thevenin s theorem

7/30/2019 Thevenin s Theorem

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WOC Thevenins Theorem

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Thevenins Theorem

Thevenins Theorem can be used for two purposes:

1. To calculate the current through (or voltage across) a component in any circuit,

or

2. To develop a constant voltage equivalent circuit which may be used to simplifythe analysis of a complex circuit.

Any linear one-port network can be replaced with a single voltage source in serieswith a single resistor (see Fig. 1 below). The voltage source is called the Theveninequivalent voltage, and the resistor is called the Thevenin equivalent resistance. Thismeans that the single voltage source and series resistor must behave identically to theactual network it is replacing.

You can use Thevenins theorem to solve a complex DC circuit.

Figure 1 A network replaced with its Thevenin equivalent circuit


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The steps used for implementing Thevenins Theorem are listed below:

Step 1Remove the resistor, R through which you wish to calculate the current or across whichyou want to know the voltage. Label these terminals (where the resistor was removed)a and b. Calculate the voltage that appears across these open terminals. This is

called the open circuit voltage or the Thevenin equivalent voltage, VTH.

Figure 2

Lets consider the example shown in Fig. 2. Use the voltage source, V1, and the voltagedividing network made up of R4, R3 and R2. Here resistor R2 does not influence the

voltage that appears across the a and b terminals. This is because no current is drawnthrough R2 when measuing the voltage across the a and b terminals. This leaves onlyR3 and R4. What is left looks remarkably like a series circuit. From Kirchoffs laws weknow that the series circuit will divide V1 as given in Eq. 1.

43

31TH

RR

RVV

+

= (1)

Step 2From the open terminals, (a and b) calculate the resistance looking back from theopen terminals into the network. Each voltage source must be replaced by a resistor

equal to the internal resistance of the voltage source before the Thevenin resistance isevaluated. If RInternal = 0, then replace the voltage source with a zero ohm resistor(short). This resistance is RTH.

Figure 3

Let us consider the example shown in Fig. 3. After the sources are removed we can findthe resistance looking back from the open terminals of the network by measuring theresistance with an ohmmeter connected to terminals a and b. This is just like anequivalent resistance as we saw in the Kirchhoff lab. We can also calculate thisresistance. It is easiest to calculate the equivalent resistance starting from the left sideof the network shown in Fig. 3. We can see that R3 is in parallel with R4. Rememberthat the resistance of 2 resistors in parallel is:

+VTH

RTH


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43

43P

RR

RRR

+

= (2)

This parallel resistance is in series with R2. This gives us a Thevenin resistance of:

2

43

43TH R

RR

RRR +

+

= (3)

Now we have the components we need to create the Thevenin equivalent circuit shownin Fig. 1. Next the load resistor is replaced and we can write the equations for thecurrent and voltage this resistor is exposed to. Fig. 4 shows the Thevenin equivalentcircuit with the load resistor, R, replaced .

Figure 4

Step 3From the Kirchhoff lab we know the current through R is:

RR

VI

TH

THR

+

= (4)

and the voltage across R is:

RR

RVIRV

TH

THR

+

== (5)

VTH is the Thevenin equivalent voltage obtained in Step 1, RTH is the Theveninequivalent resistance obtained in Step 2, and R is the load resistor removed in Step 1.

thevenin s theorem

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