report on Thevenin's theorem

1. SUBJECT: CIRCUIT THEORY & NETWORKS
DEPARTMENT: ELECTRONICS AND COMMUNICATION ENGINEERING
YEAR: SECOND SEM: THIRD
TOPIC: THEVENIN’S THEOREM
SUBMITTED TO- PROF. JOYITA CHAKRABORTY (SUBJECT TEACHER)
SUBMITTED BY-
1. ARPITA BANERJEE
2. SOUMYA GHOSH
CHOWDHURY
3. ROHAN HORE
4. RANIK AHAMED

2. 1.0 THEVENIN’S THEOREM
1.1.0 ABSTRACT
1.1.1 CIRCUIT THEOREMS – SCOPE AND LIMITATIONS
1.2.0 INTRODUCTION
1.2.1 ORIGINATION
1.2.2 THEVENIN’S EQUIVALENT CIRCUIT
1.2.3 EXPLANATION
1.2.4 THEVENIN VOLTAGE
1.2.5 THEVININ RESISTANCE
1.2.6 WHY THEVENIN'S THEOREM IS NOT APPLICABLE TO
NON-LINEAR CIRCUITS?
1.2.7 CAN THEVENIN THEOREM BE APPLIED TO CIRCUIT
HAVING A.C SOURCES?
1.2.8 WHY THEVENIN EQUIVALENT CIRCUIT IS NOT VERY
USEFUL AT MICROWAVE FREQUENCIES?
1.2.9.1 THE BASIC REQUIREMENTS TO PROOF THEVENIN
THEOREM IN LAB
1.2.9.2 PROCEDURE
1.2.10 APPLICATIONS
1.2.11 ADVANTAGES
1.2.12 LIMITATIONS
1.3.0 CONCLUSION
1.3.1 REFERENCES

3. 1.1.0 ABSTRACT
1.1.1 CIRCUIT THEOREMS – SCOPE AND LIMITATIONS
SOURCES: DR. T. S. RATHORE, SENIOR MEMBER, IEEE DEPARTMENT OF
ELECTRICAL ENGINEERING, INDIAN INSTITUTE OF TECHNOLOGY, GOA,
PHARMAGUDI, PONDA, GOA 403401 INDIA
 THEVENIN THEOREMS
THIS IS THE FIRST PART OF THREE PARTS OF THE ABOVE TITLED PAPER.
THIS PART WILL DEAL WITH SOURCE TRANSFORMATION AND
THEVENIN/NORTON THEOREMS. THE TRADITIONAL SOURCE
TRANSFORMATION GIVES ONLY ONE CURRENTTO-VOLTAGE OR
VOLTAGE-TO-CURRENT EQUIVALENT CIRCUIT. IT IS SHOWN THAT THERE
IS A LARGE NUMBER OF CURRENT-TO-VOLTAGE, VOLTAGETO-CURRENT,
CURRENT-TO-CURRENT AND VOLTAGE-TO-VOLTAGE SOURCE
TRANSFORMATIONS POSSIBLE UNDER CERTAIN GIVEN TERMINAL
CONDITION. THIS RESULT IS NOT GIVEN IN THE TEXT BOOKS. NEXT,
RATHORE’S ONE-CIRCUIT AND ONE-STEP PROCEDURE FOR EVALUATION
OF THE TWO PARAMETERS OF THEVENIN AND NORTON EQUIVALENT
CIRCUITS IS DESCRIBED. UNLIKE MURTI’S METHOD, IT CAN HANDLE THE
CONTROLLED SOURCES AS WELL.
THERE ARE CIRCUITS WHOSE THEVENIN EQUIVALENTS ARE
INTERESTING. SOME SUCH CIRCUITS WHICH ARE DESCRIBED HERE ARE-
(i) CIRCUITS WITHOUT ANY INDEPENDENT SOURCE;
(ii) CIRCUITS HAVE LOOP OR NODE METHOD-BASED DELTA ZERO AND
(iii) (III) CIRCUITS WHICH HAVE THEVENIN EQUIVALENT ACROSS A
VOLTAGE SOURCE.

4. 1.2.0 INTRODUCTION
THEVENIN’S THEOREM IS THAT ANY LINEAR ACTIVE NETWORK CONSISTING OF INDEPENDENT
OR DEPENDENT VOLTAGE AND CURRENT SOURCE AND THE NETWORK ELEMENTS CAN BE
REPLACED BY AN EQUIVALENT CIRCUIT HAVING A VOLTAGE SOURCE IN SERIES WITH A
RESISTANCE, THAT VOLTAGE SOURCE BEING THE OPEN CIRCUITED VOLTAGE ACROSS THE OPEN
CIRCUITED LOAD TERMINALS AND THE RESISTANCE BEING THE INTERNAL RESISTANCE OF THE
SOURCE.
1.2.1 ORIGINATION
A TEACHING INSPECTOR, LÉON CHARLES THÉVENIN AT THE ÉCOLE SUPÉRIEURE DE
TÉLÉGRAPHIE IN 1882, HE BECAME INCREASINGLY INTERESTED IN THE PROBLEMS OF
MEASUREMENT IN ELECTRICAL CIRCUITS. AS A RESULT OF STUDYING KIRCHHOFF'S CIRCUIT
LAWS AND OHM'S LAW, HE DEVELOPED HIS FAMOUS THEOREM, THÉVENIN'S THEOREM,[1]
WHICH
MADE IT POSSIBLE TO CALCULATE CURRENTS IN MORE COMPLEX ELECTRICAL CIRCUITS AND
ALLOWING PEOPLE TO REDUCE COMPLEX CIRCUITS INTO SIMPLER CIRCUITS CALLED
THÉVENIN'S EQUIVALENT CIRCUITS.
HÉVENIN CONSULTED SEVERAL SCHOLARS WELL KNOWN AT THAT TIME, AND CONTROVERSY
AROSE AS TO WHETHER HIS LAW WAS CONSISTENT WITH THE FACTS OR NOT. HE DIED IN PARIS.
SHORTLY BEFORE HIS DEATH HE WAS VISITED BY A FRIEND, J. B. POMEY, AND WAS SURPRISED
TO HEAR THAT HIS THEOREM HAD BEEN ACCEPTED ALL OVER THE WORLD IN 1926.
1.2.2 THEVENIN’S EQUIVALENT CIRCUIT:
AS FAR AS THE LOAD RESISTOR RL IS CONCERNED, ANY
COMPLEX “ONE-PORT” NETWORK CONSISTING OF MULTIPLE RESISTIVE CIRCUIT ELEMENTS AND
ENERGY SOURCES CAN BE REPLACED BY ONE SINGLE EQUIVALENT RESISTANCE RS AND ONE
SINGLE EQUIVALENT VOLTAGE VS. RS IS THE SOURCE RESISTANCE VALUE LOOKING BACK INTO THE
CIRCUIT AND VS IS THE OPEN CIRCUIT VOLTAGE AT THE TERMINALS.

5. 1.2.3 EXPLANATION:
STEP- 1 :
LET US CONSIDER A SIMPLE DC CIRCUIT AS SHOWN IN THE FIGURE
ABOVE, WHERE WE HAVE TO FIND THE LOAD CURRENT IL BY THE THEVENIN’S THEOREM. IN ORDER
TO FIND THE EQUIVALENT VOLTAGE SOURCE, RL IS REMOVED FROM THE CIRCUIT AS SHOWN IN THE
FIGURE BELOW AND VOC OR VTH IS CALCULATED.
STEP-2 :
NOW, TO FIND THE INTERNAL RESISTANCE OF THE
NETWORK (THEVENIN’S RESISTANCE OR EQUIVALENT RESISTANCE) IN SERIES WITH THE OPEN
CIRCUIT VOLTAGE VOC , ALSO KNOWN AS THEVENIN’S VOLTAGE VTH, THE VOLTAGE SOURCE IS
REMOVED OR WE CAN SAY IT IS DEACTIVATED BY A SHORT CIRCUIT (AS THE SOURCE DOES NOT
HAVE ANY INTERNAL RESISTANCE).
STEP-3 :
STEP-4 :
As per Thevenin’s Statement, the load current is determined by
the circuit shown above and the equivalent Thevenin’s circuit is obtained.Where,VTH is the Thevenin’s equivalent
voltage. It is an open circuit voltage across the terminal AB known as load terminal.
RTH is the Thevenin’s equivalent resistance, as seen from the load terminals where all the sources are replaced by their
internal impedance rL is the load resistance.

6. 1.2.4 THEVENIN VOLTAGE:
THE THEVENIN VOLTAGE E USED IN THEVENIN'S
THEOREM IS AN IDEAL VOLTAGE SOURCE EQUAL TO THE OPEN CIRCUIT VOLTAGE AT THE
TERMINALS. IN THE EXAMPLE BELOW, THE RESISTANCE R2 DOES NOT AFFECT THIS VOLTAGE AND
THE RESISTANCES R1 AND R3 FROM THE VOLTAGE DIVIDER.
1.2.5 THEVININ RESISTANCE:

7. 1.2.6 WHY THEVENIN'S THEOREM IS NOT APPLICABLE TO NON-LINEAR
CIRCUITS?
– THE THEVENIN'S THEOREM CAN BE USED IN NON LINEAR CIRCUITS, AS LONG AS IT'S USED AT
LINEAR (OR APPROX LINEAR) PARTS OF THE CURVE.
FOR EXAMPLE, LET'S LOOK AT COMMON EMITTER AMPLIFIER.
THIS CIRCUIT HAS NON LINEAR ELEMENTS. BUT AS LONG AS THE
TRANSISTOR IS IN DIRECT ACTIVE REGIME THE BASE CURRENT CAN BE CONSIDERED TO BE ALMOST
ZERO. ALSO, THERE IS AN EXPONENTIAL CONNECTION BETWEEN COLLECTOR CURRENT
AND VBEVBE. IF WE TAKE VERY SMALL INPUT VOLTAGE, THEN WE ARE NOT VARYING THE
CHARACTERISTIC THAT MUCH SO WE CAN JUST USE SMALL SIGNAL MODEL. WITH THIS MODEL WE
WILL GET LINEAR DEPENDENCY BETWEEN VOUTVOUT AND VINVIN. AND WE USE THEVENIN'S
THEOREM HERE.
THE REASON WHY THIS IS ALMOST LINEAR IN SMALL SIGNAL ANALYSIS IS MORE OBVIOUS IF WE
LOOK AT DIODE SMALL SIGNAL ANALYSIS.
AS YOU CAN SEE HERE, FOR VERY SMALL INPUT AC SIGNAL WE CAN
APPROXIMATE THINGS WITH TANGENT THAT'S BEING REPRESENTED AS A DIODE RESISTANCE IN
SMALL SIGNAL ANALYSIS. THE SAME LOGIC IS USED TO GET SMALL SIGNAL MODEL OF BIPOLAR
TRANSISTOR HERE, SO WE GET LINEAR DEPENDENCY. OF COURSE, THIS IS BECAUSE WE MADE
APPROXIMATIONS, SO IT'S NOT GOING TO WORK ONCE THESE APPROXIMATIONS STOP MAKING
SENSE BECAUSE THE INPUT VOLTAGE IS TO HIGH, NOR WILL IT WORK IF THE TRANSISTOR IS IN
SOME DIFFERENT WORK REGIME.
BOTTOM LINE IS THAT THEVENIN'S THEOREM HAS GREAT APPLICATIONS EVEN IN NON LINEAR
CIRCUITS, AND IT'S QUITE HANDY.

8. 1.2.7 CAN THEVENIN THEOREM BE APPLIED TO CIRCUIT HAVING A.C SOURCES?
YES. THEVENIN THEOREM APPLICABLE FOR AC CIRCUIT.
1. THE FACT IS THAT IN DC CIRCUIT WE USE THEVENIN EQUIVALENT RESISTANCE, BUT IN AC
WE HAVE TO FIND THE EQUIVALENT IMPEDANCE.
2. IN AC NETWORK WE HAVE TO USE PHASOR SUM OF THE VOLTAGE SOURCES .
ALL OTHER CONDITIONS ARE SIMILAR TO DC SOURCE.
1.2.8 WHY THEVENIN EQUIVALENT CIRCUIT IS NOT VERY USEFUL AT
MICROWAVE FREQUENCIES?
THE SIMPLE MODELS ASSUME AIR IS AN INSULATOR, WIRES HAVE ZERO INDUCTANCE AND ZERO
CAPACITANCE TO GROUND AND TO EACH OTHER AND THAT TRANSIT TIMES ARE ZERO. NONE OF
THOSE THINGS APPLY SO WELL TO MICROWAVES.
1.2.9.1 THE BASIC REQUIREMENTS TO PROOF THEVENIN THEOREM IN LAB
I. RESISTOR: A RESISTOR IS A TWO-TERMINAL ELECTRONIC COMPONENT THAT
PRODUCES A VOLTAGE ACROSS ITS TERMINALS THAT IS PROPORTIONAL TO THE
ELECTRIC CURRENT THROUGH IT IN ACCORDANCE WITH OHM'S LAW.
II. LAMP: A LAMP IS A REPLACEABLE COMPONENT SUCH AS AN INCANDESCENT
LIGHT BULB, WHICH IS DESIGNED TO PRODUCE LIGHT FROM ELECTRICITY. THESE
COMPONENTS USUALLY HAVE A BASE OF CERAMIC, METAL, GLASS OR PLASTIC,
WHICH MAKES AN ELECTRICAL CONNECTION IN THE SOCKET OF A LIGHT
FIXTURE.
III. WIRE: A WIRE IS A SINGLE, USUALLY CYLINDRICAL, ELONGATED STRING OF
METAL. WIRES ARE USED TO BEAR MECHANICAL LOADS AND TO CARRY
ELECTRICITY AND TELECOMMUNICATIONS SIGNALS. WIRE IS COMMONLY
FORMED BY DRAWING THE METAL THROUGH A HOLE IN A DIE OR DRAW PLATE.
IV. SWITCH: IN ELECTRONICS, A SWITCH IS AN ELECTRICAL COMPONENT THAT CAN
BREAK AN ELECTRICAL CIRCUIT, INTERRUPTING THE CURRENT OR DIVERTING IT
FROM ONE CONDUCTOR TO ANOTHER.
V. BATTERY: IN ELECTRONICS, A BATTERY OR VOLTAIC CELL IS A COMBINATION OF
MANY ELECTROCHEMICAL GALVANIC CELLS OF IDENTICAL TYPE TO STORE
CHEMICAL ENERGY AND TO DELIVER HIGHER VOLTAGE OR HIGHER CURRENT
THAN WITH SINGLE CELLS.
VI. VOLTMETER: A VOLTMETER IS AN INSTRUMENT USED FOR MEASURING THE
ELECTRICAL POTENTIAL DIFFERENCE BETWEEN TWO POINTS IN AN ELECTRIC
CIRCUIT. ANALOG VOLTMETERS MOVE A POINTER ACROSS A SCALE IN
PROPORTION TO THE VOLTAGE OF THE CIRCUIT; DIGITAL VOLTMETERS GIVE A
NUMERICAL DISPLAY OF VOLTAGE BY USE OF AN ANALOG TO DIGITAL
CONVERTER.
VII. AMMETER: AN AMMETER IS A MEASURING INSTRUMENT USED TO MEASURE THE
ELECTRIC CURRENT IN A CIRCUIT. ELECTRIC CURRENTS ARE MEASURED IN
AMPERES (A), HENCE THE NAME.
• VIII. NON-CONTACT AMMETER: A TYPE OF AMMETER THAT NEED NOT BE A PART OF THE
CIRCUIT.

9. 1.2.9.2 PROCEDURE
➢ I. THE COMPONENTS ARE GIVEN ON THE RIGHT SIDE OF THE SIMULATOR. YOU CAN CLICK ON
THE DESIRED COMPONENT AND DRAG IT TO THE SIMULATOR SCREEN.
• II. CONNECTION WIRES ARE PROVIDED. THE CONNECTION CAN BE CONFIRMED BY NOTICING THE
COLOUR CHANGE IN THE NODE.
• III. FIRST, DESIGN THE ORIGINAL CIRCUIT , AND THEN NOTICE THE CURRENT AND VOLTAGE
THROUGH THE LOAD RESISTANCE.
• IV. THEN CALCULATE THE THEVENIN'S EQUIVALENT RESISTANCE AND VOLTAGE. DESIGN
THEVENIN'S EQUIVALENT CIRCUIT. MEASURE THE CURRENT THROUGH THE LOAD RESISTANCE.
V. COMPARE THE TWO RESULTS TO VERIFY THE THEOREM.
➢ 1.2.10 APPLICATIONS:
➢ I. TO DETERMINE CHANGE IN LOAD VOLTAGE: TO PREDICT RANGE OF LOAD VOLTAGE
VARIATION DUE TO CHANGE IN LOAD RESISTANCE.
➢ II. TO OBTAIN NORTON’S EQUIVALENT CIRCUIT.
➢ III. TO DETERMINE MAXIMUM POWER THAT CAN BE TRANSFERRED TO LOAD FROM THE
NETWORK.
➢ IV. SOURCE MODELING AND RESISTANCE MEASUREMENT USING THE WHEATSTONE BRIDGE
PROVIDE APPLICATIONS FOR THEVENIN’S THEOREM.
➢ THIS HELPS IN MAKING INTEGRATED CIRCUITS.
➢ 1.2.11. ADVANTAGES:
➢ I. IT REDUCES A COMPLEX CIRCUIT TO A SIMPLE CIRCUIT VIZ A SINGLE SOURCE OF E.M.F
➢ II. IT GREATLY SIMPLIFIES THE PORTION OF THE CIRCUIT OF THE LESSER IMPORTANCE AND
ENABLES US TO VIEW THE ACTION OF THE OUTPUT PART DIRECTLY.
➢ III. THE THEOREM IS PARTICULARLY USEFUL TO FIND CURRENT IN A PARTICULAR BRANCH OF A
NETWORK AS THE RESISTANCE OF THAT BRANCH IS VARIED WHILE ALL OTHER RESISTANCES
AND E.M.F SOURCE REMAIN CONSTANT.
➢
➢ 1.2.12 LIMITATIONS:
➢ I. MANY, IF NOT MOST CIRCUITS ARE ONLY LINEAR OVER A CERTAIN RANGE OF
VALUES, THUS THE THÉVENIN EQUIVALENT IS VALID ONLY WITHIN THIS
LINEAR RANGE AND MAY NOT BE VALID OUTSIDE THE RANGE.
➢ II. THE THÉVENIN EQUIVALENT HAS AN EQUIVALENT I-V CHARACTERISTIC
ONLY FROM THE POINT OF VIEW OF THE LOAD.
➢ III. THE POWER DISSIPATION OF THE THÉVENIN EQUIVALENT IS NOT
NECESSARILY IDENTICAL TO THE POWER DISSIPATION OF THE REAL SYSTEM.
➢

10. ➢ 1.3.0 CONCLUSION
➢ It has been shown that a large number of equivalent circuits for each of the four source transformations (C-V, V-C,
C-C and V-V) can be obtained if either the current through or voltage across the output terminals is known.
Thevenin equivalent is the special case of the proposed C-V (V-C) transformation where the source voltage (current)
is the open (short) circuit voltage (current). Since the general forms of the source transformations are network-
specific, they are not recommended for simplifying the networks. However, if the current through or voltage across
the output terminals is known, these transformations are capable of giving a number of equivalent circuits. It may be
noted that the Thevenin equivalent circuits are not the only equivalent circuits, but there are many other possible
equivalent circuits for a given circuit (network N3 ).
➢ T.S. Rathore’s procedure for evaluating the two parameters of the Thevenin equivalent circuit has been described
and illustrated with two examples: one with controlled sources and the other without them. Unlike Murti’s method
[3], the method is capable of handling the controlled sources, is simple to apply and no extra step is required
irrespective of the number of independent sources present. There are circuits whose Thevenin equivalents are
interesting. Some such circuits which have been described are (i) circuits without any independent source; (ii)
circuits have loop or node method-based delta 0 and (iii) circuits which have Thevenin equivalent across an ideal
voltage source.
➢ 1.3.1 REFERENCES
➢ 1. T. S. RATHORE, “SOURCE TRANSFORMATION THEOREM REVISITED,” IETE J. EDUC., VOLUME 49,
NUMBER 1, JAN-APR 2008, PP. 13-17. [3]. V. G. K. MURTI, “ONE-STEP EVALUATION OF THE
THEVENIN EQUIVALENT CIRCUIT”, IETE J EDUCATION, VOLUME 44, NUMBER 2, APRIL-JUNE 2003,
PP 53-57. [
2. T.S. RATHORE, “ONE-CIRCUIT AND ONE-STEP EVALUATION OF THE THEVENIN EQUIVALENT
CIRCUIT”, IETE J EDUCATION, VOLUME 48, NUMBER 1, JAN-MARCH 2007, PP. 9-12.
3. T.S. RATHORE, “THEVENIN EQUIVALENTS OF SOME INTERESTING NETWORKS WITH
DEPENDENT SOURCES”, IETE J EDUCATION, VOLUME 53, NUMBER 1, JAN-JUNE 2012.
4. L. TH´EVENIN. SUR LA MESURE DE LA R´ESISTANCE SP´ECIFIQUE DES FILS [ON MEASURING THE
SPECIFIC
RESISTANCE OF WIRE]. ANNALES T´EL´EGRAPHIQUES, 10:167–178, 1883. TROISIEME S´ERIE.
5. L. TH´EVENIN. SUR LES CONDITIONS DE SENSIBILIT´E DU PONT DE WHEATSTONE [ON THE
SENSITIVITY
CONDITIONS OF THE WHEATSONE BRIDGE]. ANNALES T´EL´EGRAPHIQUES, 10:225–234, 1883.
TROISIEME
S´ERIE.
6. L. TH´EVENIN. SUR LA MESURE DES DIFF´ERENCES DE POTENTIEL AU MOYEN DU
GALVANOM`ETRE [ON
MEASURING THE POTENTIAL DIFFERENCE BY GALVANOMETERS]. ANNALES T´EL´EGRAPHIQUES,
10:446–449,1883. TROISIEME S´ERIE.