Capacitance

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Dept. of ECE

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Examination Schedule

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AEM ECE351 Friday, February. 24, 2012 9:00 9 :40 p.m. Elec & Comp Eng. Room 123Dept. of ECE

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Applied Electromagnetics(Ref. ECE 351 2011 - 2012)

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CapacitanceNorth Dakota State University

Dr. M. [email protected] Tel: (701) 231 Ext. 8816Thursday, 16 February 2012Dept. of ECE Department of Electrical and Computer Engineering North Dakota State University

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Electronic Circuit Elements

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CapacitorsA C = dDept. of ECE

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Capacitorsa device that stores energy by maintaining a separation between positive and negative charge

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(Symbol:

)

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What is a capacitor? Electronic component

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2 conducting surfaces separated by an insulating material Stores charge UsesTime delays Filters Tuned circuitsDept. of ECE

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Capacitors

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Store electric charge. Consist of 2 conducting objects placed near one another with a dielectric material in between them.

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Capacitor construction

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2 metal plates Separated by insulating material Sandwich construction Swiss roll structure Capacitance set by...

A C = dDept. of ECE

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Parallel-Plate Capacitor

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The capacitance of a device depends on the geometric arrangement of the conductors For a parallel-plate capacitor whose plates are separated by air:

A C = o dDept. of ECE

o = 8.85x10-12 F/m9

Permittivity of free spacesmsreyhani smsreyhani

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In AC circuits Power in a capacitor

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Instantaneous power (p)The product of V and I Positive and negative power Positive power indicates that the energy is stored by the capacitor Negative power indicates that the energy is returned from the capacitor Power fluctuation is twice that of the voltage or currentDept. of ECE

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ESR (equivalent series resistance) is the sum of in-phase AC resistance ESL (Equivalent Series Inductance)

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In AC circuits Power in a capacitor

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True power (Ptrue)Ideally, all the stored energy in the capacitor is returned to the source No true power In real world, leakage current and the ESL and ESR consume true power.Dept. of ECE

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ESR (equivalent series resistance) is the sum of in-phase AC resistance ESL (Equivalent Series Inductance)

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In AC circuit Power in a capacitorReactive power (Pr)

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The rate at which a capacitor stores or returns energy Non-zero quantity Does not represents an energy loss Unit is volt-ampere reactive (VAR)

P = Vrms I rms r2 Vrms P = r XC 2 P = I rms X C rDept. of ECE

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Capacitor applications Electrical storage Backup source

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Power supply filtering

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Capacitor applications DC blocking and AC coupling

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Capacitor applications Power line decoupling Bypassing Signal filtering Timing circuits Computer memories

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Applications of Capacitors Camera Flash

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The flash attachment on a camera uses a capacitorA battery is used to charge the capacitor The energy stored in the capacitor is released when the button is pushed to take a picture The charge is delivered very quickly, illuminating the subject when more light is neededDept. of ECE

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Applications of Capacitors -- Computers Computers use capacitors in many ways Some keyboards use capacitors at the bases of the keys When the key is pressed, the capacitor spacing decreases and the capacitance increases The key is recognized by the change in capacitanceDept. of ECE

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A C = dsmsreyhani 18

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Defining capacitance Good capacitors store a lot of chargewhen only a small voltage is applied Capacitance is charge stored per volt Capacitance is measured in farads F Big unit so nF, mF and F are usedDept. of ECE

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Q C= V19 smsreyhani smsreyhani

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Graphical representationEquating to the equation of a straight line

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Q C= V Q = CV y = mxDept. of ECE

Q

Gradient term is the capacitance of the capacitor Charge stored is directly proportional to the applied V voltagesmsreyhani smsreyhani

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Capacitors in Series Total voltage is the sum of the individual voltages across every capacitor. Total capacitance is the inverse of the sum of the inverse of individual capacitances. Current will flow until capacitors are charged.

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Capacitors in Parallel Voltage is the same across every capacitor. Total capacitance is the sum of the capacitances. Current will flow until capacitors are charged.Dept. of ECE

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Equivalent Capacitance

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Ceq

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Energy stored by a capacitor By general definition E=QV product of charge and voltage By graphical consideration...

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Q

1 E = QV 2Area term is the energy stored in the capacitor24

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Other expressions for energy By substitution of

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Q=CV

1 E = QV 2 1 2 E = CV 2 2 1Q E= 2 Csmsreyhani smsreyhani

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Charging a capacitor Current flow Initially High Finally Zero Exponential model Charging factors Capacitance ResistanceI

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Charge of Capacitors

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Discharging a capacitor Current flow Initially High Opposite to charging Finally Zero Exponential model Discharging factors Capacitance ResistanceDept. of ECE

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t

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Discharge of Capacitors

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Voltage and charge characteristicsV or Q V or Q

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Charging

tt RC

Discharging

tt RC30

V = V0 (1 eDept. of ECE

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Q = Q0 e

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Time constant

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Product of Capacitance of the capacitor being charged Resistance of the charging circuit CR Symbol Tau Unit seconds

Q V CR = V Q t CR = tDept. of ECE

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When t equals tau during discharge

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Q = Q0 e Q = Q0 e Q = Q0 eDept. of ECE

t

RC RC

RC 1

At t = tau the capacitor has fallen to 37% of its original value. By a similar analysis tau can be considered to be the time taken for the capacitor to reach 63% of full charge.

Q = Q0 0.37

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Graphical determination of tau V at 37% Q at 37% Compared to initial maximum discharge V or Q

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t = t = RC C= t RDept. of ECE

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Logarithmic discharge analysis Mathematical consideration of discharge Exponential relationship Taking natural logs equates expression to y=mx+c Gradient is -1/Tau

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V = V0 e

t

RC

t V = e RC V0

ln V ln V0 = t

RC34

1 ln V = t + ln V0 RCsmsreyhani smsreyhani

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Logarithmic discharge graphlnV

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Gradient term is the -1/Tau

t

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The EndWhat a wonderful world

Strings & Arrays in C

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Questions?

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Questions?

? ?

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