NETWORKS 2: 090920201

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CHAPTER 9

• NETWORKS 2 0909202-01
• 13 December 2004 Lecture 13
• ROWAN UNIVERSITY
• College of Engineering
• Dr Peter Mark Jansson, PP PE
• DEPARTMENT OF ELECTRICAL COMPUTER ENGINEERING
• Autumn Semester 2005 Quarter Two

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admin

• Next Thursday 7.30-1000AM (15 Dec)
• Final Exam
• Thursday noon Lab Report due
• No Late Homework will be accepted after the
  Final Exam

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Chapter 9 key concepts

• Todays learning objectives
• forced response of RLC circuit
• complete response of RLC circuit
• review types of problems that will be on final
  test

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forced response of an RLC circuit
The forced response of a circuit described by a
2nd order differential equation to a forcing
function will often be of the same form as the
forcing function
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forced response of an RLC circuit
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process to find forced response

• KVL, KCL, etc. to get 2nd order diff eq
• divide by LC etc. to get standard form
• substitute component values
• assume a response (of same form)
• solve for unknown

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KVL, KCL, etc. to get 2nd order diff eq
R 6? L 7H C 1/42F is 8e-2t A
KVL v/R i C dv/dt is v L di/dt
dv/dt L di2/dt2
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divide by LC, etc. to get standard form
KVL L di/dt /R i CL di2/dt2 is
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substitute component values
R 6? L 7H C 1/42F is 8e-2t A
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assume a response (of same form)
Response if Be-2t
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solve for unknown
LC1 Write the final equation for the forced
response for i(t)
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complete response of an RLC circuit

• the complete response of a circuit with two
  irreducible energy storage elements x(t) can be
  represented by its two components, namely the
  natural response (xn) and the forced response
  (xf)

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process to find complete response

• KVL, KCL, etc. to get 2nd order diff eq
• get standard form of natural response
• examine form of forcing function
• assume a forced response (of same form)
• solve for unknowns with equations and initial
  conditions using Cramers rule

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complete response of an RLC circuit
When L1H, C1/6F, R5O and Vs 2/3(e-t)V
Initial conditions v(0) 10V, dv(0)/dt -2V
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complete response of an RLC circuit1) KVL to get
circuits 2nd order diff. eqn.
KVL for the loop -vs Ldi/dt vC Ri 0
Equation for capacitor i Cdv/dt Substituting
value of i from capacitor into KVL
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complete response of an RLC circuit2) get
standard form of natural response
When L1H, C1/6F, R5O and Vs 2/3(e-t)V
Substituting L,C R values s2 5s 6 0
Use Characteristic Equation to get roots
(s2)(s3) 0, s1 -2, s2 -3
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REMEMBERforced response of an RLC circuit
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complete response of an RLC circuit3) examine
form of forcing function4) assume forced
response of same form
When L1H, C1/6F, R5O and Vs 2/3(e-t)V
Forcing Function Vs 2/3 (e-t)V
Using previous table Ke-at will have response
Ae-at
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complete response of an RLC circuit5) solve for
unknowns with initial conditions
Initial conditions v(0) 10V, dv(0)/dt -2V
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complete response of an RLC circuit5) solve for
unknowns with initial conditions
Initial conditions v(0) 10V, dv(0)/dt -2V
LC2 Write the final equation for the complete
response for v(t)
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complete response of an RLC circuit

• HW problem 9.9.9

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Tables 9.14-1, 9.14-2, 9.14-3

• good study aids

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Final Test Review

• contributors to ECE knowledge
• sinusoidal functions and plotting
• real, reactive and apparent power
• power triangle
• RLC circuits and solutions
• Laplace transforms and inverse
• transfer function