1. Introductory Circuit Analysis Robert L. Boylestad
Chapter 10 - Capacitors
Introductory Circuit Analysis
Robert L. Boylestad 1

2. Introduction
Capacitors display their total characteristics only when a change in voltage is made the circuit in which they exist 2

3. The Electric Field
The electric field is represented by electric flux lines, which are drawn to indicate the strength of the electric field at any point around the charged body; that is, the denser the lines of flux, the stronger the electric field 3

4. The Electric Field
The electric field strength at a point is the force acting on a unit positive charge at that point
Electric flux lines always extend from a positively charged body to a negatively charge body, always extend or terminate perpendicular to the charged surface, and never intersect 4

5. Capacitance
A capacitor is constructed of two parallel conducting plates separated by an insulating material
Capacitance is a measure of a capacitor’s ability to store charge on its plates
A capacitor has capacitance of 1 farad if 1 coulomb of charge is deposited on the plates by potential difference of 1 volt across the plates
A farad is named after Michael Faraday, a nineteenth century English chemist and physicist 5

6. Capacitance
The farad is generally too large a measure of capacitance for most practical applications, so the microfarad (10-6 ) or picofarad (10-12 ) is more commonly used
Different capacitors for the same voltage across their plates will acquire greater or lesser amounts of charge on their plates, hence the capacitors have greater or lesser capacitance 6

7. Capacitance
Fringing – At the edge of the capacitor plates the flux lines extend outside the common surface area of the plates 7

8. Capacitance Dielectric – Insulator of the capacitor
The purpose of the dielectric is to create an electric field to oppose the electric field setup by free charges on the parallel plates
Di for “opposing” and electric for “electric field”
Dipoles – Formed within the insulator of a capacitor when the electrons of the insulating material are unable to leave the parent atom and travel to the positive plate of the capacitor 8

9. Capacitance
Different dielectric materials between the same two parallel plates, different amounts of charge will deposit on the plates
Permittivity – The ratio of the flux density to the electric field intensity in the dielectric – a measure of how easily the dielectric will “permit” the establishment of flux lines within the dielectric
Relative permittivity – Often called the dielectric constant, it is the ratio of the permittivity of any dielectric to that of a vacuum 9

10. Dielectric Strength
For every dielectric there is a potential that, if applied across the dielectric, will break the bonds within the dielectric and cause current to flow. The voltage required per unit length (electric field intensity) to establish conduction in a dielectric is an indication of its dielectric strength and is called the breakdown voltage 10

11. Leakage Current
In an ideal situation current flow of electrons will occur in a dielectric only when the breakdown voltage is reached
In actuality, there are free electrons in every dielectric due in part to impurities and forces within the material itself
When a voltage is applied across the plates of a capacitor, a leakage current due to the free electrons flows from one plate to the other 11

12. Types of Capacitors
Like resistors, capacitors are classified into two general headings: Fixed and Variable
Fixed – mica, ceramic, electrolytic, tantalum and polyester-film
Mica capacitor consists of mica sheets separated by sheets of metal foil. The plates are connected to two electrodes. The entire system is encased in a plastic insulating material
The mica capacitor exhibits excellent characteristics under stress of temperature variations and high voltage applications 12

13. Types of Capacitors
Ceramic capacitor – Made in different shapes and sizes but the basic construction is the same
A ceramic base is coated on both sides with a metal, such as copper or silver, to act as the two plates. The leads are then attached through electrodes to the plates. An insulating coating of ceramic or plastic is then applied over the plates and dielectric.
Very low leakage current and can be used in both dc and ac networks 13

14. Types of Capacitors
Electrolytic capacitor – most commonly used in situations where capacitances of the order of one to several thousand microfarads are required.
Primarily for use in dc networks because they have good insulating characteristics (high leakage current) between the plates in one direction but take on the characteristics of a conductor in the other direction
Basic construction consists of a roll of aluminum foil coated on one side with an aluminum oxide, the aluminum being the positive plate and the oxide the dielectric. A layer of paper or gauze saturated with an electrolyte is place over the aluminum oxide on the positive plate. Another layer of aluminum without the oxide is then placed over this layer to assume the role of the negative plate. 14

15. Types of Capacitors
Working voltage – the voltage that can be applied across a capacitor for long periods of time with out breakdown
Surge voltage – The maximum dc voltage that can be applied for a short period of time 15

16. Types of Capacitors Tantalum capacitors: solid and wet-slug
Tantalum powder of high purity is pressed into a rectangular or cylindrical shape. Next the anode (+) is simply pressed into the resulting structure. The resulting unit is then sintered (baked) in a vacuum at very high temperatures to establish a very porous material
The resulting structure with a very large surface area in a limited volume. It is then immersed in an acid solution which creates a very thin manganese dioxide coating on the large porous surface area
An electrolyte is then added to establish contact between the surface and the cathode
If an appropriate “wet” acid is introduced, it is called a wet-slug tantalum capacitor 16

17. Types of Capacitors Polyester-film capacitor
Basic construction consists of two metal foils separated by a strip of polyester material such as Mylar®. The outside layer of polyester is applied to act as an insulating jacket.
Each metal jacket is connected to a lead that extends either axially or radially from the capacitor
The rolled construction results in a large surface, and the use of the plastic dielectric results in a very thin layer between the conducting surfaces
The capacitor can be used for both dc and ac networks 17

18. Types of Capacitors Variable resistors
Most common are shown in the figure below. The dielectric for each is air. The capacitance is changed by turning the shaft at one end to vary the common area of the movable and fixed plates. The greater the common area the larger the capacitance. 18

19. Types of Capacitors Measuring and testing
The digital reading capacitance meter shown will allow you to simply place the capacitor between the provided clips with the proper polarity and the meter will display the level of capacitance
Insert Fig 10.20 19

20. 10.7 - Transients in Capacitive Networks: Changing Phase
A capacitor can be replaced by an open-circuit equivalent once the charging phase in a dc network has passed
The current of ic of a capacitive network is essentially zero after five time constants of the charging phase have passed in a dc network
The voltage across a capacitor cannot change instantaneously 20

21. Discharge Phase
The network above is designed to both charge and discharge the capacitor. Charging occurs when the switch is in position 1 and discharging occurs when the switch is in position 2. If the switch is switched from 1 to 2 during the charging process the capacitor will begin to discharge at a rate sensitive to the same time constant  = RC 21

22. Initial Values
The voltage across a capacitor at the instant of the start of the charging phase is called the initial value. Once the voltage is applied the transient phase will commence until a leveling off occurs after five time constants called steady-state as shown in the figure above 22

23. 10.10 - Instantaneous Values
To determine the voltage (or current) at a particular instant of time that is not an integral multiple of the time constant ()
Charging:
Discharging: 23

24. 10.11 - Thévenin Equivalent :  = RThC
In a network that is not a simple series form, it will be necessary to first find the Thévenin equivalent circuit for the network external to the capacitive element
ETh will then be the source voltage E, and RTh will be the resistance R. The time constant is then:  = RThC 24

25. The Current ic
Current ic associated with the capacitance C is related to the voltage across the capacitor by
Where dvcldt is a measure of the change in vc in a vanishingly small period of time
The function dvcldt is called the derivative of the voltage vc with respect to time t 25

26. 10.13 - Capacitors in Series and Parallel
Capacitors, like resistors, can be placed in series and in parallel
Placing capacitors in series, the charge is the same on each capacitor 26

27. Capacitors in Series and Parallel
Placing capacitors in parallel the voltage across each capacitor is the same
The total charge is the sum of that on each capacitor 27

28. 10.14 - Energy Stored by a Capacitor
The ideal capacitor does not dissipate any energy supplied to it. It stores the energy in the form of an electric field between the conducting surfaces
The power curve can be obtained by finding the product of the voltage and current at selected instants of time and connecting the points obtained
WC is the area under the curve 28

29. Stray Capacitance
Stray capacitances exist not through design but simply because two conducting surfaces are relatively close to each other
Two conducting wires in the same network will have a capacitive effect between them 29

30. 10.16 - Application Capacitors find applications in:
Electronic flash lamps for cameras
Line conditioners
Timing circuits
Electronic power supplies 30