Circuit Analysis Techniques Key Concepts Node voltage analysis and equations Super node Mesh current analysis and equations Super mesh Source transformation Linearity Nonlinear loads Superposition Thevenin and Norton models Maximum Signal Transfer Interface Design -1- Circuit Analysis Techniques Key Words Node-voltage KVL constraint KCL constraint Reference node Supernode Supermesh Nonreference nodes Mesh currents Planar circuit Source transformation Linear circuits. Homogeneity Additivity Proportionality Superposition Unit output method Lookback resistance Maximum signal transfer Maximum power transfer -2- Circuit Analysis Techniques Reading The Analysis & Design of Linear Circuits Sections 3-1 to 3-6 Pages 73-153. Roland E. Thomas, Albert J. Rosa Gregory J. Toussaint, -3- Circuit Analysis Techniques Node Voltage Analysis and Equations Node Voltage Analysis – Getting Started • What is a node? • What does node-voltage analysis find? • Using KCL what do we know about node currents? • What is the current that flows through the resistor? -4- Circuit Analysis Techniques Node Voltage Analysis and Equations Node Voltage Analysis – Doing the Analysis 1. Find ground 2. Assume currents leaving a node are positive and those entering are negative 3. Let’s analyze the circuit… V V A S V V V V V 0 B S B C 0 B R R R 1 2 3 -5- Circuit Analysis Techniques Super Node Working with Super Nodes The circuit has a voltage source between two non-ground nodes 1. Draw a node around the non-grounded source 2. Treat the exiting currents as if they were exiting from one node VA 0 VA VS1 VC VS1 IS 0 R2 R1 R3 -6- Circuit Analysis Techniques Mesh Current Analysis and Equations Mesh Current Analysis – Getting Started • How many loops? • How many meshes? • How many KVL equations? -7- Circuit Analysis Techniques Mesh Current Analysis and Equations Mesh Current Analysis – Multiple Currents in one Branch There are two types of voltage drops in a branch element • The drop with one mesh current flowing through that element • The drop with two branch currents flowing in opposite directions -8- Circuit Analysis Techniques Super Mesh Mesh Current Analysis – Working with Super Meshes • The super mesh is the dual of the super node R2I A R1 ( I A IC ) R3 ( IB IC ) R4IB 0 VS R3 ( IC IB ) R1 ( IC I A ) 0 -9- Circuit Analysis Techniques Linearity Linear Circuit Analysis – Proportionality • • • • The relationship between input and output – Gain We call the gain K Gain may be positive or negative What is the gain – K – in this circuit? - 10 - Circuit Analysis Techniques Linearity Linear Circuit Analysis – Superposition • For a linear circuit with multiple sources…. • We can compute the desired output by -Turning off all sources but one - Computing the output from the one remaining source - Repeating for each source - Summing the results • What are the outputs Vx and Vy Current Source 0 : VXV 100 10 5V 100 100 1 0.1 Voltage Source 0 : VXI 100 100 5 V 1 1 100 100 - 11 - Circuit Analysis Techniques Linearity Linear Circuit Analysis – Unit Output Modeling Unit Output Modeling – An application of proportionality 1. Objective is to find the gain – K of a circuit 2. Once K is known – we can find the output for any input 3. Start with easy numbers - Let i0 = 1A - Work backwards… - 12 - Circuit Analysis Techniques Thévenin and Norton Equivalent Models Thévenin and Norton Equivalent Circuits 1. The key initial concept…Any linear circuit can be represented by - A Thévenin source VT in series with a Thévenin resistor RT 2. The key to the solution… - Find VT and RT Problem… What value of RL will give us Vout of 2V? Solution… Find the Thévenin equivalent circuit then RL - 13 - Circuit Analysis Techniques Interface Design Interface Circuit Design Things to think about when designing an interface to a load… 1. What i, V, or p is available without the interface? - This is the maximum i, V, or p available from the source 2. Does the load require less than the maximum? Design an interface that will enable 3 V across the load - 14 - Circuit Analysis Techniques SUMMARY: This unit introduced basic functional circuit analysis, developed the Thevenin and Norton circuit models, then extended these concepts and techniques to interface circuit design. - 15 - Circuit Analysis Techniques REMINDERS: Assignments from Unit 1 are due at start of next unit. Prepare for the next unit by reading: Thomas, Rosa, and Toussaint, Sections 4-1 to 4-6 and 5-1 to 5-6, prior to coming to class. - 16 -