EGR 277

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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

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Lecture 19 EGR 260 Circuit Analysis
Series RLC Circuit - develop expressions for ?
and wo
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Lecture 19 EGR 260 Circuit Analysis
Parallel RLC Circuit - develop expressions for ?
and wo
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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

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