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


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


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


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.


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


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


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


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.


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


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


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


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.


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)


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.)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.)


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)


DC Circuits AC Circuits


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 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*



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



Engineering

ECE203 Lecture 2