ECE 4991 Electrical and Electronic Circuits Chapter 3

2 Where are we? Chapter 2 - The basic concepts and practice at analyzing simple electric circuits with sources and resistors Chapter 3 – More harder networks to analyze and the notion of equivalent circuits Chapter 4 – Capacitors and inductors added to the mix Chapter 5 – Analyzing transient situations in complex passive networks Chapter 8 – New subject – the wonders of operational amplifiers as system elements Chapter 9 – Introduction to semiconductors – the basics and diodes – more network analysis Chapter 10 – Bipolar junction transistors and how they work – now you can build your own op amp

3 What’s Important in Chapter 3 1.Definitions 2.Nodal Analysis 3.Mesh Analysis 4.The Principle of Superposition 5.Thevenin and Norton Equivalent Circuits 6.Condition for Maximum Power Transfer

4 1. Definitions Node voltages Branch currents “Ground” KCL Nodal Analysis Mesh currents KVL Mesh Analysis Principle of Superposition Equivalent circuit Thevenin theorem Norton theorem One-port networks Source loading

5 2. Nodal Analysis Used to “analyze” circuits Solve for currents, voltages, power, etc., throughout circuits Applies KCL to nodes –Often used in concert with Ohm’s Law

6 Node Method Find nodes – Identify ground node Label branch currents & node voltages Node voltages, if not defined by a voltage source, are independent variables Write KCL for nodes Solve for unknowns

7 Working with Nodal Analysis

8 I R1R1 R2R2 R3R3 R4R4 V

9 I R1R1 R2R2 R3R3 R4R4 V R5R5 R6R6

10 Working with Nodal Analysis

11 For Next Time 1.Sign onto Blackboard, if still have not 2.Practice Nodal Analysis 3.Learn about rest of chapter 3, particularly about mesh analysis

12 3. Mesh Analysis Also used to “analyze” circuits Solve for currents, voltages, power, etc., throughout circuits Applies KVL to meshes –Often used in concert with Ohm’s Law

13 Node Method Identify meshes and mesh currents For n meshes and m current sources, there are n-m independent variables Write KVL for all meshes with unknown mesh currents Solve for unknowns I

14 Working with Mesh Analysis I

15 Working with Mesh Analysis I R1R1 R2R2 R3R3 R4R4 V

16 Working with Mesh Analysis I R1R1 R2R2 R3R3 R4R4 V R5R5 R6R6

17 Working with Mesh Analysis

18 For Next Time 1.Sign onto Blackboard, if still have not 2.Keep practicing Nodal Analysis 3.Practice Mesh Analysis 4.Learn about rest of chapter 3, particularly about equivalent circuits

19 4. The Principle of Superposition When working with linear circuits, can find the solution for each energy source and combine the results Procedure: –Remove all but one energy source V sources  wires I sources  opens –Solve the circuit –Repeat for a different energy source –Add up the solutions

20 5. Thévenin and Norton Equivalent Circuits Thévenin Theorem When viewed from the load, any network composed of ideal voltage and current sources and of linear resistors, may be represented by an equivalent circuit consisting of an ideal voltage source V T in series with an equivalent resistance R T I  VTVT RTRT

21 Thévenin and Norton Equivalent Circuits Norton Theorem When viewed from the load, any network composed of ideal voltage and current sources and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source I N in parallel with an equivalent resistance R N I  ININ RNRN I

22 Thévenin Equivalence Equivalent Resistance 1.Remove load 2.Zero all current and voltage sources V sources  wires I sources  opens 3.Compute the resistance between the load terminals Equivalent Voltage 1.Remove the load 2.Define V OC as the open-circuit voltage across the load terminals 3.Solve for V OC

23 Thévenin Equivalent Circuits R1R1 R2R2 RLRL V R T = ?V T = ?

24 Thévenin Equivalent Circuits VTVT RTRT V R2R2 R1R1

25 Working with Thévenin Equivalent Circuits I R1R1 R2R2 R3R3 V R T = ?V T = ?

26 Working with Thévenin Equivalent Circuits VTVT RTRT

27 Practice with Thévenin Equivalent Circuits I R1R1 R3R3 R5R5 V R T = ?V T = ? R4R4 R2R2

28 Practice with Thévenin Equivalent Circuits

29 Chapter 2 and 3 Practice for Test

30 Chapter 2 and 3 Practice for Test

31 Chapter 2 and 3 Practice for Test

32 Chapter 2 and 3 Practice for Test

33 Chapter 2 and 3 Practice for Test

34 Chapter 2 and 3 Practice for Test