A capacitor is a passive two-terminal electrical component that stores
potential energy in an electric field. The effect of a capacitor is
known as capacitance. While some capacitance exists between any two
electrical conductors in proximity in a circuit, a capacitor is a
component designed to add capacitance to a circuit. The capacitor was
originally known as a condenser.[1]
The physical form and construction of practical capacitors vary widely
and many capacitor types are in common use. Most capacitors contain at
least two electrical conductors often in the form of metallic plates
or surfaces separated by a dielectric medium. A conductor may be a
foil, thin film, sintered bead of metal, or an electrolyte. The
nonconducting dielectric acts to increase the capacitor's charge
capacity. Materials commonly used as dielectrics include glass,
ceramic, plastic film, paper, mica, and oxide layers. Capacitors are
widely used as parts of electrical circuits in many common electrical
devices. Unlike a resistor, an ideal capacitor does not dissipate
energy.
When two conductors experience a potential difference, for example,
when a capacitor is attached across a battery, an electric field
develops across the dielectric, causing a net positive charge to
collect on one plate and net negative charge to collect on the other
plate. No current actually flows through the dielectric, however,
there is a flow of charge through the source circuit. If the condition
is maintained sufficiently long, the current through the source
circuit ceases. However, if a time-varying voltage is applied across
the leads of the capacitor, the source experiences an ongoing current
due to the charging and discharging cycles of the capacitor.
Contents 1 History 2 Theory of operation 2.1 Overview 2.2 Hydraulic analogy 2.3 Parallel-plate model 2.4 Energy stored in a capacitor 2.5 Current–voltage relation 2.6 DC circuits 2.7 AC circuits 2.8 Laplace circuit analysis (s-domain) 2.9 Circuit analysis 3 Non-ideal behavior 3.1 Breakdown voltage
3.2 Equivalent circuit
3.3 Q factor
3.4 Ripple current
3.5
4
4.1
5
5.1 Letter and digit code 5.2 Historical 6 Applications 6.1 Energy storage
6.2 Digital memory
6.3
6.4.1 Power factor correction 6.5 Suppression and coupling 6.5.1 Signal coupling 6.5.2 Decoupling 6.5.3 High-pass and low-pass filters 6.5.4 Noise suppression, spikes, and snubbers 6.6 Motor starters 6.7 Signal processing 6.7.1 Tuned circuits 6.8 Sensing 6.9 Oscillators 6.10 Producing light 7 Hazards and safety 8 See also 9 References 10 Bibliography 11 External links History[edit] Battery of four Leyden jars in Museum Boerhaave, Leiden, the Netherlands In October 1745,
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 capacitor made of two parallel metal plates, using an air gap as the dielectric. A capacitor consists of two conductors separated by a non-conductive
region.[17] The non-conductive region can either be a vacuum or an
electrical insulator material known as a dielectric. Examples of
dielectric media are glass, air, paper, plastic, ceramic, and even a
semiconductor depletion region chemically identical to the conductors.
From
C = Q V displaystyle C= frac Q V A capacitance of one farad (F) means that one coulomb of charge on each conductor causes a voltage of one volt across the device.[19] Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance. In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes: C = d Q d V displaystyle C= frac mathrm d Q mathrm d V Hydraulic analogy[edit] In the hydraulic analogy, a capacitor is analogous to a rubber membrane sealed inside a pipe— this animation illustrates a membrane being repeatedly stretched and un-stretched by the flow of water, which is analogous to a capacitor being repeatedly charged and discharged by the flow of charge In the hydraulic analogy, charge carriers flowing through a wire are analogous to water flowing through a pipe. A capacitor is like a rubber membrane sealed inside a pipe. Water molecules cannot pass through the membrane, but some water can move by stretching the membrane. The analogy clarifies a few aspects of capacitors: The current alters the charge on a capacitor, just as the flow of water changes the position of the membrane. More specifically, the effect of an electric current is to increase the charge of one plate of the capacitor, and decrease the charge of the other plate by an equal amount. This is just as when water flow moves the rubber membrane, it increases the amount of water on one side of the membrane, and decreases the amount of water on the other side. The more a capacitor is charged, the larger its voltage drop; i.e., the more it "pushes back" against the charging current. This is analogous to the fact that the more a membrane is stretched, the more it pushes back on the water. Charge can flow "through" a capacitor even though no individual electron can get from one side to the other. This is analogous to water flowing through the pipe even though no water molecule can pass through the rubber membrane. The flow cannot continue in the same direction forever; the capacitor experiences dielectric breakdown, and analogously the membrane will eventually break. The capacitance describes how much charge can be stored on one plate of a capacitor for a given "push" (voltage drop). A very stretchy, flexible membrane corresponds to a higher capacitance than a stiff membrane. A charged-up capacitor is storing potential energy, analogously to a stretched membrane. Parallel-plate model[edit] Parallel plate capacitor model consists of two conducting plates, each of area A, separated by a gap of thickness d containing a dielectric. The simplest model capacitor consists of two thin parallel conductive plates each with an area of A displaystyle A separated by a uniform gap of thickness d displaystyle d filled with a dielectric with permittivity ϵ displaystyle epsilon . It is assumed the gap d displaystyle d is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of the capacitor. Since the separation between the plates is uniform over the plate area, the electric field between the plates E displaystyle E is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area is approximately the same width as the plate separation, d displaystyle d , and assuming d displaystyle d is small compared to the plate dimensions, it is small enough to be ignored. Therefore if a charge of + Q displaystyle +Q is placed on one plate and − Q displaystyle -Q on the other plate, the charge on each plate will be spread evenly in a surface charge layer of constant charge density σ = ± Q / A displaystyle sigma =pm Q/A coulombs per square meter, on the inside surface of each plate. From
E = σ / ϵ displaystyle E=sigma /epsilon . The voltage V displaystyle V between the plates is defined as the line integral of the electric field over a line from one plate to another V = ∫ 0 d E ( z ) d z = E d = σ ϵ d = Q d ϵ A displaystyle V=int _ 0 ^ d E(z),mathrm d z=Ed= sigma over epsilon d= Qd over epsilon A The capacitance is defined as C = Q / V displaystyle C=Q/V . Substituting V displaystyle V above into this equation C = ϵ A d displaystyle C= epsilon A over d Therefore in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between the plates. Since the area A displaystyle A of the plates increases with the square of the linear dimensions and the separation d displaystyle d increases linearly, the capacitance scales with the linear dimension of a capacitor ( C ∝ L displaystyle Cvarpropto L ), or as the cube root of the volume. A parallel plate capacitor can only store a finite amount of energy before dielectric breakdown occurs. The capacitor's dielectric material has a dielectric strength Ud which sets the capacitor's breakdown voltage at V = Vbd = Udd. The maximum energy that the capacitor can store is therefore E = 1 2 C V 2 = 1 2 ϵ A d ( U d d ) 2 = 1 2 ϵ A d U d 2 displaystyle E= frac 1 2 CV^ 2 = frac 1 2 frac epsilon A d (U_ d d)^ 2 = frac 1 2 epsilon AdU_ d ^ 2 The maximum energy is a function of dielectric volume, permittivity, and dielectric strength. Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that the electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called parasitic capacitance. For some simple capacitor geometries this additional capacitance term can be calculated analytically.[20] It becomes negligibly small when the ratios of plate width to separation and length to separation are large. Energy stored in a capacitor[edit] To increase the charge and voltage on a capacitor, work must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field.[21][22] If the voltage on the capacitor is V displaystyle V , the work d W displaystyle dW required to move a small increment of charge d q displaystyle dq from the negative to the positive plate is d W = V d q displaystyle dW=Vdq . The energy is stored in the increased electric field between the plates. The total energy stored in a capacitor is equal to the total work done in establishing the electric field from an uncharged state.[23][22][21] W = ∫ 0 Q V ( q ) d q = ∫ 0 Q q C d q = 1 2 Q 2 C = 1 2 V Q = 1 2 C V 2 displaystyle W=int _ 0 ^ Q V(q)mathrm d q=int _ 0 ^ Q frac q C mathrm d q= 1 over 2 Q^ 2 over C = 1 over 2 VQ= 1 over 2 CV^ 2 where Q displaystyle Q is the charge stored in the capacitor, V displaystyle V is the voltage across the capacitor, and C displaystyle C is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between the plates, the charge moving under the influence of the electric field will do work on the external circuit. If the gap between the capacitor plates d displaystyle d is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value E = V / d displaystyle E=V/d . In this case the stored energy can be calculated from the electric field strength W = 1 2 C V 2 = 1 2 ϵ A d ( E d ) 2 = 1 2 ϵ A d E 2 = 1 2 ϵ E 2 ( volume of electric field ) displaystyle W= 1 over 2 CV^ 2 = 1 over 2 epsilon A over d (Ed)^ 2 = 1 over 2 epsilon AdE^ 2 = 1 over 2 epsilon E^ 2 ( text volume of electric field ) The last formula above is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field. Current–voltage relation[edit] The current I(t) through any component in an electric circuit is defined as the rate of flow of a charge Q(t) passing through it, but actual charges—electrons—cannot pass through the dielectric layer of a capacitor. Rather, one electron accumulates on the negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the integral of the current as well as 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:[24] V ( t ) = Q ( t ) C = 1 C ∫ t 0 t I ( τ ) d τ + V ( t 0 ) displaystyle V(t)= frac Q(t) C = frac 1 C int _ t_ 0 ^ t I(tau )mathrm d tau +V(t_ 0 ) Taking the derivative of this and multiplying by C yields the derivative form:[25] I ( t ) = d Q ( t ) d t = C d V ( t ) d t displaystyle I(t)= frac mathrm d Q(t) mathrm d t =C frac mathrm d V(t) mathrm d t The dual of the capacitor is the inductor, which stores energy in a magnetic field rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance L. DC circuits[edit] See also: RC circuit 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.[26] If the capacitor is initially uncharged while the switch is open, and the switch is closed at t0, it follows from Kirchhoff's voltage law that V 0 = v resistor ( t ) + v capacitor ( t ) = i ( t ) R + 1 C ∫ t 0 t i ( τ ) d τ displaystyle V_ 0 =v_ text resistor (t)+v_ text capacitor (t)=i(t)R+ frac 1 C int _ t_ 0 ^ t i(tau )mathrm d tau Taking the derivative and multiplying by C, gives a first-order differential equation: R C d i ( t ) d t + i ( t ) = 0 displaystyle RC frac mathrm d i(t) mathrm d t +i(t)=0 At t = 0, the voltage across the capacitor is zero and the voltage across the resistor is V0. The initial current is then I(0) =V0/R. With this assumption, solving the differential equation yields I ( t ) = V 0 R ⋅ e − t τ 0 V ( t ) = V 0 ( 1 − e − t τ 0 ) Q ( t ) = C ⋅ V 0 ( 1 − e − t τ 0 ) displaystyle begin aligned I(t)&= frac V_ 0 R cdot e^ frac -t tau _ 0 \V(t)&=V_ 0 left(1-e^ frac -t tau _ 0 right)\Q(t)&=Ccdot V_ 0 left(1-e^ frac -t tau _ 0 right)end aligned where τ0 = RC, the time constant of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially. In the case of a discharging capacitor, the capacitor's initial voltage (VCi) replaces V0. The equations become I ( t ) = V C i R ⋅ e − t τ 0 V ( t ) = V C i ⋅ e − t τ 0 Q ( t ) = C ⋅ V C i ⋅ e − t τ 0 displaystyle begin aligned I(t)&= frac V_ Ci R cdot e^ frac -t tau _ 0 \V(t)&=V_ Ci cdot e^ frac -t tau _ 0 \Q(t)&=Ccdot V_ Ci cdot e^ frac -t tau _ 0 end aligned AC circuits[edit]
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.
X = − 1 ω C = − 1 2 π f C Z = 1 j ω C = − j ω C = − j 2 π f C displaystyle begin aligned X&=- frac 1 omega C =- frac 1 2pi fC \Z&= frac 1 jomega C =- frac j omega C =- frac j 2pi fC end aligned where j is the imaginary unit and ω is the angular frequency of the sinusoidal signal. The −j phase indicates that the AC voltage V = ZI 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. 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 is 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. A capacitor connected to a sinusoidal voltage source causes a displacement current to flow through it. In the case that the voltage source is V0cos(ωt), the displacement current can be expressed as: I = C d V d t = − ω C V 0 sin ( ω t ) displaystyle I=C frac dV dt =-omega C V_ text 0 sin(omega t) At sin(ωt) = -1, the capacitor has a maximum (or peak) current whereby I0 = ωCV0. The ratio of peak voltage to peak current is due to capacitive reactance (denoted XC). X C = V 0 I 0 = V 0 ω C V 0 = 1 ω C displaystyle X_ C = frac V_ text 0 I_ text 0 = frac V_ text 0 omega CV_ text 0 = frac 1 omega C XC approaches zero as ω approaches infinity. If XC approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. XC approaches infinity as ω approaches zero. If XC approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies. The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source: I = − I 0 sin ( ω t ) = I 0 cos ( ω t + 90 ∘ ) displaystyle I=- I_ text 0 sin( omega t )= I_ text 0 cos( omega t + 90^ circ ) In this situation, the current is out of phase with the voltage by
+π/2 radians or +90 degrees, i.e. the current leads the voltage by
90°.
Laplace circuit analysis (s-domain)[edit]
When using the
Z ( s ) = 1 s C displaystyle Z(s)= frac 1 sC where C is the capacitance, and s is the complex frequency. Circuit analysis[edit] See also: Series and parallel circuits For capacitors in parallel Several capacitors in parallel Illustration of the parallel connection of two capacitors 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. C e q = ∑ i C i = C 1 + C 2 + ⋯ + C n displaystyle C_ mathrm eq =sum _ i C_ i =C_ 1 +C_ 2 +cdots +C_ n For capacitors in series Several capacitors in series Illustration of the serial connection of two capacitors 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. 1 C e q = ∑ i 1 C i = 1 C 1 + 1 C 2 + ⋯ + 1 C n displaystyle frac 1 C_ mathrm eq =sum _ i frac 1 C_ i = frac 1 C_ 1 + frac 1 C_ 2 +cdots + frac 1 C_ n 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, if capacitance and leakage currents for each capacitor are identical. In such an application, on occasion, series strings are connected in parallel, forming a matrix. The goal is to maximize the energy storage of the network without overloading any capacitor. For high-energy storage with capacitors in series, some safety considerations must be applied to ensure one capacitor failing and leaking current does not apply too much voltage to the other series capacitors. Series connection is also sometimes used to adapt polarized electrolytic capacitors for bipolar AC use. See electrolytic capacitor#Designing for reverse bias. Voltage distribution in parallel-to-series networks. To model the distribution of voltages from a single charged capacitor ( A ) displaystyle left(Aright) connected in parallel to a chain of capacitors in series ( B n ) displaystyle left(B_ text n right) : ( v o l t s ) A e q = A ( 1 − 1 n + 1 ) ( v o l t s ) B 1..n = A n ( 1 − 1 n + 1 ) A − B = 0 displaystyle begin aligned (volts)A_ mathrm eq &=Aleft(1- frac 1 n+1 right)\(volts)B_ text 1..n &= frac A n left(1- frac 1 n+1 right)\A-B&=0end aligned Note: This is only correct if all capacitance values are equal. The power transferred in this arrangement is: P = 1 R ⋅ 1 n + 1 A volts ( A farads + B farads ) displaystyle P= frac 1 R cdot frac 1 n+1 A_ text volts left(A_ text farads +B_ text farads right) Non-ideal behavior[edit] 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 analyzed as nearly linear, and can be dealt with by adding virtual components to the equivalent circuit of an ideal 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 ordinary (normal, e.g., 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. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at variable frequencies of operation. Breakdown voltage[edit] 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,[27] V bd = E ds d displaystyle V_ text bd =E_ text ds d 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.[28]
For air dielectric capacitors the breakdown field strength is of the
order 2 to 5 MV/m; for mica the breakdown is 100 to 300 MV/m; for oil,
15 to 25 MV/m; it can be much less when other materials are used for
the dielectric.[29] The dielectric is used in very thin layers and so
absolute breakdown voltage of capacitors is limited. Typical ratings
for capacitors used for general electronics applications range from a
few volts to 1 kV. As the voltage increases, the dielectric must be
thicker, making high-voltage capacitors larger per capacitance than
those rated for lower voltages. The breakdown voltage is critically
affected by factors such as the geometry of the capacitor conductive
parts; sharp edges or points increase the electric field strength at
that point and can lead to a local breakdown. Once this starts to
happen, the breakdown quickly tracks through the dielectric until it
reaches the opposite plate, leaving carbon behind and causing a short
(or relatively low resistance) circuit. The results can be explosive
as the short in the capacitor draws current from the surrounding
circuitry and dissipates the energy.[30] However, in capacitors with
particular dielectrics[31][32] and thin metal electrodes shorts are
not formed after breakdown. It happens because a metal melts or
evaporates in a breakdown vicinity, isolating it from the rest of the
capacitor.[33][34]
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.
Two different circuit models of a real capacitor An 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: Z C = Z + R ESR = 1 j ω C + R ESR displaystyle Z_ text C =Z+R_ text ESR = frac 1 jomega C +R_ text ESR 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 =
VRMS² /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 is
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,[36] and slowly discharges over time (time
may vary greatly depending on the capacitor material and quality).
Q factor[edit]
The quality factor (or Q) of a capacitor is the ratio of its reactance
to its resistance at a given frequency, and is a measure of its
efficiency. The higher the
Q = X C R = 1 ω C R displaystyle Q= frac X_ C R = frac 1 omega CR where ω displaystyle omega is angular frequency, C displaystyle C is the capacitance, X C displaystyle X_ C is the capacitive reactance, and R displaystyle R is the equivalent series resistance (ESR) of the capacitor. Ripple current[edit] Ripple current is the AC component of an applied source (often a switched-mode power supply) whose frequency may be constant or varying. Ripple current causes heat to be generated within the capacitor due to the dielectric losses caused by the changing field strength together with the current flow across the slightly resistive supply lines or the electrolyte in the capacitor. The equivalent series resistance (ESR) is the amount of internal series resistance one would add to a perfect capacitor to model this. Some types of capacitors, primarily tantalum and aluminum electrolytic capacitors, as well as some film capacitors have a specified rating value for maximum ripple current.
Most capacitors have a dielectric spacer, which increases their
capacitance compared to air or a vacuum. In order to maximise the
charge that a capacitor can hold, the dielectric material needs to
have as high a permittivity as possible, while also having as high a
breakdown voltage as possible. The dielectric also needs to have as
low a loss with frequency as possible.
However, low value capacitors are available with a vacuum between
their plates to allow extremely high voltage operation and low losses.
Variable capacitors with their plates open to the atmosphere were
commonly used in radio tuning circuits. Later designs use polymer foil
dielectric between the moving and stationary plates, with no
significant air space between the plates.
Several solid dielectrics are available, including paper, plastic,
glass, mica and ceramic.
Solid electrolyte, resin-dipped 10 μF 35 V tantalum capacitors. The + sign indicates the positive lead. Polymer capacitors (OS-CON, OC-CON, KO, AO) use solid conductive
polymer (or polymerized organic semiconductor) as electrolyte and
offer longer life and lower ESR at higher cost than standard
electrolytic capacitors.
A feedthrough capacitor is a component that, while not serving as its
main use, has capacitance and is used to conduct signals through a
conductive sheet.
Several other types of capacitor are available for specialist
applications. Supercapacitors store large amounts of energy.
Supercapacitors made from carbon aerogel, carbon nanotubes, or highly
porous electrode materials, offer extremely high capacitance (up to
5 kF as of 2010[update]) and can be used in some applications
instead of rechargeable batteries.
d Q = C ( V ) d V displaystyle dQ=C(V),dV where the voltage dependence of capacitance, C(V), suggests that the capacitance is a function of the electric field strength, which in a large area parallel plate device is given by ε = V/d. This field polarizes the dielectric, which polarization, in the case of a ferroelectric, is a nonlinear S-shaped function of the electric field, which, in the case of a large area parallel plate device, translates into a capacitance that is a nonlinear function of the voltage.[46][47] Corresponding to the voltage-dependent capacitance, to charge the capacitor to voltage V an integral relation is found: Q = ∫ 0 V C ( V ) d V displaystyle Q=int _ 0 ^ V C(V),dV which agrees with Q = CV only when C does not depend on voltage V. By the same token, the energy stored in the capacitor now is given by d W = Q d V = [ ∫ 0 V d V ′ C ( V ′ ) ] d V . displaystyle dW=Q,dV=left[int _ 0 ^ V dV' C(V')right] dV . Integrating: W = ∫ 0 V d V ∫ 0 V d V ′ C ( V ′ ) = ∫ 0 V d V ′
∫ V ′ V d V C ( V ′ ) = ∫ 0 V d V ′ ( V − V ′ ) C ( V ′ ) , displaystyle W=int _ 0 ^ V dV int _ 0 ^ V dV' C(V')=int _ 0 ^ V dV' int _ V' ^ V dV C(V')=int _ 0 ^ V dV'left(V-V'right)C(V') , where interchange of the order of integration is used. The nonlinear capacitance of a microscope probe scanned along a ferroelectric surface is used to study the domain structure of ferroelectric materials.[48] Another example of voltage dependent capacitance occurs in semiconductor devices such as semiconductor diodes, where the voltage dependence stems not from a change in dielectric constant but in a voltage dependence of the spacing between the charges on the two sides of the capacitor.Template:Sze This effect is intentionally exploited in diode-like devices known as varicaps. Frequency-dependent capacitors[edit] If a capacitor is driven with a time-varying voltage that changes rapidly enough, at some frequency the polarization of the dielectric cannot follow the voltage. As an example of the origin of this mechanism, the internal microscopic dipoles contributing to the dielectric constant cannot move instantly, and so as frequency of an applied alternating voltage increases, the dipole response is limited and the dielectric constant diminishes. A changing dielectric constant with frequency is referred to as dielectric dispersion, and is governed by dielectric relaxation processes, such as Debye relaxation. Under transient conditions, the displacement field can be expressed as (see electric susceptibility): D ( t ) = ε 0 ∫ − ∞ t
ε r ( t − t ′ ) E ( t ′ ) d t ′ , displaystyle boldsymbol D(t) =varepsilon _ 0 int _ -infty ^ t varepsilon _ r (t-t') boldsymbol E (t') dt', indicating the lag in response by the time dependence of εr, calculated in principle from an underlying microscopic analysis, for example, of the dipole behavior in the dielectric. See, for example, linear response function.[49][50] The integral extends over the entire past history up to the present time. A Fourier transform in time then results in: D ( ω ) = ε 0 ε r ( ω ) E ( ω ) , displaystyle boldsymbol D (omega )=varepsilon _ 0 varepsilon _ r (omega ) boldsymbol E (omega ) , where εr(ω) is now a complex function, with an imaginary part
related to absorption of energy from the field by the medium. See
permittivity. The capacitance, being proportional to the dielectric
constant, also exhibits this frequency behavior. Fourier transforming
I ( ω ) = j ω Q ( ω ) = j ω ∮ Σ D ( r , ω ) ⋅ d Σ
displaystyle I(omega )=jomega Q(omega )=jomega oint _ Sigma boldsymbol D ( boldsymbol r , omega )cdot d boldsymbol Sigma = [ G ( ω ) + j ω C ( ω ) ] V ( ω ) = V ( ω ) Z ( ω ) , displaystyle =left[G(omega )+jomega C(omega )right]V(omega )= frac V(omega ) Z(omega ) , where j is the imaginary unit, V(ω) is the voltage component at angular frequency ω, G(ω) is the real part of the current, called the conductance, and C(ω) determines the imaginary part of the current and is the capacitance. Z(ω) is the complex impedance. When a parallel-plate capacitor is filled with a dielectric, the measurement of dielectric properties of the medium is based upon the relation: ε r ( ω ) = ε r ′ ( ω ) − j ε r ″ ( ω ) = 1 j ω Z ( ω ) C 0 = C cmplx ( ω ) C 0 , displaystyle varepsilon _ r (omega )=varepsilon '_ r (omega )-jvarepsilon ''_ r (omega )= frac 1 jomega Z(omega )C_ 0 = frac C_ text cmplx (omega ) C_ 0 , where a single prime denotes the real part and a double prime the imaginary part, Z(ω) is the complex impedance with the dielectric present, Ccmplx(ω) is the so-called complex capacitance with the dielectric present, and C0 is the capacitance without the dielectric.[51][52] (Measurement "without the dielectric" in principle means measurement in free space, an unattainable goal inasmuch as even the quantum vacuum is predicted to exhibit nonideal behavior, such as dichroism. For practical purposes, when measurement errors are taken into account, often a measurement in terrestrial vacuum, or simply a calculation of C0, is sufficiently accurate.[53]) Using this measurement method, the dielectric constant may exhibit a resonance at certain frequencies corresponding to characteristic response frequencies (excitation energies) of contributors to the dielectric constant. These resonances are the basis for a number of experimental techniques for detecting defects. The conductance method measures absorption as a function of frequency.[54] Alternatively, the time response of the capacitance can be used directly, as in deep-level transient spectroscopy.[55] Another example of frequency dependent capacitance occurs with MOS capacitors, where the slow generation of minority carriers means that at high frequencies the capacitance measures only the majority carrier response, while at low frequencies both types of carrier respond.[56][57] At optical frequencies, in semiconductors the dielectric constant exhibits structure related to the band structure of the solid. Sophisticated modulation spectroscopy measurement methods based upon modulating the crystal structure by pressure or by other stresses and observing the related changes in absorption or reflection of light have advanced our knowledge of these materials.[58] Styles[edit]
The arrangement of plates and dielectric has many variations in different styles depending on the desired ratings of the capacitor. For small values of capacitance (microfarads and less), ceramic disks use metallic coatings, with wire leads bonded to the coating. Larger values can be made by multiple stacks of plates and disks. Larger value capacitors usually use a metal foil or metal film layer deposited on the surface of a dielectric film to make the plates, and a dielectric film of impregnated paper or plastic – these are rolled up to save space. To reduce the series resistance and inductance for long plates, the plates and dielectric are staggered so that connection is made at the common edge of the rolled-up plates, not at the ends of the foil or metalized film strips that comprise the plates. The assembly is encased to prevent moisture entering the dielectric – early radio equipment used a cardboard tube sealed with wax. Modern paper or film dielectric capacitors are dipped in a hard thermoplastic. Large capacitors for high-voltage use may have the roll form compressed to fit into a rectangular metal case, with bolted terminals and bushings for connections. The dielectric in larger capacitors is often impregnated with a liquid to improve its properties. Several axial-lead electrolytic capacitors Capacitors may have their connecting leads arranged in many
configurations, for example axially or radially. "Axial" means that
the leads are on a common axis, typically the axis of the capacitor's
cylindrical body – the leads extend from opposite ends. Radial
leads might more accurately be referred to as tandem; they are rarely
actually aligned along radii of the body's circle, so the term is
inexact, although universal. The leads (until bent) are usually in
planes parallel to that of the flat body of the capacitor, and extend
in the same direction; they are often parallel as manufactured.
Small, cheap discoidal ceramic capacitors have existed from the 1930s
onward, and remain in widespread use. After the 1980s, surface mount
packages for capacitors have been widely used. These packages are
extremely small and lack connecting leads, allowing them to be
soldered directly onto the surface of printed circuit boards. Surface
mount components avoid undesirable high-frequency effects due to the
leads and simplify automated assembly, although manual handling is
made difficult due to their small size.
Mechanically controlled variable capacitors allow the plate spacing to
be adjusted, for example by rotating or sliding a set of movable
plates into alignment with a set of stationary plates. Low cost
variable capacitors squeeze together alternating layers of aluminum
and plastic with a screw. Electrical control of capacitance is
achievable with varactors (or varicaps), which are reverse-biased
semiconductor diodes whose depletion region width varies with applied
voltage. They are used in phase-locked loops, amongst other
applications.
Example A capacitor labeled or designated as 473K 330V has a capacitance of 47
× 103 pF = 47 nF (±10%) with a maximum working voltage of
330 V. The working voltage of a capacitor is nominally the
highest voltage that may be applied across it without undue risk of
breaking down the dielectric layer.
Letter and digit code[edit]
The notation to state a capacitor's value in a circuit diagram varies.
The letter and digit code for capacitance values following IEC 60062
and
This mylar-film, oil-filled capacitor has very low inductance and low resistance, to provide the high-power (70 megawatt) and high speed (1.2 microsecond) discharge needed to operate a dye laser. Energy storage[edit]
A capacitor can store electric energy when disconnected from its
charging circuit, so it can be used like a temporary battery, or like
other types of rechargeable energy storage system.[63] Capacitors are
commonly used in electronic devices to maintain power supply while
batteries are being changed. (This prevents loss of information in
volatile memory.)
A capacitor can facilitate conversion of kinetic energy of charged
particles into electric energy and store it.[64]
Conventional capacitors provide less than 360 joules per kilogram of
specific energy, whereas a conventional alkaline battery has a density
of 590 kJ/kg. There is an intermediate solution: Supercapacitors,
which can accept and deliver charge much faster than batteries, and
tolerate many more charge and discharge cycles than rechargeable
batteries. They are however 10 times larger than conventional
batteries for a given charge. On the other hand, it has been shown
that the amount of charge stored in the dielectric layer of the thin
film capacitor can be equal or can even exceed the amount of charge
stored on its plates.[65]
In car audio systems, large capacitors store energy for the amplifier
to use on demand. Also for a flash tube a capacitor is used to hold
the high voltage.
Digital memory[edit]
In the 1930s, John Atanasoff applied the principle of energy storage
in capacitors to construct dynamic digital memories for the first
binary computers that used electron tubes for logic.[66]
A 10,000 microfarad capacitor in an amplifier power supply Reservoir capacitors are used in power supplies where they smooth the output of a full or half wave rectifier. They can also be used in charge pump circuits as the energy storage element in the generation of higher voltages than the input voltage. Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. This is used in car audio applications, when a stiffening capacitor compensates for the inductance and resistance of the leads to the lead-acid car battery. Power factor correction[edit] A high-voltage capacitor bank used for power factor correction on a power transmission system In electric power distribution, capacitors are used for power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in volt-amperes reactive (var). The purpose is to counteract inductive loading from devices like electric motors and transmission lines to make the load appear to be mostly resistive. Individual motor or lamp loads may have capacitors for power factor correction, or larger sets of capacitors (usually with automatic switching devices) may be installed at a load center within a building or in a large utility substation. Suppression and coupling[edit] Signal coupling[edit] Main article: capacitive coupling Polyester film capacitors are frequently used as coupling capacitors. Because capacitors pass AC but block DC signals (when charged up to
the applied dc voltage), they are often used to separate the AC and DC
components of a signal. This method is known as
f = 1 2 π L C displaystyle f= frac 1 2pi sqrt LC where L is in henries and C is in farads. Sensing[edit] Main article: capacitive sensing Main article: Capacitive displacement sensor Most capacitors are designed to maintain a fixed physical structure. However, various factors can change the structure of the capacitor, and the resulting change in capacitance can be used to sense those factors. Changing the dielectric: The effects of varying the characteristics of the dielectric can be used for sensing purposes. Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors are used to accurately measure the fuel level in airplanes; as the fuel covers more of a pair of plates, the circuit capacitance increases. Squeezing the dielectric can change a capacitor at a few tens of bar pressure sufficiently that it can be used as a pressure sensor.[68] A selected, but otherwise standard, polymer dielectric capacitor, when immersed in a compatible gas or liquid, can work usefully as a very low cost pressure sensor up to many hundreds of bar. Changing the distance between the plates: Capacitors with a flexible plate can be used to measure strain or pressure. Industrial pressure transmitters used for process control use pressure-sensing diaphragms, which form a capacitor plate of an oscillator circuit. Capacitors are used as the sensor in condenser microphones, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some accelerometers use MEMS capacitors etched on a chip to measure the magnitude and direction of the acceleration vector. They are used to detect changes in acceleration, in tilt sensors, or to detect free fall, as sensors triggering airbag deployment, and in many other applications. Some fingerprint sensors use capacitors. Additionally, a user can adjust the pitch of a theremin musical instrument by moving their hand since this changes the effective capacitance between the user's hand and the antenna. Changing the effective area of the plates: Capacitive touch switches are now used on many consumer electronic products. Oscillators[edit] Further information: Hartley oscillator Example of a simple oscillator incorporating a capacitor A capacitor can possess spring-like qualities in an oscillator
circuit. In the image example, a capacitor acts to influence the
biasing voltage at the npn transistor's base. The resistance values of
the voltage-divider resistors and the capacitance value of the
capacitor together control the oscillatory frequency.
Producing light[edit]
Main article: light emitting capacitor
A light-emitting capacitor is made from a dielectric that uses
phosphorescence to produce light. If one of the conductive plates is
made with a transparent material, the light is visible. Light-emitting
capacitors are used in the construction of electroluminescent panels,
for applications such as backlighting for laptop computers. In this
case, the entire panel is a capacitor used for the purpose of
generating light.
Hazards and safety[edit]
The hazards posed by a capacitor are usually determined, foremost, by
the amount of energy stored, which is the cause of things like
electrical burns or heart fibrillation. Factors such as voltage and
chassis material are of secondary consideration, which are more
related to how easily a shock can be initiated rather than how much
damage can occur.[44]
Capacitors may retain a charge long after power is removed from a
circuit; this charge can cause dangerous or even potentially fatal
shocks or damage connected equipment. For example, even a seemingly
innocuous device such as a disposable-camera flash unit, powered by a
1.5 volt AA battery, has a capacitor which may contain over 15 joules
of energy and be charged to over 300 volts. This is easily capable of
delivering a shock. Service procedures for electronic devices usually
include instructions to discharge large or high-voltage capacitors,
for instance using a Brinkley stick. Capacitors may also have built-in
discharge resistors to dissipate stored energy to a safe level within
a few seconds after power is removed. High-voltage capacitors are
stored with the terminals shorted, as protection from potentially
dangerous voltages due to dielectric absorption or from transient
voltages the capacitor may pick up from static charges or passing
weather events.[44]
Some old, large oil-filled paper or plastic film capacitors contain
polychlorinated biphenyls (PCBs). It is known that waste PCBs can leak
into groundwater under landfills. Capacitors containing PCB were
labelled as containing "Askarel" and several other trade names.
PCB-filled paper capacitors are found in very old (pre-1975)
fluorescent lamp ballasts, and other applications.
Capacitors may catastrophically fail when subjected to voltages or
currents beyond their rating, or as they reach their normal end of
life.
Swollen electrolytic capacitors – the special design of the capacitor tops allows them to vent instead of bursting violently This high-energy capacitor from a defibrillator has a resistor connected between the terminals for safety, to dissipate stored energy.
See also[edit]
References[edit] ^ a b Duff, Wilmer (1908–1916). A Text-Book of Physics (4th ed.).
Philadelphia: P. Blakiston's Son & Co. p. 361. Retrieved 1
December 2016.
^ Bird, John (2010). Electrical and Electronic Principles and
Technology. Routledge. pp. 63–76. ISBN 9780080890562.
Retrieved 2013-03-17.
^ Floyd, Thomas (1984–2005). Electronic Devices (7th ed.). Upper
Saddle River, NJ: Pearson Education. p. 10.
ISBN 0-13-127827-4.
^ Williams, Henry Smith. "A History of Science Volume II, Part VI: The
Leyden Jar Discovered". Retrieved 2013-03-17.
^ Keithley, Joseph F. (1999). The Story of Electrical and Magnetic
Measurements: From 500 BC to the 1940s. John Wiley & Sons.
p. 23. ISBN 9780780311930. Retrieved 2013-03-17.
^ Houston, Edwin J. (1905).
Bibliography[edit] Dorf, Richard C.; Svoboda, James A. (2001). Introduction to Electric
Circuits (5th ed.). New York: John Wiley & Sons.
ISBN 9780471386896.
Philosophical Transactions of the Royal Society LXXII, Appendix 8,
1782 (Volta coins the word condenser)
Ulaby, Fawwaz Tayssir (1999). Fundamentals of Applied
Electromagnetics. Upper Saddle River, New Jersey: Prentice Hall.
ISBN 9780130115546.
Zorpette, Glenn (2005). "Super Charged: A Tiny South Korean Company is
Out to Make Capacitors Powerful enough to Propel the Next Generation
of Hybrid-Electric Cars". IEEE
External links[edit] Wikimedia Commons has media related to Capacitors and Capacitors (SMD). The Wikibook
Look up capacitor in Wiktionary, the free dictionary. The First Condenser – A Beer
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