Eye And Foot Problems In Diabetic related diseases
The term diabetes mellitus refers to a group of medical disorders of varying causes which are usually accompanied by long standing elevations of blood glucose levels over and above what is generally acceptable as normal.
Blood glucose elevation in this situation being a direct consequence of inadequate production of insulin by the body part called the pancreas. Insulin can best be described as a body chemical medically referred to as “hormone.” It is usually released by the pancreas in response to meal or glucose-containing drink.
Diabetes and the Eye
Eye problems which can affect people with diabetes more commonly include cataract (clouding of the lens of the eye), glaucoma (increase of fluid pressure inside the eye, leading to optic nerve damage and loss of vision), diabetic retinopathy (the most common diabetic eye disease) and some less dangerous others.
These eye complications are commonly seen in those with a longer duration of diabetes, those with poorly controlled or uncontrolled diabetes, and those with other organ problems.
These eye problems are often unknown to the sufferer at the early stages when their treatments are better assured, unless they undergo regular eye examinations by an eye doctor.
Eye examinations should be done every six months or yearly. Treatments depend on the advice of the eye care specialist in conjunction with other diabetic care specialists. Cataracts are usually curable with operation; glaucoma is better treated early with drugs, laser and/or operation, while diabetic retinopathy requires laser therapy.
What are the risk factors for diabetic retinopathy?
The longer a person has diabetes, the greater the chance of developing diabetic retinopathy. Almost 80 per cent of people, who have diabetes for 15 years or more, have some damage done on the blood vessels in their retina.
What can be done to prevent diabetic retinopathy?
There is no treatment that can prevent diabetic retinopathy altogether. Persons with any form of diabetes may develop diabetic retinopathy. It has, however, been proven that a good control of diabetes can delay and slow down the rate of progress of diabetic retinopathy and its complications.
Besides good control of blood glucose, one must exercise regularly, keep the blood pressure under control, avoid smoking, and avoid excessive weight.
How do I know if I have diabetic retinopathy?
You might not know that you are having diabetic retinopathy, as there are no symptoms in the early stages of the disease. Therefore, it is essential to have a periodic evaluation of your eye by an eye doctor to detect the condition early.
Early diagnosis and timely treatment are very essential in preventing the complications of this disease and thus, maintaining vision.
How frequently should I get my eye examined?
Because a person with diabetes can have retinopathy and not know it, a regular check-up with an eye care professional is essential. If one has diabetes, it is advised to get a bi-annual or yearly examination with the eye doctor.
The pupils may be dilated with eye drops, so that the eye doctor may have a good look at the back of the eye. Once there is diabetic retinopathy, then the eye doctor will advise if there will be a need for some investigations, treatment or just a follow-up. In these cases, the frequency of follow-up visits is decided on the basis of the severity of the disease.
Treatment for diabetic retinopathy
Specific treatment will be determined by the doctor(s) based on: age, overall health condition, and medical history, extent of the disease involvement, individual tolerance for specific medications, procedures, or therapies, expectations for the course of the disease, personal opinion or preference.
Diabetic retinopathy is often treated with laser surgery to shrink the abnormal blood vessels or to seal the leaking ones.
What are the other possible eye conditions in diabetes?
Glaucoma
People with diabetes are 40 per cent more likely to suffer from glaucoma than people without diabetes. The longer someone has had diabetes, the more common glaucoma is. Risk also increases with age. Glaucoma occurs when pressure builds up in the eye.
In most cases, the pressure causes drainage of the aqueous humour to slow down so that it builds up in the front chamber of the eye. The pressure pinches the blood vessels that carry blood to the retina and optic nerve.
Vision is gradually lost because the retina and nerves are damaged. There are several treatments for glaucoma. Some use drugs to reduce pressure in the eye, while others involve surgery.
Cataracts
Many people without diabetes get cataracts, but people with diabetes are 60 per cent more likely to develop this eye condition. People with diabetes also tend to develop cataracts at a younger age and have them progress faster.
With cataracts, the clear eye lens becomes cloudy, blocking light. To help deal with mild cataracts, one may need to wear sunglasses.
For cataracts that interfere greatly with vision, doctors usually remove the lens of the eye. Sometimes, the patient gets a new transplanted lens. In people with diabetes, retinopathy can get worse after removal of the lens and glaucoma may start to develop.
Foot problems in diabetes
People with diabetes can develop different types of foot problems. Even what appears to be a minor problem can get worse and lead to serious complications.
Foot ulcerations are a common cause for hospital admissions among persons with diabetes, resulting in prolonged hospital stay, loss of the limb (amputation) and even death.
Many of these serious foot problems can, however, be prevented through proper foot care, early identification of foot problems and prompt treatment by a skilled health care provider.
Monday, October 26, 2009
Wednesday, October 21, 2009
CAPACITORS
Capacitors
Modern capacitors, by a cm rule.
Type Passive
Invented Ewald Georg von Kleist (October 1745)
Electronic symbol
A capacitor or condenser is a passive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force between the plates. The effect is greatest between wide, flat, parallel, narrowly separated conductors.
An ideal capacitor is characterized by a single constant value, capacitance, which is measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. In practice, the dielectric between the plates passes a small amount of leakage current. The conductors and leads introduce an equivalent series resistance and the dielectric has an electric field strength limit resulting in a breakdown voltage.
Capacitors are widely used in electronic circuits to block the flow of direct current while allowing alternating current to pass, to filter out interference, to smooth the output of power supplies, and for many other purposes. They are used in resonant circuits in radio frequency equipment to select particular frequencies from a signal with many frequencies.
[edit] History
Battery of four Leyden jars in Museum Boerhave, Leiden.In October 1745, Ewald Georg von Kleist of Pomerania in Germany found that charge could be stored by connecting a high voltage electrostatic generator by a wire to a volume of water in a hand-held glass jar.[1] Von Kleist's hand and the water acted as conductors and the jar as a dielectric (although details of the mechanism were incorrectly identified at the time). Von Kleist found that after removing the generator, touching the wire resulted in a painful spark. In a letter describing the experiment, he said "I would not take a second shock for the kingdom of France."[2] The following year, the Dutch physicist Pieter van Musschenbroek invented a similar capacitor, which was named the Leyden jar, after the University of Leyden where he worked.[3] Daniel Gralath was the first to combine several jars in parallel into a "battery" to increase the charge storage capacity.[citation needed]
Benjamin Franklin investigated the Leyden jar and proved that the charge was stored on the glass, not in the water as others had assumed.[citation needed] He also created the term "battery",[4][5] (as in a battery of cannon), subsequently applied to clusters of electrochemical cells.[6] Leyden jars were later to be made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils.[citation needed] The earliest unit of capacitance was the 'jar', equivalent to about 1 nanofarad.[citation needed]
Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of wireless (radio) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance. A more compact construction began to be used of a flexible dielectric sheet such as oiled paper sandwiched between sheets of metal foil, rolled or folded into a small package.
Early capacitors were also known as condensers, a term that is still occasionally used today. The term was first used for this purpose by Alessandro Volta in 1782, with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor.[citation needed]
[edit] Theory of operation
Main article: Capacitance
Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.
A simple demonstration of a parallel-plate capacitorA capacitor consists of two conductors separated by a non-conductive region.[7] The non-conductive substance is called the dielectric medium, although this may also mean a vacuum or a semiconductor depletion region chemically identical to the conductors. A capacitor is assumed to be self-contained and isolated, with no net electric charge and no influence from an external electric field. The conductors thus contain equal and opposite charges on their facing surfaces,[8] and the dielectric contains an electric field. The capacitor is a reasonably general model for electric fields within electric circuits.
An ideal capacitor is wholly characterized by a constant capacitance 'C', defined as the ratio of charge ±'Q' on each conductor to the voltage 'V' between them
Sometimes charge buildup affects the mechanics of the capacitor, causing the capacitance to vary. In this case, capacitance is defined in terms of incremental changes:
In SI units, a capacitance of one farad means that one coulomb of charge on each conductor causes a voltage of one volt across the device.[9]
[edit] Energy storage
Work must be done by an external influence to move charge between the conductors in a capacitor. When the external influence is removed, the charge separation persists and energy is stored in the electric field. If charge is later allowed to return to its equilibrium position, the energy is released. The work done in establishing the electric field, and hence the amount of energy stored, is given by:[10]
[edit] Current-voltage relation
The current i (t ) through a component in an electric circuit is defined as the rate of change of the charge q (t ) that has passed through it. Physical charges cannot pass through the dielectric layer of a capacitor, but rather build up in equal and opposite quantities on the electrodes: as each electron accumulates on the negative plate, one leaves the positive plate. Thus the accumulated charge on the electrodes is equal to the integral of the current, as well as being proportional to the voltage (as discussed above). As with any antiderivative, a constant of integration is added to represent the initial voltage v (t0). This is the integral form of the capacitor equation,[11]
.
Taking the derivative of this, and multiplying by C, yields the derivative form,[12]
.
The dual of the capacitor is the inductor, which stores energy in the magnetic field rather than the electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance L.
[edit] DC circuits
A simple resistor-capacitor circuit demonstrates charging of a capacitor.A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V0 is known as a charging circuit.[13] If the capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0, it follows from Kirchhoff voltage.
As the capacitor reaches equilibrium with the source voltage, the voltage across the resistor and the current through the entire circuit decay exponentially. The case of discharging a charged capacitor likewise demonstrates exponential decay, but with the initial capacitor voltage replacing V0 and the final voltage being zero.
[edit] AC circuits
See also: reactance (electronics) and electrical impedance#Deriving the device specific impedances
Impedance, the vector sum of reactance and resistance, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. Fourier analysis allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively
where j is the imaginary unit and ω is the angular velocity of the sinusoidal signal. The - j phase indicates that the AC voltage V = Z I lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc.
Note that impedance decreases with increasing capacitance and increasing frequency. This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude—an AC "short circuit" or AC coupling. Conversely, for very low frequencies, the reactance will be high, so that a capacitor is nearly an open circuit in AC analysis—those frequencies have been "filtered out".
Capacitors are different from resistors and inductors in that the impedance is inversely proportional to the defining characteristic, i.e. capacitance.
[edit] Parallel plate model
Dielectric is placed between two conducting plates, each of area A and with a separation of d.The simplest capacitor consists of two parallel conductive plates separated by a dielectric with permittivity ε (such as air). The model may also be used to make qualitative predictions for other device geometries. The plates are considered to extend uniformly over an area A and a charge density ±ρ = ±Q/A exists on their surface. Assuming that the width of the plates is much greater than their separation d, the electric field near the centre of the device will be uniform with the magnitude E = ρ/ε. The voltage is defined as the line integral of the electric field between the plates
Solving this for C = Q/V reveals that capacitance increases with area and decreases with separation
.
The capacitance is therefore greatest in devices made from materials with a high permittivity.
[edit] Networks
See also: Series and parallel circuits
For capacitors in parallel
Several capacitors in parallel.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.
For capacitors in series
Several capacitors in series.Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. 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.
Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. The voltage ratings, which are based on plate separation, add up. In such an application, several series connections may in turn be connected in parallel, forming a matrix. The goal is to maximize the energy storage utility of each capacitor without overloading it.
Series connection is also used to adapt electrolytic capacitors for AC use.
[edit] Non-ideal behaviour
Capacitors deviate from the ideal capacitor equation in a number of ways. Some of these, such as leakage current and parasitic effects are linear, or can be assumed to be linear, and can be dealt with by adding virtual components to the equivalent circuit of the capacitor. The usual methods of network analysis can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and normal (i.e., linear) network analysis cannot be used, the effect must be dealt with separately. There is yet another group, which may be linear but invalidate the assumption in the analysis that capacitance is a constant. Such an example is temperature dependence.
[edit] Breakdown voltage
Main article: Breakdown voltage
Above a particular electric field, known as the dielectric strength Eds, the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage of the device, and is given by the product of the dielectric strength and the separation between the conductors,[14]
Vbd = Edsd
The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage. Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum energy density, to the extent that the dielectric dominates their volume.[15]
For air dielectric capacitors the breakdown field strength is of the order 107 V/m and will be much less when other materials are used for the dielectric. The absolute breakdown voltage of most capacitors is nowhere near such a high number because of the very small distance between the plates. Typical ratings for capacitors used for general electronics applications range from a few volts to 100V or so. For high voltage applications physically much larger capacitors have to be used. In this field, there are a number of factors that can dramatically reduce the breakdown voltage below that to be expected by considering the breakdown field strength of the dielectric alone. For one thing, the geometry of the capacitor conductive parts (plates and connecting wires) is important. In particular, sharp edges or points hugely increase the electric field strength at that point and can lead to a local breakdown. Once this starts to happen, the breakdown will quickly "track" through the dielectric till it reaches the opposite plate and cause a short circuit.[16]
The usual breakdown route is that the field strength becomes large enough to pull electrons in the dielectric from their atoms thus causing conduction. Other scenarios are possible, such as impurities in the dielectric, and, if the dielectric is of a crystalline nature, imperfections in the crystal structure can result in an avalanche breakdown as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.[17]
[edit] Equivalent circuit
Two equivalent circuits of a real capacitorAn ideal capacitor only stores and releases electrical energy, without dissipating any. In reality, all capacitors have imperfections within the capacitor's material that create resistance. This is specified as the equivalent series resistance or ESR of a component. This adds a real component to the impedance:
As frequency approaches infinity, the capacitive impedance (or reactance) approaches zero and the ESR becomes significant. As the reactance becomes negligible, power dissipation approaches PRMS. = VRMS.² /RESR.
Similarly to ESR, the capacitor's leads add equivalent series inductance or ESL to the component. This is usually significant only at relatively high frequencies. As inductive reactance is positive and increases with frequency, above a certain frequency capacitance will be canceled by inductance. High frequency engineering involves accounting for the inductance of all connections and components.
If the conductors are separated by a material with a small conductivity rather than a perfect dielectric, then a small leakage current flows directly between them. The capacitor therefore has a finite parallel resistance,[9] and slowly discharges over time (time may vary greatly depending on the capacitor material and quality).
[edit] Ripple current
Ripple current is the AC component of an applied source (often a switched-mode power supply) whose frequency may be constant or varying. Certain types of capacitors, such as electrolytic tantalum capacitors, usually have a rating for maximum ripple current (both in frequency and magnitude). This ripple current can cause damaging heat to be generated within the capacitor due to the current flow across resistive imperfections in the materials used within the capacitor, more commonly referred to as equivalent series resistance (ESR). For example electrolytic tantalum capacitors are limited by ripple current and generally have the highest ESR ratings in the capacitor family, while ceramic capacitors generally have no ripple current limitation and have some of the lowest ESR ratings.
[edit] Instability of capacitance
The capacitance of certain capacitors decreases as the component ages. In ceramic capacitors, this is caused by degradation of the dielectric. The type of dielectric and the ambient operating and storage temperatures are the most significant aging factors, while the operating voltage has a smaller effect. The aging process may be reversed by heating the component above the Curie point. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.[18] Electrolytic capacitors age as the electrolyte evaporates. In contrast with ceramic capacitors, this occurs towards the end of life of the component.
Temperature dependence of capacitance is usually expressed in parts per million (ppm) per °C. It can usually be taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature coefficient can be either positive or negative, sometimes even amongst different samples of the same type. In other words, the spread in the range of temperature coefficients can encompass zero. See the data sheet in the leakage current section above for an example.
Capacitors, especially older components, can absorb sound waves resulting in a microphonic effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate piezoelectricity. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker. This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any.
[edit] Capacitor types
Main article: Types of capacitor
Practical capacitors are available commercially in many different forms. The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications.
Modern capacitors, by a cm rule.
Type Passive
Invented Ewald Georg von Kleist (October 1745)
Electronic symbol
A capacitor or condenser is a passive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force between the plates. The effect is greatest between wide, flat, parallel, narrowly separated conductors.
An ideal capacitor is characterized by a single constant value, capacitance, which is measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. In practice, the dielectric between the plates passes a small amount of leakage current. The conductors and leads introduce an equivalent series resistance and the dielectric has an electric field strength limit resulting in a breakdown voltage.
Capacitors are widely used in electronic circuits to block the flow of direct current while allowing alternating current to pass, to filter out interference, to smooth the output of power supplies, and for many other purposes. They are used in resonant circuits in radio frequency equipment to select particular frequencies from a signal with many frequencies.
[edit] History
Battery of four Leyden jars in Museum Boerhave, Leiden.In October 1745, Ewald Georg von Kleist of Pomerania in Germany found that charge could be stored by connecting a high voltage electrostatic generator by a wire to a volume of water in a hand-held glass jar.[1] Von Kleist's hand and the water acted as conductors and the jar as a dielectric (although details of the mechanism were incorrectly identified at the time). Von Kleist found that after removing the generator, touching the wire resulted in a painful spark. In a letter describing the experiment, he said "I would not take a second shock for the kingdom of France."[2] The following year, the Dutch physicist Pieter van Musschenbroek invented a similar capacitor, which was named the Leyden jar, after the University of Leyden where he worked.[3] Daniel Gralath was the first to combine several jars in parallel into a "battery" to increase the charge storage capacity.[citation needed]
Benjamin Franklin investigated the Leyden jar and proved that the charge was stored on the glass, not in the water as others had assumed.[citation needed] He also created the term "battery",[4][5] (as in a battery of cannon), subsequently applied to clusters of electrochemical cells.[6] Leyden jars were later to be made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils.[citation needed] The earliest unit of capacitance was the 'jar', equivalent to about 1 nanofarad.[citation needed]
Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of wireless (radio) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance. A more compact construction began to be used of a flexible dielectric sheet such as oiled paper sandwiched between sheets of metal foil, rolled or folded into a small package.
Early capacitors were also known as condensers, a term that is still occasionally used today. The term was first used for this purpose by Alessandro Volta in 1782, with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor.[citation needed]
[edit] Theory of operation
Main article: Capacitance
Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.
A simple demonstration of a parallel-plate capacitorA capacitor consists of two conductors separated by a non-conductive region.[7] The non-conductive substance is called the dielectric medium, although this may also mean a vacuum or a semiconductor depletion region chemically identical to the conductors. A capacitor is assumed to be self-contained and isolated, with no net electric charge and no influence from an external electric field. The conductors thus contain equal and opposite charges on their facing surfaces,[8] and the dielectric contains an electric field. The capacitor is a reasonably general model for electric fields within electric circuits.
An ideal capacitor is wholly characterized by a constant capacitance 'C', defined as the ratio of charge ±'Q' on each conductor to the voltage 'V' between them
Sometimes charge buildup affects the mechanics of the capacitor, causing the capacitance to vary. In this case, capacitance is defined in terms of incremental changes:
In SI units, a capacitance of one farad means that one coulomb of charge on each conductor causes a voltage of one volt across the device.[9]
[edit] Energy storage
Work must be done by an external influence to move charge between the conductors in a capacitor. When the external influence is removed, the charge separation persists and energy is stored in the electric field. If charge is later allowed to return to its equilibrium position, the energy is released. The work done in establishing the electric field, and hence the amount of energy stored, is given by:[10]
[edit] Current-voltage relation
The current i (t ) through a component in an electric circuit is defined as the rate of change of the charge q (t ) that has passed through it. Physical charges cannot pass through the dielectric layer of a capacitor, but rather build up in equal and opposite quantities on the electrodes: as each electron accumulates on the negative plate, one leaves the positive plate. Thus the accumulated charge on the electrodes is equal to the integral of the current, as well as being proportional to the voltage (as discussed above). As with any antiderivative, a constant of integration is added to represent the initial voltage v (t0). This is the integral form of the capacitor equation,[11]
.
Taking the derivative of this, and multiplying by C, yields the derivative form,[12]
.
The dual of the capacitor is the inductor, which stores energy in the magnetic field rather than the electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance L.
[edit] DC circuits
A simple resistor-capacitor circuit demonstrates charging of a capacitor.A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V0 is known as a charging circuit.[13] If the capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0, it follows from Kirchhoff voltage.
As the capacitor reaches equilibrium with the source voltage, the voltage across the resistor and the current through the entire circuit decay exponentially. The case of discharging a charged capacitor likewise demonstrates exponential decay, but with the initial capacitor voltage replacing V0 and the final voltage being zero.
[edit] AC circuits
See also: reactance (electronics) and electrical impedance#Deriving the device specific impedances
Impedance, the vector sum of reactance and resistance, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. Fourier analysis allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively
where j is the imaginary unit and ω is the angular velocity of the sinusoidal signal. The - j phase indicates that the AC voltage V = Z I lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc.
Note that impedance decreases with increasing capacitance and increasing frequency. This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude—an AC "short circuit" or AC coupling. Conversely, for very low frequencies, the reactance will be high, so that a capacitor is nearly an open circuit in AC analysis—those frequencies have been "filtered out".
Capacitors are different from resistors and inductors in that the impedance is inversely proportional to the defining characteristic, i.e. capacitance.
[edit] Parallel plate model
Dielectric is placed between two conducting plates, each of area A and with a separation of d.The simplest capacitor consists of two parallel conductive plates separated by a dielectric with permittivity ε (such as air). The model may also be used to make qualitative predictions for other device geometries. The plates are considered to extend uniformly over an area A and a charge density ±ρ = ±Q/A exists on their surface. Assuming that the width of the plates is much greater than their separation d, the electric field near the centre of the device will be uniform with the magnitude E = ρ/ε. The voltage is defined as the line integral of the electric field between the plates
Solving this for C = Q/V reveals that capacitance increases with area and decreases with separation
.
The capacitance is therefore greatest in devices made from materials with a high permittivity.
[edit] Networks
See also: Series and parallel circuits
For capacitors in parallel
Several capacitors in parallel.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.
For capacitors in series
Several capacitors in series.Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. 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.
Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. The voltage ratings, which are based on plate separation, add up. In such an application, several series connections may in turn be connected in parallel, forming a matrix. The goal is to maximize the energy storage utility of each capacitor without overloading it.
Series connection is also used to adapt electrolytic capacitors for AC use.
[edit] Non-ideal behaviour
Capacitors deviate from the ideal capacitor equation in a number of ways. Some of these, such as leakage current and parasitic effects are linear, or can be assumed to be linear, and can be dealt with by adding virtual components to the equivalent circuit of the capacitor. The usual methods of network analysis can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and normal (i.e., linear) network analysis cannot be used, the effect must be dealt with separately. There is yet another group, which may be linear but invalidate the assumption in the analysis that capacitance is a constant. Such an example is temperature dependence.
[edit] Breakdown voltage
Main article: Breakdown voltage
Above a particular electric field, known as the dielectric strength Eds, the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage of the device, and is given by the product of the dielectric strength and the separation between the conductors,[14]
Vbd = Edsd
The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage. Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum energy density, to the extent that the dielectric dominates their volume.[15]
For air dielectric capacitors the breakdown field strength is of the order 107 V/m and will be much less when other materials are used for the dielectric. The absolute breakdown voltage of most capacitors is nowhere near such a high number because of the very small distance between the plates. Typical ratings for capacitors used for general electronics applications range from a few volts to 100V or so. For high voltage applications physically much larger capacitors have to be used. In this field, there are a number of factors that can dramatically reduce the breakdown voltage below that to be expected by considering the breakdown field strength of the dielectric alone. For one thing, the geometry of the capacitor conductive parts (plates and connecting wires) is important. In particular, sharp edges or points hugely increase the electric field strength at that point and can lead to a local breakdown. Once this starts to happen, the breakdown will quickly "track" through the dielectric till it reaches the opposite plate and cause a short circuit.[16]
The usual breakdown route is that the field strength becomes large enough to pull electrons in the dielectric from their atoms thus causing conduction. Other scenarios are possible, such as impurities in the dielectric, and, if the dielectric is of a crystalline nature, imperfections in the crystal structure can result in an avalanche breakdown as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.[17]
[edit] Equivalent circuit
Two equivalent circuits of a real capacitorAn ideal capacitor only stores and releases electrical energy, without dissipating any. In reality, all capacitors have imperfections within the capacitor's material that create resistance. This is specified as the equivalent series resistance or ESR of a component. This adds a real component to the impedance:
As frequency approaches infinity, the capacitive impedance (or reactance) approaches zero and the ESR becomes significant. As the reactance becomes negligible, power dissipation approaches PRMS. = VRMS.² /RESR.
Similarly to ESR, the capacitor's leads add equivalent series inductance or ESL to the component. This is usually significant only at relatively high frequencies. As inductive reactance is positive and increases with frequency, above a certain frequency capacitance will be canceled by inductance. High frequency engineering involves accounting for the inductance of all connections and components.
If the conductors are separated by a material with a small conductivity rather than a perfect dielectric, then a small leakage current flows directly between them. The capacitor therefore has a finite parallel resistance,[9] and slowly discharges over time (time may vary greatly depending on the capacitor material and quality).
[edit] Ripple current
Ripple current is the AC component of an applied source (often a switched-mode power supply) whose frequency may be constant or varying. Certain types of capacitors, such as electrolytic tantalum capacitors, usually have a rating for maximum ripple current (both in frequency and magnitude). This ripple current can cause damaging heat to be generated within the capacitor due to the current flow across resistive imperfections in the materials used within the capacitor, more commonly referred to as equivalent series resistance (ESR). For example electrolytic tantalum capacitors are limited by ripple current and generally have the highest ESR ratings in the capacitor family, while ceramic capacitors generally have no ripple current limitation and have some of the lowest ESR ratings.
[edit] Instability of capacitance
The capacitance of certain capacitors decreases as the component ages. In ceramic capacitors, this is caused by degradation of the dielectric. The type of dielectric and the ambient operating and storage temperatures are the most significant aging factors, while the operating voltage has a smaller effect. The aging process may be reversed by heating the component above the Curie point. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.[18] Electrolytic capacitors age as the electrolyte evaporates. In contrast with ceramic capacitors, this occurs towards the end of life of the component.
Temperature dependence of capacitance is usually expressed in parts per million (ppm) per °C. It can usually be taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature coefficient can be either positive or negative, sometimes even amongst different samples of the same type. In other words, the spread in the range of temperature coefficients can encompass zero. See the data sheet in the leakage current section above for an example.
Capacitors, especially older components, can absorb sound waves resulting in a microphonic effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate piezoelectricity. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker. This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any.
[edit] Capacitor types
Main article: Types of capacitor
Practical capacitors are available commercially in many different forms. The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications.
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