CHAPTERS 9

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CHAPTERS 9 12

• NETWORKS 2 ECE09.202.01
• 6 December 2006 Lecture 14
• ROWAN UNIVERSITY
• College of Engineering
• Dr Peter Mark Jansson, PP PE
• DEPARTMENT OF ELECTRICAL COMPUTER ENGINEERING
• Autumn Semester 2006 Quarter Two

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admin

• HW 7 due in lab next Tuesday
• Lab 2 will be due at final
• FINAL EXAM
• Monday Room 239
• 1230 230

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Chapters 9 12 key concepts

• Todays learning objectives
• complete response of RLC circuit
• forced response of RLC circuit
• undamped series RLC circuits
• introduce three-phase circuits

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complete response of an RLC circuit

• The complete response of an RLC circuit is the
  sum of the natural response and the forced
  response.

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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
KCL 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
KCL 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
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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
LC1 Write the final equation for the complete
response for v(t)
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complete response of an RLC circuit

• HW problem 9.8-9

Determine i(t) when is5u(t) and i(0)0 and
vc(0)0
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Where to begin 9.8-9?
What is characteristic equation? What are its
roots? What is ?? What is ??
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Where to begin 9.8-9?
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natural response Type 3underdamped unforced
parallel RLC circuit
The roots in this case are 2 complex roots
Complex underdamped
The natural response will be of the form
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HW 9.8-9
Substituting (1) into (2) yields
Is this right?
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Tables 9.13-1, 9.13-2, 9.13-3

• on page 399
• good study aids

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Chapter 12

• three phase circuits
• three phase voltages
• Wye (Y) and Delta (?) connections

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But first.
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What is 3-phase power?
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Wye and Delta configurations