1. CIRCUITS by Ulaby & Maharbiz
3. Analysis Techniques
CIRCUITS by Ulaby & Maharbiz

2. Overview

3. Node-Voltage Method
Node 1
Node 3
Node 2
Node 2
Node 3

4. Node-Voltage Method Three equations in 3 unknowns:
Solve using Cramer’s rule, matrix
inversion, or MATLAB

6. Supernode
A supernode is formed when a voltage source connects two extraordinary nodes
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

7. KCL at Supernode =
Note that “internal” current in supernode cancels, simplifying KCL expressions
Takes care of unknown current in a voltage source

8. Example 3-3: Supernode
Solution:
Supernode
Determine: V1 and V2

9. Mesh-Current Method Two equations in 2 unknowns:
Solve using Cramer’s rule, matrix
inversion, or MATLAB

10. Example 3-5: Mesh Analysis
But
Mesh 1
Hence
Mesh 2
Mesh 3

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)

12. Example 3-6: Supermesh Mesh 1 Solution gives: Mesh 2 SuperMesh 3/4
Supermesh Auxiliary Equation

14. 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

15. Nodal Analysis by Inspection
Requirement: All sources are independent current sources

16. Example 3-7: Nodal by Inspection
Off-diagonal elements
Currents into nodes
G11
G13
@ node 1
@ node 2
@ node 3
@ node 4

17. Mesh by Inspection
Requirement: All sources are independent voltage sources

18. A circuit is linear if output is proportional to input
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

19. Superposition
Superposition trades off the examination of several simpler circuits in place of one complex circuit

20. Example 3-9: Superposition
Contribution from I0
alone
Contribution from V0
alone
I1 = 2 A
I2 = ‒3 A
I = I1 + I2 = 2 ‒ 3 = ‒1 A

21. Cell Phone
Today’s systems are complex. We use a block diagram approach to represent circuit sections.

22. 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?

23. voltage across output with no load (open circuit)
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

24. 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

25. 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.

26. Example 3-10: Thévenin Equivalent

27. How Do We Find Thévenin/Norton Equivalent Circuits?
Method 2: Equivalent Resistance 1. Analyze circuit to find either or
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
Note: This method does not apply to circuits that contain dependent sources.

28. Example 3-11: RTh (Circuit has no dependent sources) Replace with SC
Replace with OC

29. How Do We Find Thévenin/Norton Equivalent Circuits?
Method 3:

30. Example

31. To find

32. In many situations, we want to maximize power transfer to the load

35. Tech Brief 5: The LED

36. BJT: Our First 3 Terminal Device!
Active device with dc sources
Allows for input/output, gain/amplification, etc

37. BJT Equivalent Circuit
Looks like a current amplifier
with gain b

38. Digital Inverter With BJTs
Out 1
BJT Rules:
Vout cannot exceed Vcc=5V
Vin cannot be negative
Output high
Input low In
Out
Output low
Input high

39. Nodal Analysis with Multisim
See examples on DVD

40. Multisim Example: SPDT Switch

41. Tech Brief 6: Display Technologies

42. Tech Brief 6: Display Technologies
Digital Light Processing (DLP)

43. Summary