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Chapter 4 Circuit Analysis Techniques A) Node Voltage B) Mesh Current

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Node Voltage and Mesh Current methods derive a minimal set of equations solve all circuit variables Node Voltage uses KCL Mesh Current uses KVL NV more powerful than MC –MC only solves "planar circuits"

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Non Planar Circuit Node Voltage CAN solve, MC cannot

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Node Voltage Method Basic idea—What is the current i ?

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Node Voltage Method What if unknown voltages

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Node Voltage Method v1,v2 label unknown node voltages

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NV solves unknown node voltages Node: point where two or more components connect Essential node: point where 3 or more components connect all currents can then be derived

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CleoCleo: determine the number of nodes in each circuit. Draw closed contours around each node

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Now encircle the "Essential Nodes"

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It can be proven... The number of NV equations needed to fully solve a circuit is Ne – 1 –Ne is number of essential node voltages (including the reference node)

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Encircle the "Essential Nodes" in this circuit

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Node Voltage Method 1.establish a ground node 2.label unknown essential node voltages (v1 is voltage relative to ground) 3.write KCL for each unknown essential node 4.solve system of eqns

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Find v1, v2

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Remember Matlab/Freemat To solve systems of equations such as 9v1 – v2 = 36 -3v1 + 11v2 = 180 use the following A = [ 9 -1 ; -3 11]; b = [36; 180] A\b ans = 6 18

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Cleo: Problem 2Cleo: Problem 2 Find all the node voltages in the circuit. V50k = 2.86V (Watch video 4:42)

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Do handout problems 1,2

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NV Special Cases Dependent sources Voltage source applied between 1 essential node and ground Voltage source applied between 2 essential nodes (not ground)

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Voltage Source between Essential Node and ground How to figure current down that branch? –you don't have to! –don't write node equation at v1 –v1 = 15V by inspection –one less unknown node to solve

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Problem 3Problem 3 Find the indicated currents; use NV I A = -27 μA, I B = -133 μA, I C = 17.1 μA Only 1 unknown node

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Can't write NV at v1 (current thru source?) nor V2 (same reason) SOLN: –SUPERNODE! –KCL applies to regions as well as nodes 1) Circle V1+V2 2) write KCL for Supernode 3) KVL v1, v2 and 10V Floating Voltage Source (Supernode)

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Use Supernode NV to Find v1,v2

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Dependent Sources all types possible adds another unknown (ix) but ix can be expressed in terms of node voltages eventually removed from node equations not difficult to handle

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Cleo: Problem 1 Use nodal analysis to determine Ix (.027A) Video 6:47Problem 1

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Do Handout problems 3, 4

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Handout Problems

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1) Cleo:Problem 1 Write 1 NV eq at V2 and solveProblem 1

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2) Use NV to find v1, v2 and i1 (60,10,10) b) how much power delivered by 15A src? (-900W, del) c) how about 5A source? (50W absorb)

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3) Write a Supernode NV to find V1, V2(6,18)

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4) Find v1, v2, ix (16,10,6/5)

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