Capacitor
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Charge Before Initial Final No more electrons to leave V 0 V 0 i c = C d v c d t crowded electrons prevent other electrons from arriving Energy stored in Electric Field v c (0 ) = v c (0 ) i c (0 ) i c (0 ) unyielding voltage current jump v c ( ) = V 0 i c ( ) = 0 Capacitor 3
Discharge Initial Final i c = C d v c d t No more electrons moving v c (0 ) = v c (0 ) i c (0 ) i c (0 ) unyielding voltage current jump v c ( ) = 0 i c ( ) = 0 Capacitor 4
Charge V R I V in R C V c i c = C d v c d t unyielding voltage current jump the capacitor voltage slowly follows the shape of the applied step input voltage continuous v = v R v C v c (0 ) = v c (0 ) i = i R = i C jump the capacitor current changes abruptly by the applied step input voltage and then slowly becomes zero i c (0 ) i c (0 ) Capacitor 5
Discharge V R I V in R C V c i c = C d v c d t unyielding voltage current jump continuous v = v R v C the capacitor voltage slowly follows the the shape of the applied step input voltage v c (0 ) = v c (0 ) i = i R = i C jump the capacitor current changes abruptly by the applied step input voltage and then slowly becomes zero i c (0 ) i c (0 ) Capacitor 6
Pulse v = v R v C i = i R = i C Capacitor 7
Pulse v C i C i C = C d v C d t ω i C X C v C v C i C i C Capacitor 8
Everchanging signal pairs decreasing increasing decreasing increasing decreasing increasing d d t v C i L negative positive charge discharge negative positive i C v L charge discharge Capacitor 9
Capacitor Current positive charge (positive ions) insulator negative charge (free electrons) Think as electrons move to the left Displacement Current Capacitor 10
Continuous Charing and Discharging Operations Incremental Voltage Increment Incremental Voltage Decrement Charging incrementally Charging incrementally charging incrementaly - charging incrementally - charging incrementally charging incrementaly Capacitor 11
Fully Charged and Fully Discharged Incremental Voltage Increment Incremental Voltage Decrement Fully charged Continuous Charging Continuous Discharging Fully Charged Fully Discharged Fully Discharged Fully Discharged Fully - Charged Capacitor 12
Fully Discharged : Large Current Incremental Voltage Increment Incremental Voltage Decrement Continuous Charging Continuous Discharging Fully Charged Fully Discharged Fully Discharged Fully Discharged Fully - Charged Capacitor 13
y[n1] y[n] y(t)=sin(t) 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 [n] y [n1] = y(nt ) y ((n1)t )=sin(nt ) sin((n1)t ) Capacitor 14
Fully Charged and Fully Discharged y [n] y [n1] 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 7-1 1]); y [n] y [n1] = y(nt ) y ((n1)t )=sin(nt ) sin((n1)t ) Capacitor 15
Fully Charged and Fully Discharged Fully Charged y(t)=sin(t) h = bar(t1, y2*7, "hist") set(h(1), "facecolor", "y"); hold on plot(t1, y1) axis([0 7-1 1]); Fully Discharged Fully Discharged Fully Discharged ( y [n] y[n1]) 7 Fully - Charged dy dt Capacitor 16
Everchanging signal pairs Positive Discharge Negative Discharge Positive Charge Negative Charge Negative Charge Positive Charge electrons move to the left electrons move to the right electrons move to the right electrons move to the left Capacitor 17
Everchanging signal pairs charge discharge charge discharge Capacitor 18
Everchanging signal pairs charge discharge charge discharge Capacitor 19
Everchanging signal pairs charge discharge charge discharge Capacitor 20
Everchanging signal pairs decreasing increasing decreasing increasing decreasing increasing d d t v C i L negative positive charge discharge negative positive i C v L charge discharge Capacitor 21
I leads V by 90 Initial charge Full charge I V SHORT OPEN V = 0 I = 0 I : peak V : peak Capacitor 22
References [1] http://en.wikipedia.org/ [2] J.H. McClellan, et al., Signal Processing First, Pearson Prentice Hall, 2003