ELECTRIC CIRCUITS ECSE2010 Spring 2003 Class 6

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ELECTRIC CIRCUITSECSE-2010Spring 2003 Class 6

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ASSIGNMENTS DUE

• Today (Monday)
• HW 2 Due
• Experiment 1 Report Due
• Activities 6-1, 6-2, 6-3, 6-4 (In Class)
• Activities 6-2 and 6-3 will use an ILM
• Tuesday/Wednesday
• Will do Experiment 2 In Class (EP-2)
• Activities 7-1, 7-2, (In Class)
• Thursday
• Will do Experiment 3 In Class (EP-3)
• Activities 8-1, 8-2, (In Class)

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OPEN SHOP HOURS

• All in JEC 4104 (Studio)
• Wednesdays
• 9-10 am Prof. Nagy
• 2-4 pm Prof. Jennings
• Thursdays
• 9-10 am Prof. Millard
• May Add More Later

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REVIEW

• Node Equations
• Technique to Solve Any Linear Circuit
• Label Unknown Node Voltages, v1, v2, v3, etc.
• Unknown Nodes Nodes - Voltage Sources 1
  (Reference)
• Write a KCL at Each Unknown Node Voltage
• Sum of Currents OUT of Node 0
• Relate Currents to Node Voltages (Ohms Law)
• Will Always Get the Same Number of Equations as
  Unknowns
• Solve Linear, Algebraic Equations using any
  Technique that Works for You

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ADD CONTROLLED SOURCES

• Controlled/Dependent Sources Always Make Things
  Harder
• Must Now Find a Constraint Equation
• Must Relate Controlling Voltage or Current to
  Unknown Node Voltages (or unknown Mesh Currents
  as we will see a little later today)
• Must Do By Inspection THINK!
• No Systematic Way of finding the Constraint
  Equation
• Will Explore with Activity 6-1

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ACTIVITY 6-1

• Define v, i using Active Convention

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ACTIVITY 6-1

• Use Node Equations to find v1, v2
• 4 Nodes - 1 Voltage Source - 1 (Ref) 2 Unknown
  Node Voltages
• v1, v2 vs is assumed to be known
• Constraint Equation
• Need to Relate ix to v1, v2
• ix (vs - v1) / 5k
• 6ix 1.2 vs - 1.2 v1

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ACTIVITY 6-1

• Define v, i using Active Convention

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ACTIVITY 6-1
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ACTIVITY 6-1
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NODE EQUATIONS WITH CONTROLLED SOURCES

• Find the Constraint Equation
• Must Relate Controlling Voltage or Current to
  Unknown Node Voltages
• Proceed with Usual Node Equations
• Write KCLs in Usual Way
• Will have an Extra Step of Algebra
• Matrix is no longer Symmetric

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MESH EQUATIONS

• Another Systematic Technique for Solving ANY
  Linear Circuit
• Will Always Work!
• Not Always the Easiest Technique
• Can Use Either Node Equations or Mesh Equations,
  But Cannot Mix
• Usually Must Choose Which to Use
• Will Say More About This Later

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EXAMPLE
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MESH EQUATIONS

• Mesh Equation Procedure
• Label and Define ALL Mesh Currents
• Mesh Window Pane in Circuit
• Mesh Current A Current defined as flowing all
  the way around a Mesh
• Some Circuit Elements will have more than 1 Mesh
  Current flowing in them
• Mesh Currents must satisfy KCL
• Must Define Both Unknown Mesh Currents and Known
  Currents from Current Sources
• May Choose Any Direction for Unknown Mesh Currents

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EXAMPLE
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MESH EQUATIONS

• Mesh Equation Procedure
• Label and Define ALL Mesh Currents
• Unknown Mesh Currents and Currents from Current
  Sources
• of Unknown Mesh Currents of Meshes - of
  Current Sources
• Example 2 Meshes - 0 Current Sources 2
  Unknown Mesh Currents i1 and i2
• Write a KVL around Each Unknown Mesh Current
• Sum of Voltages due to All Mesh Currents 0
• Express vs in terms of Mesh Currents using Ohms
  Law

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EXAMPLE
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EXAMPLE
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MESH EQUATIONS

• Write KVL Around Each Unknown Mesh Current (i1,
  i2 in Example)
• Go Backwards Around Current Arrow
• Why Backwards? gt Makes terms involving Unknown
  Mesh Currents Positive
• For This Example
• i1 R2 - i2 R2 i1 R1 - Vin 0
• i2 R4 i2 R3 i2 R2 - i1 R2 0
• 2 Equations, 2 Unknowns gt Can Solve for i1 and
  i2

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MESH EQUATIONS

• Writing a KVL around Each Unknown Mesh Current
  will Always Provide of Linear, Algebraic
  Equations Unknown Mesh Currents
• Can Always Solve for i1, i2, .
• For a Large Number of Unknown Mesh Currents,
  usually write equations in Matrix Form to solve
  using MAPLE, MATLAB, Cramers Rule, etc.

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CIRCUIT SOLVER

• An Interactive Learning Module (ILM) developed by
  Academy for Electronic Media
• 1 of Many ILMs developed at Rensselaer
• http//www.academy.rpi.edu/projects/ccli
• Click on Circuit Solver version 2
• Choose 2 Mesh First - Then Activity 4-3
• Activity 4-3 should read Activity 6-3
• Activity 6-3 is same as Activity 6-4
• Will do with ILM (6-3) and by Hand (6-4)

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2 MESH ACTIVITY 6-2

• Same Circuit as Example
• Define Mesh Currents i1 and i2
• Drag and Drop Mesh Currents
• Create KVL Around i1
• Click to Add or Delete a Term
• KVL Around i1 i1 R2 - i2 R2 i1 R1 Vin 0
• KVL Around i2 i2 R4 i2 R3 i2 R2 i1 R2 0
• Click to Solve for all Rs 1 ohm
• vout .2 vin

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ACTIVITY 6-2
ACTIVITY 6-2
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ACTIVITY 6-2

• KVL Around Mesh i1 i1 - i2 i1 Vin 0
• gt 2i1 - i2 Vin
• KVL Around Mesh i2 i2 i2 i2 i1 0
• gt - i1 3i2 0
• gt - 2i1 6i2 0
• Add 5i2 Vin gt i2 .2 Vin Amps
• vout i2 (1 ohm) .2 Vin Volts
• Checks with Series/Parallel Method

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ACTIVITY 6-3 (4-3 in ILM)

• Same as Activity 6-4
• First Solve using Circuit Solver
• Just Write Answer Down on Paper to be Turned In
• Then solve by Hand (Activity 6-4)
• Feel Free to Comment on Whether ILM was Helpful
  to You

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ACTIVITY 6-4
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ACTIVITY 6-4

• 5 Meshes 2 Current Sources 3 Unknown Mesh
  Currents
• ii, i2, i3
• Must Define All Mesh Currents Known and Unknown
• Must be Careful with these to make sure Mesh
  Currents are Unique
• This Takes Practice!

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ACTIVITY 6-4
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ACTIVITY 6-4

• Write KVLs around Unknown Meshes
• Mesh 1 - 10 9 (i1 - i3) 7 i1 0
• (16) i1 (0) i2 (- 9) i3 10
• Mesh 2 5 ( i2 4) 2 (i2 - i3) 10 0
• (0) i1 (7) i2 (- 2) i3 - 30
• Mesh 3 8 (i3 - 3) 9 (i3 - i1) 2 (i3 - i2)
  6 (i3 4) 0
• (- 9) i1 (- 2) i2 (25) i3 0
• KVLs Will Always Work
• Can now Solve for i1, i2, i3

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ACTIVITY 6-4
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ADD CONTROLLED SOURCES

• Always Makes Things Harder
• Must Find a Constraint Equation
• Relate Controlling Voltage or Current to Unknown
  Mesh Currents (or Unknown Node Voltages if using
  Node Equations)
• Must Do By Inspection THINK!
• Algebra becomes more difficult