### Lifetime of Aluminum Electrolytic Capacitors

Contents

Lifetime of Aluminum Electrolytic Capacitors

1. Ambient Temperature Effect on Lifetime

2. Applying Voltage Effect on Lifetime

3. Ripple Current Effect on Lifetime

4. Charge and Discharge Operation Effect on Lifetime

5. Inrush Current

6.Abnormal Voltage Effect on Lifetime

A ：Frequency factor

E ：Activation energy

R：Gas constant (8.31J/deg)

T ：Absolute temperature (K)

Applying Equation (5) to the lifetime of the capacitors brings Equation (6), which is converted to Equation (7):

Practical estimation of the lifetime has been using Equation (8) as an approximation:

Lo：Specified lifetime (hour) with the rated voltage applied (or the rated ripple current superimposed to a DC voltage) at the upper limit of the category temperature. Refer to the lifetime specifications of individual products.

Lx：Estimated life on actual usage (hour)

To：Maximum Category Temperature（℃）

Tx：Actual Ambient Temperature（℃）

Bt：Temperature acceleration factor

Where, the temperature acceleration factor (BT) is approximately 2 over an ambient temperature range from 60°C to 95°C, which means that the lifetime is approximately halved for every 10°C rise in ambient temperature. However, according to the Arrhenius Equation (6), the reciprocal of T is directly proportional to the logarithm of lifetime, which means that, strictly speaking, there is the temperature range where the theory of lifetime reducing by half at every 10°C rise is not applied. (Fig. 19).

Especially for capacitors whose maximum operating temperature is a 105°C or higher, the temperature acceleration factor (BT) needs to be modified depending on temperature ranges of the lifetime estimation. For details, please consult us.

For lifetime estimation at a lower-temperature range, evaluation test data have not been obtained, and for evaluating long term endurance, it is necessary to take into account some additional factors such as deterioration of the rubber seal materials as well as the diffusion of electrolyte. Accordingly, in Equation (8), Tx should be 40°C at the lowest for the lifetime calculation purpose, and also the estimated lifetime (Lx) should be 15 years at the longest.

However, for capacitors of larger size and higher rated voltage contain a larger volume of electrolyte, difference in applying voltages can affect degradation of the oxide layer, other than the diffusion of electrolyte. Therefore, for screw mount terminal type capacitors with the rated voltage of 350Vdc or higher, the lifetime estimation includes the effect of applying a lower voltage than the rated voltage (derating voltage).

3-1 Heat Generation due to Ripple Current

Power consumption by the ripple current can be expressed as follows:

W：Internal power dissipation

IR ：Ripple Current

R：Internal Resistance (Equivalent Series Resistance)

V ：Applied voltage

IL ：Leakage Current

Leakage current IL at the maximum operating temperature can be 5 to 10 times higher than the valuesmeasured at 20°C. However, considering IR >> IL, the above equation can be simplified as Equation (10).

To obtain the temperature at which equilibrium is achieved between heat generation and dissipation, derive Equation (11).

β ：Radiation Constant

A ：Surface area of can case （m2） ΔT：Temperature-rise due to the Ripple Current（℃）

D：Can Diameter (m)

L ：Can Length (m)

From the above equation, the internal temperature rise (ΔT) is given by Equation (12):

Also, for a ripple frequency of 120Hz, Equation (12) for calculating ΔT is rewritten as Equation (13):

tanδ ：Dissipation Factor at 120Hz

ω ：2πf（f = 120Hz）

C ：Capacitance at 120Hz（F）

An approximate value of ripple current-caused ΔT can be calculated using Equation (14): Io：Rated ripple current (Arms), frequency compensated, at the upper limit of the category temperature range

Ix：Operating ripple current (Arms) actually flowing in the capacitor

ΔTo：Rise in internal temperature due to the rated ripple current (℃): different for each product series. Please consult us.

There are some product families that can accept a higher ripple current than the rated value providing that ambient temperature Tx is lower than the upper limit of the category temperature range. However, in this case, remember that the lifetime decreases due to the higher ΔT due to the ripple current. Be sure that ΔT does not exceed the specified limit that has been determined as a function of ambient temperature. Note that the core temperature limit of the element is shown by [Tx + ΔT limit]. Examples of ΔT limits at some ambient temperatures are shown below

Each product family has a different ΔT limit. For details, consult us.

3-2 Ripple Current and Frequency

The ripple current rating is specified normally by the effective value (r.m.s value) of 120Hz or 100kHz sine wave. However, since the equivalent series resistance

(ESR) of a capacitor is frequency-dependent, the allowable ripple current depends on the frequency. Where the operating ripple current consists of a mains power frequency element and switching frequency element(s) like switching mode power supplies do, the internal power loss is expressed by Equation (15):

W：Power consumption

If1、 If2、…Ifn：Ripple current (Arms) at frequency f1···fn

Given a frequency compensation factor (Frequency Multiplier) = Ffn and reference frequency for the ripple current = fo, Rfn ＝ Rfo/Ffn2 is obtained. Therefore, the ripple current at any frequency can be converted into its r.m.s. value at the reference frequency (Ifo) using Equation (16): Ifo ：Reference ripple current (Arms), i.e., that at the reference frequency

Ff1、 Ff2、…Ffn ：Frequency compensation factor (Frequency Multiplier) at frequency f1···fn (Refer to the catalogs)

Note that the ESR depends on the temperature and the value of βdepends on the installation conditions of the capacitor on the board. To determine more accurate values of ΔT, they can be actually measured using a thermocouple

3-3 Lifetime Estimation

Equations (17) through (19) can be used for estimating the lifetime of a non-solid aluminum electrolytic capacitor based on the ambient temperature, the rise of internal temperature due to ripple current, and operating voltage applied.

For a surface mount type or radial lead type capacitor :

Endurance specifications are defined by the rated voltage For a surface mount type or radial lead type capacitor :

Endurance specifications are defined by “the rated ripple current superimposition”. For a snap-in type or screw terminal type capacitor Lo : Specified lifetime (hour) at the upper limit of the category temperature range and at the rated voltage

Lr : Specified lifetime (hour) at the upper limit of the category temperature range and at the rated ripple current superimposed to a DC voltage

Lx : Estimation of actual lifetime (hour)

To : Upper limit of the category temperature range (℃)

Tx : Actual ambient temperature of the capacitor (℃) Use 40℃ if the actual ambient temperature is below it.

ΔT : Rise of internal temperature due to actual ripple current (℃)

*ΔTo : Rise of internal temperature due to the rated ripple current (℃)

*Kt : Correction factor of ambient temperature acceleration factor

*Kv : Derating voltage factor (a snap-in type capacitor with the rated voltage of less than 160Vdc and a screw terminal type capacitor with the rated voltage of less than 350Vdc :1)

*A : Acceleration factor of temperature-rise due to the ripple current(This factor depends on use conditions.)

For the values marked with * , consult us.

Please consult us about lifetime equations for the series of the category temperature 125℃ or more

Subject series : MXB, MHS, MVH, MHL, MHB, MHJ, MHK, GPA, GVA, GXF, GXE, GXL, GPD, GVD, GQB, GXA.

Note that the calculation results above are not considered as a guaranteed value. When designing the lifetime of a device, please select a capacitor that has an extra margin against the device lifetime requirements. Also, where the estimation result calculated exceeds 15 years, please consider 15 years to be a maximum. If 15 years or more may be required as an expected lifetime, please consult us.

When this charge and discharge is repeatedly operated, the chemical reactions proceed to further form the oxide layer on the cathode foil, causing the capacitance of the cathode foil to reduce and thereby reducing the capacitance of the capacitor. Moreover, the chemical reactions bring heat and gases. Depending on the charge and discharge conditions, the internal pressure may increase, the pressure relief vent may open or the capacitor may have destructive failures. Consult us for using a capacitor with the following applications:

・Frequently repeating power on/off.

・Repeating rapid charge and discharge operations at a short interval cycle.

・Repeating charge and discharge operations with a large voltage drop.

Figures 23 through 25 show some test data of special-design capacitors for charge and discharge application, compared with general-purpose capacitors.

However, frequently repeating inrush currents may heat up the element inside a capacitor more than the allowable limit and/or overheat the external terminal connections or the connections between the internal lead and foil electrode.

6-1 Overvoltage

Applying a voltage higher than the rated voltage will cause chemical reactions (formation of dielectric) to occur on the anode foil with the leakage current rapidly increasing, which produces heat and gases and thereby increases the internal pressure. The reactions are accelerated by the voltage, current density and ambient temperature, causing the pressure relief vent to open or the capacitor to have destructive failures. It may also accompany a reduction in capacitance and an increase in tanδ as well as an increase in the leakage current, which can lead to internal short-circuiting failure. An example of capacitor overvoltage characteristics is shown in Fig. 26

6-2 Reverse Voltage

Applying a reverse voltage will cause chemical reactions (formation of dielectric) to occur on the cathode foil, and, as is the case with overvoltage, the leakage current will rapidly increase with heat and gases generating and thus the internal pressure increases. The reactions are accelerated by the voltage, current density and ambient temperature. It may also accompany a reduction in capacitance and an increase in tanδ as well as an increase in the leakage current. An example of capacitor reverse-voltage characteristics is shown in Fig. 27. A reverse voltage of as small as 1V can cause the capacitance to decrease. A reverse voltage of 2 to 3V can shorten lifetime due to a reduction in capacitance, increase in tanδ, and/or increase in leakage current. A reverse voltage of even higher value can open the pressure relief vent or lead to destructive failures (Fig. 27).

6-3 Do not Use Aluminum Electrolytic Capacitors in an AC Circuit

Using an aluminum electrolytic capacitor in an AC circuit will result in the same situation as that with a positive potential being applied to the cathode (like a reverse voltage) and with an excessively large ripple current flowing in the capacitor, which may increase the internal pressure due to the generation of heat and gases, open the pressure relief vent, leak the electrolyte with the rubber seal bung expelled or cause the capacitor to blow up or catch fire in the worst case. If the capacitor blows up, it may scatter flammable materials such as electrolyte and element-supporting wax materials, which can lead to short-circuiting of the device. Therefore, do not use aluminum electrolytic capacitors in any of the AC circuits.

Lifetime of Aluminum Electrolytic Capacitors

1. Ambient Temperature Effect on Lifetime

2. Applying Voltage Effect on Lifetime

3. Ripple Current Effect on Lifetime

4. Charge and Discharge Operation Effect on Lifetime

5. Inrush Current

6.Abnormal Voltage Effect on Lifetime

##### Lifetime of Aluminum Electrolytic Capacitors

The lifetime of aluminum electrolytic capacitors is largely dependent on the application conditions. Environmental factors include temperature, humidity, atmospheric pressure and vibrations. Electrical factors include operating voltage, ripple current and chargedischarge. Where the capacitors are used in a normal filtering circuit, ambient temperature and heating due to the ripple current are crucial factors for determining the lifetime of the capacitors. These factors are included to the lifetime specifications titled “Endurance” on the catalogs or product specifications. For applications subject to high humidity and/or continuous vibrations, or subject to frequent charge and discharge operations, the endurance of individual conditions should be considered.##### 1 Ambient Temperature Effect on Lifetime

The lifetime of aluminum electrolytic capacitors is affected mainly by the loss of electrolyte as the result of diffusion through the rubber seal materials, which leads to a decrease in capacitance and increase in tanδ . The relationship of temperature to the diffusion of electrolyte follows the Arrhenius’ Law (Equations (4) and (5)): k ：Reaction rate constantA ：Frequency factor

E ：Activation energy

R：Gas constant (8.31J/deg)

T ：Absolute temperature (K)

Applying Equation (5) to the lifetime of the capacitors brings Equation (6), which is converted to Equation (7):

Practical estimation of the lifetime has been using Equation (8) as an approximation:

Lo：Specified lifetime (hour) with the rated voltage applied (or the rated ripple current superimposed to a DC voltage) at the upper limit of the category temperature. Refer to the lifetime specifications of individual products.

Lx：Estimated life on actual usage (hour)

To：Maximum Category Temperature（℃）

Tx：Actual Ambient Temperature（℃）

Bt：Temperature acceleration factor

Where, the temperature acceleration factor (BT) is approximately 2 over an ambient temperature range from 60°C to 95°C, which means that the lifetime is approximately halved for every 10°C rise in ambient temperature. However, according to the Arrhenius Equation (6), the reciprocal of T is directly proportional to the logarithm of lifetime, which means that, strictly speaking, there is the temperature range where the theory of lifetime reducing by half at every 10°C rise is not applied. (Fig. 19).

Especially for capacitors whose maximum operating temperature is a 105°C or higher, the temperature acceleration factor (BT) needs to be modified depending on temperature ranges of the lifetime estimation. For details, please consult us.

For lifetime estimation at a lower-temperature range, evaluation test data have not been obtained, and for evaluating long term endurance, it is necessary to take into account some additional factors such as deterioration of the rubber seal materials as well as the diffusion of electrolyte. Accordingly, in Equation (8), Tx should be 40°C at the lowest for the lifetime calculation purpose, and also the estimated lifetime (Lx) should be 15 years at the longest.

##### 2 Applying Voltage Effect on Lifetime

Where a capacitor is used at lower than the rated voltage, the lifetime may not be adversely affected, which means that the effect of the applying voltage is negligibly small, while the effect of the ambient temperature and heat generation due to ripple current is significant.However, for capacitors of larger size and higher rated voltage contain a larger volume of electrolyte, difference in applying voltages can affect degradation of the oxide layer, other than the diffusion of electrolyte. Therefore, for screw mount terminal type capacitors with the rated voltage of 350Vdc or higher, the lifetime estimation includes the effect of applying a lower voltage than the rated voltage (derating voltage).

##### 3 Ripple Current Effect on Lifetime

Since an aluminum electrolytic capacitor has a larger tanδ than other types of capacitors, the capacitor produces more internal heat when a ripple current flows through it. The temperature rise due to this heat may significantly affect the lifetime of the capacitor. This is the reason why ripple current ratings are specified for capacitors3-1 Heat Generation due to Ripple Current

Power consumption by the ripple current can be expressed as follows:

W：Internal power dissipation

IR ：Ripple Current

R：Internal Resistance (Equivalent Series Resistance)

V ：Applied voltage

IL ：Leakage Current

Leakage current IL at the maximum operating temperature can be 5 to 10 times higher than the valuesmeasured at 20°C. However, considering IR >> IL, the above equation can be simplified as Equation (10).

To obtain the temperature at which equilibrium is achieved between heat generation and dissipation, derive Equation (11).

β ：Radiation Constant

A ：Surface area of can case （m2） ΔT：Temperature-rise due to the Ripple Current（℃）

D：Can Diameter (m)

L ：Can Length (m)

From the above equation, the internal temperature rise (ΔT) is given by Equation (12):

Also, for a ripple frequency of 120Hz, Equation (12) for calculating ΔT is rewritten as Equation (13):

tanδ ：Dissipation Factor at 120Hz

ω ：2πf（f = 120Hz）

C ：Capacitance at 120Hz（F）

An approximate value of ripple current-caused ΔT can be calculated using Equation (14): Io：Rated ripple current (Arms), frequency compensated, at the upper limit of the category temperature range

Ix：Operating ripple current (Arms) actually flowing in the capacitor

ΔTo：Rise in internal temperature due to the rated ripple current (℃): different for each product series. Please consult us.

There are some product families that can accept a higher ripple current than the rated value providing that ambient temperature Tx is lower than the upper limit of the category temperature range. However, in this case, remember that the lifetime decreases due to the higher ΔT due to the ripple current. Be sure that ΔT does not exceed the specified limit that has been determined as a function of ambient temperature. Note that the core temperature limit of the element is shown by [Tx + ΔT limit]. Examples of ΔT limits at some ambient temperatures are shown below

Each product family has a different ΔT limit. For details, consult us.

3-2 Ripple Current and Frequency

The ripple current rating is specified normally by the effective value (r.m.s value) of 120Hz or 100kHz sine wave. However, since the equivalent series resistance

(ESR) of a capacitor is frequency-dependent, the allowable ripple current depends on the frequency. Where the operating ripple current consists of a mains power frequency element and switching frequency element(s) like switching mode power supplies do, the internal power loss is expressed by Equation (15):

W：Power consumption

If1、 If2、…Ifn：Ripple current (Arms) at frequency f1···fn

Given a frequency compensation factor (Frequency Multiplier) = Ffn and reference frequency for the ripple current = fo, Rfn ＝ Rfo/Ffn2 is obtained. Therefore, the ripple current at any frequency can be converted into its r.m.s. value at the reference frequency (Ifo) using Equation (16): Ifo ：Reference ripple current (Arms), i.e., that at the reference frequency

Ff1、 Ff2、…Ffn ：Frequency compensation factor (Frequency Multiplier) at frequency f1···fn (Refer to the catalogs)

Note that the ESR depends on the temperature and the value of βdepends on the installation conditions of the capacitor on the board. To determine more accurate values of ΔT, they can be actually measured using a thermocouple

3-3 Lifetime Estimation

Equations (17) through (19) can be used for estimating the lifetime of a non-solid aluminum electrolytic capacitor based on the ambient temperature, the rise of internal temperature due to ripple current, and operating voltage applied.

For a surface mount type or radial lead type capacitor :

Endurance specifications are defined by the rated voltage For a surface mount type or radial lead type capacitor :

Endurance specifications are defined by “the rated ripple current superimposition”. For a snap-in type or screw terminal type capacitor Lo : Specified lifetime (hour) at the upper limit of the category temperature range and at the rated voltage

Lr : Specified lifetime (hour) at the upper limit of the category temperature range and at the rated ripple current superimposed to a DC voltage

Lx : Estimation of actual lifetime (hour)

To : Upper limit of the category temperature range (℃)

Tx : Actual ambient temperature of the capacitor (℃) Use 40℃ if the actual ambient temperature is below it.

ΔT : Rise of internal temperature due to actual ripple current (℃)

*ΔTo : Rise of internal temperature due to the rated ripple current (℃)

*Kt : Correction factor of ambient temperature acceleration factor

*Kv : Derating voltage factor (a snap-in type capacitor with the rated voltage of less than 160Vdc and a screw terminal type capacitor with the rated voltage of less than 350Vdc :1)

*A : Acceleration factor of temperature-rise due to the ripple current(This factor depends on use conditions.)

For the values marked with * , consult us.

Please consult us about lifetime equations for the series of the category temperature 125℃ or more

Subject series : MXB, MHS, MVH, MHL, MHB, MHJ, MHK, GPA, GVA, GXF, GXE, GXL, GPD, GVD, GQB, GXA.

Note that the calculation results above are not considered as a guaranteed value. When designing the lifetime of a device, please select a capacitor that has an extra margin against the device lifetime requirements. Also, where the estimation result calculated exceeds 15 years, please consider 15 years to be a maximum. If 15 years or more may be required as an expected lifetime, please consult us.

##### 4 Charge and Discharge Operation Effect on Lifetime

Applying a voltage to an aluminum electrolytic capacitor makes the electric charges accumulate on the anode foil dielectric. Discharging the electricity through a discharging resistance makes the electric charges move to the cathode foil and cause chemical reactions between the cathode aluminum and electrolyte, thereby forming a dielectric oxide layerWhen this charge and discharge is repeatedly operated, the chemical reactions proceed to further form the oxide layer on the cathode foil, causing the capacitance of the cathode foil to reduce and thereby reducing the capacitance of the capacitor. Moreover, the chemical reactions bring heat and gases. Depending on the charge and discharge conditions, the internal pressure may increase, the pressure relief vent may open or the capacitor may have destructive failures. Consult us for using a capacitor with the following applications:

・Frequently repeating power on/off.

・Repeating rapid charge and discharge operations at a short interval cycle.

・Repeating charge and discharge operations with a large voltage drop.

Figures 23 through 25 show some test data of special-design capacitors for charge and discharge application, compared with general-purpose capacitors.

##### 5 Inrush Current

For the power supply inrush current that can occur on the start-up of a power supply or on the charge of a welding machine lasts only milliseconds, but its magnitude may reach 10 to 1,000 times more than the normal current. Usually, a single, non-repeated inrush current produces a negligibly small amount of heat, so it does not matter.However, frequently repeating inrush currents may heat up the element inside a capacitor more than the allowable limit and/or overheat the external terminal connections or the connections between the internal lead and foil electrode.

##### 6 Abnormal Voltage Effect on Lifetime

Applying abnormal voltage can increase the internal pressure with heat and gases produced, causing the pressure relief vent to open or the capacitor to have destructive failures6-1 Overvoltage

Applying a voltage higher than the rated voltage will cause chemical reactions (formation of dielectric) to occur on the anode foil with the leakage current rapidly increasing, which produces heat and gases and thereby increases the internal pressure. The reactions are accelerated by the voltage, current density and ambient temperature, causing the pressure relief vent to open or the capacitor to have destructive failures. It may also accompany a reduction in capacitance and an increase in tanδ as well as an increase in the leakage current, which can lead to internal short-circuiting failure. An example of capacitor overvoltage characteristics is shown in Fig. 26

6-2 Reverse Voltage

Applying a reverse voltage will cause chemical reactions (formation of dielectric) to occur on the cathode foil, and, as is the case with overvoltage, the leakage current will rapidly increase with heat and gases generating and thus the internal pressure increases. The reactions are accelerated by the voltage, current density and ambient temperature. It may also accompany a reduction in capacitance and an increase in tanδ as well as an increase in the leakage current. An example of capacitor reverse-voltage characteristics is shown in Fig. 27. A reverse voltage of as small as 1V can cause the capacitance to decrease. A reverse voltage of 2 to 3V can shorten lifetime due to a reduction in capacitance, increase in tanδ, and/or increase in leakage current. A reverse voltage of even higher value can open the pressure relief vent or lead to destructive failures (Fig. 27).

6-3 Do not Use Aluminum Electrolytic Capacitors in an AC Circuit

Using an aluminum electrolytic capacitor in an AC circuit will result in the same situation as that with a positive potential being applied to the cathode (like a reverse voltage) and with an excessively large ripple current flowing in the capacitor, which may increase the internal pressure due to the generation of heat and gases, open the pressure relief vent, leak the electrolyte with the rubber seal bung expelled or cause the capacitor to blow up or catch fire in the worst case. If the capacitor blows up, it may scatter flammable materials such as electrolyte and element-supporting wax materials, which can lead to short-circuiting of the device. Therefore, do not use aluminum electrolytic capacitors in any of the AC circuits.

If you have any questions or inquiries that do not apply to the above, please contact us at the following address.