Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Notes > Chapter - Network Theorems, PPT, DC Circuits, Semester, Engineering
Chapter - Network Theorems, PPT, DC Circuits, Semester, Engineering - Electronics and Communication Engineering (ECE) PDF Download
Introduction
The slides cover the following topics:
- Network Theorem
- Superposition Theorem
- Thevenin and Norton Equivalent Circuits
- Norton's Theorem
- Maximum Power Transfer
- Circuit Transformation
Networks Theorem---------------------------------------------------Next slide
Network Theorems
Networks Theorem---------------------------------------------------Next slide
Objectives
•At the end of this topic, you should be able to:
- apply the superposition theorem for circuit analysis
- apply Thevenin’s theorem to simplify the circuit for analysis
- apply Norton’s theorem to simplify the circuit for analysis
- understand maximum power transfer and perform circuit conversion
Networks Theorem---------------------------------------------------Next slide
Superposition Theorem
•The Superposition theorem states that if a linear system is driven by more than one independent power source, the total response is the sum of the individual responses. The following example will show the step of finding branches current using superpostion theorem
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Refer to the Figure 1, determine the branches current using superposition theorem.
•Solution
•The application of the superposition theorem is shown in Figure 1, where it is used to calculate the branch current. We begin by calculating the branch current caused by the voltage source of 120 V. By substituting the ideal current with open circuit, we deactivate the current source, as shown in Figure 2.
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•To calculate the branch current, the node voltage across the 3Ω resistor must be known. Therefore
The equations for the current in each branch,
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In order to calculate the current cause by the current source, we deactivate the ideal voltage source with a short circuit, as shown
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•To determine the branch current, solve the node voltages across the 3Ω and 4Ω resistors as shown in Figure 4
•The two node voltages are
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•By solving these equations, we obtain
•v3 = -12 V
•v4 = -24 V
Now we can find the branches current,
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To find the actual current of the circuit, add the currents due to both the current and voltage source,
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Networks Theorem---------------------------------------------------Next slide
Thevenin & Norton Equivalent Circuits
Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
A series combination of Thevenin equivalent voltage source V0 and Thevenin equivalent resistance Rs
Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load. Norton form:
A parallel combination of Norton equivalent current source I0 and Norton equivalent resistance Rs
Networks Theorem---------------------------------------------------Next slide
Networks Theorem---------------------------------------------------Next slide
•Example
Refer to the Figure 6, find the Thevenin equivalent circuit.
Refer to the Figure 6, find the Thevenin equivalent circuit.
•Solution
•In order to find the Thevenin equivalent circuit for the circuit shown in Figure 6, calculate the open circuit voltage, vab. Note that when the a, b terminals are open, there is no current flow to 4Ω resistor. Therefore, the voltage vab is the same as the voltage across the 3A current source, labeled v1.
•To find the voltage v1, solve the equations for the singular node voltage. By choosing the bottom right node as the reference node,
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•By solving the equation, v1 = 32 V. Therefore, the Thevenin voltage Vth for the circuit is 32 V.
•The next step is to short circuit the terminals and find the short circuit current for the circuit shown in Figure 7. Note that the current is in the same direction as the falling voltage at the terminal.
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Current isc can be found if v2 is known. By using the bottom right node as the reference node, the equationfor v2 becomes
By solving the above equation, v2 = 16 V. Therefore, the short circuit current isc is
The Thevenin resistance RTh is
Figure 8 shows the Thevenin equivalent circuit for the Figure 6.
Networks Theorem---------------------------------------------------Next slide
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Norton’s Theorem
•The Norton equivalent circuit contains an independent current source which is parallel to the Norton equivalent resistance. It can be derived from the Thevenin equivalent circuit by using source transformation. Therefore, the Norton current is equivalent to the short circuit current at the terminal being studied, and Norton resistance is equivalent to Thevenin resistance.
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Example 3
Derive the Thevenin and Norton equivalent circuits of Figure 6.
•Solution
•Step 1: Source transformation (The 25V voltage source is converted to a 5 A current source.)
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Step 2: Combination of parallel source and parallel resistance
Step 3: Source transformation (combined serial resistance to produce the Thevenin equivalent circuit.)
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•Step 4: Source transformation (To produce the Norton equivalent circuit. The current source is 4A (I = V/R = 32 V/8 ?))
Figure 9 Steps in deriving Thevenin and Norton equivalent circuits.
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Maximum Power Transfer
•Maximum power transfer can be illustrated by Figure 10. Assume that a resistance network contains independent and dependent sources, and terminals a and b to which the resistance RL is connected. Then determine the value of RL that allows the delivery of maximum power to the load resistor.
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•Maximum power transfer happens when the load resistance RL is equal to the Thevenin equivalent resistance, RTh. To find the maximum power delivered to RL,
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Circuit Transformation
•The configuration of circuit connection can be changed to make the calculation easier. There are TWO type of transformations which are Delta (Δ) to star connection (U) and vice versa.
Figure 12 Delta and Star Circuit Connection
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Delta (Δ) to star (Y) transformation:
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Star (Y) to Delta (D) transformation:
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Objectives
•At the end of this topic, you should be able to:
- apply the superposition theorem for circuit analysis
- apply Thevenin’s theorem to simplify the circuit for analysis
- apply Norton’s theorem to simplify the circuit for analysis
- understand maximum power transfer and perform circuit conversion
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FAQs on Chapter - Network Theorems, PPT, DC Circuits, Semester, Engineering - Electronics and Communication Engineering (ECE)
| 1. What are the different network theorems covered in the chapter? |  |
Ans. The chapter on Network Theorems covers several important theorems such as Kirchhoff's laws, Ohm's law, Norton's theorem, Thevenin's theorem, Maximum Power Transfer theorem, and Superposition theorem. These theorems are used to analyze and solve complex DC circuits.
| 2. How can I apply Kirchhoff's laws to solve a DC circuit? | |
Ans. Kirchhoff's laws, which include Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL), are used to analyze and solve DC circuits. KCL states that the sum of currents flowing into a node is equal to the sum of currents flowing out of that node. KVL states that the sum of voltages around any closed loop in a circuit is zero. By applying these laws, you can write down a set of equations and solve them to find the unknown currents and voltages in the circuit.
| 3. How does Thevenin's theorem simplify circuit analysis? | |
Ans. Thevenin's theorem allows complex circuits to be simplified into an equivalent circuit consisting of a single voltage source in series with a resistor. This equivalent circuit is called the Thevenin equivalent circuit. By replacing a part of a circuit with its Thevenin equivalent, you can simplify the circuit analysis. The Thevenin voltage is the open-circuit voltage across the terminals where you want to find the equivalent circuit, and the Thevenin resistance is the equivalent resistance when all the independent sources are turned off.
| 4. What is the purpose of the Maximum Power Transfer theorem? | |
Ans. The Maximum Power Transfer theorem states that the maximum power is transferred from a source to a load when the load resistance is equal to the Thevenin resistance of the source. This theorem is useful in designing circuits for maximum power transfer efficiency. By matching the load resistance to the Thevenin resistance, you can ensure that the maximum power is delivered to the load.
| 5. How does the Superposition theorem simplify circuit analysis? | |
Ans. The Superposition theorem states that in a linear circuit with multiple independent sources, the total response (current or voltage) at any point in the circuit is the algebraic sum of the individual responses due to each source acting alone. This theorem allows you to analyze the circuit by considering the effect of each source separately, making it easier to calculate the overall response. By turning off all but one independent source at a time and calculating the response, you can then add up the individual responses to obtain the total response.
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