Chapter 4 Circuit Analysis Techniques A) Node Voltage B) Mesh Current.
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Transcript of Chapter 4 Circuit Analysis Techniques A) Node Voltage B) Mesh Current.
![Page 1: Chapter 4 Circuit Analysis Techniques A) Node Voltage B) Mesh Current.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649c785503460f9492dfe6/html5/thumbnails/1.jpg)
Chapter 4Circuit 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 ?
![Page 5: Chapter 4 Circuit Analysis Techniques A) Node Voltage B) Mesh Current.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649c785503460f9492dfe6/html5/thumbnails/5.jpg)
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 currentscan then be derived
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Cleo: 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 Method1. 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 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 3 Find the indicated currents; use NV
IA = -27 μA, IB = -133 μA, IC = 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 6:47
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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 solve
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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)