1 / 8

Application of Laplace Transforms: Circuit Analysis

EGR 261 – Inverse Laplace Transforms using MATLAB. Application of Laplace Transforms: Circuit Analysis MATLAB is a powerful tool for analyzing circuits using Laplace transforms. One approach might be: Determine the s-domain circuit (find initial conditions first)

foy
Télécharger la présentation

Application of Laplace Transforms: Circuit Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. EGR 261 – Inverse Laplace Transforms using MATLAB • Application of Laplace Transforms: Circuit Analysis • MATLAB is a powerful tool for analyzing circuits using Laplace transforms. One approach might be: • Determine the s-domain circuit (find initial conditions first) • Use MATLAB to find complex impedances (XC = 1/(sC), XL = sL) • Write any required circuit equations (KVL, KCL, etc) • Use solve( ) solve the circuit equations. The result will be functions of s. • Use ilaplace( ) to find the corresponding time-domain expressions. • In class the s-domain relationships for each type of circuit element are developed. They are summarized on the following slide.

  2. EGR 261 – Inverse Laplace Transforms using MATLAB R R C 1/(sC) v(0)/s sL L Li(0) 10V 10/s 2mA 0.002/s s-domain circuit models time-domain s-domain

  3. Lecture #22 EGR 267 – Engineering Analysis Tools • Procedure: Circuit Analysis using the Laplace-transformed Circuit • Draw the circuit at t = 0-. • Assume that the circuit is in steady state. • Draw inductors as short circuits and capacitors as open circuits. • Find vC(0-) and iL(0-) – these are needed for step 2. • Draw the s-domain circuit for t > 0. • Analyze the circuit as you might analyze a DC circuit (using any circuit analysis method). Recall that the s-domain impedances sL and 1/(sC) act essentially like resistors. Determine the desired result in the s-domain (V(s), I(s), etc). • Convert the result back to the time domain. In other words, use inverse Laplace transforms to find v(t) or i(t) from V(s) or I(s). • Note: If the circuit has zero initial conditions then the voltage sources in the capacitor and inductor models will be zero.

  4. EGR 261 – Inverse Laplace Transforms using MATLAB + VC(t) _ 28 ohms 4 H + - 160 V 0.025 F Example 1: Use Laplace transforms and MATLAB to determine i(t) and vC(t) in the circuit shown below (for t > 0). Assume that all initial conditions are zero. i(t)

  5. EGR 261 – Inverse Laplace Transforms using MATLAB Example 1 (continued)

  6. EGR 261 – Inverse Laplace Transforms using MATLAB Example 2: Use Laplace transforms and MATLAB to determine ia(t) and ib(t) in the circuit shown below (for t > 0). Assume that all initial conditions are zero. ia(t) ib(t)

  7. EGR 261 – Inverse Laplace Transforms using MATLAB Example 2 (continued)

  8. EGR 261 – Inverse Laplace Transforms using MATLAB Example 3: (class example) Use Laplace transforms and MATLAB to determine i(t) and v(t) in the circuit shown below (for t > 0). Assume that vC(0) = 50V and i(0) = 100 mA. 8 mH 10 uF i(t) + v(t) - + - 336 V 4k 2k

More Related