ece203 lecture 3,4
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ECE203 Lecture 3, 4 SlidesTRANSCRIPT
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.)
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.)
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.)
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
5. Draw the Thévenin equivalent circuit with the portion
of the circuit previously removed replaced between the
terminals of the equivalent circuit.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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)
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
DC Circuits
AC Circuits
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
Possible to find Norton equivalent circuit
from Thévenin equivalent circuit
Use source transformation method
ZN = ZTh
IN = ETh/ZTh
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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*
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
L
2
Th
R4
V
22
2 L
LTh
R
RVpmax = =
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
Mathematically the Tellegen’s Theorem
states:
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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’
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
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 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University