18. For each circuit in Figure 8–81, determine the Thevenin equivalent as seen from terminals A and B.
20. Using Thevenin’s theorem, find the voltage across R4
in Figure 8–83.
22. Determine the current into point A when R8 is 1.0kΩ, 5kΩ, and 10kΩ in Figure 8–85.
24. Determine the Thevenin equivalent looking from terminals A and B for the circuit in Figure 8–87.
30. Reduce the circuit between terminals A and B in Figure 8–88 to its Norton equivalent.
Thevenin and Norton theorems
EET310 Circuit analysis
Thevenin theorem
Applicable to linear electrical circuits
Linearity is the property of an element describing a linear relationship between cause and effect.
Although the property applies to many circuit elements, we shall limit its applicability to resistors here.
The property is a combination of both the homogeneity (scaling) property and the additivity property
The homogeneity property requires that if the input (also called the excitation) is multiplied by a constant, then the output (also called the response) is multiplied by the same constant.
For a resistor, for example, Ohm’s law relates the input i to the output v,
If the current is increased by a constant k, then the voltage increases corresponding
Linearity
The additivity property requires that the response to a sum of inputs is the sum of the responses to each input applied separately.
Using the voltage-current relationship of a resistor, if
Then applying (i1 + i2) gives
Linearity
We say that a resistor is a linear element because the voltage-current relationship satisfies both the homogeneity and the additivity properties.
In general, a circuit is linear if it is both additive and homogeneous.
A linear circuit consists of only linear elements, linear dependent sources, and independent sources.
Thevenin’s theorem
Thevenin’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:
Thevenin’s theorem
V T H is defined as the open circuit voltage between the two output terminals of a circuit.
R T H is defined as the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.
Thevenin’s theorem
Example:
Find the Thevenin voltage and resistance for the circuit.
To find V T H, apply a voltage divider to R1 and R2.
Thevenin’s theorem
Follow up:
What is the voltage across R L?
Since we know the Thevenin circuit, the easiest way to answer the question is to use it and apply the voltage divider theorem.
Thevenin’s theorem
Thevenin’s theorem is useful for solving the Wheatstone bridge. One way to Thevenize the bridge is to create two Thevenin circuits – from A to ground and from B to ground.
The resistance between point A and ground is R1||R3 and the resistance from B to ground is R2||R4. The voltage on each side of the bridge is found using the voltage divider rule.
Thevenin’s theorem
Example:
For the bridge shown, R1||R3 = 165 Ω and R2||R4 = 179 Ω. The voltage from A to ground (with no load) is 7.5 V and from B to ground (with no load) is 6.87 V.
The Thevenin circuits for each side of the bridge are shown on the following slide.
Thevenin’s theorem
Putting the load on the Thevenin circuits and applying the superposition theorem allows you to calculate the load current. The load current is: 1.27 mA
The dual Thevenin circuits used in this analysis have the advantage of retaining the ground from the original circuit.
Thevenin’s Theorem
Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh where
VTh is the open circuit voltage at the terminals and
RTh is the input or equivalent resistance at the terminals when the independent source are turn off.
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Thevenin’s Theorem
Steps in determining the Thevenin Equivalent Circuit
Remove the load from the circuit.
Label the resulting two terminals. We will label them as a and b, although any notation may be used.
Set all sources in the circuit to zero.
Voltage sources are set to zero by replacing them with short circuits (zero volts).
Current sources are set to zero by replacing them with open circuits (zero amps).
Determine the Thévenin equivalent resistance, RTh, by calculating the resistance “seen” between terminals a and b.
It may be necessary to redraw the circuit to simplify this step.
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Thevenin’s Theorem
Steps in determining the Thevenin Equivalent Circuit
Replace the sources removed in Step 3 and determine the open-circuit voltage between the terminals.
If the circuit has more than one source, it may be necessary to use the superposition theorem.
In that case, it will be necessary to determine the open-circuit voltage due to each source separately and then determine the combined effect.
The resulting open-circuit voltage will be the value of the Thévenin voltage, ETh.
Draw the Thévenin equivalent circuit using the resistance determined in Step 4 and the voltage calculated in Step 5. As part of the resulting circuit, include that portion of the network removed in Step 1.
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Thevenin’s Theorem
Thevenin Theorem Steps
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Input resistance of the dead circuit b/n a and b
Turn of all independent sources
Thevenin’s Theorem
Case 1:
If the network has no dependent sources:
Turn off all independent source.
RTH: can be obtained via simplification of either parallel or series connection seen from a-b
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Thevenin’s Theorem
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Case 2:
If the network has dependent sources:
Turn off all independent sources.
Apply a voltage source vo at a-b
Alternatively, apply a current source io at a-b
Thevenin’s Theorem
Find the Thevenin equivalent circuit of the circuit shown below
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Thevenin’s Theorem
Determine the Thevenin equivalent of the circuit below
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Thevenin’s Theorem
Determine the Thevenin equivalent circuit
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Thevenin’s Theorem
Determine the Thevenin equivalent to the left of the load
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Norton’s theorem
Norton’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:
Norton’s theorem
I N is defined as the output current when the output terminals are shorted.
R N is defined as the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.
Norton’s Theorem
Norton’s theorem states that a linear two-terminal circuit can be replaced by equivalent circuit consisting of a current source IN in parallel with a resistor RN
where IN is the short-circuit current through the terminals and
RN is the input or equivalent resistance at the terminals when the independent source are turn off.
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