CAPACITORS Capacitors are devices which can store electric charge They have many applications in electronic circuits They include: forming timing elements, waveform shaping, limiting current in AC circuits CHARGING AND DISCHARGING A CAPACITOR Capacitors are made up from two metal plates separated by a thin insulating layer The insulator is called the dielectric Electron flow 1 2 1 2 Electron flow DC 123456789 DC SUPPLY - SUPPLY - - - - - - 123456789 Fig 1a Charging a capacitor Fig 1b Discharging a capacitor Consider an uncharged capacitor in the circuit shown in Fig 1a When the switch is moved to position 1, the positive terminal of the battery draws electrons off the top plate of the capacitor and transfers the same number to the bottom plate As a result, the top plate becomes positively charged and the bottom plate becomes negatively charged Lamp LP1 would glow while electrons are being transferred from one plate to the other The build up of charge on the plates develops a voltage across the capacitor Transfer of charge continues until the voltage across the capacitor is the same as the battery voltage The capacitor is then fully charged When the switch is moved to position 2 (Fig 1b), the capacitor provides a voltage across lamp LP2 Electrons on the bottom plate are attracted to the top plate through the filament of the lamp The lamp would glow brightly for a while then gradually dim as the voltage across the capacitor falls When all of the electrons have been transferred back to the top plate the capacitor is fully discharged The action can be repeated by moving the switch to position 1 then back to position 2 When used in this way the capacitor behaves like a small rechargeable battery 1
UNITS OF CAPACITANCE The value of a capacitor is governed by its ability to store charge The unit used for capacitance is the farad A capacitor has a capacity of 1 farad if the addition, or removal, of 1 coulomb of charge changes the voltage across it by 1V The farad (F) is a very large unit Capacitor values are usually given in microfarads (mf), nanofarads (nf) or picofarads (pf) 1µF = 1 F = 10-6 F 1,000,000 1nF = 1 F = 10-9 F 1µF = 1,000nF 1,000,000,000 1pF = 1 F = 10-12 F 1µF =1,000,000pF 1,000,000,000,000 DIELECTRICS The insulator, or dielectric, between the plates of a capacitor is strained by the electric field formed by the charges The field draws electrons from their normal orbit, centred on the nucleus, towards the positive plate Electric dipoles are formed in the dielectric This has the effect of reducing the voltage across the capacitor The capacitor is now able to hold more charge at a certain voltage Various types of dielectrics are used in capacitors Each will have advantages and disadvantages The material selected will depend upon the application required for the capacitor It can be shown that in order to provide high capacitance, the area of the plate should be large and the separation small Rolling the plates into a spiral enables a large area to be fitted into a small volume Some insulating materials, eg mica, are not flexible enough for this technique to be used 2
CIRCUIT SYMBOLS There are two main types of capacitors, polarised and non-polarised Polarised capacitors are usually referred to as electrolytic capacitors Symbols used for the two types are shown below General symbol Electrolytic capacitor Fig 2 Symbols used for capacitors In the next Exercise you will be using electrolytic capacitors They are used because they provide a much larger capacity than non-polarised capacitors of the same physical size Considerable care is required when using electrolytic capacitors Their positive terminal must be nearer the positive supply rail than their negative terminal If electrolytic capacitors are connected the wrong way around they will heat up and probably explode IDENTIFYING THE LEADS ON ELECTROLYTIC CAPACITORS Polarity is always clearly marked on electrolytic capacitors The following diagrams illustrate some conventions in common use Ask your tutor for examples of axial and radial aluminium type Axial Radial Tantalum Fig 3 Polarity of electrolytic capacitors 3
TYPES AND SPECIFICATION A good Electronic Components catalogue will offer a wide range of capacitor types Technical specification will usually provide the following data: values available in the range tolerance working voltage leakage current physical size All of these must be considered when making your selection The working voltage is the maximum voltage that the capacitor can withstand before its dielectric breaks down Care must be taken to ensure that the working voltage is higher than any DC voltage that will be applied across the capacitor In AC circuits, it must be remembered that the maximum voltage applied on the capacitor is û2 times the RMS voltage Leakage current provides a value for the current that flows directly between the plates through the dielectric Its value depends upon the dielectric used and the voltage on the capacitor The following table provides information about types of capacitor that are often used in electronic circuits TYPE APPEARANCE PROPERTIES AND APPLICATIONS Polar Aluminium Electrolytic Available in range of values from 1µF - 50,000µF Tolerance about -10% to 50% Working voltage from about 6V to 400V available Size increases with working voltage value Main advantage is small size for capacitance provided Used for smoothing in power power supplies Not suitable for high frequency operation 4
TYPE APPEARANCE PROPERTIES AND APPLICATIONS Tantalum Available in range of values from about 01µF to 100µF Tolerance 20% Working voltage from about 6V to 35V available Smaller in size than aluminium type of same value Very easily damaged by reverse voltage Often used in timing circuits Polyester Available in range of values from about 001µF to 47µF Colour code often used to indicate value Tolerance 5% to 20% Working voltage from about 250V to 400V Disc Ceramic Available in range of values from about 22pF to 01µF Tolerance 10% to 50% Working voltage up to 10kV available Often used to remove high frequency noise signals in switching circuits Variable Capacitors Used in tuning stages of radio receivers Rotating the shaft varies area of overlap between plates This sets value of capacitance Air, or thin sheets of mica, used as dielectric Also available as trimmer capacitors for direct mounting onto printed circuit boards (PCB) Values available up to 500pF 5
COLOUR CODING ON POLYESTER CAPACITORS A five band colour code is often used to indicate the value, tolerance and working voltage of polyester capacitors The numbers associated with the colours in the value code are the same as for resistors } Band 1 Band 2 Value Code Band 3 Band 4 Tolerance Band 5 Working Voltage Fig 4 Capacitor colour code COLOR VALUE COLOR TOLERANCE Bands 1,2 & 3 Band 4 Black 0 Green ± 5% Brown 1 White ±10% Red 2 Orange 3 Yellow 4 Green 5 COLOR WORKING Blue 6 Band 5 VOLTAGE Violet 7 Grey 8 Red 250V DC White 9 Yellow 400V DC Value code is used in the same way as for resistors Bands 1 and 2 indicate the first two digits and band 3 indicates the number of 0 s Value of the capacitor is given in picofarads (pf) 6
EXAMPLE Yellow (4) Value = 47000pF = 0047µF Violet (7) Orange (3) Tolerance = ±10% White Red Working voltage = 250V DC PRINTED CODE Printed code is used in a similar way to that for resistors eg 4u7 is used to indicate a value of 47µF Ceramic disc capacitors often carry a 3-digit code to indicate their values in picofarads The first digits indicate the first two numbers and the third the number of zeros to be added eg 223 indicates 22000pF 7
USING CAPACITORS AS TIMING ELEMENTS We shall now investigate how the voltage across a capacitor varies with time as it is being charged and discharged from a constant voltage source A CHARGING A CAPACITOR FROM A CONSTANT VOLTAGE SOURCE V R V S V C Fig 5 Charging a capacitor Let us assume that the capacitor carries no initial charge When the switch is closed, there is no voltage across the capacitor and all of the supply voltage will appear across R In this case V R = V S The initial charging current is given by: I = V R = V S R R As time goes by, the voltage across the capacitor will increase, due to the build up of charge, and the voltage across the resistor will decrease When the voltage across the capacitor has reached a value V C, the charging current is given by: I = V R = V S - V C R R Since the charging current decreases, the rate of flow of charge on to the capacitor plates will decrease As a result, the rate at which the voltage increases across the capacitor will decrease A graph of voltage against time will be steep when the switch is closed and the slope will decrease as time goes by (Fig 6) It can be shown that the charging curve is an exponential curve and that the voltage across the capacitor and resistor at a time t are given by: V C = V S (1 - e -t/rc ) and V R = V S e -t/rc 8
You will not be expected to use these equations in any test If you would like to know how they are used, consult your tutor V S V C V S2 0 0 RC 2RC 3RC 4RC 5RC 069RC time Fig 6 Charging curve RC (R x C) is called the time constant of the circuit Remember the following points about an exponential charging curve: Voltage across capacitor reaches half way to the supply voltage, V S, in a time 069RC Voltage across capacitor reaches 063V S after a time RC Voltage across capacitor reaches 099V S after a time 5RC 9
B DISCHARGING A CAPACITOR THROUGH A RESISTOR Consider a capacitor being charged up from a voltage source V o 1 2 V o V o C R V C V o 2 0 0 RC 2RC 3RC 4RC 5RC 069RC time Fig 7 Discharging a capacitor When the switch is moved over to position 2, the capacitor discharges through resistor R A voltage V o is applied across the resistor and the initial discharging current I is given by : I = V o R Voltage across the capacitor starts to fall at a rapid rate As charge flows off the capacitor, the voltage across the resistor is reduced The discharging current reduces and the slope of a graph of Vc against time would decreases It can be shown (proof provided on request) that: V C = V R = V o e -t/rc V o has been used in this case to serve as a reminder that it is the starting, or original, voltage across the capacitor The curve in Fig 7 is known as an exponential decay curve You should be able to show that: the voltage falls to V o /2 after a time 069RC the voltage across the capacitor is 037V o after a time RC the voltage across the capacitor is near zero after 5RC RC is the time constant of the circuit 10