1. 3. ANALYSIS TECHNIQUES CIRCUITS by Ulaby & Maharbiz All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

2. All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

3. Node-Voltage Method Node 1 Node 2 Node 3 Node 2 Node 3 All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

4. Node-Voltage Method Three equations in 3 unknowns: Solve using Cramer’s rule, matrix inversion, or MATLAB All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

6. Supernode  Current through voltage source is unknown  Less nodes to worry about, less work!  Write KVL equation for supernode  Write KCL equation for closed surface around supernode A supernode is formed when a voltage source connects two extraordinary nodes All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

7. KCL at Supernode  Note that “internal” current in supernode cancels, simplifying KCL expressions  Takes care of unknown current in a voltage source = All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

8. Example 3-3: Supernode Determine: V1 and V2 Solution: Supernode All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

9. Mesh-Current Method Two equations in 2 unknowns: Solve using Cramer’s rule, matrix inversion, or MATLAB All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

10. Example 3-5: Mesh Analysis Mesh 1 Mesh 2 Mesh 3 But Hence All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

11. Supermesh A supermesh results when two meshes have a current source( with or w/o a series resistor) in common  Voltage across current source is unknown  Write KVL equation for closed loop that ignores branch with current source  Write KCL equation for branch with current source (auxiliary equation) All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

12. Example 3-6: Supermesh Mesh 2 SuperMesh 3/4 Mesh 1 Supermesh Auxiliary Equation Solution gives: All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

13. Nodal versus Mesh When do you use one vs. the other? What are the strengths of nodal versus mesh?  Nodal Analysis  Node Voltages (voltage difference between each node and ground reference) are UNKNOWNS  KCL Equations at Each UNKNOWN Node Constrain Solutions (N KCL equations for N Node Voltages)  Mesh Analysis  “Mesh Currents” Flowing in Each Mesh Loop are UNKNOWNS  KVL Equations for Each Mesh Loop Constrain Solutions (M KVL equations for M Mesh Loops) Count nodes, meshes, look for supernode/supermesh All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

14. Nodal Analysis by Inspection  Requirement: All sources are independent current sources All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

15. Example 3-7: Nodal by Inspection @ node 1 @ node 2 @ node 3 @ node 4 Off-diagonal elementsCurrents into nodes G 13 G 11 All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

16. Mesh by Inspection Requirement: All sources are independent voltage sources All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

17. Linearity A circuit is linear if output is proportional to input  A function f(x) is linear if f(ax) = af(x)  All circuit elements will be assumed to be linear or can be modeled by linear equivalent circuits  Resistors V = IR  Linearly Dependent Sources  Capacitors  Inductors We will examine theorems and principles that apply to linear circuits to simplify analysis All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

18. Superposition Superposition trades off the examination of several simpler circuits in place of one complex circuit All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

19. Example 3-9: Superposition Contribution from I 0 Contribution from V 0 I 1 = 2 A I = I 1 + I 2 = 2 ‒ 3 = ‒ 1 A alone I 2 = ‒ 3 A All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

20. Cell Phone Today’s systems are complex. We use a block diagram approach to represent circuit sections. All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

21. Equivalent Circuit Representation  Fortunately, many circuits are linear  Simple equivalent circuits may be used to represent complex circuits  How many points do you need to define a line? All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

22. Thévenin’s Theorem Linear two-terminal circuit can be replaced by an equivalent circuit composed of a voltage source and a series resistor voltage across output with no load (open circuit) Resistance at terminals with all independent circuit sources set to zero All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

23. Norton’s Theorem Linear two-terminal circuit can be replaced by an equivalent circuit composed of a current source and parallel resistor Current through output with short circuit Resistance at terminals with all circuit sources set to zero All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

24. How Do We Find Thévenin/Norton Equivalent Circuits ?  Method 1: Open circuit/Short circuit 1. Analyze circuit to find 2. Analyze circuit to find Note: This method is applicable to any circuit, whether or not it contains dependent sources. All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

25. Example 3-10: Thévenin Equivalent All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

26. How Do We Find Thévenin/Norton Equivalent Circuits? Method 2: Equivalent Resistance 1. Analyze circuit to find either or Note: This method does not apply to circuits that contain dependent sources. 2. Deactivate all independent sources by replacing voltage sources with short circuits and current sources with open circuits. 3. Simplify circuit to find equivalent resistance All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

27. Example 3-11: R Th Replace with SC Replace with OC (Circuit has no dependent sources) All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

28. How Do We Find Thévenin/Norton Equivalent Circuits? Method 3: All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

29. Example All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

30. To find Example (cont.) All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

31. Power Transfer In many situations, we want to maximize power transfer to the load All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

34. Tech Brief 4: The LED All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

35. Tech Brief 4: The LED All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

36. Tech Brief 4: The LED All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

37. BJT: Our First 3 Terminal Device!  Active device with dc sources  Allows for input/output, gain/amplification, etc All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

38. BJT Equivalent Circuit Looks like a current amplifier with gain  All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

39. Digital Inverter With BJTs Output high Input low Output low Input high InOut 01 10 InOut BJT Rules: Vout cannot exceed Vcc=5V Vin cannot be negative All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

40. Nodal Analysis with Multisim See examples on DVD All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

41. Multisim Example: SPDT Switch All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press

42. Summary All rights reserved. Do not reproduce or distribute. © 2013 National Technology and Science Press