ELECTRIC CIRCUITS ECSE2010 Spring 2003 Class 5

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ELECTRIC CIRCUITSECSE-2010Spring 2003 Class 5

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ASSIGNMENTS DUE

• Today (Thursday)
• Activities 5-1, 5-2, 5-3 (In Class)
• Next Monday
• HW 2 Due
• Experiment 1 Report Due
• Activities 6-1, 6-2, 6-3, 6-4 (In Class)
• Next Tuesday/Wednesday
• Will do Experiment 2 In Class (EP-2)
• Activities 7-1, 7-2, (In Class)

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REVIEW

• Controlled/Dependent Sources
• VCVS, VCCS, CCVS, CCCS
• Used to Model Electronic Devices
• Make Circuits Interesting (and Harder)
• Equivalent Resistance
• Replace any Load Network with Req
• Load Network Rs, Controlled Sources, No
  Independent Sources

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CONTROLLED SOURCES
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CONTROLLED SOURCES
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CONTROLLED SOURCES
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CONTROLLED SOURCES
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EQUIVALENT RESISTANCE
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Req with Controlled Sources
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REVIEW

• Req with Controlled Sources
• Connect Test Voltage vt
• Define it Using Active Convention
• Find it in terms of vt (Use KCL, KVL, Ohms Law,
  etc.)
• Req vt / it

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WHERE ARE WE?

• Circuit Elements
• Ideal, Independent i and v sources
• Ideal, Controlled i and v sources
• Resistors
• Potentiometers
• Have Learned How to Define all is and vs using
  Active/Passive Convention
• Have Begun to do Circuit Analysis Solving for
  all is and vs

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WHERE ARE WE?

• Circuit Analysis Techniques
• Ohms Law for Rs
• KCL and KVL
• Simplify Circuits using Series/Parallel Rs
• Replace Load Network with Req
• Sometimes Hard to Know Where to Start
• Will Now Develop Systematic Techniques that will
  Always Work
• Node Equations Today
• Mesh Equations on Monday

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NODE EQUATIONS

• Systematic Technique for Solving ANY Linear
  Circuit
• Will Always Work!
• Not Always the Easiest Technique
• Will Also Learn About Mesh Equations
• Can Use Either Technique But Cannot Mix
• Very Powerful Techniques!!
• Will Use For Rest of Course

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EXAMPLE
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NODE EQUATIONS

• See Example Ckt
• Node Equation Procedure
• Label Unknown Node Voltages (v1, v2, )

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EXAMPLE
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NODE EQUATIONS

• Node Equation Procedure
• Label Unknown Node Voltages (v1, v2, )
• of Unknown Node Voltages of Nodes - of
  Voltage Sources - 1 (Reference)
• Example 4 Nodes - 1 Voltage Source - 1 2
  Unknown Node Voltages v1, v2
• Write a KCL at Each Unknown Node Voltage
• Sum of Currents Out 0
• Express is in terms of Node Voltages

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EXAMPLE
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NODE EQUATIONS

• Example

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NODE EQUATIONS

• Example

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NODE EQUATIONS

• Writing a KCL at Each Unknown Node Voltage will
  Always Provide of Linear Equations
  Unknowns
• Can Always Solve for v1, v2, .
• Node Equations will ALWAYS work
• Can take it to the bank

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ACTIVITY 5-1

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ACTIVITY 5-1

• 6 Nodes - 2 Voltage Sources - 1 (Ref)
• gt 3 Unknown Node Voltages
• v1, v2, v3

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ACTIVITY 5-1

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ACTIVITY 5-1

• 6 Nodes - 2 Voltage Sources - 1 (Ref)
• gt 3 Unknown Node Voltages
• v1, v2, v3
• Write a KCL at each Unknown Node Voltage,
  relating Currents to the Node Voltages using
  Ohms Law
• Usually best to sum Currents OUT of the Node

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ACTIVITY 5-1

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ACTIVITY 5-1
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ACTIVITY 5-1
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ACTIVITY 5-1
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ACTIVITY 5-1
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ACTIVITY 5-2

• For Large Matrices, Use MAPLE
• Usually for n gt 2
• Must Include with (linalg)
• Two Ways to Solve using MAPLE
• See MAPLE Scripts
• Must Be Careful with Syntax

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ACTIVITY 5-2

• MAPLE SCRIPT Classic Method
• gtwith (linalg)
• gtGR-gtmatrix(3,3,1/51/101/R,
  -1/R,-1/10,-1/R,1/201/41/R,0,
  -1/10,0,1/10)
• gtG(R)
• gtIsmatrix(3,1,14,-10,-2)

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ACTIVITY 5-2

• gtvR-gtevalm(inverse(G(R))Is)
• means matrix multiplication
• gtv(R)
• gtv(1)
• gtiaR-gt(v(R)2,1-2)
• gtia(R)
• gtia(1)

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ACTIVITY 5-2

• MAPLE SCRIPT Gaussjord Method
• gtwith (linalg)
• gtGR-gtmatrix(3,4,1/51/101/R,
  -1/R,-1/10,14,-1/R,1/201/41/R,0,
  -10,-1/10,0,1/10,-2)
• gtG(R)
• gtBR-gtguassjord(G(R))
• gtB(R)
• leads to same result

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ACTIVITY 5-3a
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ACTIVITY 5-3a

• KCL at Node v
• Sum of Currents Out of Node 0
• (v-30)/6 (v8)/2 (v8-30)/10 - 5 0
• v (1/6 1/2 1/10) 30/6 8/2 22/10 5
• gt (23/30) v 8.2 gt v 10.7 V
• Writing a KCL at each Unknown Node always works!

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ACTIVITY 5-3b
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ACTIVITY 5-3b

• 5 Nodes - 2 Voltage Sources - 1 (Ref)
• 2 Unknown Node Voltages, v1, v2
• Write a KCL at each Unknown Node
• Sum of Currents Out 0

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ACTIVITY 5-3b
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ACTIVITY 5-3b
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ACTIVITY 5-3b
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ACTIVITY 5-3b