Capacitor in an AC circuit

Transcription

1 Capacitor in an AC circuit

2 Copyright (c) Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to youngwlim@hotmail.com. This document was produced by using OpenOffice and Octave.

3 Everchanging signal pairs decreasing increasing decreasing increasing decreasing increasing d dt negative positive charge discharge negative positive vc il ic vl charge discharge 3

4 Capacitor Current positive charge (positive ions) Think as insulator negative charge (free electrons) electrons move to the left Displacement Current 4

5 Positive ions and free electrons positive charge (positive ions) insulator negative charge (free electrons) [[commons:user crap ]] (original work by commons:user:greg Robson) /thumb/f/f7/electron_shell_029_copper no_label.svg/200pxelectron_shell_029_copper_-_no_label.svg.png + + 5

6 Three States positive charge (positive ions) negative charge (free electrons) Positive Charged State fully charged no current Negative Charged State fully charged no current Fully Discharged State large current 6

7 Inter-State Current Flowing Under Positive Charging Under Negative Charging (+) current flow direction ( ) current flow direction electron flow direction electron flow direction 7

8 Inter-State Current Flowing Fully Discharged State Under Positive Charging Initial large current no current (+) current flow direction (+) current flow direction electron flow direction electron flow direction Positive Charged State 8 Crowded No more space

9 Inter-State Current Flowing Fully Discharged State Under Negative Charging Initial large current no current ( ) current flow direction ( ) current flow direction electron flow direction electron flow direction Negative Charged State 9 Crowded No more space

10 An AC Voltage Source Under Positive Charging Fully Discharged State Fully Discharged State Under Negative Charging 10 Positive Charged State Negative Charged State

11 An AC Voltage Source Fully Discharged State Under Positive Charging Positive Charged State Under Negative Charging Fully Discharged State Under Negative Charging Negative Charged State Under Positive Charging Fully Discharged State 11

12 Fully Charged and Fully Discharged Fully + Charged Fully Discharged Fully Discharged Fully Discharged Fully Charged (+) current (+) Charging ( ) Charging ( ) Charging (+) Charging (+) current ( ) current ( ) current (+) current (+) Charging (+) Discharging ( ) Charging ( ) Discharging 12

13 A Cycle Fully Discharged State Fully Discharged State 13

14 State Transition Diagram Fully Discharged State Fully Discharged State 14

15 Current Flow Positive Charged State Fully Discharged State Fully Discharged State Negative Charged State 15

16 Fully Charged and Fully Discharged y [ n] y [n+1] y [ n] h = bar(t1, [y1' y2'], "stacked") set(h(1), "facecolor", "g"); set(h(2), "facecolor", "y"); hold on plot(t1, y1) axis([ ]); y [n ] y [n+1] = y (n T ) y ((n+1)t )=sin(n T ) sin ((n+1)t ) 16

17 Continuous Charing and Discharging Operations Incremental Voltage Increment + Charging incrementally Incremental Voltage Decrement Charging incrementally + charging incrementally - charging incrementally - charging incrementally + charging incrementally + charging incrementally - discharging incrementally - charging incrementally + discharging incrementally 17

18 Fully Discharged : Large Current Incremental Voltage Increment Continuous Charging Incremental Voltage Decrement Continuous Discharging Fully + Charged Fully Discharged Fully Discharged Fully Discharged Fully Charged 18

19 y[n+1] y[n] t = linspace(0, pi*2, 50); t1 = t; t2 = t + t(2); y1 = sin(t1); y2 = sin(t2) - sin(t1); stem(t1, y2) hold on plot(t1, y1) y (t)=sin (t) y [n ] y [n+1] = y (n T ) y ((n+1)t )=sin(n T ) sin ((n+1)t ) 19

20 Fully Charged and Fully Discharged y [ n] y [n+1] y [ n] h = bar(t1, [y1' y2'], "stacked") set(h(1), "facecolor", "g"); set(h(2), "facecolor", "y"); hold on plot(t1, y1) axis([ ]); y [ n] y [n+1] = y (n T ) y ((n+1)t )=sin(n T ) sin ((n+1)t ) 20

21 Fully Charged and Fully Discharged Fully + Charged Fully Discharged y (t)=sin (t) h = bar(t1, y2/t(2), "hist") set(h(1), "facecolor", "y"); hold on plot(t1, y1) axis([ ]); Fully Discharged Fully Discharged Fully Charged 21 y [n] y [n+1] T dy dt

22 Fully Charged and Fully Discharged y [ n] y [n+1] y [ n] h = bar(t1, [y1' y2'], "stacked") set(h(1), "facecolor", "g"); set(h(2), "facecolor", "y"); hold on plot(t1, y1) axis([0 pi]); y [n ] y [n+1] = y (n T ) y ((n+1)t )=sin(n T ) sin ((n+1)t ) 22

23 Everchanging signal pairs Positive Discharge Positive Charge electrons move to the left Negative Discharge Negative Charge Negative Charge electrons move to the right electrons move to the right 23 Positive Charge electrons move to the left

24 Everchanging signal pairs charge discharge charge discharge 24

25 Everchanging signal pairs charge discharge charge discharge 25

26 Everchanging signal pairs charge discharge charge discharge 26

27 Everchanging signal pairs decreasing increasing decreasing increasing decreasing increasing d dt negative positive charge discharge negative positive vc il ic vl charge discharge 27

28 I leads V by 90 Initial charge Full charge SHORT OPEN V=0 I=0 I : peak V : peak 28 I V

29 References [1] [2] J.H. McClellan, et al., Signal Processing First, Pearson Prentice Hall, 2003