ECE201Lect-22

ECE201Lect-22 - L as short circuit; find I L (0 ) and/or V...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE201 Lect-22 1 Second-Order Circuits Cont’d
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECE201 Lect-22 2 Important Concepts The differential equation for the circuit Forced (particular) and natural (complementary) solutions Transient and steady-state responses 1st order circuits: the time constant ( τ ) • 2nd order circuits: natural frequency 0 ) and the damping ratio (ζ)
Background image of page 2
ECE201 Lect-22 3 Building Intuition Even though there are an infinite number of differential equations, they all share common characteristics that allow intuition to be developed: Particular and complementary solutions Effects of initial conditions Roots of the characteristic equation
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ECE201 Lect-22 4 The second-order ODE has a form of To find the natural solution, we solve the characteristic equation : • Which has two roots: s 1 and s 2 . Second-Order Natural Solution 0 2 2 0 0 2 = + + ϖ ζϖ s s 0 ) ( ) ( 2 ) ( 2 0 0 2 2 = + + t x dt t dx dt t x d
Background image of page 4
ECE201 Lect-22 5 Step-by-Step Approach 1. Assume solution (only dc sources allowed): i. x ( t ) = K 1 + K 2 e -t/ τ ii. x ( t ) = K 1 + K 2 e s 1 t + K 3 e s 2 t i. At t =0 , draw circuit with C as open circuit and
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L as short circuit; find I L (0 ) and/or V C (0 ) ii. At t =0 + , redraw circuit and replace C and/or L with appropriate source of value obtained in step #2, and find x (0)=K 1 +K 2 (+K 3 ) iii. At t = , repeat step #2 to find x ( )=K 1 ECE201 Lect-22 6 Step-by-Step Approach 5. Find time constant ( ), or characteristic roots ( s ) i. Looking across the terminals of the C or L element, form Thevenin equivalent circuit; =R Th C or =L/R Th ii. Write ODE at t >0; find s from characteristic equation 5. Finish up 1. Simply put the answer together. 2. Typically have to use d x ( t )/d t t =0 to generate another algebraic equation to solve for K 2 & K 3 (try repeating the circuit analysis of step #5 at t =0 + , which basically means using the values obtained in step #3) ECE201 Lect-22 7 Class Examples Learning Extension E7.10 Learning Extension E7.11...
View Full Document

Page1 / 7

ECE201Lect-22 - L as short circuit; find I L (0 ) and/or V...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online