capacitance and its application

7/31/2019 Capacitance and Its Application

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Department of physics

ELECTROMAGNETISM

SFT 3013

ASSIGNMENT: CAPACITANCE AND ITS APPLICATION

GROUP MEMBER MATRIX NUMBER

KU MOHD SYAFIQ D20091035089

MUHAMAD FADLILAH BIN

MUKHLAS

D20091035126

SUARDI BIN NANANG D20091035131

MOHD AIDIL UBAIDILLAH B

RAZILAN

D20091035132

Lecturer name:

PROF. DR ROSLY BIN JAAFAR


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1.0 INTRODUCTION

1.1 Capacitor and Capacitance

Capacitors are used in virtually every area of electronics, and they perform a variety of

different tasks. Some capacitors are used for coupling, others for decoupling, while others may

be used in filters, and some may be used for power supply smoothing. Again some capacitorswill be used in low frequency circuits, and others in high frequency circuits.

Capacitance (symbol C) is a measure of a capacitor's ability to store charge. A large

capacitance means that more charge can be stored. Capacitance is measured in farads, symbol F.

However 1F is very large, so prefixes (multipliers) are used to show the smaller values:

(micro) means 10-6

(millionth), so 1000000F = 1F

n (nano) means 10-9

(thousand-millionth), so 1000nF = 1F

p (pico) means 10-12

(million-millionth), so 1000pF = 1nF

1.1.1 Capacitance of Parallel Plates

The electric field between two large parallel plates isgiven by

The voltage difference between the two plates can be expressed in terms of the workdone on apositive test charge q when it moves from the positive to the negative plate.

It then follows from the definition ofcapacitance that
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1.1.2 Cylindrical Capacitor

The capacitance for cylindrical or spherical conductors can be obtained by evaluating the voltage

difference between the conductors for a given charge on each. By applying Gauss' law to aninfinite cylinder in a vacuum, the electric field outside a charged cylinder is found to be

The voltage between the cylinders can be found by integrating the electric field along a radialline:

From the definition ofcapacitance and including the case where the volume is filled by a

dielectric ofdielectric constant k, the capacitance per unit length is defined as
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1.1.3 Spherical Capacitor

The capacitance for spherical or cylindrical conductors can be obtained by evaluating the voltage

difference between the conductors for a given charge on each. By applying Gauss' law to ancharged conducting sphere, the electric field outside it is found to be

The voltage between the spheres can be found by integrating the electric field along a radial line:

From the definition of capacitance, the capacitance is

1.2 Charge and Energy Stored

The amount of charge (symbol Q) stored by a capacitor is given by:

Charge, Q = C V where: Q = charge in coulombs (C)

C = capacitance in farads (F)

V = voltage in volts (V)

When they store charge, capacitors are also storing energy:

Energy,

E = QV = CV where E = energy in joules (J).
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1.3 Capacitive Reactance,Xc

Capacitive reactance (symbol Xc) is a measure of a capacitor's opposition to AC (alternating

current). Like resistance it is measured in ohms, , but reactance is more complex thanresistance because its value depends on the frequency (f) of the electrical signal passing through

the capacitor as well as on the capacitance, C.

Capacitive reactance, Xc = 1 where: Xc = reactance in ohms ()f = frequency in hertz (Hz)

C = capacitance in farads (F)2fC

The reactance Xc is large at low frequencies and small at high frequencies. For steady DC whichis zero frequency, Xc is infinite (total opposition), hence the rule that capacitors pass AC but

block DC.

1.4 Capacitors in Series and Parallel

Combinedcapacitance (C)

of

capacitorsconnected in

series

1/C=1/C1 + 1/C2 + 1/C3..

Combinedcapacitance (C)

of

capacitors

connected in

parallel

C = C1 + C2 + C3 ...


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1.5 Charging and Discharging of capacitor

1.5.1 Capacitor Charging

With the switch at A, the capacitor is charging. Current flows from the battery throughthe capacitor. The electrons move to one plate, but they do not jump the insulating gap inside the

capacitor. They collect on the surface of the plate.Meanwhile, electrons are removed from theother plate from the abundance that is always there in metals. That gives the plate a net positive

charge. And removing the charge completes the path around which current flows.The current is

always the same on both terminals of a capacitor. You can't move charge into one terminalwithout removing it from the other.As the current flows from the battery to the capacitor, it

travels through the LED. This emits light during the charging cycle, and then dims and finally

turns dark when the capacitor is fully charged.

The transient behavior of a circuit with a battery, a resistor and acapacitor is governed by Ohm's law, the voltage law and the definition

ofcapacitance. Development of the capacitor charging relationship

requires calculus methods and involves a differential equation. Forcontinuously varying charge the current is defined by a derivative

This kind ofdifferential equation has a general solution of the form:

and the detailed solution is formed by substitution of the generalsolution and forcing it to fit the boundary conditions of this problem.The result is
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1.5.2 Capacitor Discharging

With the switch at C, the capacitor is connected to the 1-ohm resistor. The charges storedin the capacitor's electric field now have an escape route. They can finally flow from one plate to

the other, by travelling through the resistor.

The rate of charge travel (current) depends on the circuit resistance, and a lot on how

hard it is pushed by the strength of the internal electric field (voltage).

2.0 TYPE OF CAPACITOR

There are a very large variety of different types of capacitor available in the market placeand each one has its own set of characteristics and applications from small delicate trimming

capacitors up to large power metal-can type capacitors used in high voltage power correction and

smoothing circuits. Like resistors, there are also variable types of capacitors which allow us to

vary their capacitance value for use in radio or "frequency tuning" type circuits.

Commercial types of capacitor are made from metallic foil interlaced with thin sheets ofeither paraffin-impregnated paper or Mylar as the dielectric material. Some capacitors look like

tubes, this is because the metal foil plates are rolled up into a cylinder to form a small package

with the insulating dielectric material sandwiched in between them. Small capacitors are oftenconstructed from ceramic materials and then dipped into an epoxy resin to seal them. Either way,capacitors play an important part in electronic circuits so here are a few of the more "common"

types of capacitor available.

Choosing the right capacitor use for the right capacitor is all part of the design process for

a circuit. Using the wrong type of capacitor can easily mean that a circuit will not work.


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2.1 Dielectric Capacitor

Dielectric Capacitors are usually of the variable type were a continuous variation of

capacitance is required for tuning transmitters, receivers and transistor radios. Variable dielectric

capacitors are multi-plate air-spaced types that have a set of fixed plates (the stator vanes) and a

set of movable plates (the rotor vanes) which move in between the fixed plates. The position ofthe moving plates with respect to the fixed plates determines the overall capacitance value. The

capacitance is generally at maximum when the two sets of plates are fully meshed together. Highvoltage type tuning capacitors have relatively large spacings or air-gaps between the plates with

breakdown voltages reaching many thousands of volts.

2.1.1 Variable Capacitor Symbols

As well as the continuously variable types, preset type variable capacitors are alsoavailable called Trimmers. These are generally small devices that can be adjusted or "pre-set" to

a particular capacitance value with the aid of a small screwdriver and are available in very smallcapacitances of 500pF or less and are non-polarized.

2.2 Film Capacitor

Film Capacitors are the most commonly available of all types of capacitors, consisting of arelatively large family of capacitors with the difference being in their dielectric properties. These

include polyester (Mylar), polystyrene, polypropylene, polycarbonate, metallized paper, Teflon

etc. Film type capacitors are available in capacitance ranges from as small as 5pF to as largeas 100uF depending upon the actual type of capacitor and its voltage rating. Film capacitors also

come in an assortment of shapes and case styles which include:

Wrap & Fill (Oval & Round) - where the capacitor is wrapped in a tight plastic tape

and have the ends filled with epoxy to seal them.

Epoxy Case (Rectangular & Round) - where the capacitor is encased in a moulded

plastic shell which is then filled with epoxy.

Metal Hermetically Sealed (Rectangular & Round) - where the capacitor is encased

in a metal tube or can and again sealed with epoxy.

with all the above case styles available in both Axial and Radial Leads.


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Film Capacitors which use polystyrene, polycarbonate or Teflon as their dielectrics are

sometimes called "Plastic capacitors". The construction of plastic film capacitors is similar tothat for paper film capacitors but use a plastic film instead of paper. The main advantage of

plastic film capacitors compared to impregnated-paper types is that they operate well under

conditions of high temperature, have smaller tolerances, a very long service life and high

reliability. Examples of film capacitors are the rectangular metallized film and cylindrical film &foil types as shown below.

2.2.1 Radial Lead Type

2.2.2 Axial Lead Type

The film and foil types of capacitors are made from long thin strips of thin metal foil with

the dielectric material sandwiched together which are wound into a tight rolland then sealed in paper or metal tubes. These film types require a much

thicker dielectric film to reduce the risk of tears or punctures in the film, and

is therefore more suited to lower capacitance values and larger case sizes.


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Metallized foil capacitors have the conductive film metallized sprayed directly onto each

side of the dielectric which gives the capacitor self-healing properties and can therefore usemuch thinner dielectric films. This allows for higher capacitance values and smaller case sizes

for a given capacitance. Film and foil capacitors are generally used for higher power and more

precise applications.

2.3 Ceramic Capacitors

Ceramic CapacitorsorDisc Capacitors as they are generally called, are made by coatingtwo sides of a small porcelain or ceramic disc with silver and are then stacked together to make a

capacitor. For very low capacitance values a single ceramic disc of about 3-6mm is used.

Ceramic capacitors have a high dielectric constant (High-K) and are available so that relativelyhigh capacitances can be obtained in a small physical size. They exhibit large non-linear changes

in capacitance against temperature and as a result are used as de-coupling or by-pass capacitors

as they are also non-polarized devices. Ceramic capacitors have values ranging from a few pico-farads to one or two microfarads but their voltage ratings are generally quite low.

Ceramic Capacitor

Ceramic types of capacitors generally have a 3-digit code printed onto their body toidentify their capacitance value in pico-farads. Generally the first two digits indicate the

capacitors value and the third digit indicates the number of zero's to be added. For example, aceramic disc capacitor with the markings 103 would indicate 10 and 3 zero's in pico-farads

which is equivalent to 10,000 pF or 10nF. Likewise, the digits 104 would indicate 10 and 4

zero's in pico-farads which is equivalent to 100,000 pF or 100nF and so on. Then on the image ofa ceramic capacitor above the numbers 154 indicate 15 and 4 zero's in pico-farads which is

equivalent to 150,000 pF or 150nF. Letter codes are sometimes used to indicate their tolerance

value such as: J = 5%, K = 10% or M = 20% etc.

2.4 Electrolytic Capacitors

Electrolytic Capacitors are generally used when very large capacitance values arerequired. Here instead of using a very thin metallic film layer for one of the electrodes, a semi-

liquid electrolyte solution in the form of a jelly or paste is used which serves as the second


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electrode (usually the cathode). The dielectric is a very thin layer of oxide which is grown

electro-chemically in production with the thickness of the film being less than ten microns. Thisinsulating layer is so thin that it is possible to make capacitors with a large value of capacitance

for a small physical size as the distance between the plates, d is very small.

Electrolytic Capacitor

The majority of electrolytic types of capacitors are Polarized, that is the DC voltage

applied to the capacitor terminals must be of the correct polarity, i.e. positive to the positiveterminal and negative to the negative terminal as an incorrect polarization will break down the

insulating oxide layer and permanent damage may result. All polarized electrolytic capacitors

have their polarity clearly marked with a negative sign to indicate the negative terminal and thispolarity must be followed.

Electrolytic Capacitors are generally used in DC power supply circuits due to their largecapacitances and small size to help reduce the ripple voltage or for coupling and decoupling

applications. One main disadvantage of electrolytic capacitors is their relatively low voltage

rating and due to the polarization of electrolytic capacitors, it follows then that they must not be

used on AC supplies. Electrolytic's generally come in two basic forms; Aluminum ElectrolyticCapacitorsand Tantalum Electrolytic Capacitors.

Electrolytic Capacitor


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2.4.1 Aluminium Electrolytic Capacitors

There are basically two types of Aluminium Electrolytic Capacitor, the plain foil type and

the etched foil type. The thickness of the aluminium oxide film and high breakdown voltage give

these capacitors very high capacitance values for their size. The foil plates of the capacitor are

anodized with a DC current. This anodizing process sets up the polarity of the plate material anddetermines which side of the plate is positive and which side is negative. The etched foil type

differs from the plain foil type in that the aluminium oxide on the anode and cathode foils hasbeen chemically etched to increase its surface area and permittivity. This gives a smaller sized

capacitor than a plain foil type of equivalent value but has the disadvantage of not being able to

withstand high DC currents compared to the plain type. Also their tolerance range is quite largeat up to 20%. Typical values of capacitance for an aluminium electrolytic capacitor range from

1uF up to 47,000uF.

Etched foil electrolytic's are best used in coupling, DC blocking and by-pass circuitswhile plain foil types are better suited as smoothing capacitors in power supplies. But

aluminiumelectrolytic 's are "polarized" devices so reversing the applied voltage on the leads willcause the insulating layer within the capacitor to become destroyed along with the capacitor.However, the electrolyte used within the capacitor helps heal a damaged plate if the damage is

small. Since the electrolyte has the properties to self-heal a damaged plate, it also has the ability

to re-anodize the foil plate. As the anodizing process can be reversed, the electrolyte has theability to remove the oxide coating from the foil as would happen if the capacitor was connected

with a reverse polarity. Since the electrolyte has the ability to conduct electricity, if the

aluminum oxide layer was removed or destroyed, the capacitor would allow current to pass from

one plate to the other destroying the capacitor

2.4.2 Tantalum Electrolytic Capacitors

Tantalum Electrolytic CapacitorsandTantalum Beads, are available in both wet (foil) and

dry (solid) electrolytic types with the dry or solid tantalum being the most common. Solid

tantalum capacitors use manganese dioxide as their second terminal and are physically smallerthan the equivalent aluminium capacitors. The dielectric properties of tantalum oxide is also

much better than those of aluminium oxide giving a lower leakage currents and better

capacitance stability which makes them suitable for use in blocking, by-passing, decoupling,filtering and timing applications.

Also, Tantalum Capacitors although polarized, can tolerate being connected to a reversevoltage much more easily than the aluminium types but are rated at much lower workingvoltages. Solid tantalum capacitors are usually used in circuits where the AC voltage is small

compared to the DC voltage. However, some tantalum capacitor types contain two capacitors in-

one, connected negative-to-negative to form a "non-polarized" capacitor for use in low voltageAC circuits as a non-polarized device. Generally, the positive lead is identified on the capacitor

body by a polarity mark, with the body of a tantalum bead capacitor being an oval geometrical

shape. Typical values of capacitance range from 47nF to 470F


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Aluminium& Tantalum Electrolytic Capacitor

Electrolytic's are widely used capacitors due to their low cost and small size but there are three

easy ways to destroy an electrolytic capacitor:

Over-voltage - excessive voltage will cause current to leak through the dielectric

resulting in a short circuit condition.

Reversed Polarity - reverse voltage will cause self-destruction of the oxide layer and

failure.

Over Temperature - excessive heat dries out the electrolytic and shortens the life of an

electrolytic capacitor.

3.0 CHARACTERISTIC OF CAPACITOR

Even though two capacitors may have exactly the same capacitance value, they may havedifferent voltage ratings. If a smaller rated voltage capacitor is substituted in place of a higher

rated voltage capacitor, the increased voltage may damage the smaller capacitor. Also we

remember from the last tutorial that with a polarised electrolytic capacitor, the positive lead mustgo to the positive connection and the negative lead to the negative connection otherwise it may

again become damaged. So it is always better to substitute an old or damaged capacitor with the

same type as the specified one. An example of capacitor markings is given below.


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The capacitor, as with any other electronic component, comes defined by a series ofcharacteristics. These Capacitor Characteristics can always be found in the datasheets that the

capacitor manufacturer provides to us so here are just a few of the more important ones.

3.1 Nominal Capacitance, (C)

The nominal value of the Capacitance, C of a capacitor is measured in pico-Farads (pF),nano-Farads (nF) or micro-Farads (F) and is marked onto the body of the capacitor as numbers,

letters or coloured bands. The capacitance of a capacitor can change value with the circuitfrequency (Hz) y with the ambient temperature. Smaller ceramic capacitors can have a nominal

value as low as one pico-Farad, ( 1pF ) while larger electrolytic's can have a nominal capacitance

value of up to one Farad, ( 1F ). All capacitors have a tolerance rating that can range from -20%

to as high as +80% for aluminiumelectrolytic's affecting its actual or real value. The choice ofcapacitance is determined by the circuit configuration but the value read on the side of a

capacitor may not necessarily be its actual value.

3.2 Working Voltage, (WV)

The Working Voltage is the maximum continuous voltage either DC or AC that can beapplied to the capacitor without failure during its working life. Generally, the working voltage

printed onto the side of a capacitors body refers to its DC working voltage, ( WV-DC ). DC and

AC voltage values are usually not the same for a capacitor as the AC voltage value refers to the

r.m.s. value and NOT the maximum or peak value which is 1.414 times greater. Also, the

specified DC working voltage is valid within a certain temperature range, normally - 30C to +70C. Any DC voltage in excess of its working voltage or an excessive AC ripple current maycause failure. It follows therefore, that a capacitor will have a longer working life if operated in acool environment and within its rated voltage. Common working DC voltages are 10V, 16V,

25V, 35V, 50V, 63V, 100V, 160V, 250V, 400V and 1000V and are printed onto the body of the

capacitor.


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3.3 Tolerance, (%)

As with resistors, capacitors also have a Tolerance rating expressed as a plus-or-minus

value either in picofarad's (pF) for low value capacitors generally less than 100pF or as a

percentage (%) for higher value capacitors generally higher than 100pF. The tolerance value is

the extent to which the actual capacitance is allowed to vary from its nominal value and canrange anywhere from -20% to +80%. Thus a 100F capacitor with a 20% tolerance could

legitimately vary from 80F to 120F and still remain within tolerance. Capacitors are ratedaccording to how near to their actual values they are compared to the rated nominal capacitance

with coloured bands or letters used to indicated their actual tolerance. The most common

tolerance variation for capacitors is 5% or 10% but some plastic capacitors are rated as low as1%.

3.4 Leakage Current

The dielectric used inside the capacitor to separate the conductive plates is not a perfect

insulator resulting in a very small current flowing or "leaking" through the dielectric due to the

influence of the powerful electric fields built up by the charge on the plates when applied to aconstant supply voltage. This small DC current flow in the region of nano-amps (nA) is called

the capacitors Leakage Current. Leakage current is a result of electrons physically making their

way through the dielectric medium, around its edges or across its leads and which will over timefully discharging the capacitor if the supply voltage is removed.

When the leakage is very low such as in film or foil type capacitors it is generallyreferred to as "insulation resistance" ( Rp ) and can be expressed as a high value

resistance in parallel with the capacitor as shown. When the leakage current ishigh as in electrolytic's it is referred to as a "leakage current" as electrons flowdirectly through the electrolyte. Capacitor leakage current is an important

parameter in amplifier coupling circuits or in power supply circuits, with the bestchoices for coupling and/or storage applications being Teflon and the other

plastic capacitor types (polypropylene, polystyrene, etc) because the lower thedielectric constant, the higher the insulation resistance.

Electrolytic-type capacitors (tantalum and aluminum) on the other hand may have veryhigh capacitances, but they also have very high leakage currents (typically of the order of about

5-20 A per F) due to their poor isolation resistance, and are therefore not suited for storage or

coupling applications. Also, the flow of leakage current for aluminiumelectrolytic's increaseswith temperature.


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3.5 Working Temperature, (T)

Changes in temperature around the capacitor affect the value of the capacitance because

of changes in the dielectric properties. If the air or surrounding temperature becomes to hot or tocold the capacitance value of the capacitor may change so much as to affect the correct operationof the circuit. The normal working range for most capacitors is -30C to +125C with nominal

voltage ratings given for a Working Temperature of no more than +70C especially for the

plastic capacitor types. Generally for electrolytic capacitors and especially aluminiumelectrolytic capacitor, at high temperatures (over +85C the liquids within the electrolyte can be

lost to evaporation, and the body of the capacitor (especially the small sizes) may become

deformed due to the internal pressure and leak outright. Also, electrolytic capacitors can not be

used at low temperatures, below about -10C, as the electrolyte jelly freezes.

3.6 Temperature Coefficient, (TC)

The Temperature Coefficient of a capacitor is the maximum change in its capacitance

over a specified temperature range. The temperature coefficient of a capacitor is generally

expressed linearly as parts per million per degree centigrade (PPM/C), or as a percent changeover a particular range of temperatures. Some capacitors are non linear (Class 2 capacitors) and

increase their value as the temperature rises giving them a temperature coefficient that is

expressed as a positive "P". Some capacitors decrease their value as the temperature rises giving

them a temperature coefficient that is expressed as a negative "N". For example "P100" is +100ppm/C or "N200", which is -200 ppm/C etc. However, some capacitors do not change their

value and remain constant over a certain temperature range, such capacitors have a zerotemperature coefficient or "NPO". These types of capacitors such as Mica or Polyester aregenerally referred to as Class 1 capacitors.

Most capacitors, especially electrolytic's lose their capacitance when they get hot buttemperature compensating capacitors are available in the range of at least P1000 through to

N5000 (+1000 ppm/C through to -5000 ppm/C). It is also possible to connect a capacitor with a

positive temperature coefficient in series or parallel with a capacitor having a negativetemperature coefficient the net result being that the two opposite effects will cancel each other

out over a certain range of temperatures. Another useful application of temperature coefficient

capacitors is to use them to cancel out the effect of temperature on other components within a

circuit, such as inductors or resistors etc.

3.7 Polarization

Capacitor Polarization generally refers to the electrolytic type capacitors but mainly theAluminiumElectrolytic's, with regards to their electrical connection. The majority are polarized


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types, that is the voltage connected to the capacitor terminals

must have the correct polarity, i.e. positive to positive andnegative to negative. Incorrect polarization can cause the

oxide layer inside the capacitor to break down resulting in

very large currents flowing through the device resulting in

destruction as we have mentioned earlier.

The majority of electrolytic capacitors have their

negative, -ve terminal clearly marked with either a blackstripe, band, arrows or chevrons down one side of their body

as shown, to prevent any incorrect connection to the DC

supply. Some larger electrolytic's have their metal can orbody connected to the negative terminal but high voltage types have their metal can insulated

with the electrodes being brought out to separate spade or screw terminals for safety. Also, when

using aluminiumelectrolytic's in power supply smoothing circuits care should be taken to prevent

the sum of the peak DC voltage and AC ripple voltage from becoming a "reverse voltage".

3.8 Equivalent Series Resistance, (ESR)

The Equivalent Series Resistanceor ESR, of a capacitor is the AC impedance of the

capacitor when used at high frequencies and includes the resistance of the dielectric material, theDC resistance of the terminal leads, the DC resistance of the connections to the dielectric and the

capacitor plate resistance all measured at a particular frequency and temperature.

ESR Model

In some ways, ESR is the opposite of the insulation resistance which is presented as a

pure resistance (no capacitive or inductive reactance) in parallel with the capacitor. An idealcapacitor would have only capacitance but ESR is presented as a pure resistance in series with

the capacitor and which is frequency dependent making it a "DYNAMIC" quantity.

As ESR defines the energy losses of the "equivalent" series resistance of a capacitor itmust therefore determine the capacitor's overall I2R heating losses especially when used in power

and switching circuits. Capacitors with a relatively high ESR have less ability to pass current to

and from its plates to the external circuit because of their longer charging and discharging RCtime constant. The ESR of electrolytic capacitors increases over time as their electrolyte dries

out. Capacitors with very low ESR ratings are available and are best suited when using the

capacitor as a filter.


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4.0 APPLICATIONS

4.1 Capacitive coupling

In electronics, capacitive coupling is the transfer of energy within an electrical network by

means of the capacitance between circuit nodes. This coupling can have an intentional oraccidental effect. Capacitive coupling is typically achieved by placing a capacitor in series with

the signal to be coupled.

1. analog circuits

Capacitive coupling

Polyester film capacitors, commonly used for

coupling between two circuits.

In analog circuits, a coupling capacitor is used to connect two circuits such that only theAC signal from the first circuit can pass through to the next while DC is blocked. This technique

helps to isolate the DC bias settings of the two coupled circuits. Capacitive coupling is also

known asAC coupling and the capacitor used for the purpose is known as a coupling or DC

blocking capacitor. The term decoupling capacitoris also used, emphasizing the DC isolation.

Capacitive coupling has the disadvantage of degrading the low frequency performance of a

system containing capacitively coupled units.


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4.2 Filter capacitor

Filter capacitors are any capacitors used for filtering. Filter capacitors are common in electrical

and electronic work, and cover a number of applications.

1. Transformers

Transformer Full-wave rectifier with a capacitor filter.

The main purpose of filter capacitor is to change AC power to DC power. The simple

capacitor filter is the most basic type of power supply filter. The application of the simple

capacitor filter is very limited. It is sometimes used on extremely high-voltage, low-current

power supplies for cathode-ray and similar electron tubes, which require very little load current

from the supply. The capacitor filter is also used where the power-supply ripple frequency is not

critical; this frequency can be relatively high. The capacitor (C1) shown in figure 4-15 is a

simple filter connected across the output of the rectifier in parallel with the load.

When this filter is used, the RC charge time of the filter capacitor (C1) must be short and

the RC discharge time must be long to eliminate ripple action. In other words, the capacitor must

charge up fast, preferably with no discharge at all.

Half-wave rectifier without filtering.

Half-wave rectifier with filtering.


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4.3 Capacitor used as smoothing

To provide a steady DC output. The raw rectified DC requires a smoothing capacitor

circuit to enable the rectified DC to be smoothed so that it can be used to power electronics

circuits without large levels of voltage variation.

The raw DC supplied by a rectifier on its own would consist of a series of half sine waves withthe voltage varying between zero and 2 times the RMS voltage (ignoring any diode and otherlosses). A supply of this nature would not be of any use for powering circuits because any

analogue circuits would have the huge level of ripple superimposed on the output, and any digitalcircuits would not function because the power would be removed every half cycle.

To smooth the output of the rectifier a reservoir capacitor is used - placed across the output of thereciter and in parallel with the load.. This capacitor charges up when the voltage from the

rectifier rises above that of the capacitor and then as the rectifier voltage falls, the capacitor

provides the required current from its stored charge.

As there will always be some ripple on the output of a rectifier using a smoothing capacitor

circuit, it is necessary to be able to estimate the approximate value. Over-specifying a capacitortoo much will add extra cost, size and weight - under-specifying it will lead to poor performance.

The diagram above shows the ripple for a full wave rectifier with capacitor smoothing. If a halfwave rectifier was used, then half the peaks would be missing and the ripple would be

approximately twice the voltage.


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For cases where the ripple is small compared to the supply voltage - which is almost always the

case - it is possible to calculate the ripple from a knowledge of the circuit conditions:

Fullwave rectifier:

Half-wave rectifier

These equations provide more than sufficient accuracy. Although the capacitor discharge for apurely resistive load is exponential, the inaccuracy introduced by the linear approximation is

very small for low values of ripple.

It is also worth remembering that the input to a voltage regulator is not a purely resistive load but

a constant current load. Finally, the tolerances of electrolytic capacitors used for rectifier

smoothing circuits are large - 20% at the very best, and this will mask any inaccuraciesintroduced by the assumptions in the equations.

Two of the major specifications of a capacitor are its capacitance and working voltage. Howeverfor applications where large levels of current may flow, as in the case of a rectifier smoothing

capacitor, a third parameter is of importance - its maximum ripple current.

The ripple current is not just equal to the supply current. There are two scenarios:

Capacitor discharge current: On the discharge cycle, the maximum current supplied bythe capacitor occurs as the output from the rectifier circuit falls to zero. At this point all

the current from the circuit is supplied by the capacitor. This is equal to the full current of

the circuit.


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Capacitor charging current: On the charge cycle of the smoothing capacitor, the

capacitor needs to replace all the lost charge, but it can only achieve this when thevoltage from the rectifier exceeds that from the smoothing capacitor. This only occurs

over a short period of the cycle. Consequently the current during this period is much

higher. The large the capacitor, the better it reduces the ripple and the shorter the charge

period.

In view of the large currents involved, care must be taken to ensure that the ripple current doesnot exceed the rated values for the capacitor.


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4.4 Capacitor used as timing

In this application a capacitor can be used with a resistor or inductor in a resonant or time

dependent circuit. In this function the capacitor may appear in a filter, oscillator tuned circuit, or

in a timing element for a circuit, the time it takes to charge and discharge determining the

operation of the circuit. Capacitors do not keep time they do however charge at a specific rate of63% of the applied voltage from a source that can be used to relate to timing since the source

voltage can be calculated after a time lapse. So this make capacitor being used to produce a

timer. Capacitors appear as though they are short circuit whilethey are charging, but as soon as

they are charged, they appear to be open circuit. One example of capacitor used as timer is 55

integrated circuit.

The 555 integrated circuit forms the basis of lots of timing circuits. Lets look first at howCapacitors work. Try these two circuits:

The first circuit lets the capacitor charge up by connecting it to the battery. Capacitor being

discharge by flipping the switch so that the capacitor is connected to the LED. The capacitor

discharges through the LED which shines briefly. The second circuit allows the discharge to

slow down. We can plot it on the oscilloscope that Crocodile Clips provides. Flip the switch

and the capacitor charges slowly up to the battery voltage. Then flip the switch again and it

discharges slowly through the resistor. Both curves are shown below and are exponentials.


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The formula that can be used to work out the Time Constant for this kind of circuit is T = RxC;

the units are Ohms, Farads and Seconds. Since Farads are rather largeMegaOhms (M),

microfarads (uF), and seconds, or kiloohms, microfarads and millisecondscan beuse. The time

constant gives the time taken to get to 63% of the final voltage level. Theoretically an

exponential curve never reaches the target voltage, but a good approximation is five time

constants.

The circuit lets the capacitor being charge up by connecting it to the battery through the push

switch. The capacitor can be discharge directly through the LEDbut it would be too quick.Instead, slow down the discharge by using a 1k resistor and a transistor. That small current turns

the transistor on so that the LED shines. If the circuit in Crocodile Clips can the charge and

discharge be plot on the oscilloscope. Put the oscilloscope probe at the collector lead of the

transistor. Press the switch and the capacitor quickly charges up to the battery voltage. Release

the switch and it discharges slowly through the resistor. The graph is shown below.

The formula that can be used to work out the Time Constant for this kind of circuit is T= RxC;

the units are Ohms, Farads and Seconds. Since Farads are rather large MegaOhms (M),

MicroFarads (uF) and Secondscan beuse. The time constant gives the time taken to reach 63%

of the final voltage level.


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4.5 Capacitors as a tune

Type of capacitor that be used for tune are variable capacitors. This capacitor are mostly used in

radio tuning circuits and they are sometimes called 'tuning capacitors'. They have very small

capacitance values, typically between 100pF and 500pF (100pF = 0.0001F). The type

illustrated usually has trimmers built in (for making small adjustments - see below) as well as themain variable capacitor. Many variable capacitors have very short spindles which are not suitable

for the standard knobs used for variable resistors and rotary switches. It would be wise to check

that a suitable knob is available before ordering a variable capacitor. Variable capacitors are notnormally used in timing circuits because their capacitance is too small to be practical and the

range of values available is very limited. Instead timing circuits use a fixed capacitor and a

variable resistor if it is necessary to vary the time period.

A voltage controlled variable capacitor varactor. can be constructed using switchable MEMs

capacitors as the control element. As the MEMscapacitors are binary onoff.controlled, the most useful configuration for a variable capacitor is MEMs capacitor with binary weightedcapacitance selection. Theschematic of one possible topology is shown in Figure 9. This

arrangement constructs each binarycapacitor bit as a single branch containing one or more

MEMs capacitors and a fixed capacitor.The total capacitance of each branch is the series

combination of the two sets of capacitors.In the schematic, the largest bit consists of sixswitchable MEMs capacitors at 3.4 pF each for atotal of 20 pF in combination with the series 74

pF capacitor. This yields the desired 16 pF oftotal capacitance for the largest bit. The smaller bits

are similarly constructed, and contain 8, 4, 2,1, and .5 pF total capacitance. The bits with a

total capacitance of less than 3.4 pF use a singlecapacitor membrane, and a series capacitor thatacts as a divider to reduce the total capacitance tothe desired value. For example, the smallest bit

isrealized with a single MEMs capacitor in serieswith a 0.6 pF capacitor, with an effectivecapacitanceof 0.5 pF when the MEMs capacitor isactuated.


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Figure 8.Typical switching speed measurements for a

MEMs capacitor

Figure 9.Schematic of a tunable capacitor using numerous shunt MEMs capacitor elements.


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Figure 10.Micrograph of a tunable RF MEMs capacitor.

Each of the MEMs capacitors is actuated byapplication of a control voltage to the capacitor

electrode. Each control signal is decoupled fromthe RF through a 5 kV thin-film resistor. The

series capacitor serves to block the control voltagefrom interfering with adjoining circuitry.As each MEMs draws negligible current, biasingthe device through a high resistance servesas an effective means of minimizing DC]RFinteractions.A completed RF MEMs shunt variable

capacitoris shown in Figure 10. The overall chip size is3.2=3.2 mm=0.53 mm. The layout of the

devicewas not optimized for minimum size, and waslaid out in a fashion very similar to theschematic.The capacitor RF port is on the left side of thechip while the DC control pads are on

the top ofthe IC. Unused areas were filled with groundplane to minimize coupling between bits

and theDC control lines.


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Figure 11.Capacitance of the tunable MEMs capacitor vs. binary state

The measured capacitance of the variable capacitor ranges from 1.5 pF with none of the bits

actuated to 33.2 pF with all of the bits actuated. A graph of this response is shown in Figure11.This represents a maximum onroff ratio of approximately 22; the highest the authors believe

has been reported to date. The highest five bits of the capacitor exhibit a differential capacitance

within 5% of the desired values. The smallest bitsare impacted by fringing capacitance of theinterconnects. The off-capacitance of the 14 individualMEMs capacitors is approximately

500]700 fF.Therefore, a bulk of the 1.5 pF zero-state capacitanceis due to fringing between the

capacitorinterconnects and the closely spaced groundplane. With proper layout to reduce this

parasiticcapacitance, capacitance tuning ranges in the40-50 range should be achievable. Figure12demonstrates the capacitance of the IC as a functionof frequency. As the IC is actuated

throughits various states, the variable capacitor changesseries-resonant frequency. This change is

a functionof the capacitance to ground in each state,and the line length between the input and

thatcapacitance. Future designs will be improved byreducing all line lengths, and by positioningthelarger capacitance states _which are more sensitive to line length. closer to the input

terminal.The quality factor _Q. of this variable capacitor isless than 20 at 1 GHz. This is due

mainly to thelong line lengths and the addition of the multipleelectrode resistances in series.Future designs willmodify the connections between membranes to amore parallel arrangement,

greatly reducing theoverall resistance. It is estimated that quality factorsgreater than 50 are

achievable with improvedlayout and thicker conductor interconnects.


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4.6 Capacitors as storing energy

Element of energy stored:

If Q is the amount of charge stored when the whole battery voltage appears across the capacitor,

then the stored energy is obtained from the integral:

This energy expression can be put in three equivalent forms by just permutations based on thedefinition of capacitance C=Q/V.

The energy stored on a capacitor can be expressed in terms of the work done by the battery.

Voltage represents energy per unit charge, so the work to move a charge element dq from the

negative plate to the positive plate is equal to V dq, where V is the voltage on the capacitor. Thevoltage V is proportional to the amount of charge which is already on the capacitor.


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When the switch is closed to connect the battery to the capacitor, there is zero voltage across the

capacitor since it has no charge buildup. The voltage on the capacitor is proportional to the

charge

Storing energy on the capacitor involves doing work to transport charge from one plate of the

capacitor to the other against the electrical forces. As the charge builds up in the charging

process, each successive element of charge dq requires more work to force it onto the positive

plate. Summing these continuously changing quantities requires an integral. plate of the capacitorto the other against the electrical forces. As the charge builds up in the charging process, each

successive element of charge dq requires more work to force it onto the positive plate. Summingthese continuously changing quantities requires an integral.

Note that the total energy stored QV/2 is exactly half of the energy QV which is supplied by thebattery, independent of R!


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Transporting differential charge dq to theplate of the capacitor requires work

But as the voltage rises toward the battery voltage in the process of storing energy, eachsuccessive dq requires more work. Summing all these amounts of work until the total charge is

reached is an infinite sum, the type of task an integral is essential for. The form of the integral

shown above is a polynomial integral and is a good example of the power of integration.

capacitance and its application

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