First Order Circuits, Systems, and Differential Equations

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• First Order Circuits, Systems, and Differential
  Equations

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HOMEWORK

• Read Sections 7.4, 5, 6.8
• Work Problems
• 7.4-1, 4, 6
• 7.5-1, 4
• Section 6.8, End of Section Quiz Question Q6.8-1

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SYNONYMS

• Realization
• Design
• System Diagram
• Block Diagram
• Simulation

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Nondynamic System Elements

• Summer/Adder

• Splitter/Takeoff

• Scalar Multiplier

• Function Multiplier

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Dynamic System Elements

• Differentiator

• Integrator

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ExampleDraw a Simulation Diagram for the
Differential Equation dy/dt ay x(t)

• Step 1 Convert to Operator Form

• Step 2 Move ay(t) to the Right Side

• Step 3 Multiply Both Sides by 1/p

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• Step 3 (Repeated for Convenience)

• Step 4 Read the Equation Left to Right, Draw the
  Diagram Right to Left!

• Definition This Configuration is Called a
  "Recursive" Realization

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Another Form

• The Original Differential Equation

• Use the First Order Solution Operator

• Read the Equation Right to Left, Draw the Diagram
  Left to Right!

Non-Recursive
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Example Draw a Recursive Simulation Diagram with
no Differentiators for H(p) 2p/(p2)
Solution
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1st Order Block
1/(p2)
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Can Realize with either the Recursive or
Nonrecursive Diagrams Previously Discussed
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Example Draw a Recursive Simulation Diagram for
v(t) in the Circuit below and find its Unit Step
Response
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Solution
8/p
Z1(p)
4/p
Z2(p)
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Solution (continued)
v(t)
v1(t)
v2(t)
v1(t)
v(t)

vs(t)
v2(t)
1/(p8/3)
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Solution (continued)

-
1
1
3
2
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Plot (for t gt 0)
s(t)
t