1. Circuit Analysis Techniques 1.Circuit Reduction 2.Node-Voltage method 3.Mesh- Current method. 4.Superposition method. 5.Thevenin’s and Norton’s circuits. 6.Maximum Power Transfer theorem Lecture #4 OUTLINE

2. this technique is based on reducing the circuit to a simpler form and then applying voltage and current division rules. Example find V0 1.Circuit Reduction

3. For the circuit shown Find the equivalent resistance seen from the source terminals. Use voltage and current division rules to find the current Ix.

4. 1.Choose a reference node (“ground”) Look for the one with the most connections! 2.Define unknown node voltages those which are not fixed by voltage sources 3.Write KCL at each unknown node, expressing current in terms of the node voltages (using the I-V relationships of branch elements) 4.Solve the set of independent equations N equations for N unknown node voltages Node-Voltage Circuit Analysis Method

5. Node Voltage equations

6. R 4 V 1 R 2 + - ISIS R 3 R1R1 Nodal Analysis: Example #1

7. V 2 V 1 R 2 R 1 R 4 R 5 R 3 I 1 VaVa Nodal Analysis: Example #2

8. Node-Voltage Method and Dependent Sources Dependent current source: treat as independent current source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages. Dependent voltage source: treat as independent voltage source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages.

9. Nodal Analysis with dependent sources

10. Find io