ECE201 Exam #2 Review1 Exam #2 Review Dr. Holbert March 27, 2006

ECE201 Exam #2 Review2 Don’t Forget the Fundamentals Polarity and Passive Sign Convention Ohm’s Law; KCL; KVL Voltage and Current Division Phasors, Impedance, and Complex numbers

ECE201 Exam #2 Review3 Steps of Nodal Analysis 1.Choose a reference (ground) node, V=0. 2.Assign node voltages to the other nodes. 3.Apply KCL to each node but the reference node; express currents in terms of node voltages. 4.Solve the resulting system of linear equations. V1V1 V2V2 Z

ECE201 Exam #2 Review4 Steps of Mesh/Loop Analysis 1.Identify mesh (loops). 2.Assign a current to each mesh. 3.Apply KVL around each loop to get an equation in terms of the loop currents. 4.Solve the resulting system of linear equations. I1I1 +– VZVZ I2I2 V Z = (I 1 - I 2 ) Z Z

ECE201 Exam #2 Review5 Nodal and Loop Analyses Nodal Analysis Recipe 1&2) Identify and label N nodal voltages plus the ground node (V=0) 3) Apply KCL at N nodes (supernode makes constraint eq.) 4) Solve for the nodal voltages Loop Analysis Recipe 1&2) Identify and label N mesh currents 3) Apply KVL at the N meshes 4) Solve for the mesh currents

ECE201 Exam #2 Review6 Linearity More important as a concept than as an analysis methodology, but allows scaling of current/voltage values Leads to superposition: “In any linear circuit containing multiple independent sources, the current or voltage at any point in the circuit may be calculated as the algebraic sum of the individual contributions of each source acting alone.”

ECE201 Exam #2 Review7 Superposition Procedure 1.For each independent voltage and current source (repeat the following): a) Replace the other independent voltage sources with a short circuit (i.e., V = 0). b) Replace the other independent current sources with an open circuit (i.e., I = 0). Note: Dependent sources are not changed! c) Calculate the contribution of this particular voltage or current source to the desired output parameter. 2.Algebraically sum the individual contributions (current and/or voltage) from each independent source.

ECE201 Exam #2 Review8 Source Transformation VSVS ISIS +–+– Z Z V S = Z I S

ECE201 Exam #2 Review9 Thevenin/Norton Analysis 1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable). 2. Thevenin: Compute the open circuit voltage, V OC. Norton: Compute the short circuit current, I SC. For case 3(b) both V OC =0 and I SC =0 [so skip step 2]

ECE201 Exam #2 Review10 Thevenin/Norton Analysis 3. Compute the Thevenin equivalent resistance, R Th (or impedance, Z Th ). (a) If there are only independent sources, then short circuit all the voltage sources and open circuit the current sources (just like superposition). (b) If there are only dependent sources, then must use a test voltage or current source in order to calculate R Th (or Z Th ) = V Test /I test (c) If there are both independent and dependent sources, then compute R Th (or Z Th ) from V OC /I SC.

ECE201 Exam #2 Review11 Thevenin/Norton Analysis 4. Thevenin: Replace circuit with V OC in series with R Th, Z Th. Norton: Replace circuit with I SC in parallel with R Th, Z Th. Note: for 3(b) the equivalent network is merely R Th (or Z Th ), that is, no voltage (or current) source. Only steps 2 & 4 differ from Thevenin & Norton!

ECE201 Exam #2 Review12 Thevenin/Norton Analysis V oc Thevenin equivalent circuit Z Th +–+– Norton equivalent circuit Z Th I sc