Exam #1 Review

1. Exam #1 Review Dr. Holbert February 18, 2008 EEE 202

2. Basic Circuit Analysis Methods • While Obeying Passive Sign Convention • Ohm’s Law; KCL; KVL • Voltage and Current Division • Series/Parallel Resistance combinations EEE 202

3. I Circuit Element – + Default Sign Convention • Passive sign convention : current should enter the positive voltage terminal • Consequence for P = I V • Positive (+) Power: element absorbs power • Negative (-) Power: element supplies power EEE 202

4. Ohm’s Law V = I R I + The Rest of the Circuit R V – EEE 202

5. i1(t) i5(t) i2(t) i4(t) i3(t) KCL (Kirchhoff’s Current Law) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction EEE 202

6. KVL (Kirchhoff’s Voltage Law) The sum of voltages around a loop is zero: Analogy: pressure drop through pipe loop + – + v2(t) + – v1(t) v3(t) – EEE 202

7. KVL Polarity • A loop is any closed path through a circuit in which no node is encountered more than once • Voltage Polarity Convention • A voltage encountered + to – is positive • A voltage encountered – to + is negative EEE 202

8. In General: Voltage Division • Consider N resistors in series: • Source voltage(s) are divided between the resistors in direct proportion to their resistances EEE 202

9. In General: Current Division • Consider N resistors in parallel: • Special Case (2 resistors in parallel) EEE 202

10. Equivalent Impedance • If we wish to replace two parallel resistances with a single resistor whose voltage-current relationship is the same, the equivalent resistance has a value of: • Parallel elements share the same two (distinct) end nodes EEE 202

11. V1 V2 R 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. • Solve the resulting system of linear equations for the nodal voltages. EEE 202

12. I2 VR + – R I1 VR = (I1 –I2 ) R 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. • Solve the resulting system of linear equations for the mesh/loop currents. EEE 202

13. 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 M mesh currents 3) Apply KVL at the M meshes (a current source makes a constraint equation) 4) Solve for the mesh currents Nodal and Loop Analyses EEE 202

14. Superposition Procedure • For each independent voltage and current source (repeat the following): • Replace the other independent voltage sources with a short circuit (i.e., V = 0). • Replace the other independent current sources with an open circuit (i.e., I = 0). Note: Dependent sources are not changed! • 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. EEE 202

15. Source Transformation A voltage source in series with a resistor is transformed into a current source in parallel with that resistor; and vice versa. Rs + – Vs Is Rs EEE 202

16. Basic Approach to Finding the Thevenin/Norton Equivalent • Circuits with independent sources: • Find Voc and/or Isc • Compute RTh (= Voc/Isc) • Circuits without independent sources: • Apply a test voltage (current) source • Find resulting current (voltage) • Compute RTh (= Vtest/Itest) EEE 202

17. RTh + – Voc Isc RTh Thevenin equivalent circuit Norton equivalent circuit Thevenin/Norton Equivalent EEE 202

18. Generally apply KCL or nodal analysis Ideal Op-Amp Relations i– = 0 = i+ v– = v+ + – Op Amps EEE 202