Title: EGR 277
1Lecture 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
2Lecture 19 EGR 260 Circuit Analysis
Series RLC Circuit - develop expressions for ?
and wo
3Lecture 19 EGR 260 Circuit Analysis
Parallel RLC Circuit - develop expressions for ?
and wo
4Lecture 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
5Lecture 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
6Lecture 19 EGR 260 Circuit Analysis
Example B) Continued with R 2
7Lecture 19 EGR 260 Circuit Analysis
Example C) Continued with R
8Lecture 19 EGR 260 Circuit Analysis
Example Determine v(t) in the circuit shown
below for t gt 0.