Books on Reserve for EE 42 and 100 in the Bechtel Engineering Library

1. 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.

2. New topics – energy storage elements Capacitors Inductors

3. The Capacitor Two conductors (a,b) separated by an insulator: difference in potential = Vab => equal & opposite charges Q on conductors Q = CVab where C is the so-called capacitance of the structure, • positive (+) charge is on the conductor at higher potential +Q + Vab Q = Magnitude of charge stored on each conductor - -Q • Parallel-plate capacitor: • area of the plates = A (m2) • separation between plates = d (m) • dielectric permittivity of insulator • =  (F/m) • => capacitance (F) F

5. Electrolytic (polarized) capacitor has + sign on one plate Symbol: Units: Farads (Coulombs/Volt) Current-Voltage relationship: or C C (typical range of values: 1 pF to 1 mF; for “supercapa- citors” up to a few F!) ic + vc – If C (geometry) is unchanging, iC = dvC/dt Note: Q(t) must be a continuous function of time

7. 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

8. Schematic Symbol and Water Model for a Capacitor

9. Capacitor Uses Capacitors 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 boards

10. 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. 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.

11. Application 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) g1 g2 FIXED OUTER PLATES

12. Application: Condenser Microphone Vout = dx Econst

13. Capacitor Voltage in Terms of Current Charge is integral of current through capacitor and also equals capacitance C time capacitor voltage:

14. Thus, energy is . Stored 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 CAPACITORS STORE ELECTRIC ENERGY 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!)

15. A more rigorous derivation ic + vc –

16. Example: Current, Power & Energy for a Capacitor i(t) v (V) v(t) – + 10 mF 1 t (s) 0 1 2 3 4 5 vc and q must be continuous functions of time; however, ic can be discontinuous. i (mA) t (s) 0 1 2 3 4 5 Note:In “steady state” (dc operation), time derivatives are zero  C is an open circuit

17. p (W) i(t) v(t) – + 10 mF t (s) 0 1 2 3 4 5 w (J) t (s) 0 1 2 3 4 5

18. Capacitors in Parallel i1(t) i2(t) + v(t) – i(t) C1 C2 + v(t) – i(t) Ceq Equivalent capacitance of capacitors in parallel is the sum

19. 1 1 1 = + C C C 1 2 eq Capacitors in Series + v1(t) – + v2(t) – + v(t)=v1(t)+v2(t) – C1 C2 i(t) i(t) Ceq

20. The Inductor • An inductor is constructed by coiling a wire around some type of form. • 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 voltage across the coil is induced: + vL(t) iL _ Note: In “steady state” (dc operation), time derivatives are zero  L is a short circuit

21. Symbol: Units: Henrys (Volts • second / Ampere) Current in terms of voltage: L (typical range of values: mH to 10 H) iL + vL – Note: iL must be a continuous function of time

22. Schematic Symbol and Water Model of an Inductor

23. Stored Energy INDUCTORS STORE MAGNETIC ENERGY Consider an inductor having an initial current i(t0) = i0 = = p ( t ) v ( t ) i ( t ) t ò = t t = w ( t ) p ( ) d t 0 1 1 2 = - 2 w ( t ) Li Li 0 2 2

24. Inductors in Series + v1(t) – + v2(t) – + v(t)=v1(t)+v2(t) – L1 L2 i(t) i(t) + – + – v(t) v(t) Leq Equivalent inductance of inductors in series is the sum

25. Inductors in Parallel + v(t) – + v(t) – i1 i2 i(t) i(t) Leq L1 L2

26. Summary • Capacitor • v cannot change instantaneously • i can change instantaneously • Do not short-circuit a charged • capacitor (-> infinite current!) • n cap.’s in series: • n cap.’s in parallel: • Inductor • i cannot change instantaneously • v can change instantaneously • Do not open-circuit an inductor with current flowing (-> infinite voltage!) • n ind.’s in series: • n ind.’s in parallel: q = CvC

27. Transformer – Two Coupled Inductors + + v1 v2 - - N1 turns N2 turns |v2|/|v1| = N2/N1 See Hambley pp. 712-4 on Ideal Transformer

28. AC Power System

29. Relative advantages of HVDC over HVAC power transmission • Asynchronous interconnections (e.g., 50 Hz to 60 Hz system) • Environmental – smaller footprint, can put in underground cables more economically, ... • Economical -- cheapest solution for long distances, smaller loss on same size of conductor (skin effect), terminal equipment cheaper • Power flow control (bi-directional on same set of lines) • Added benefits to the transmission (system stability, power quality, etc.)

30. High-voltage DC power systems * Highest DC voltage system: +/- 600 kV, in Brazil – brings 50 Hz power from 12,600 MW Itaipu hydropower plant to 60 Hz network in Sao Paulo

31. Summary of Electrical Quantities

32. Summary of Electrical Quantities (concluded)