NETWORK ANALYSIS AND SYNTHESIS
Subject code-NEC-301
Unit -1 and 2 Slides
(Session 2014-15)
BY
Mr. Rakesh Kumar
&
Mr. Abhay Goyal
ECE Department
ABES Engineering College
Ghaziabad,u.p
Introduction
– It is concerned with determining
the response, given the excitation and the network.
Network Synthesis – In this, the problem is to design
the network given the excitation and the desired
response.
Network Analysis
SIGNAL ANALYSIS
 Excitation
and response are given in
terms of voltage and current
 Signal can be described well in terms of
spectral or frequency information
 Time and frequency translation can be
done by Fourier series ,fourier integral
and the Laplace transform.
 Consider
the sinusoidal signal
Representation of signal in time domain
Representation of signal amplitude & phase against
frequency
 Consider
the signal having 2n+1 sinusoidal
components
Then , Discrete amplitude and phase spectrum will be given as
 Consider
the case having infinite spectral lines. Then,
Then Amplitude and phase spectrum will be continuous
Inference
 For
a real periodic signal, magnitude plot
is always an even function of frequency
and phase plot is always an odd function
of frequency.
 The spectrum of continuous time period
signal is discrete and a periodic in nature.
Complex frequency
Where real part describe growth and decay of the
amplitudes of signals
While imaginary part describe the angular
frequency
 Consider the case when the velocity is inclined at
any arbitrary angle.
Rotating phasor with exponentially decreasing amplitude
Rotating phasor with exponentially increasing amplitude
Therefore, generalized cisoidal signal
Describe the growth & decay of the amplitudes in addition to
angular frequency in the usual sense.
Conclusion
 when
,Sinusoid is undamped
 When jw = 0,signal is an exponential signal.
 When
then the signal is a constant.
Network Analysis
This part consist of characterizing the network itself in
terms of time & frequency and determining how the
network behaves as a signal processor.
Basic Definitions
I.
a)
b)
Linear
A linear system holds
Principal of superposition
Principal of proportionality
2) Passive
A linear network is passive if
a) Energy delivered to the network is non
negative for any arbitrary excitation.
b) If no voltage or current appear between
any two terminals before an excitation is
applied.
3) Reciprocal
A network is said to be reciprocal if when
the point of excitation and measurement
of response are interchanged.
4) Causal or Non- Causal
A system is said to be causal if the output at any
time depends only on present and past values of
input otherwise the system is Non-causal.
5) Time Invariant
A system is said to be time invariant if time
shift in input signal results in an identical
time shift in the output signal.
Ideal models
1) Amplifier
An amplifier scales up the magnitude of the input.
2) Differentiator
The input signal is differentiated and possibly scaled up or
down.
3) Integrator
The output signal is the integral of the input.
4) Time delayer
The output is delayed by an amount T, but retains the same
wave shape as input.

Consider triangular pulse as the input signal, the different
output signal from amplifier, differentiator, integrator and
delayed output are given as
Ideal elements
Current voltage relationship as function of time
 Expressing
the previous function as
complex frequency variable,s we have
Conclusion
In time domain, voltage-current relationship are
given in terms of differential equations while in
complex frequency domain, the voltage- current
relationship are expressed in algebraic
equations. Thus algebraic equations are more
easily solved than differential equations.
Network synthesis
In this, the problem is to design the network given
the excitation and the desired response.
Driving point impedance is given as
Signals and waveforms
 General
Characteristics of signals
1)Periodic or aperiodic
Periodic signal repeats itself with minimum fundamental
period,T.
Where,T is the period of the Signal
In Aperiodic Signal, Pulse pattern do not repeat after a
certain finite interval,T.
2) Even or odd
An even function obeys the relation
s(t) = s(-t)
An odd function obeys the relation
s(t) = -s(-t)
General Descriptions of signals
1)Time constant
It determines how quickly a waveform decays.
2) RMS value
Root mean square value of a periodic waveform e(t) is
3) DC value
Dc value of a waveform has meaning only when the
waveform is periodic.
4) Duty cycle
it is defined as the ratio of the time duration of
the positive cycle to of a periodic waveform to
the period,T.
5) Crest factor
It is defined as the ratio of peak voltage of a periodic
waveform to the rms value with dc component removed
Step function and associated waveforms
The unit step function u(t) is defined as
Sgn function
It is defined as
Ramp function
It is shown as
The unit impulse
The unit impulse function has zero width,
infinite height and an integral (area) of one.
Kirchhoff’s current law
At any node (junction) in an electrical circuit, the sum
of currents flowing into that node is equal to the sum of
currents flowing out of that node
Here, i2+i3=i1+i4
Kirchhoff’s voltage law
The directed sum of the electrical potential differences
(voltage) around any closed network is zero,
Here,v1+v2+v3-v4=0
Superposition theorem
In any linear bilateral circuit having more than one source, the
response in any one of the branches is equal to algebraic
sum of the responses caused by individual sources while
rest of the sources are replaced by their internal resistances.
 Consider the linear network with n voltage and m current
sources
Figure-Superposition in linear circuits
Thus by superposition principal, the total current is due to
all of the sources is equal to the algebraic sum.
Network elements
1) Resistor
It defines linear proportionality relationship between v(t)
and i(t)
V(t)= R i(t)
i(t)= G v(t)
Where R is in ohms and G in mho
G = 1/R
2) Capacitor
V-I relationship are given as
3) Inductor
The V-I relationship between current and voltage are given
as
Initial and final conditions
1)Initial conditions for a capacitor
The voltage-current relationship at t = 0+ is
If i(t) does not contain impulses or derivatives of
impulses. then, Vc(0+) = Vc(0-)
If q is the charge on the capacitor at t = 0-,the initial
voltage is
When there is no initial charge on capacitor then Vc(0+) = 0
2)Initial conditions for an inductor
The voltage-current relationship at t = 0+ is
If v(t) does not contain impulses. then, iL(0+) = iL(0-)
When there is no initial current current then iL(0+) = 0 which
corresponds to an open circuit at t = 0+
Final conditions for sinusoidal excitations
Step and impulse response
Solution of network equations
 In
this section we will apply our knowledge of
differential equations to the analysis of linear
networks.
 Two important points in network analysis are
I. The writing of network equations
II. The solution of these same equations
 Network equations can be written on a mesh,
node or mixed basis depending upon the
unknown quantities.
THE END