NETWORK ANALYSIS AND SYNTHESIS
Chapter 1
Introduction
INTRODUCTION
3 key words: Excitation, network and response
Network – Any structure containing interconnected elements.
Circuit –physical structure constructed from electrical
components
Network analysis:
o Determining the response given the excitation and the
network .
Network synthesis:
o To design the network given the excitation and the desired
response .
Excitation Network Response
1.1 SIGNAL ANALYSIS
For electric networks, excitation and response are
given in terms of voltages and currents.
These signals are a function of time and frequency.
We use transforms (Fourier and Laplace) to transform
from time domain to frequency domain and vice versa.
HOW A SIGNAL IS DESCRIBED IN TERMS
OF BOTH FREQUENCY AND TIME
Example:
s (t ) Ao Sin( wo t o )
1.2 NETWORK ANALYSIS
Characterization of the excitation and response
is only half of the problem.
The other half is describing the network.
BASIC DEFINITIONS
Linear system
A network is linear if and only if
c1e1(t) c1r1(t)
System
c2e2(t) c2r2(t)
System
c1e1(t) +c2e2(t) c1r1(t)+c2r2(t)
System
i.e. if it satisfies the principle of superposition and
proportionality
BASIC DEFINITIONS
Passive
A linear network is passive if
a) The energy delivered is non negative for any excitation.
b) No voltages or currents appear between any two terminals
before excitation is applied.
Reciprocal
A network is said to be reciprocal if when the point of
excitation and response are interchanged, the relation between
excitation and response remains the same.
RECIPROCITY EXAMPLE
I= 0.35294A
Non-linear element
I = 0.3798A I = 0.3397A
The inclusion of controlled sources or active elements may also
destroy reciprocity.
A non-bilateral element, such as a diode, destroys reciprocity
BASIC DEFINITIONS
Causal
A network is causal if the response is zero before any
excitation.
e(t ) 0 for t T then r (t ) 0 for t T
Time invariant
A network is time invariant if e(t ) r (t ) then e(t T ) r (t T )
i.e. a network that doesn’t contain time variant
components.
IDEAL MODELS
The following ideal models are useful in signal
processing
Amplifier r (t ) ke (t )
Differentiator d
r (t ) e(t )
dt
Integrator r (t ) e(t )dt
Time Delay
r (t ) e(t T )
IDEAL ELEMENTS
The elements encountered most are resistor,
capacitor and inductor.
When the currents and voltages are given as a
function of time
v(t ) Ri (t ) Resistor
di (t )
v(t ) L Inductor
dt
t
1
v(t ) i ( x)dx v(0) Capacitor
C0
IDEAL ELEMENTS
In frequency domain, using Laplace transform
1.3 NETWORK SYNTHESIS
In network synthesis, we are given the excitation
and response and we are required to synthesize the
network from the system function.
R( s)
H (s)
E ( s)
The end points of elements are called terminals.
A port is defined as any pair of two terminals into
which energy is supplied, drawn or variables
measured.
DRIVING POINT SYNTHESIS
Deriving point immittance: the excitation and
response are taken from the same port.
A driving point impedance is thus given as
V (s)
Z ( s)
I (s)
TWO PORT NETWORK
Transfer function: excitation and response are taken
from different ports.
The transfer function can take different forms.
V2 ( s )
Z 21 ( s )
I1 ( s )
V2 ( s )
H (s)
V1 ( s )
FILTER DESIGN
One of the most important aspect of transfer
function synthesis.
A filter is defined as a network that passes a certain
portion of a frequency and blocks the remainder of
the spectrum.
Ideal Low pass filter
FILTER DESIGN
Two aspects of filter design
1. Obtaining a suitable and realizable
transmittance H(s) given the specification.
2. Realizing the transmittance H(S).
FILTER DESIGN
The first step is an approximation step.
Because there are no ideal filters.
End!
