ECE203 Lecture 3,4

 For DC Circuits
 Any two-terminal, linear, bilateral, active dc network
can be replaced by an equivalent circuit consisting of
an equivalent voltage source(Thévenin’s Voltage
Source) and an equivalent series resistor (Thévenin’s
Resistance)
 For AC Circuits
 Any two-terminal, linear, bilateral, active ac network
can be replaced by an equivalent circuit consisting of
an equivalent voltage source(Thévenin’s Voltage
Source) and an equivalent series impedance
(Thévenin’s Impedance)
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

 DC Circuits  AC Circuits

 Thévenin’s theorem can be used to:
 Analyze networks with sources that are not in
series or parallel.
 Reduce the number of components required to
establish the same characteristics at the output
terminals.
 Investigate the effect of changing a particular
component on the behaviour of a network
without having to analyze the entire network
after each change.

 Procedure to determine the proper values
of RTh and Eth
 1. Remove the portion of the network across
which the Thévenin’s equivalent circuit is to
be found
 2. Mark the terminals of the remaining two-
terminal network. (The importance of this
step will become obvious as we progress
through some complex networks.)

 3. Calculate RTh by first setting all sources to zero
(voltage sources are replaced by short circuits, and
current sources by open circuits) and then finding the
resultant resistance between the two marked terminals.
(If the internal resistance of the voltage and/or current
sources is included in the original network, it must
remain when the sources are set to zero.)

 4. Calculate ETh by first returning all sources to
their original position and finding the open-
circuit voltage between the marked terminals.
(This step is invariably the one that will lead to
the most confusion and errors. In all cases, keep
in mind that it is the open-circuit potential
between the two terminals marked in step 2.)

 5. Draw the Thévenin equivalent circuit with the portion
of the circuit previously removed replaced between the
terminals of the equivalent circuit.

 Dual of Thévenin's theorem
 For DC Networks
 Any two-terminal, linear, bilateral, active dc network can
be replaced by an equivalent circuit consisting of an
equivalent current source(Norton’s Current Source) and an
equivalent parallel resistor (Norton’s Conductance)
 For AC Circuits
 Any two-terminal, linear, bilateral, active ac network can
be replaced by an equivalent circuit consisting of an
equivalent current source(Norton’s Current Source) and an
equivalent shunt admittance (Norton’s Admittance)

 Procedure
 1. Remove that portion of the network across
which the Norton equivalent circuit is found
 2. Mark the terminals of the remaining two-
terminal network

 3. Calculate RN by first setting all sources to zero
(voltage sources are replaced with short circuits,
and current sources with open circuits) and then
finding the resultant resistance between the two
marked terminals. (If the internal resistance of
the voltage and/or current sources is included in
the original network, it must remain when the
sources are set to zero.) Since RN = RTh the
procedure and value obtained using the approach
described for Thévenin’s theorem will determine
the proper value of RN.

 4. Calculate IN by first returning all the sources to
their original position and then finding the short-
circuit current between the marked terminals.
 5. Draw the Norton equivalent circuit with the
portion of the circuit previously removed
replaced between the terminals of the
equivalent circuit.

 Possible to find Norton equivalent circuit
from Thévenin equivalent circuit
 Use source transformation method
 ZN = ZTh
 IN = ETh/ZTh

 DC Circuits
A load will receive maximum power from a linear bilateral dc
network when its load resistive value is exactly equal to the
Thévenin’s resistance
RL = RTh
 AC Circuits
A load will receive maximum power from a linear
bilateral ac network when its load impedance is
complex conjugate of the Thévenin’s impedance
ZL = ZTh*

L
2
Th
R4
V
 2
2
2 L
LTh
R
RV
pmax = =
Resistance
network which
contains
dependent and
independent
sources

 The current I in any branch of a linear
bilateral passive network, due to a single
voltage source E anywhere in the network,
will equal the current through the branch in
which the source was originally located if the
source is placed in the branch in which the
current I was originally measured
 The location of the voltage source and the
resulting current may be interchanged without a
change in current

 Any element in a linear bilateral electrical
network can be replaced by a voltage source
of magnitude equal to the current passing
through the element multiplied by the value
of the element, provided the currents and
voltages in other parts of the circuit remain
the same.

 In any linear bilateral Electrical Network If in
any Branch have it’s initial resistance (or
impedance “Z” in case of AC) “R” conducting a
current of “I” through it, and if the resistance of
the branch is changed by a factor of ΔR (ΔZ in
case of AC), with it’s final resistance R+ ΔR (final
impedance Z+ΔZ), the final effect in various
branches due to the change in the resistance of
the branch can be calculated by injecting an
extra voltage source I ΔR (I ΔZ) along with the
resistance (impedance) in modified branch

Answer =
fig 2.b =
fig2.d =
fig 2.a + fig 2.c

 In any linear bilateral active network, any
branch within a circuit may be placed by an
equivalent branch, provided the replacement
branch has the same current through it and
the voltage across it as the original branch.

 In any electrical network which
satisfies Kirchhoff’s laws , the algebraic sum
of instantaneous power in all the branches is
equal to zero.
 Or, the algebraic sum of powers delivered by
all sources is equal to the algebraic sum of
powers absorbed by all elements

 Mathematically the Tellegen’s Theorem
states:

 Applicable only to circuit made of branches
in parallel with only one resistance and
voltage source in a branch
 In any network, if the voltage sources V1, V2… Vn
in series with internal resistances R1, R2… Rn
respectively, are in parallel, then the sources
may be replaced by a single voltage source V’ in
series with R’

 Limitations of Superposition theorem
 Superposition theorem only applicable to Linear
Networks
 Superposition theorem is not valid for power
responses; Applicable only for computing voltage
and current responses.
 Properties of Superposition theorem:
 Homogeneity or proportionality
 Additivity

 Thévenin's theorem limitations
 Applicable only for linear bilateral networks
 There should not be any magnetic coupling present in between the load & the
network.
 The power dissipation by the Thévenin equivalent circuit is not always identical
to the power dissipation by the real circuit
 The Thévenin equivalent has an equivalent I-V characteristic only from the point
of view of the load.
 Thévenin's theorem applications
 Thevenin's Theorem is especially useful in analyzing power systems and other
circuits where one particular resistor in the circuit (called the “load” resistor) is
subject to change, and re-calculation of the circuit is necessary with each trial
value of load resistance, to determine voltage across it and current through it.
 Source modelling and resistance measurement using the Wheatstone bridge
provide applications for Thevenin’s theorem.
 Norton’s theorem has the same applications and limitations as that of
Thévenin's theorem as they are equivalent

ECE203 Lecture 3,4

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ECE203 Lecture 3,4