Fundamentals of Electric Circuits (EE201) CIRCUIT...

Fundamentals of Electric

Circuits (EE201)

CIRCUIT THEOREMS

By

Dr. Eng. Omar Abdel-Gaber M. Aly

[email protected]

Assistant Professor

Electrical Engineering Department

College of Engineering Al-Majmaa

Al-Majmaa University

SUPERPOSITION

The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone.

Fundamentals of Electric Circuits, by Dr. Omar Aly

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to apply the superposition principle, we

must keep two things in mind:

1. We consider one independent source at a time while all other independent sources are turned off. This implies that we replace every voltage source by 0 V (or a short circuit), and every current source by 0 A (or an open circuit). This way we obtain a simpler and more manageable circuit.

2. Dependent sources are left intact because they are controlled by circuit variables.


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Steps to Apply Superposition

Principle:

1. Turn off all independent sources except one source. Find the output (voltage or current) due to that active source using nodal or mesh analysis.

2. Repeat step 1 for each of the other independent sources.

3. Find the total contribution by adding algebraically all the contributions due to the independent sources.


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EXAMPLE 4.3

Use the superposition theorem to find v in the circuit in Fig.


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EXAMPLE 4.4

Find io in the circuit in Fig. using superposition.


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EXAMPLE 4.5

For the circuit in Fig, use the superposition theorem to find i.


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SOURCE TRANSFORMATION

A source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa.


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SOURCE TRANSFORMATION we should keep the following points in

mind when dealing with source transformation.

1. The arrow of the current source is directed toward the positive terminal of the voltage source.

2. Source transformation is not possible when R = 0, which is the case with an ideal voltage source. Or an ideal current source with R =∞ cannot be replaced by a finite voltage source.


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EXAMPLE 4.6

Use source transformation to find vo in the circuit in Fig.


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EXAMPLE 4.7

Find vx in Fig using source transformation.


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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 sources are turned off.


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Thus VTh is the open-circuit voltage across the terminals as shown in Fig.

RTh is the input resistance at the terminals when the independent sources are turned off.


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Finding RTH If the network has no dependent sources, we

turn off all independent sources. RTh is the input resistance of the network looking between terminals a and b.

If the network has dependent sources, we turn off all independent sources. We apply a voltage source vo at terminals a and b and determine the resulting current io.

Then RTh = vo/io


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Thevenin’s theorem is very important a linear circuit with a variable load can be replaced by the Thevenin equivalent, exclusive of the load. The current IL through the load and the voltage VL across the load are:


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EXAMPLE 4.8

Find the Thevenin equivalent circuit of the circuit shown, to the left of the terminals a-b. Then find the current through RL = 6, 16, and 36 Ω.


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EXAMPLE 4.9

Find the Thevenin equivalent of the circuit shown.


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EXAMPLE 4.10

Determine the Thevenin equivalent of the circuit shown.


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NORTON’S THEOREM

Norton’s theorem states that a linear two-terminal circuit can be replaced by an 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 sources are turned off.


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EXAMPLE 4.11

Find the Norton equivalent circuit of the circuit in Fig.


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EXAMPLE 4.12

Using Norton’s theorem, find RN and IN of the circuit in Fig.


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MAXIMUM POWER

TRANSFER In many practical situations, a circuit is

designed to provide power to a load. It is desirable to maximize the power delivered to a load.

The Thevenin equivalent is useful in finding the maximum power a linear circuit can deliver to a load.

the power delivered to the load is


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EXAMPLE 4.13

Find the value of RL for maximum power transfer in the circuit of Fig. Find the maximum power.


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MAXIMUM POWER

TRANSFER

For a given circuit, VTh and RTh are fixed. By varying the load resistance RL, the power delivered to the load varies as sketched in Fig.

Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as seen from the load (RL = RTh).


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Problems Chp4 , page 154

6, 7, 8, 9, 10, 11, 12, 13, 14,

27, 28, 30, 33, 34

36, 37, 40, 41, 43, 46, 54, 55, 56, 57


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