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

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.


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)


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 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

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


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

Engineering

resistance network

original network

entire network

thvenins equivalent

active ac network

active dc network

norton equivalent circuit

linear bilateral ac