Network-theorems.pptx hahajakaksmmssjsjjsjsjs

Hi

1. Network Theorems

2. Elements of an Electric circuit Types of elements: Active Elements and Passive Elements Bilateral and Unilateral Elements Lumped and Distributed Elements

3. Active elements Active elements : Active elements are the elements of a circuit which possess energy of their own and can impart it to other element of the circuit. Active elements are of two types a) Voltage source b) Current source A Voltage source has a specified voltage across its terminals, independent of current flowing through it. A current source has a specified current through it independent of the voltage appearing across it.

4. Passive Elements The passive elements of an electric circuit do not possess energy of their own. They receive energy from the sources. The passive elements are the resistance, the inductance and the capacitance. When electrical energy is supplied to a circuit element, it will respond in one and more of the following ways If the energy is consumed, then the circuit element is a pure resistor. If the energy is stored in a magnetic field, the element is a pure inductor. And if the energy is stored in an electric field, the element is a pure capacitor.

5. Linear and Non-Linear Elements Linear elements show the linear characteristics of voltage & current. That is its voltage-current characteristics are at all-times a straight-line through the origin. For example, the current passing through a resistor is proportional to the voltage applied through its and the relation is expressed as V I or V = IR. Resistors, inductors and capacitors are the examples of the linear elements and their properties do not change with a change in the applied voltage and the circuit current. Non linear element’s V-I characteristics do not follow the linear pattern i.e. the current passing through it does not change linearly with the linear change in the voltage across it. Examples are the semiconductor devices such as diode, transistor.

6. Bilateral and Unilateral Elements An element is said to be bilateral, when the same relation exists between voltage and current for the current flowing in both directions. Ex: Voltage source, Current source, resistance, inductance & capacitance. The circuits containing them are called bilateral circuits. An element is said to be unilateral, when the same relation does not exist between voltage and current when current is flowing in both directions. The circuits containing them are called unilateral circuits. Ex: Vacuum diodes, Silicon Diodes, Selenium Rectifiers etc.

7. Lumped and Distributed Elements Lumped elements are those elements which are very small in size & in which simultaneous actions takes place. Typical lumped elements are capacitors, resistors, inductors. Distributed elements are those which are not electrically separable for analytical purposes. For example a transmission line has distributed parameters along its length and may extend for hundreds of miles. The circuits containing them are called unilateral circuits

8. Superposition Theorem In an active linear network containing several sources (including dependent sources), the overall response (branch current or voltage) in any branch in the network is equal to the algebraic sum of the responses of individual source considered separately, with all other sources made inoperative, it means replacing them with their internal resistances or impedances. The current in any branch of a circuit equals the sum of the currents produced in that branch by each individual independent source with all others zeroed.

9. Procedure of Superposition Theorem Step 1  − Find the response in a particular branch by considering one independent source and eliminating the remaining independent sources present in the network. Step 2  − Repeat Step 1 for all independent sources present in the network. Step 3  − Add all the responses in order to get the overall response in a particular branch when all independent sources are present in the network.

10. Find the current flowing through 20 Ω resistor of the following circuit using  superposition theorem .

11. Step 1  − Let us find the current flowing through 20 Ω resistor by considering only  20 V voltage source . In this case, we can eliminate the 4 A current source by making open circuit of it. The modified circuit diagram is shown in the following figure.

12. There is only one principal node except Ground in the above circuit. So, we can use  nodal analysis  method. The node voltage V 1  is labelled in the following figure. Here, V 1  is the voltage from node 1 with respect to ground. Therefore, the current flowing through 20 Ω resistor is  0.4 A , when only 20 V voltage source is considered.

13. Step 2  − Let us find the current flowing through 20 Ω resistor by considering only  4 A current source . In this case, we can eliminate the 20 V voltage source by making shortcircuit of it. The modified circuit diagram is shown in the following figure . n the above circuit, there are three resistors to the left of terminals A & B. We can replace these resistors with a single  equivalent resistor . Here, 5 Ω & 10 Ω resistors are connected in parallel and the entire combination is in series with 10 Ω resistor. The  equivalent resistance  to the left of terminals A & B will be

14. CONTINUED Therefore, the current flowing through 20 Ω resistor is  1.6 A , when only 4 A current source is considered. Step 3  − We will get the current flowing through 20 Ω resistor of the given circuit by doing the  addition of two currents  that we got in step 1 and step 2. Mathematically, it can be written as I = I 1 + I 2 Substitute, the values of  I 1  and  I 2  in the above equation. Substitute, the values of  I 1  and  I 2  in the above equation.

15. CONTINUED

16. Thevenin’s Theorem Any two terminal network is composed of an ideal voltage source V TH and a series resistor R TH .

17. Norton’s theorem Any two terminal network is equivalent to an ideal current source I N and a parallel resistor R N .