NodeAnalysispp2

NodeAnalysispp2 - NODAL AND LOOP ANALYSIS TECHNIQUES...

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1 NODAL AND LOOP ANALYSIS TECHNIQUES LEARNING GOALS CIRCUITS WITH OPERATIONAL AMPLIFIERS Develop systematic techniques to determine all the voltages and currents in a circuit NODAL ANALYSIS LOOP ANALYSIS Op-amps are very important devices, widely available, that permit the design of very useful circuits; e.g., integrators, sensors, timing circuits, just to name a few. ...and they can be modeled by circuits with dependent sources NODE ANALYSIS • One of the systematic ways to determine every voltage and current in a circuit The variables used to describe the circuit will be “Node Voltages” -- The voltages of each node with respect to a pre-selected reference node
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2 IT IS INSTRUCTIVE TO START THE PRESENTATION WITH A RECAP OF A PROBLEM SOLVED BEFORE USING SERIES/ PARALLEL RESISTOR COMBINATIONS COMPUTE ALL THE VOLTAGES AND CURRENTS IN THIS CIRCUIT SECOND: “BACKTRACK” USING KVL, KCL OHM’S k V I a 6 2 = : S OHM' 0 3 2 1 = I I I : KCL 3 * 3 I k V b = : S OHM' …OTHER OPTIONS. .. 4 3 4 * 4 12 4 12 I k V I I b = + = 5 3 4 5 * 3 0 I k V I I I C = = + : S OHM' : KCL k 12 k k 12 || 4 k 6 k k 6 || 6 k V I 12 12 1 = ) 12 ( 9 3 3 + = a V 3 I FIRST REDUCE TO A SINGLE LOOP CIRCUIT
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3 THE NODE ANALYSIS PERSPECTIVE THERE ARE FIVE NODES. IF ONE NODE IS SELECTED AS REFERENCE THEN THERE ARE FOUR VOLTAGES WITH RESPECT TO THE REFERENCE NODE a S a S V V V V V V = = + + 1 1 0 b a b a V V V V V V = = + + 3 3 0 ______ = ca V QUESTION DRILL REFERENCE S V a V b V c V + 1 V KVL + 3 V KVL + 5 V WHAT IS THE PATTERN??? KVL 0 5 = + b c V V V ONCE THE VOLTAGES ARE KNOWN THE CURRENTS CAN BE COMPUTED USING OHM’S LAW THEOREM: IF ALL NODE VOLTAGES WITH RESPECT TO A COMMON REFERENCE NODE ARE KNOWN THEN ONE CAN DETERMINE ANY OTHER ELECTRICAL VARIABLE FOR THE CIRCUIT A GENERAL VIEW + R v N m R v v v = c b V V V = 5 THE REFERENCE DIRECTION FOR CURRENTS IS IRRELEVANT ' i + R v USING THE LEFT-RIGHT REFERENCE DIRECTION THE VOLTAGE DROP ACROSS THE RESISTOR MUST HAVE THE POLARITY SHOWN R v v i N m = LAW S OHM' IF THE CURRENT REFERENCE DIRECTION IS REVERSED . .. + ' R v THE PASSIVE SIGN CONVENTION WILL ASSIGN THE REVERSE REFERENCE POLARITY TO THE VOLTAGE ACROSS THE RESISTOR R v v i m N = ' LAW S OHM' ' i i = PASSIVE SIGN CONVENTION RULES!
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4 DEFINING THE REFERENCE NODE IS VITAL S MEANINGLES IS 4V V STATEMENT THE 1 = UNTIL THE REFERENCE POINT IS DEFINED BY CONVENTION THE GROUND SYMBOL SPECIFIES THE REFERENCE POINT. + V 4 ALL NODE VOLTAGES ARE MEASURED WITH RESPECT TO THAT REFERENCE POINT + V 2 _____? 12 = V + 12 V THE STRATEGY FOR NODE ANALYSIS 1. IDENTIFY ALL NODES AND SELECT A REFERENCE NODE 2. IDENTIFY KNOWN NODE VOLTAGES 3. AT EACH NODE WITH UNKNOWN VOLTAGE WRITE A KCL EQUATION (e.g.,SUM OF CURRENT LEAVING =0) 0 : @ 3 2 1 = + + I I I V a 0 3 6 9 = + + k V V k V k V V b a a s a 4. REPLACE CURRENTS IN TERMS OF NODE VOLTAGES AND GET ALGEBRAIC EQUATIONS IN THE NODE VOLTAGES . ..
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NodeAnalysispp2 - NODAL AND LOOP ANALYSIS TECHNIQUES...

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