Slide 1Slide 2The CapacitorSlide 4Slide 5Slide 6Practical CapacitorsSlide 8Slide 9Slide 10Application Example: MEMS Accelerometer to deploy the airbag in a vehicle collisionSlide 12Capacitor Voltage in Terms of CurrentStored EnergyA more rigorous derivationExample: Current, Power & Energy for a CapacitorSlide 17Capacitors in ParallelCapacitors in SeriesThe InductorSlide 21Slide 22Slide 23Inductors in SeriesInductors in ParallelSummarySlide 27Slide 28Relative advantages of HVDC over HVAC power transmissionSlide 30Slide 31Slide 32Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 1Books on Reserve for EE 42 and 100 in the Bechtel Engineering Library“The Art of Electronics” by Horowitz and Hill (2nd edition) -- A terrific source book on practical electronics (also a copy in 140 Cory lab bookcase)“Electrical Engineering Uncovered” by White and Doering (2nd edition) – Freshman intro to aspects of engineering and EE in particular”Newton’s Telecom Dictionary: The authoritative resource for Telecommunications” by Newton (18th edition – he updates it annually) – A place to find definitions of all terms and acronyms connected with telecommunications. TK5102.N486 Shelved withdictionaries to right of entry gate.AnnouncementsWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 2New topics – energy storage elements Capacitors InductorsWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 3The CapacitorTwo conductors (a,b) separated by an insulator:difference in potential = Vab=> equal & opposite charges Q on conductorsQ = CVabwhere C is the so-called capacitance of the structure, positive (+) charge is on the conductor at higher potentialParallel-plate capacitor:• area of the plates = A (m2)• separation between plates = d (m) • dielectric permittivity of insulator = (F/m)=> capacitancedACQ = Magnitude of charge stored on each conductorFVab+-+Q-Q(F)Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 4Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 5Symbol:Units: Farads (Coulombs/Volt)Current-Voltage relationship:orNote: Q(t) must be a continuous function of time+vc–icdtdCvdtdvCdtdQicccCC(typical range of values: 1 pF to 1 F; for “supercapa-citors” up to a few F!)Electrolytic (polarized)capacitor has + sign on one plateIf C (geometry) is unchanging, iC = dvC/dtWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 6Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 7•A capacitor can be constructed by interleaving the plates with two dielectric layers and rolling them up, to achieve a compact size.•To achieve a small volume, a very thin dielectric with a high dielectric constant is desirable. However, dielectric materials break down and become conductors when the electric field (units: V/cm) is too high.–Real capacitors have maximum voltage ratings–An engineering trade-off exists between compact size and high voltage ratingPractical CapacitorsWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 8Schematic Symbol and Water Model for a CapacitorWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 9Capacitor UsesCapacitors are used to: store energy for camera flashbulbs; in filters that separate signals having different fre-quencies in resonant circuits to tune a radio and oscillators that generate a time-varying voltage at a desired frequency;Capacitors also appear as undesired “parasitic” elements in circuits where they usually degrade circuit perfor- mance (example, conductors on printed circuit boardsWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 10Capacitors used in MEMS Airbag Deployment Accelerometer (MEMS = MicroElectroMechanical Systems)Chip about 1 cm2 holding in themiddle an electromechanicalaccelerometer around which areelectronic test and calibrationcircuits (Analog Devices, Inc.) Hundreds of millions have beensold.Airbag of car that crashed into the back of a stopped Mercedes. Within 0.3 seconds after deceleration the bag is supposed to be empty. Driver was not hurt in any way; chassis distortion meant that this car was written off.Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 11Application Example: MEMS Accelerometerto deploy the airbag in a vehicle collision•Capacitive MEMS position sensor used to measure acceleration (by measuring force on a proof mass)FIXED OUTER PLATESg1g2Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 12Flexible conducting diaphragmSound wavesCylindrical air-filled cavityConducting rigid cupCondenser microphone Electret microphoneElectret: insulator(e.g., teflon) that wasbombarded with electronsthat remain imbeddedin it to “bias” thecondenser.Widely used in tele-phone handsets;available at RadioShackGX1EconstxVoutVout ~ xx EconstEconstX1GGGVoutVout ~ x EconstApplication: Condenser MicrophoneVout = x EconstWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 13Capacitor Voltage in Terms of Current)0()(1)0()(1)()0()()(000ctctcctcvdttiCCQdttiCtvQdttitQCharge is integral of current through capacitor and alsoequals capacitance C time capacitor voltage:Week 3b. Prof. WhiteEE 42 and 100, Spring 2006 14You might think the energy stored on a capacitor charged to voltage V is QV = CV2, which has the dimension of Joules. But during charging, the average voltage across the capacitor was only half the final value of VThus, energy is .221 21CVQV Example: The energy stored in a 1 pF capacitance charged to 5 Volts equals ½ (1pF) (5V)2 = 12.5 pJ (A 5F supercapacitor charged to 5 volts stores 63 J; if it discharged at a constant rate in 1 ms, energy is discharged at a 63 kW rate!)Stored EnergyCAPACITORS STORE ELECTRIC ENERGYWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 15FinalInitialcFinalInitialFinalInitialcccVvVvdQ vdttttt dtdQVvVvvdt ivw2CV212CV21VvVvdv CvwInitialFinalFinalInitialcc+vc–icA more rigorous derivationWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 16Example: Current, Power & Energy for a CapacitordtdvCi –+v(t)10 Fi(t)t (s)v (V)0 2 3 4 51t (s)02 3 4 511i (A)vc and q must be continuousfunctions of time; however,ic can be discontinuous.)0()(1)(0vdiCtvtNote: In “steady state”(dc operation), timederivatives are zero C is an open circuitWeek 3b. Prof. WhiteEE 42 and 100, Spring 2006 17vip 0 2 3 4 51w (J)–+v(t)10 Fi(t)t (s)02 3 4 51p (W)t (s)2021CvpdwtWeek 3b. Prof. WhiteEE
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