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Network Theory

Mesh and Node Analysis

jinto007mathew
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Network Theory

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  1. Mar Baselios Institute of Technology and Science [MBITS] Nellimattom, Kerala ECT205 NETWORK THEORY Prepared by: Asst. Prof. Jinto Mathew Dept. of ECE

  2. Network • Network is an interconnection of electrical components or electrical elements.

  3. Syllabus Module 1 : Mesh and Node Analysis. Module 2 : Network Theorems. Module 3 : Application of Laplace Transforms. Module 4 : Network functions. Module 5 : Two port network Parameters.

  4. Network Parameters Network Parameters • Node • Path • Loop • Branch 2 1 3

  5. Circuit Variables Voltage,V= dW/dQ Current, I= dQ/dt Power, P=dW/dt

  6. Circuit elements : Passive Elements Resistor, V=IR Inductor, V= L*(dI/dt) Capacitor, V= (1/C)*∫ V dt

  7. Circuit elements : Active Elements Deliver Power to other elements. Eg: BJT, FET, MOSFETS

  8. Classification of Sources Independent Sources Dependent Sources

  9. Independent Sources Not dependent on any other parameters. Independent Voltage Sources. Independent Current Sources.

  10. Independent Voltage Sources

  11. Independent Current Sources

  12. Dependent Sources Dependent sources produce the amount of voltage or current that is dependent on some other voltage or current. Dependent sources are also called as controlled sources. Dependent Voltage Sources Dependent Current Sources

  13. Dependent Voltage Sources Voltage Dependent Voltage Source (VDVS) Current Dependent Voltage Source (CDVS) μ- Voltage Gain. r- Trans Resistance

  14. Dependent Current Sources Voltage Dependent Current Source (VDCS) Current Dependent Current Source (CDCS) g- Transconductance. β- Current Gain

  15. Kirchhoff’s laws Kirchhoff’s Current Law(KCL) Kirchhoff’s Voltage Law(KVL)

  16. Kirchhoff’s Current Law Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents leaving (or entering) a node is equal to zero.

  17. Kirchhoff’s Voltage Law Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around a loop or mesh is equal to zero.

  18. Voltage Division

  19. Current Division

  20. Q. Find voltage Vx using voltage division?

  21. Voltage Division

  22. Solution: Two 10 ohm resistors are in parallel. Ie, effective resistance: Req=(10*10)/ (10+10)=5 ohm. 5 Ohm in series with 3 ohm. Net Resistance=8 ohm

  23. Q. Find current through 3ohm resistor in the network?

  24. Current Division

  25. Q: Find i1,i2 and V3 using current Division?

  26. Q. Find the current supplied by 60V source?

  27. Q. Compute the current through resistor R3 if it is known that the voltage source supplies a current of 3A?

  28. Q. Count the number of branches and nodes in the network. If Ix= 3 A and the 18v source delivers 8 A of current, what is the value of RA?

  29. Q. Find I1 and I2 in the given network?

  30. Q. Find Vx using KVL?

  31. Q. Determine Vx in the circuit?

  32. Q. Find V in the network?

  33. Fig 1.17

  34. Fig 1.27

  35. Mesh Analysis Mesh analysis is a method that is used to solve planar circuits for the currents at any place in the electrical circuit.

  36. Procedure of Mesh Analysis Step 1 − Identify the meshes and label the mesh currents in either clockwise or anti-clockwise direction. Step 2 − Observe the amount of current that flows through each element in terms of mesh currents. Step 3 − Write mesh equations to all meshes. Mesh equation is obtained by applying KVL first and then Ohm’s law. Step 4 − Solve the mesh equations obtained in Step 3 in order to get the mesh currents.

  37. Find the currents in each element using Mesh analysis?

  38. Step 1

  39. Step 2 Analyse current flows through each element in terms of mesh currents.

  40. Step 3 Find Mesh equations for all meshes. Mesh 1 Mesh 2

  41. Step 4 Solve the mesh equations obtained in Step 3 in order to get the mesh currents.

  42. Q. What is the power loss in 10ohm resistor? Use mesh analysis.

  43. Q.Find V by mesh analysis such that the current through 5V source is zero?

  44. Q. Use mesh analysis to find ix in the circuit?

  45. Q. Find the loop current and Vx?

  46. Q.Find the mesh current in the given network?

  47. Node Analysis A node is a common point of two or more branches. We will consider the node voltages with respect to Ground……. Node-voltage method.

  48. Procedure of Nodal Analysis Step 1 − Identify the principal nodes and choose one of them as reference node. We will treat that reference node as the Ground. Step 2 − Label the node voltages with respect to Ground from all the principal nodes except the reference node. Step 3 − Write nodal equations at all the principal nodes except the reference node. Nodal equation is obtained by applying KCL first and then Ohm’s law. Step 4 − Solve the nodal equations obtained in Step 3 in order to get the node voltages.

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