Announcements Books 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 with dictionaries to right of entry gate EE 42 and 100 Spring 2006 Week 3b Prof White 1 New topics energy storage elements Capacitors Inductors EE 42 and 100 Spring 2006 Week 3b Prof White 2 The Capacitor Two conductors a b separated by an insulator difference in potential Vab equal opposite charges Q on conductors Q Q Vab Q CVab Q Magnitude of charge stored on each conductor where C is the so called capacitance of the structure positive charge is on the conductor at higher potential Parallel plate capacitor area of the plates A m2 separation between plates d m dielectric permittivity of insulator F m capacitance A C d EE 42 and 100 Spring 2006 F F Week 3b Prof White 3 EE 42 and 100 Spring 2006 Week 3b Prof White 4 or Symbol C C Electrolytic polarized capacitor has sign on one plate Units Farads Coulombs Volt typical range of values 1 pF to 1 F for supercapacitors up to a few F Current Voltage relationship dQ dvc dC ic C vc dt dt dt If C geometry is unchanging iC dvC dt ic vc Note Q t must be a continuous function of time EE 42 and 100 Spring 2006 Week 3b Prof White 5 EE 42 and 100 Spring 2006 Week 3b Prof White 6 Practical Capacitors 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 rating EE 42 and 100 Spring 2006 Week 3b Prof White 7 Schematic Symbol and Water Model for a Capacitor EE 42 and 100 Spring 2006 Week 3b Prof White 8 Capacitor Uses Capacitors are used to store energy for camera flashbulbs in filters that separate signals having different frequencies 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 performance example conductors on printed circuit boards EE 42 and 100 Spring 2006 Week 3b Prof White 9 Capacitors used in MEMS Airbag Deployment Accelerometer MEMS MicroElectroMechanical Systems Chip about 1 cm2 holding in the middle an electromechanical accelerometer around which are electronic test and calibration circuits Analog Devices Inc Hundreds of millions have been sold EE 42 and 100 Spring 2006 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 White 10 Application Example MEMS Accelerometer to deploy the airbag in a vehicle collision Capacitive MEMS position sensor used to measure acceleration by measuring force on a proof mass g1 g2 FIXED OUTER PLATES EE 42 and 100 Spring 2006 Week 3b Prof White 11 Application Condenser Microphone Condenser microphone G Sound waves Econst Electret microphone E c onst X1 G Vout x x Cylindrical air filled cavity Flexible conducting diaphragm Conducting rigid cup Vout x E c onst Vout x Econst EE 42 and 100 Spring 2006 Vout Week 3b Prof White X1 Vout x Econst Electret insulator e g teflon that was bombarded with electrons that remain imbedded in it to bias the condenser Widely used in telephone handsets available at RadioShack 12 Capacitor Voltage in Terms of Current Charge is integral of current through capacitor and also equals capacitance C time capacitor voltage t Q t ic t dt Q 0 0 t t 1 Q 0 1 vc t ic t dt ic t dt vc 0 C0 C C0 EE 42 and 100 Spring 2006 Week 3b Prof White 13 Stored Energy CAPACITORS STORE ELECTRIC ENERGY You 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 V Thus energy is 1 QV 1 CV 2 2 2 Example The energy stored in a 1 pF capacitance charged to 5 Volts equals 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 EE 42 and 100 Spring 2006 Week 3b Prof White 14 A more rigorous derivation ic t t Final v VFinal dQ v VFinal w v c ic dt dt v c v c dQ dt t t Initial v VInitial v VInitial vc v VFinal 1 1 2 2 w Cv dv CV CV c c Final Initial 2 2 v VInitial EE 42 and 100 Spring 2006 Week 3b Prof White 15 Example Current Power Energy for a Capacitor t 1 v t i d v 0 C0 0 1 i A 0 1 2 3 4 5 EE 42 and 100 Spring 2006 3 4 10 F t s vc and q must be continuous functions of time however ic can be discontinuous dv i C dt 2 v t v V 1 i t 5 t s Week 3b Prof White Note In steady state dc operation time derivatives are zero C is an open circuit 16 p W i t 0 1 2 3 4 5 v t 10 F t s p vi w J 0 t 1 2 EE 42 and 100 Spring 2006 3 4 5 t s Week 3b Prof White 1 2 w pd Cv 2 0 17 Capacitors in Parallel i t i1 t i2 t C1 C2 v t i t Ceq v t Ceq C1 C2 dv i Ceq dt Equivalent capacitance of capacitors in parallel is the sum EE 42 and 100 Spring 2006 Week 3b Prof White 18 Capacitors in Series v1 t v2 t i t C1 C2 i t Ceq v t v1 t v2 t 1 1 1 Ceq C1 C2 EE 42 and 100 Spring 2006 Week 3b Prof White 19 The Inductor An inductor is constructed by coiling a wire around some type of form vL t iL Current flowing through the coil creates a magnetic field and a magnetic flux that links the coil LiL When the current changes the magnetic flux changes a …
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