EGR 277 - PowerPoint PPT Presentation

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EGR 277

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Lecture #19 EGR 260 Circuit Analysis Reading Assignment: ... Two common second-order circuits are now considered: series RLC circuits parallel RLC circuits. – PowerPoint PPT presentation

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Title: EGR 277


1
Lecture 19 EGR 260 Circuit Analysis
Reading Assignment Chapter 8 in Electric
Circuits, 9th Ed. by Nilsson
  • Series and Parallel RLC Circuits
  • Two common second-order circuits are now
    considered
  • series RLC circuits
  • parallel RLC circuits.
  • Relationships for these circuits can be easily
    developed such that the characteristic equation
    can be determined directly from component values
    without writing a differential equation for each
    example.
  • A general 2nd-order characteristic equation has
    the form
  • A general 2nd-order characteristic equation has
    the form s2 2?s wo2 0
  • where
  • ? damping coefficient
  • wo resonant frequency

2
Lecture 19 EGR 260 Circuit Analysis
Series RLC Circuit - develop expressions for ?
and wo
3
Lecture 19 EGR 260 Circuit Analysis
Parallel RLC Circuit - develop expressions for ?
and wo
4
Lecture 19 EGR 260 Circuit Analysis
  • Procedure for analyzing 2nd-order circuits
    (series RLC and parallel RLC)
  • 1. Find the characteristic equation and the
    natural response
  • Is the circuit a series RLC or parallel RLC? (for
    t gt 0 with independent sources killed)
  • Find ? and wo2 and use these values in the
    characteristic equation s2 2?s wo2.
  • Find the roots of the characteristic equation
    (characteristic roots or natural frequencies).
  • Determine the form of the natural response based
    on the type of characteristic roots
  • Overdamped Real, distinct roots (s1 and s2)
  • Underdamped Complex roots (s1,s2 ??j?)
  • Critically damped Repeated roots (ss1s2)
  • Find the forced response - Analyze the circuit
    at t ? to find xf x(?).
  • Find the initial conditions, x(0) and x(0).
  • A) Find x(0) by analyzing the circuit at t 0-
    (find all capacitor voltages and inductor
    currents)
  • Analyze the circuit at t 0 (using vC(0) and iL
    (0) from step 3B) and find
  • 4. Find the complete response

5
Lecture 19 EGR 260 Circuit Analysis
Example Determine v(t) in the circuit shown
below for t gt 0 if A) R 7 B) R 2 C) R
6
Lecture 19 EGR 260 Circuit Analysis
Example B) Continued with R 2
7
Lecture 19 EGR 260 Circuit Analysis
Example C) Continued with R
8
Lecture 19 EGR 260 Circuit Analysis
Example Determine v(t) in the circuit shown
below for t gt 0.
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