and
(ii) the principle of proportionality hold
By the superposition principle
If for the given excitation-response pairs networks e1 (t ), r1 t and
e2 (t ), r2 t then if the excitation were e(t ) e1 (t ) e2 (t ), the response would
be
r (t ) r1 (t ) r2 (t )
By the proportionality principle
If the excitation were C1e1 (t ), where C1 a constant is, then the response woul
be C1 r1 (t ),
We say that network N 1 is linear and N2
is nonlinear as the principle of superposition holds for N1 but not for N2
2. Time-invariant and Time-variant Networks
The network parameter is dependent on
time.
Let a linear resistor be characterized by v(t ) R(t )i(t ) where R (t )
is a prescribed time function
A time – invariant network is characterized by a constant coefficient
equation
Time-invariant
the response (output) depends on the shape of
the excitation (input) but not on the time of application. A network
3.Passive and Active Networks
Let v(t) and i(t) be the two voltage and current at the terminals of a
network. Then the energy delivered to the network is given by
A network is said to be passive if, and only if , the energy
delivered to the network is non-negative for all time and
input
W(t,t0) + E(t0) ≥ 0 where E(t0) is the energy in the
network at t = t0
Basis Active Component Passive Component
Nature of source Deliver or produce Utilizes or store energy
energy in the form of in the form of voltage
voltage or current or current
Examples Diodes,Transistors,SCR Resistor,
,LED,Integrated Capacitor,Inductor
circuits,Voltage
¤t sourses
Function of the Devises which produce Devises which store
component energy in the form of energy in the form of
voltage or current voltage or current
Power Gain They are capable of They are incapable of
providing power gain providing power gain
Flow of current Active component can Passive component can
control the flow of not control the flow of
current current
The active components The passive
requires an external components do not
source for the requires any external
Active Networks
Assignment
- Detail
Characteristics
- Examples
