1 / 17

Lecture - 5 Nodal analysis  

Lecture - 5 Nodal analysis  . Outline. Terms of describing circuits. The Node-Voltage method. The concept of supernode . Terms of describing circuits . Example 1. For the circuit in the figure, identify a) all nodes. b) all essential nodes. c) all branches.

scout
Download Presentation

Lecture - 5 Nodal analysis  

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture - 5 Nodal analysis  

  2. Outline • Terms of describing circuits. • The Node-Voltage method. • The concept of supernode.

  3. Terms of describing circuits

  4. Example 1 • For the circuit in the figure, identify a) all nodes. b) all essential nodes. c) all branches. d) all essential branches. e) all meshes. f) two paths that are not loops or essential branches. g) two loops that are not meshes.

  5. Example 1 • The nodes are a, b, c, d, e, f, and g. b) The essential nodes are b, c, e, and g. c) The branches are v1, v2, R1, R2, R3, R4, R5, R6, R7 and I. d) The essential branches are: v1 – R1 , R2 – R3 , v2 – R4 , R5, R6, R7 and I

  6. Example 1 e) The meshes are: v1 – R1– R5 – R3 – R2, v2–R2 – R3 – R6 –R4, R5– R7 – R6 and R7 –I f) The two paths that are not loops or essential branches are R1 – R5 – R6 and v2 - R2 , because they do not have the same starting and ending nodes), nor are they an essential branch (because they do not connect two essential nodes). g)The two loops that are not meshes are v1 — R1 — R5 – R6 - R4 - v2 and I — R5 —R6 , because there are two loops within them.

  7. The Node-Voltage method • Steps to determine Node Voltages: • Select a node as the reference node. Assign voltage v1, v2, …vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node. • Apply KCL to each of the n-1 non-reference nodes. • Use Ohm’s law to express the branch currents in terms of node voltages. • Solve the resulting simultaneous equations to obtain the unknown node voltages.

  8. Example 2 a) Use the node-voltage method of circuit analysis to find the branch currents ia, ib, and icin the circuit shown. b) Find the power associated with each source, and state whether the source is delivering or absorbing power.

  9. Example 2 a) There are two essential nodes; thus we need to write a single node voltage expression. We select the lower node as the reference node and define the unknown node voltage as v1. Summing the currents away from node 1 generates the node-voltage equation: Solving for v1 gives  v1=40V Hence b) P50V = -50ia = -100 W (delivering). P3A= -3v1 = -3(40) = -120 W (delivering).

  10. Example 3 Use the node-voltage method to find the power dissipated in the 5Ω resistor in the circuit shown. -------------------------------------------------------- We begin by noting that the circuit has three essential nodes. Hence we need two node-voltage equations to describe the circuit. Four branches terminate on the lower node, so we select it as the reference node. The two unknown node voltages are defined on the circuit. Summing the currents away from node 1 generates the equation.

  11. Example 3 • Summing the currents away from node 2 yields • As written, these two node-voltage equations contain three unknowns, namely, v1, v2, and iΦ . To eliminate i Φwe must express this controlling current in terms of the node voltages

  12. Example 3 Substituting this relationship into the node 2 equation simplifies the two node-voltage equations to Solving for v1 and v2 gives v1=16V and v2= 10V Then

  13. The Concept of a Supernode • A supernode is formed by enclosing a (dependent or independent) voltage source connected between two non-reference nodes and any elements connected in parallel with it. • The required two equations for regulating the two non-reference node voltages are obtained by the KCL of the super node and the relationship of node voltages due to the voltage source

  14. Example 4 Use the node-voltage method to find v in the circuit shown. ---------------------------------------------------

  15. Example 4 Note that the dependent voltage source and the node voltages v and v2 form a supernode. The v1 node voltage equation is The supernode equation is The constraint equation due to the dependent source is

  16. Example 4 The constraint equation due to the supernode is: Place this set of equations in standard form: Solving this set of equations gives v1 = 15 V, v2 = 10 V, ix = 2 A, and v = 8 V.

  17. Summary • Those terms are node, essential node, path, branch, essential branch, mesh, and planar circuit. • The node-voltage method works with both planar and non-planar circuits. • A reference node is chosen from among the essential nodes. • Voltage variables are assigned at the remaining essential nodes, and Kirchhoff s current law is used to write one equation per voltage variable. • The number of equations is ne — 1, where ne is the number of essential nodes

More Related