ECE203 Lecture 2
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Transcript of ECE203 Lecture 2
07, July, 2014
Lecture 4
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits
Corollaries of the Maxwell equations in the low-frequency limit
Accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
Also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule)
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,
or: The algebraic sum of currents in a network of conductors meeting at a point is zero.
Based on principle of conservation of electric charge
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
The current entering any
junction is equal to the current
leaving that
junction. i1 + i4 =i2 + i3
Also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule
The directed sum of the electrical potential differences (voltage) around any closed network is zero,
or: More simply, the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop,
or: The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.
Based on the conservation of energy whereby voltage is defined as the energy per unit charge.
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
The sum of all the voltages around the
loop is equal to zero. v1 + v2 + v3 - v4 = 0
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Applicable only to lumped network models
KCL is valid only if the total electric charge, Q , remains constant in the region being considered
KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop.
KCL and KVL only apply to circuits with steady currents (DC). However, for AC circuits having dimensions much smaller than a wavelength, KCL, KVL are also approximately applicable.
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Series circuit – Voltage divider
Same current flows; Voltage drops
proportional to value of resistors/impedance;
Different voltage from single source; So
called voltage divider
Power in series circuit: Sum of powers in
each resistor in series
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Current from source divides in all branches
of parallel circuit; So called current divider
Power in parallel circuit: Sum of powers in
each resistor in parallel
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Important fundamental theorems of network analysis. They are the
Superposition theorem
Thévenin’s theorem
Norton’s theorem
Maximum power transfer theorem
Substitution theorem
Millman’s theorem
Reciprocity theorem
Tellegen’s theorem
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
The current through, or voltage across, an
element in a linear bilateral network is
equal to the algebraic sum of the currents
or voltages produced independently by
each source.
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Used to find the solution to networks with two or more sources that are not in series or parallel.
The current through, or voltage across, an element in a network is equal to the algebraic sum of the currents or voltages produced independently by each source.
Since the effect of each source will be determined independently, the number of networks to be analyzed will equal the number of sources.
A circuit is linear when superposition theorem can be used to obtain its currents and voltages
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
For a two-source network, if the current produced by one source is in one direction, while that produced by the other is in the opposite direction through the same resistor, the resulting current is the difference of the two and has the direction of the largerIf the individual currents are in the same direction, the resulting current is the sum of two in the direction of either current
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
Superposition theorem can be applied only to voltage and current
It cannot be used to solve for total power dissipated by an element
Power is not a linear quantity
Follows a square-law relationship
The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source
Diode and transistor circuits will have both dc and ac sources
Superposition can still be applied
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
For applying Superposition theorem:-
Replace all other independent voltage sources with a short circuit (thereby eliminating difference of potential. i.e. V=0, internal impedance of ideal voltage source is ZERO (short circuit)).
Replace all other independent current sources with an open circuit (thereby eliminating current. i.e. I=0, internal impedance of ideal current source is infinite (open circuit).When this theorem is applied to an ac circuit, it has to be remembered that the voltage and current sources are in the phasor form and the passive elements are impedances.
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University
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 - K20-07-2014.Jeya Prakash - Kalasalingam University
DC Circuits AC Circuits
ECE203 - Network Analysis - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.Jeya Prakash - Kalasalingam University
DC Circuits AC Circuits
ECE203 - Network Analysis - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.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 - K20-07-2014.Jeya Prakash - Kalasalingam University
DC CircuitsA 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 - K20-07-2014.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K20-07-2014.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 - K20-07-2014.Jeya Prakash - Kalasalingam University
ECE203 - Network Analysis - K20-07-2014.Jeya Prakash - Kalasalingam University