Series-equivalent circuit Discrete capacitors deviate from the ideal capacitor. An ideal capacitor only stores and releases electrical energy, with no dissipation. Capacitor components have losses and parasitic inductive parts. These imperfections in material and construction can have positive implications such as linear frequency and temperature behavior in class 1 ceramic capacitors. Conversely, negative implications include the non-linear, voltage-dependent capacitance in class 2 ceramic capacitors or the insufficient dielectric insulation of capacitors leading to leakage currents. All properties can be defined and specified by a series equivalent circuit composed out of an idealized capacitance and additional electrical components which model all losses and inductive parameters of a capacitor. In this series-equivalent circuit the electrical characteristics are defined by: •
C, the capacitance of the capacitor •
Rinsul, the
insulation resistance of the dielectric, not to be confused with the insulation of the housing •
Rleak, the resistance representing the
leakage current of the capacitor •
RESR, the
equivalent series resistance which summarizes all ohmic losses of the capacitor, usually abbreviated as "ESR" •
LESL, the
equivalent series inductance which is the effective self-inductance of the capacitor, usually abbreviated as "ESL". Using a series equivalent circuit instead of a parallel equivalent circuit is specified by
IEC/EN 60384–1.
Standard capacitance values and tolerances The
rated capacitance CR or
nominal capacitance CN is the value for which the capacitor has been designed. Actual capacitance depends on the measured frequency and ambient temperature. Standard measuring conditions are a low-voltage AC measuring method at a temperature of 20 °C with frequencies of • 100 kHz, 1 MHz (preferred) or 10 MHz for non-electrolytic capacitors with CR ≤ 1 nF: • 1 kHz or 10 kHz for non-electrolytic capacitors with 1 nF R ≤ 10 μF • 100/120 Hz for electrolytic capacitors • 50/60 Hz or 100/120 Hz for non-electrolytic capacitors with CR > 10 μF For supercapacitors a voltage drop method is applied for measuring the capacitance value. . Capacitors are available in geometrically increasing
preferred values (
E series standards) specified in IEC/EN 60063. According to the number of values per decade, these were called the E3, E6, E12,
E24 etc. series. The range of units used to specify capacitor values has expanded to include everything from pico- (pF), nano- (nF) and microfarad (μF) to farad (F). Millifarad and kilofarad are uncommon. The percentage of allowed deviation from the rated value is called
tolerance. The actual capacitance value should be within its tolerance limits, or it is out of specification. IEC/EN 60062 specifies a letter code for each tolerance. The required tolerance is determined by the particular application. The narrow tolerances of E24 to
E96 are used for high-quality circuits such as precision oscillators and timers. General applications such as non-critical filtering or coupling circuits employ E12 or E6. Electrolytic capacitors, which are often used for
filtering and
bypassing capacitors mostly have a tolerance range of ±20% and need to conform to E6 (or E3) series values.
Temperature dependence Capacitance typically varies with temperature. The different dielectrics express great differences in temperature sensitivity. The temperature coefficient is expressed in
parts per million (ppm) per degree Celsius for class 1 ceramic capacitors or in % over the total temperature range for all others.
Frequency dependence Most discrete capacitor types have more or less capacitance changes with increasing frequencies. The dielectric strength of class 2 ceramic and plastic film diminishes with rising frequency. Therefore, their capacitance value decreases with increasing frequency. This phenomenon for ceramic class 2 and plastic film dielectrics is related to
dielectric relaxation in which the time constant of the electrical dipoles is the reason for the frequency dependence of
permittivity. The graphs below show typical frequency behavior of the capacitance for ceramic and film capacitors. File:MLCC-Kap-versus-Frequenz-engl.svg | Frequency dependence of capacitance for ceramic class 2 capacitors (NP0 class 1 for comparisation) File:Folko-Kurve-C-f-Frequenz-4.png| Frequency dependence of capacitance for film capacitors with different film materials For electrolytic capacitors with non-solid electrolyte, mechanical motion of the
ions occurs. Their movability is limited so that at higher frequencies not all areas of the roughened anode structure are covered with charge-carrying ions. As higher the anode structure is roughened as more the capacitance value decreases with increasing frequency. Low voltage types with highly roughened anodes display capacitance at 100 kHz approximately 10 to 20% of the value measured at 100 Hz.
Voltage dependence Capacitance may also change with applied voltage. This effect is more prevalent in class 2 ceramic capacitors. The permittivity of ferroelectric class 2 material depends on the applied voltage. Higher applied voltage lowers permittivity. The change of capacitance can drop to 80% of the value measured with the standardized measuring voltage of 0.5 or 1.0 V. This behavior is a small source of non-linearity in low-distortion filters and other analog applications. In audio applications this can cause distortion (measured using
THD). Film capacitors and electrolytic capacitors have no significant voltage dependence. File:Delta-Cap-versus-Spannung-engl.png|Simplified diagram of the change in capacitance as a function of the applied voltage for 25 V capacitors in different kind of ceramic grades File:Delta-Cap-versus-Spannung-X7R-engl.png|Simplified diagram of the change in capacitance as a function of applied voltage for X7R ceramics with different rated voltages
Rated and category voltage The voltage at which the dielectric becomes conductive is called the breakdown voltage, and is given by the product of the dielectric strength and the separation between the electrodes. The dielectric strength depends on temperature, frequency, shape of the electrodes, etc. Because a breakdown in a capacitor normally is a short circuit and destroys the component, the operating voltage is lower than the breakdown voltage. The operating voltage is specified such that the voltage may be applied continuously throughout the life of the capacitor. In IEC/EN 60384-1 the allowed operating voltage is called "rated voltage" or "nominal voltage". The rated voltage (UR) is the maximum DC voltage or peak pulse voltage that may be applied continuously at any temperature within the rated temperature range. The voltage proof of nearly all capacitors decreases with increasing temperature. Some applications require a higher temperature range. Lowering the voltage applied at a higher temperature maintains safety margins. For some capacitor types therefore the IEC standard specify a second "temperature derated voltage" for a higher temperature range, the "category voltage". The category voltage (UC) is the maximum DC voltage or peak pulse voltage that may be applied continuously to a capacitor at any temperature within the category temperature range. The relation between both voltages and temperatures is given in the picture right.
Impedance In general, a capacitor is seen as a storage component for electric energy. But this is only one capacitor function. A capacitor can also act as an
AC resistor. In many cases the capacitor is used as a
decoupling capacitor to filter or bypass undesired biased AC frequencies to the ground. Other applications use capacitors for
capacitive coupling of AC signals; the dielectric is used only for blocking DC. For such applications the AC
resistance is as important as the capacitance value. The frequency dependent AC resistance is called
impedance \scriptstyle Z and is the
complex ratio of the voltage to the current in an AC circuit. Impedance extends the concept of resistance to AC circuits and possesses both magnitude and
phase at a particular frequency. This is unlike resistance, which has only magnitude. : \ Z = |Z| e^{j\theta} The magnitude \scriptstyle |Z| represents the ratio of the voltage difference amplitude to the current amplitude, \scriptstyle j is the
imaginary unit, while the argument \scriptstyle \theta gives the phase difference between voltage and current. In capacitor data sheets, only the impedance magnitude |Z| is specified, and simply written as "Z" so that the formula for the impedance can be written in
Cartesian form : \ Z = R + jX where the
real part of impedance is the resistance \scriptstyle R (for capacitors \scriptstyle ESR) and the
imaginary part is the
reactance \scriptstyle X. As shown in a capacitor's series-equivalent circuit, the real component includes an ideal capacitor C, an inductance L (ESL) and a resistor R (ESR). The total reactance at the angular frequency \omega therefore is given by the geometric (complex) addition of a capacitive reactance (
Capacitance) X_C= -\frac{1}{\omega C} and an inductive reactance (
Inductance): X_L=\omega L_{\mathrm{ESL}}. To calculate the impedance \scriptstyle Z the resistance has to be added geometrically and then Z is given by : Z=\sqrt{{ESR}^2 + (X_\mathrm{C} + (-X_\mathrm{L}))^2}. The impedance is a measure of the capacitor's ability to pass alternating currents. In this sense the impedance can be used like Ohms law : Z = \frac{\hat u}{\hat \imath} = \frac{U_\mathrm{eff}}{I_\mathrm{eff}}. to calculate either the peak or the effective value of the current or the voltage. In the special case of
resonance, in which the both reactive resistances : X_C= -\frac{1}{\omega C} and X_L=\omega L_{\mathrm{ESL}} have the same value (X_C=X_L), then the impedance will only be determined by {ESR}. The impedance specified in the datasheets often show typical curves for the different capacitance values. With increasing frequency as the impedance decreases down to a minimum. The lower the impedance, the more easily alternating currents can be passed through the capacitor. At the
apex, the point of resonance, where XC has the same value than XL, the capacitor has the lowest impedance value. Here only the ESR determines the impedance. With frequencies above the resonance the impedance increases again due to the ESL of the capacitor. The capacitor becomes an inductance. As shown in the graph, the higher capacitance values can fit the lower frequencies better while the lower capacitance values can fit better the higher frequencies. Aluminum electrolytic capacitors have relatively good decoupling properties in the lower frequency range up to about 1 MHz due to their large capacitance values. This is the reason for using electrolytic capacitors in standard or
switched-mode power supplies behind the
rectifier for smoothing application. Ceramic and film capacitors are already out of their smaller capacitance values suitable for higher frequencies up to several 100 MHz. They also have significantly lower parasitic inductance, making them suitable for higher frequency applications, due to their construction with end-surface contacting of the electrodes. To increase the range of frequencies, often an electrolytic capacitor is connected in parallel with a ceramic or film capacitor. Many new developments are targeted at reducing parasitic inductance (ESL). This increases the resonance frequency of the capacitor and, for example, can follow the constantly increasing switching speed of digital circuits. Miniaturization, especially in the SMD multilayer ceramic chip capacitors (
MLCC), increases the resonance frequency. Parasitic inductance is further lowered by placing the electrodes on the longitudinal side of the chip instead of the lateral side. The "face-down" construction associated with multi-anode technology in tantalum electrolytic capacitors further reduced ESL. Capacitor families such as the so-called MOS capacitor or silicon capacitors offer solutions when capacitors at frequencies up to the GHz range are needed.
Inductance (ESL) and self-resonant frequency ESL in industrial capacitors is mainly caused by the leads and internal connections used to connect the capacitor plates to the outside world. Large capacitors tend to have higher ESL than small ones because the distances to the plate are longer and every mm counts as an inductance. For any discrete capacitor, there is a frequency above DC at which it ceases to behave as a pure capacitor. This frequency, where X_C is as high as X_L, is called the self-resonant frequency. The self-resonant frequency is the lowest frequency at which the impedance passes through a minimum. For any AC application the self-resonant frequency is the highest frequency at which capacitors can be used as a capacitive component. This is critically important for
decoupling high-speed logic circuits from the power supply. The decoupling capacitor supplies
transient current to the chip. Without decouplers, the IC demands current faster than the connection to the power supply can supply it, as parts of the circuit rapidly switch on and off. To counter this potential problem, circuits frequently use multiple bypass capacitors—small (100 nF or less) capacitors rated for high frequencies, a large electrolytic capacitor rated for lower frequencies and occasionally, an intermediate value capacitor.
Ohmic losses, ESR, dissipation factor, and quality factor The summarized losses in discrete capacitors are ohmic
AC losses.
DC losses are specified as "
leakage current" or "insulating resistance" and are negligible for an AC specification. AC losses are non-linear, possibly depending on frequency, temperature, age or humidity. The losses result from two physical conditions: • line losses including internal supply line resistances, the contact resistance of the electrode contact, line resistance of the electrodes, and in "wet" aluminum electrolytic capacitors and especially supercapacitors, the limited conductivity of liquid electrolytes and •
dielectric losses from
dielectric polarization. The largest share of these losses in larger capacitors is usually the frequency dependent ohmic dielectric losses. For smaller components, especially for wet electrolytic capacitors, conductivity of liquid electrolytes may exceed dielectric losses. To measure these losses, the measurement frequency must be set. Since commercially available components offer capacitance values cover 15 orders of magnitude, ranging from pF (10−12 F) to some 1000 F in supercapacitors, it is not possible to capture the entire range with only one frequency. IEC 60384-1 states that ohmic losses should be measured at the same frequency used to measure capacitance. These are: • 100 kHz, 1 MHz (preferred) or 10 MHz for non-electrolytic capacitors with CR ≤ 1 nF: • 1 kHz or 10 kHz for non-electrolytic capacitors with 1 nF R ≤ 10 μF • 100/120 Hz for electrolytic capacitors • 50/60 Hz or 100/120 Hz for non-electrolytic capacitors with CR > 10 μF A capacitor's summarized resistive losses may be specified either as ESR, as a
dissipation factor(DF, tan δ), or as
quality factor (Q), depending on application requirements. Capacitors with higher ripple current I_R loads, such as electrolytic capacitors, are specified with
equivalent series resistance ESR. ESR can be shown as an ohmic part in the above vector diagram. ESR values are specified in datasheets per individual type. The losses of film capacitors and some class 2 ceramic capacitors are mostly specified with the dissipation factor tan δ. These capacitors have smaller losses than electrolytic capacitors and mostly are used at higher frequencies up to some hundred MHz. However the numeric value of the dissipation factor, measured at the same frequency, is independent of the capacitance value and can be specified for a capacitor series with a range of capacitance. The dissipation factor is determined as the tangent of the reactance (X_C - X_L) and the ESR, and can be shown as the angle δ between imaginary and the impedance axis. If the inductance ESL is small, the dissipation factor can be approximated as: : \tan \delta = ESR \cdot \omega C Capacitors with very low losses, such as ceramic Class 1 and Class 2 capacitors, specify resistive losses with a
quality factor (Q). Ceramic Class 1 capacitors are especially suitable for LC resonant circuits with frequencies up to the GHz range, and precise high and low pass filters. For an electrically resonant system, Q represents the effect of
electrical resistance and characterizes a resonator's
bandwidth B relative to its center or resonant frequency f_0. Q is defined as the reciprocal value of the dissipation factor. : Q = \frac{1}{\tan \delta} = \frac{f_0}{B} \ A high Q value is for resonant circuits a mark of the quality of the resonance.
Limiting current loads A capacitor can act as an AC resistor, coupling AC voltage and AC current between two points. Every AC current flow through a capacitor generates heat inside the capacitor body. These dissipation power loss P is caused by ESR and is the squared value of the effective (RMS) current I : P = I^2 \cdot ESR The same power loss can be written with the dissipation factor \tan \delta as : P = \frac{U^2 \cdot \tan \delta}{2\pi f \cdot C} The internal generated heat has to be distributed to the ambient. The temperature of the capacitor, which is established on the balance between heat produced and distributed, shall not exceed the capacitors maximum specified temperature. Hence, the ESR or dissipation factor is a mark for the maximum power (AC load, ripple current, pulse load, etc.) a capacitor is specified for. AC currents may be a: • ripple current—an effective (RMS) AC current, coming from an AC voltage superimposed of a DC bias, a • pulse current—an AC peak current, coming from a voltage peak, or an • AC current—an effective (RMS) sinusoidal current Ripple and AC currents mainly warms the capacitor body. By this currents internal generated temperature influences the breakdown voltage of the dielectric. Higher temperature lower the voltage proof of all capacitors. In wet electrolytic capacitors higher temperatures force the evaporation of electrolytes, shortening the life time of the capacitors. In film capacitors higher temperatures may shrink the plastic film changing the capacitor's properties. Pulse currents, especially in metallized film capacitors, heat the contact areas between end spray (schoopage) and metallized electrodes. This may reduce the contact to the electrodes, heightening the dissipation factor. For safe operation, the maximal temperature generated by any AC current flow through the capacitor is a limiting factor, which in turn limits AC load, ripple current, pulse load, etc.
Ripple current A "ripple current" is the
RMS value of a superimposed AC current of any frequency and any waveform of the current curve for continuous operation at a specified temperature. It arises mainly in power supplies (including
switched-mode power supplies) after rectifying an AC voltage and flows as charge and discharge current through the decoupling or smoothing capacitor. The "rated ripple current" shall not exceed a temperature rise of 3, 5 or 10 °C, depending on the capacitor type, at the specified maximum ambient temperature. Ripple current generates heat within the capacitor body due to the ESR of the capacitor. The components of capacitor ESR are: the dielectric losses caused by the changing field strength in the dielectric, the resistance of the supply conductor, and the resistance of the electrolyte. For an electric double layer capacitor (ELDC) these resistance values can be derived from a
Nyquist plot of the capacitor's complex impedance. ESR is dependent on frequency and temperature. For ceramic and film capacitors in generally ESR decreases with increasing temperatures but heighten with higher frequencies due to increasing dielectric losses. For electrolytic capacitors up to roughly 1 MHz ESR decreases with increasing frequencies and temperatures. The types of capacitors used for power applications have a specified rated value for maximum ripple current. These are primarily aluminum electrolytic capacitors, and tantalum as well as some film capacitors and Class 2 ceramic capacitors. Aluminum electrolytic capacitors, the most common type for power supplies, experience shorter life expectancy at higher ripple currents. Exceeding the limit tends to result in explosive failure. Tantalum electrolytic capacitors with solid manganese dioxide electrolyte are also limited by ripple current. Exceeding their ripple limits tends to shorts and burning components. For film and ceramic capacitors, normally specified with a loss factor tan δ, the ripple current limit is determined by temperature rise in the body of approximately 10 °C. Exceeding this limit may destroy the internal structure and cause shorts.
Pulse current The rated pulse load for a certain capacitor is limited by the rated voltage, the pulse repetition frequency, temperature range and pulse rise time. The "pulse rise time" dv/dt, represents the steepest voltage gradient of the pulse (rise or fall time) and is expressed in volts per μs (V/μs). The rated pulse rise time is also indirectly the maximum capacity of an applicable peak current I_p. The peak current is defined as: : I_p = C \cdot dv/dt where: I_p is in A; C in μF; dv/dt in V/μs The permissible pulse current capacity of a metallized film capacitor generally allows an internal temperature rise of 8 to 10 K. In the case of metallized film capacitors, pulse load depends on the properties of the dielectric material, the thickness of the metallization and the capacitor's construction, especially the construction of the contact areas between the end spray and metallized electrodes. High peak currents may lead to selective overheating of local contacts between end spray and metallized electrodes which may destroy some of the contacts, leading to increasing ESR. For metallized film capacitors, so-called pulse tests simulate the pulse load that might occur during an application, according to a standard specification. IEC 60384 part 1, specifies that the test circuit is charged and discharged intermittently. The test voltage corresponds to the rated DC voltage and the test comprises 10000 pulses with a repetition frequency of 1 Hz. The pulse stress capacity is the pulse rise time. The rated pulse rise time is specified as 1/10 of the test pulse rise time. The pulse load must be calculated for each application. A general rule for calculating the power handling of film capacitors is not available because of vendor-related internal construction details. To prevent the capacitor from overheating the following operating parameters have to be considered: • peak current per μF • Pulse rise or fall time dv/dt in V/μs • relative duration of charge and discharge periods (pulse shape) • maximum pulse voltage (peak voltage) • peak reverse voltage; • Repetition frequency of the pulse • Ambient temperature • Heat dissipation (cooling) Higher pulse rise times are permitted for pulse voltage lower than the rated voltage. Examples for calculations of individual pulse loads are given by many manufactures, e.g. WIMA and Kemet.
AC current An AC load only can be applied to a non-polarized capacitor. Capacitors for AC applications are primarily film capacitors, metallized paper capacitors, ceramic capacitors and bipolar electrolytic capacitors. The rated AC load for an AC capacitor is the maximum sinusoidal effective AC current (rms) which may be applied continuously to a capacitor within the specified temperature range. In the datasheets the AC load may be expressed as • rated AC voltage at low frequencies, • rated reactive power at intermediate frequencies, • reduced AC voltage or rated AC current at high frequencies. The rated AC voltage for film capacitors is generally calculated so that an internal temperature rise of 8 to 10 K is the allowed limit for safe operation. Because dielectric losses increase with increasing frequency, the specified AC voltage has to be derated at higher frequencies. Datasheets for film capacitors specify special curves for derating AC voltages at higher frequencies. If film capacitors or ceramic capacitors only have a DC specification, the peak value of the AC voltage applied has to be lower than the specified DC voltage. AC loads can occur in AC motor run capacitors, for voltage doubling, in
snubbers, lighting ballast and for PFC for phase shifting to improve transmission network stability and efficiency, which is one of the most important applications for large power capacitors. These mostly large PP film or metallized paper capacitors are limited by the rated reactive power VAr. Bipolar electrolytic capacitors, to which an AC voltage may be applicable, are specified with a rated ripple current.
Insulation resistance and self-discharge constant The resistance of the dielectric is finite, leading to some level of
DC "leakage current" that causes a charged capacitor to lose charge over time. For ceramic and film capacitors, this resistance is called "insulation resistance Rins". This resistance is represented by the resistor Rins in parallel with the capacitor in the series-equivalent circuit of capacitors. Insulation resistance must not be confused with the outer isolation of the component with respect to the environment. The time curve of self-discharge over insulation resistance with decreasing capacitor voltage follows the formula : u(t) = U_0 \cdot \mathrm{e}^{-t/\tau_\mathrm{s}}, With stored DC voltage U_0 and self-discharge constant : \tau_\mathrm{s} = R_\mathrm{ins} \cdot C Thus, after \tau_\mathrm{s}\, voltage U_0 drops to 37% of the initial value. The self-discharge constant is an important parameter for the insulation of the dielectric between the electrodes of ceramic and film capacitors. For example, a capacitor can be used as the time-determining component for time relays or for storing a voltage value as in a
sample and hold circuits or
operational amplifiers. Class 1 ceramic capacitors have an insulation resistance of at least 10 GΩ, while class 2 capacitors have at least 4 GΩ or a self-discharge constant of at least 100 s. Plastic film capacitors typically have an insulation resistance of 6 to 12 GΩ. This corresponds to capacitors in the uF range of a self-discharge constant of about 2000–4000 s. Insulation resistance respectively the self-discharge constant can be reduced if humidity penetrates into the winding. It is partially strongly temperature dependent and decreases with increasing temperature. Both decrease with increasing temperature. In electrolytic capacitors, the insulation resistance is defined as leakage current.
Leakage current For electrolytic capacitors the insulation resistance of the dielectric is termed "leakage current". This
DC current is represented by the resistor Rleak in parallel with the capacitor in the series-equivalent circuit of electrolytic capacitors. This resistance between the terminals of a capacitor is also finite. Rleak is lower for electrolytics than for ceramic or film capacitors. The leakage current includes all weak imperfections of the dielectric caused by unwanted chemical processes and mechanical damage. It is also the DC current that can pass through the dielectric after applying a voltage. It depends on the interval without voltage applied (storage time), the thermic stress from soldering, on voltage applied, on temperature of the capacitor, and on measuring time. The leakage current drops in the first minutes after applying DC voltage. In this period the dielectric oxide layer can self-repair weaknesses by building up new layers. The time required depends generally on the electrolyte. Solid electrolytes drop faster than non-solid electrolytes but remain at a slightly higher level. The leakage current in non-solid electrolytic capacitors as well as in manganese oxide solid tantalum capacitors decreases with voltage-connected time due to self-healing effects. Although electrolytics leakage current is higher than current flow over insulation resistance in ceramic or film capacitors, the self-discharge of modern non solid electrolytic capacitors takes several weeks. A particular problem with electrolytic capacitors is storage time. Higher leakage current can be the result of longer storage times. These behaviors are limited to electrolytes with a high percentage of water. Organic solvents such as
GBL do not have high leakage with longer storage times. Leakage current is normally measured 2 or 5 minutes after applying rated voltage.
Microphonics All ferroelectric materials exhibit
a piezoelectric effect. Because Class 2 ceramic capacitors use ferroelectric ceramics dielectric, these types of capacitors may have electrical effects called
microphonics. Microphonics (microphony) describes how electronic components transform mechanical
vibrations into an undesired electrical signal (
noise). The dielectric may absorb mechanical forces from shock or vibration by changing thickness and changing the electrode separation, affecting the capacitance, which in turn induces an AC current. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, varying the electric field between the capacitor plates exerts a physical force, turning them into an audio speaker. High current impulse loads or high ripple currents can generate audible sound from the capacitor itself, draining energy and stressing the dielectric.
Dielectric absorption (soakage) Dielectric absorption occurs when a capacitor that has remained charged for a long time discharges only incompletely when briefly discharged. Although an ideal capacitor would reach zero volts after discharge, real capacitors develop a small voltage from time-delayed dipole discharging, a phenomenon that is also called
dielectric relaxation, "soakage" or "battery action". In many applications of capacitors dielectric absorption is not a problem but in some applications, such as long-
time-constant integrators,
sample-and-hold circuits, switched-capacitor
analog-to-digital converters, and very low-distortion
filters, the capacitor must not recover a residual charge after full discharge, so capacitors with low absorption are specified. The voltage at the terminals generated by the dielectric absorption may in some cases possibly cause problems in the function of an electronic circuit or can be a safety risk to personnel. In order to prevent shocks most very large capacitors are shipped with shorting wires that need to be removed before they are used.
Energy density The capacitance value depends on the dielectric material (ε), the surface of the electrodes (A) and the distance (d) separating the electrodes and is given by the formula of a plate capacitor: : C \approx \frac{\varepsilon A}{d} The separation of the electrodes and the voltage proof of the dielectric material defines the breakdown voltage of the capacitor. The breakdown voltage is proportional to the thickness of the dielectric. Theoretically, given two capacitors with the same mechanical dimensions and dielectric, but one of them have half the thickness of the dielectric. With the same dimensions this one could place twice the parallel-plate area inside. This capacitor has theoretically 4 times the capacitance as the first capacitor but half of the voltage proof. Since the energy density stored in a capacitor is given by: : E_\mathrm{stored} = \frac{1}{2} C V^2, thus a capacitor having a dielectric half as thick as another has 4 times higher capacitance but voltage proof, yielding an equal maximum energy density. Therefore, dielectric thickness does not affect energy density within a capacitor of fixed overall dimensions. Using a few thick layers of dielectric can support a high voltage, but low capacitance, while thin layers of dielectric produce a low breakdown voltage, but a higher capacitance. This assumes that neither the electrode surfaces nor the permittivity of the dielectric change with the voltage proof. A simple comparison with two existing capacitor series can show whether reality matches theory. The comparison is easy, because the manufacturers use standardized case sizes or boxes for different capacitance/voltage values within a series. In reality modern capacitor series do not fit the theory. For electrolytic capacitors the sponge-like rough surface of the anode foil gets smoother with higher voltages, decreasing the surface area of the anode. But because the energy increases squared with the voltage, and the surface of the anode decreases lesser than the voltage proof, the energy density increases clearly. For film capacitors the permittivity changes with dielectric thickness and other mechanical parameters so that the deviation from the theory has other reasons. Comparing the capacitors from the table with a supercapacitor, the highest energy density capacitor family. For this, the capacitor 25 F/2.3 V in dimensions D × H = 16 mm × 26 mm from Maxwell HC Series, compared with the electrolytic capacitor of approximately equal size in the table. This supercapacitor has roughly 5000 times higher capacitance than the 4700/10 electrolytic capacitor but of the voltage and has about 66,000 mWs (0.018 Wh) stored electrical energy, approximately 100 times higher energy density (40 to 280 times) than the electrolytic capacitor.
Long time behavior, aging Electrical parameters of capacitors may change over time during storage and application. The reasons for parameter changings are different, it may be a property of the dielectric, environmental influences, chemical processes or drying-out effects for non-solid materials.
Aging In
ferroelectric Class 2 ceramic capacitors, capacitance decreases over time. This behavior is called "aging". This aging occurs in ferroelectric dielectrics, where domains of polarization in the dielectric contribute to the total polarization. Degradation of polarized domains in the dielectric decreases permittivity and therefore capacitance over time. The aging follows a logarithmic law. This defines the decrease of capacitance as constant percentage for a time decade after the soldering recovery time at a defined temperature, for example, in the period from 1 to 10 hours at 20 °C. As the law is logarithmic, the percentage loss of capacitance will twice between 1 h and 100 h and 3 times between 1 h and 1,000 h and so on. Aging is fastest near the beginning, and the absolute capacitance value stabilizes over time. The rate of aging of Class 2 ceramic capacitors depends mainly on its materials. Generally, the higher the temperature dependence of the ceramic, the higher the aging percentage. The typical aging of X7R ceramic capacitors is about 2.5% per decade. The aging rate of Z5U ceramic capacitors is significantly higher and can be up to 7% per decade. The aging process of Class 2 ceramic capacitors may be reversed by heating the component above the
Curie point. Class 1 ceramic capacitors and film capacitors do not have ferroelectric-related aging. Environmental influences such as higher temperature, high humidity and mechanical stress can, over a longer period, lead to a small irreversible change in the capacitance value sometimes called aging, too. The change of capacitance for P 100 and N 470 Class 1 ceramic capacitors is lower than 1%, for capacitors with N 750 to N 1500 ceramics it is ≤ 2%. Film capacitors may lose capacitance due to self-healing processes or gain it due to humidity influences. Typical changes over 2 years at 40 °C are, for example, ±3% for PE film capacitors and ±1% PP film capacitors.
Life time Electrolytic capacitors with non-solid electrolyte age as the electrolyte evaporates. This evaporation depends on temperature and the current load the capacitors experience. Electrolyte escape influences capacitance and ESR. Capacitance decreases and the ESR increases over time. In contrast to ceramic, film and electrolytic capacitors with solid electrolytes, "wet" electrolytic capacitors reach a specified "end of life" reaching a specified maximum change of capacitance or ESR. End of life, "load life" or "lifetime" can be estimated either by formula or diagrams or roughly by a so-called "10-degree-law". A typical specification for an electrolytic capacitor states a lifetime of 2,000 hours at 85 °C, doubling for every 10 degrees lower temperature, achieving lifespan of approximately 15 years at room temperature. Supercapacitors also experience electrolyte evaporation over time. Estimation is similar to wet electrolytic capacitors. Additional to temperature the voltage and current load influence the life time. Lower voltage than rated voltage and lower current loads as well as lower temperature extend the life time.
Failure rate . For electrolytic capacitors with non-solid electrolyte and supercapacitors ends this time with the beginning of wear out failures due to evaporation of electrolyte Capacitors are
reliable components with low
failure rates, achieving life expectancies of decades under normal conditions. Most capacitors pass a test at the end of production similar to a "
burn in", so that early failures are found during production, reducing the number of post-shipment failures. Reliability for capacitors is usually specified in numbers of
Failures In Time (FIT) during the period of constant random failures. FIT is the number of failures that can be expected in one billion component-hours of operation at fixed working conditions (e.g. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, at 40 °C and 0.5 UR). For other conditions of applied voltage, current load, temperature, mechanical influences and humidity the FIT can recalculated with terms standardized for industrial or military contexts. == Additional information ==