We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byAugustus Henderson
Modified over 4 years ago
E E 2315 Lecture 10 Natural and Step Responses of RL and RC Circuits
Conservation of Charge (1/4) Energy transferred if v 10 v 20 Total system charge is conserved
Conservation of Charge (2/4) Initial stored energy: At equilibrium:
Conservation of Charge (3/4) Initial Charge: Final Charge: Since
Conservation of Charge (4/4) Final stored energy: Energy consumed in R:
Conservation of Flux Linkage (1/3) Energy transferred if i 10 i 20 Total system flux linkage is conserved. Initial stored energy: At equilibrium:
Conservation of Flux Linkage (2/3) Initial flux linkage: Final flux linkage: Since
Final stored energy: Energy consumed in R: Conservation of Flux Linkage (3/3)
Natural RL Response (1/2) Inductor has initial current, i o. Switch opens at t = 0 Inductor current can’t change instantaneously
Natural RL Response (2/2) KVL: Separate the variables: Integrate: Exponential of both sides:
Natural RC Response (1/2) Capacitor has initial voltage, v o. Switch closes at t = 0. Capacitor voltage can’t change instantaneously KCL: Separate the variables:
Natural RC Response (2/2) Integrate: Exponential of both sides:
RL Step Response (1/4) Make-before-break switch changes from position a to b at t = 0. For t < 0, I o circulates unchanged through inductor.
RL Step Response (2/4) For t > 0, circuit is as below. Initial value of inductor current, i, is I o. The KVL equation provides the differential equation.
RL Step Response (3/4) Solution has two parts: Steady State Response Transient Response Determine k by initial conditions:
RL Step Response (4/4) Inductor behaves as a short circuit to DC in steady state mode
RC Step Response (1/3) Switch closes at t = 0. Capacitor has initial voltage, V o. v-i relationship: By KVL & Ohm’s Law:
RC Step Response (2/3) Response has two parts –steady state –transient Use initial voltage to determine transient Steady State ResponseTransient Response
RC Step Response (3/3) Capacitor becomes an open circuit to DC after the transient response has decayed.
Unbounded Response (1/5) Need Thévenin equivalent circuit from terminal pair connected to inductor Let initial current = 0A in this example.
Unbounded Response (2/5) Voltage divider to get v x : Then Thévenin voltage
Unbounded Response (3/5) Therefore:
Unbounded Response (4/5) Steady state: Transient:
Unbounded Response (5/5) Use initial conditions to determine k. Complete response is unbounded:
Boundary Conditions. Objective of Lecture Demonstrate how to determine the boundary conditions on the voltages and currents in a 2 nd order circuit. These.
Ch3 Basic RL and RC Circuits
Lecture 10: RL & RC Circuits Nilsson & Riedel ENG17 (Sec. 2): Circuits I Spring May 1, 2014.
Transient Analysis DC Steady-State ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall.
ECE 201 Circuit Theory I1 Step Response Circuit’s behavior to the sudden application of a DC voltage or current. Energy is being stored in the inductor.
Transient Excitation of First-Order Circuits
Department of Electronic Engineering BASIC ELECTRONIC ENGINEERING Transients Analysis.
Lecture 141 1st Order Circuits Lecture 142 1st Order Circuits Any circuit with a single energy storage element, an arbitrary number of sources, and an.
Lecture #8 Circuits with Capacitors
First Order Circuit Capacitors and inductors RC and RL circuits.
Lesson 15 – Capacitors Transient Analysis
Lecture 10: RL & RC Circuits Nilsson 7.1 – 7.4
Lecture 9, Slide 1EECS40, Fall 2004Prof. White Lecture #9 OUTLINE –Transient response of 1 st -order circuits –Application: modeling of digital logic gate.
Chapter 5 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
First Order Circuits. Objective of Lecture Explain the operation of a RC circuit in dc circuits As the capacitor releases energy when there is: a transition.
Lecture - 8 First order circuits. Outline First order circuits. The Natural Response of an RL Circuit. The Natural Response of an RC Circuit. The Step.
Chapter 8 Second-Order Circuits
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc. Lecture 12 First Order Transient.
© 2019 SlidePlayer.com Inc. All rights reserved.