1. 1 © Unitec New Zealand DE4401 DC C APACITANCE AND CAPACITORS

2. Introduction So far, we have studied circuits composed of resistances and sources. Resistors convert electrical energy into heat. Thus resistors dissipate the energy. In this section, we are looking at our first example of energy- storage element: CAPACITOR 2 © Unitec New Zealand

3. Capacitor and Capacitance 3 © Unitec New Zealand Capacitor is an electronic component used to store electric charge. Capacitance is the physical quantity describing how much electric charge can be stored in a capacitor when voltage V is applied to it. A formula commonly used in physics to calculate the capacitance is how much charge is stored per unit of voltage: C = Q / V o C is the capacitance, o Q is the amount of electric charge, o V is the applied voltage. The SI unit of capacitance is the farad (F), which is equal to one coulomb per volt. Typical capacitance values range from about 1 pF (10 −12 F) to about 1 mF (10 −3 F).

4. Storing energy in a capacitor 4 © Unitec New Zealand A capacitor consists of two conductors (Conductive Plates in the Figure) which are separated by a layer of non-conductive (insulating or dielectric) material. When you apply a voltage across the capacitor’s conductors (when a capacitor is attached across a battery), positive charge (+Q) is collected on one plate and negative charge (-Q) on the other plate. The conductors hold equal and opposite charges on their facing surfaces and an electric field develops in dielectric. The capacitance (how much charge can be stored in the capacitor) depend on physical dimensions of the conductors (shape and size of the plate) and type of dielectric (material filling the space between the two conductors).

5. Conductors and Dielectrics; Permittivity Materials in nature are either good conductors or good insulators (dielectrics). –Examples of conductors are: copper, silver, gold –Examples of dielectric are: glass, air, paper, Teflon. To describe a conductor, we have used conductivity (σ) or resistivity (ρ) of a metal. To describe a dielectric, we introduce physical quantity called permittivity (dielectric constant, ε ) of a material. Permittivity (dielectric constant) is usually given as a product of the relative permittivity of the material (ε r ) and permittivity of vacuum (ε 0 ) Permittivity of vacuum: ε 0 = 8.8541878176.. × 10 −12 F/m 5 © Unitec New Zealand

6. Parallel-plate capacitor A common form of capacitor is a parallel-plate capacitor. –Dielectric is placed between two conducting plates, each of area A and with a separation of d. 6 © Unitec New Zealand

7. Capacitance of parallel plate capacitor 7 © Unitec New Zealand C is the capacitance, in Farads; A is the area of overlap of the two plates, in square meters; ε r is the relative permittivity of the material between the plates ; ε 0 is the permittivity of vacuum (ε 0 ≈ 8.854×10−12 F m–1); and d is the separation between the plates, in meters; Capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For a parallel-plate capacitor constructed of two parallel plates both of area A separated by a distance d

8. Capacitor’s behaviour in DC and AC circuit Once it is “fully-charged” by a DC source, the capacitor blocks the flow of any more electrons onto its plates. The capacitor now acts like a temporary storage device. –A pure capacitor will maintain this charge indefinitely on its plates even if the DC supply voltage is removed. However, in AC circuit, capacitor is constantly charging and discharging at a rate determined by the frequency of the supply. –Although applying a voltage to the terminals of the capacitor cannot move a charge through dielectric, it can displace a charge within dielectric. As the voltage varies with time, the displacement of charge also varies with time, causing what is known as the displacement current. 8 © Unitec New Zealand

9. Current to voltage relationship The current through a capacitor is proportional to the rate at which the voltage across the capacitor varies with time. 9 © Unitec New Zealand Where: C is the capacitance value of the capacitor in farads (F) dv/dt is the rate of change of the supply voltage with respect to time.

10. Capacitor Charging 10 © Unitec New Zealand

11. Capacitor Discharging 11 © Unitec New Zealand

12. Voltage to current relationship 12 © Unitec New Zealand

13. RC circuit A simple resistor-capacitor circuit demonstrates charging of a capacitor. If the capacitor is initially uncharged while the switch is open, and the switch is closed at t 0, it follows from Kirchhoff's voltage law that: 13 © Unitec New Zealand

14. Solution; Time constant 14 © Unitec New Zealand The capacitor will charge up gradually through the resistor until the voltage across the capacitor reaches that of the supply voltage. This is described by a time constant of the system  0 = RC Time needed to fully charge the capacitor is equal to 5  0..

15. Capacitor discharge in a resistor 15 © Unitec New Zealand

16. Exponential function The exponential decay function is exp(-t/  ), where  is the time constant. 16 © Unitec New Zealand

17. Real capacitor The ideal capacitor is a purely reactive device, containing absolutely zero resistive (power dissipative) effects. In the real world, of course, nothing is perfect. Capacitors with significant resistive effects are said to be lossy, in reference to their tendency to dissipate (“lose”) power like a resistor. The source of capacitor loss is usually the dielectric material rather than any wire resistance, as wire length in a capacitor is very minimal. 17 © Unitec New Zealand

18. Q factor The quality factor (or Q) of a capacitor at a given frequency is a measure of its efficiency. The higher the Q factor of the capacitor, the closer it approaches the behaviour of an ideal, lossless, capacitor. 18 © Unitec New Zealand  is frequency in radians per second, C is the capacitance R C is the series resistance of the capacitor

19. Breakdown voltage Above a particular electric field, known as the dielectric strength E ds, the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage V bd of the device, and is given by the product of the dielectric strength and the separation between the conductors, d 19 © Unitec New Zealand Breakdown voltage limits the maximum energy that can be stored safely in a capacitor.

20. Series and parallel circuits Capacitors in a parallel configuration each have the same applied voltage. Their capacitances add up. –Charge is apportioned among them by size. Using the schematic diagram to visualize parallel plates, it is apparent that each capacitor contributes to the total surface area. Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The total voltage difference from end to end is apportioned to each capacitor according to the inverse of its capacitance. –The entire series acts as a capacitor smaller than any of its components 20 © Unitec New Zealand

21. Capacitor types Inside the capacitor, the terminals connect to two metal plates separated by a non-conducting substance, or dielectric. The dielectric dictates what kind of capacitor it is and for what it is best suited. Depending on the size and type of dielectric, some capacitors are better for high frequency uses, while some are better for high voltage applications. 21 © Unitec New Zealand

22. Capacitor Construction 22 © Unitec New Zealand

23. Cap Construction ceramic 23 © Unitec New Zealand

24. Rolled Capacitor 24 © Unitec New Zealand

25. Electrolytic Construction 25 © Unitec New Zealand

26. Tantalum Cap 26 © Unitec New Zealand

27. Electrolytic capacitors Electrolytic capacitors are ‘polarised’ which means they have a positive and negative lead and must be positioned in a circuit the right way round (the positive lead must go to the positive side of the circuit). They also have a much higher capacitance than non-electrolytic capacitors. Non-electrolytic capacitors usually have a lower capacitance. They are not polarised (do not have a positive and negative lead) and can be placed anyway round in a circuit. 27 © Unitec New Zealand

28. Soldering capacitors 28 © Unitec New Zealand

29. 29 © Unitec New Zealand Safety Capacitors may retain a charge long after power is removed from a circuit. This charge can cause dangerous, even fatal shocks or damage connected equipment. For example, even a seemingly innocuous device such as a disposable camera flash unit powered by a 1.5 volt AA battery contains a capacitor which may be charged to over 300 volts. This is easily capable of delivering a shock. Service procedures for electronic devices usually include instructions to discharge large or high-voltage capacitors. Capacitors may also have built-in discharge resistors to dissipate stored energy to a safe level within a few seconds after power is removed.