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Nodal Analysis

Nodal Analysis. Introducing Supernodes!!!. Nodal Analysis. Nodal Analysis provides a general procedure for analyzing circuits using node voltages as the circuit variables.

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Nodal Analysis

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  1. Nodal Analysis Introducing Supernodes!!!

  2. Nodal Analysis • Nodal Analysis provides a general procedure for analyzing circuits using node voltages as the circuit variables. • Choosing node voltages instead of element voltages as circuit variables is convenient and reduces the number of equations one must solve simultaneously.

  3. Nodal Analysis • In nodal analysis, we are interested in finding the node voltages. • The number of non-reference nodes is equal to the number of independent equations that will be derived. • Given a circuit with n nodes without voltage sources, the nodal analysis of the circuit involves taking the following steps:

  4. Nodal Analysis • 1. Select a reference node. Assign voltages v1, v2, … , vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node. • 2. 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. • 3. Solve the resulting simultaneous equations to obtain the unknown voltages. • The number of non-reference nodes is equal to the number of independent equations that will be derived.

  5. Nodal Analysis with Voltage Sources • Case 1: If a voltage source is connected between the reference node, simply set the voltage at the non-reference node equal to the voltage of the voltage source.

  6. Nodal Analysis with Voltage Sources (cont.) • Case 2: If a voltage source (dependent or independent ) is connected between two non-reference nodes, the two nodes form a supernode. • Apply both KCL and KVL to determine the node voltages.

  7. Supernodes • We treat supernodes differently because nodal analysis uses KCL, and there is no way of knowing the current through a voltage source in advance.

  8. Note the properties of a supernode: The voltage source inside the supernode provides a constraint equation needed to solve for the node voltages A supernode has no voltage of its own A supernode requires the application of both KCL and KVL Supernodes (cont.)

  9. Examples 1. Select a reference node: ground 2. Label your non-reference nodes

  10. Examples 3. Apply KCL to your non-reference nodes 4. Use Ohm’s Law to write your KCL equations in terms the node voltages. 5. Solve the resulting equations for the voltages.

  11. Examples Case 1: If you have a voltage source connected between a reference node and a non-reference node, set the voltage at the non-reference node to the value of the voltage source. V1 = 10 V

  12. Examples Case 2: If you have a voltage source connected in between two non-reference nodes, you have to apply both KCL and KVL to determine the node voltages.

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