ECE 3336 Introduction to Circuits & Electronics

1. ECE 3336 Introduction to Circuits & Electronics Lecture Set #7a Capacitors Fall 2012, TUE&TH5:30-7:00pm Dr. Wanda Wosik

2. Capacitors A capacitor is a circuit element that stores electric charges and energy in electric fields. For DC conditions it acts as an open circuit For AC conditions a current will flow through C and it will be proportional to the voltage derivative. • Capacitance C[F] is important in circuits (ex. filters, tuning circuits, electron devices etc.) but also in electromechanical applications (sensors, transducers, motors etc). • Capacitance may be also parasitic (between electronic elements, connectors etc) Charge stored when current flows

3. v p 1 2 i q p f gas 2 + + P 1 C v C p f _ _ q f v p 2 1 Analogy between fluid capacitance and electrical capacitance

4. Parallel Plate Capacitor Inserting dielectric: E V C(same Q)better charge storage efficiency • Equations without considering fringe electric field. • A note on fringe electric field: The fringe field is frequently ignored in first-order analysis. It is nonetheless important Dielectric=air But can be low or high er materials solid or liquid Fringe electric field (ignored in first order analysis) Differential form Integral form Electric field (Gauss law) Capacitance Energy stored in the capacitor

5. Defining Equation, Integral Form, Derivation Charge storage The defining equation for the capacitor, If we want to express the voltage in terms of the current, we can integrate both sides. Q=CxV icdt=dQ dQ=Cxdvc Meaning: [A]•[s]=[C] [C]=[F]•[V] We pick t0(initial time, ex. 0) andt (variable)for limits of the integral- The capacitance, CX, is constant – does not change with current or voltage

6. Figure 4.2, 4.3 Combining capacitors in a circuit

7. Power and Energy in Capacitors Power: d(energy)/dt Energy:

8. Applications (others than EE)Basic Principles • Sensing • capacitance between moving and fixed plates change as • distance and position is changed • media is replaced • Actuation • electrostatic force (attraction) between moving and fixed plates as • a voltage is applied between them. • Two major configurations Parallel plate configuration Interdigitated finger configuration

9. Stored energy Force is derivative of energy with respect to pertinent dimensional variable Plug in the expression for capacitor We arrive at the expression for force Forces of Capacitor Actuators

10. An Equivalent Electromechanical Model Note: direction definition of variables d Mechanical force develops to balance the electrical force No forces applied to the structure “d” will change with increasing voltage

11. Micromotors Power AA’ so that they would align That would misalign BB’ so now apply bias to BB’ Then repeat the steps for CC’ Slightly smaller pitch and misaligned electrodes Similar idea in rotary motors but the main problem comes from the bearings in the rotors. Electrodes are in the rotor and stator are misaligned. That generates electrostatic force that moves the rotor. There is more poles in the stator than in the rotor 3:2. The motor rotates with 10,000 rmp so there is a problem with wearing and lubrication; tribology concentrate on these issues. 2µm µm 20-25µm Hsu

12. Three phase electrostatic actuator. Arrows indicate electric field and electrostatic force. The tangential components cause the motor to rotate. Actuators that Use Fringe Electric Field - Rotary Motor

13. Electrostatic Micromotor ROTOR rotor has moved new electrodes biased

14. Three Phase Motor Operation Principle

15. Starting Position -> Apply voltage to group A electrodes

16. Motor tooth aligned to A -> Apply voltage to Group C electrodes

17. Motor tooth aligned to C -> Apply voltage to Group B electrodes

18. Motor tooth aligned to B -> Apply voltage to Group A electrodes

19. Motor tooth aligned to A -> Apply voltage to Group C electrodes

20. Capacitors in Circuits Polarities • Polarity is important for current sources and voltages sources. • Resistors, inductors and capacitors (except for electrolityc) do not have this restriction. • We will use the same passive and active sign conventions as for resistors to find relations between currents and voltages in capacitors Passive Sign Convention Active Sign Convention

23. Circuit Symbols of Capacitor

24. “How an Ultracapacitor Works An ultracapacitor, also known as a double-layer capacitor, polarizes an electrolytic solution to store energy electrostatically. Though it is an electrochemical device, no chemical reactions are involved in its energy storage mechanism – it is electrostatic. This mechanism is highly reversible, and allows the ultracapacitor to be charged and discharged hundreds of thousands of times.” source: NREL http://www.nrel.gov/vehiclesandfuels/energystorage/ultracapacitors.html

25. Time dependence in ic(t) and vc(t) If there is no voltage change there is no current flowing through the capacitor. If charge is stored there is a constant voltage that can be measured (be careful – it can be large), but a capacitor will still have no current (unless it is leaky). and

26. Change in voltage is limited Current is not infinitive The voltage change across a capacitor cannot be infinitively fast. The current cannot be infinitebut it can be very large and

27. Comparison of Rules for Inductors and Capacitors • For inductors, we had the following rules and equations: Passive sign convention

28. Comparison of Rules for Inductors and Capacitors • For capacitors, we had the following rules and equations: Passive sign convention