TECHNICALNOTETECHNICAL NOTEALUMINUM ELECTROLYTIC
ALUMINUM ELECTROLYTICCAPACITORSCAPACITORS®

1 General Description of Aluminum Electrolytic Capacitors
1-1 The Principle of Capacitor
The principle of capacitor can be presented by theprinciple drawing as in Fig.1-1.
When a voltage is applied between the metal electrodes placed opposite on both surfaces of a dielectric, electric charge can be stored proportional to thevoltage.
Q＝C・V
Q : Quantity of electricity (C)V : Voltage (V)C : Capacitance (F)Separator sheet
impregnated with electrolyte
Anode foil

Cathode foil
(Virtually, electrode forcathode extraction)

Anodic oxide film
Natural air oxide film
Electrolyte(True cathode)Fig.1-2

1-2 Equivalent Circuit of the Capacitor
The electrical equivalent circuit of the aluminum electrolytic capacitor is as presented in the following figure.

tS

D1
R1

C1

R2C2L

R3

Fig.1-1

C. called the capacitance of capacitor, is expressed by
the following expression with the electrode area S[m2],the electrode spacing t [m] and the dielectric constantof dielectric “ε”:
SC[F]＝ε0・ε・——t
ε0 : Dielectric constant in vacuum (＝8.85×10­12F/m)
The dielectric constant of an aluminum oxide film is
7 to 8. Larger capacitances can be obtained by enlarging the electrode area S or reducing t.
Table 1-1 shows the dielectric constants of typical dielectrics used in the capacitor. In many cases, capacitor
names are determined by the dielectric material used,
for example, aluminum electrolytic capacitor, tantalum
capacitor, etc.
Table 1

DielectricDielectric ConstantDielectricDielectric ConstantAluminum oxide film

7 to 8Porcelain (ceramic)

10 to 120

Mylar

3.2

Polystyrene

Mica

6 to 8

Tantalum oxide film

2.5
10 to 20

Although the aluminum electrolytic capacitor is small,it has a large capacitance. It is because the electrodearea is roughened by electrochemical etching, enlarging the electrode area and also because the dielectric is very thin.
The schematic cross section of the aluminum electrolytic capacitor is as in Fig.1-2.

NOTE : ‌Design, Specifications are subject to change without notice.
It is recommended that you shall obtain technical specifications
from ELNA to ensure that the component is suitable for your use.

R1 : Resistance of terminal and electrodeR2 : Resistances of anodic oxide film and electrolyte
R3 : Insulation resistance because of defective anodicoxide film
D1 : Oxide semiconductor of anode foil
C1 : Capacity of anode foil
C2 : Capacity of cathode foil
L : Inductance caused by terminals, electrodes, etc.

2 About the Life of an Aluminum Electrolytic
Capacitor
2-1 Concept of Life Estimation

2-1-1 Estimation of life with minimal ripple current(negligible).
Generally, the life of an aluminum electrolytic capacitor
is closely related with its ambient temperature and thelife will be approximately the same as the one obtainedby Arrhenius’ equation.
T0−T̶
10………………(1)
L＝ L0× 2
Where L : Life at temperature T
L0 : Life at temperature T0))

CAT.No.2023/2024E

TECHNICAL NOTETECHNICAL NOTEALUMINUM ELECTROLYTIC
ALUMINUM ELECTROLYTICCAPACITORSCAPACITORS®

2-1-2 Estimation of life considering the ripple current.
The ripple current affects the life of a capacitor
because the internal loss (ESR) generates heat. The
generated heat will be :P ＝Ⅰ2R………………(2)WhereⅠ : Ripple current (Arms)
R : ESR (Ω)
With increase in the temperature of the capacitor:2xR
̶………………(3)Δ T ＝Ⅰ
A xH
Where Δ T : Temperature increase in the capacitorcore(deg.)
Ⅰ : Ripple current (Arms)
R : ESR (Ω)
A : Surface area of the capacitor (cm2)
H : Radiation coefficient (Approx. 1.5 to 2.0
× 10 -3W/cm2×℃)
The above equation (3) shows that the temperature ofa capacitor increases in proportion to the square of
the applied ripple current and ESR, and in inverse
proportion to the surface area. Therefore, the amountof the ripple current determines the heat generation,
which affects the life. The value of Δ T varies depending on the capacitor types and operating conditions. The usage is generally desirable if Δ T remains
less than 5℃. The measuring point for temperature
increase due to ripple current is shown below ;Measuring point)) )ー0ーTTΔT̶̶
1010
L ＝ Ld × 2×K)………………(4)Where Ld : Life at DC operation (h)at Upper category temperature
K : Ripple acceleration factor(K＝2, within allowable ripple current)
T0 : Upper category temperature (℃)
T : Operating temperature (℃)Δ T : Temperature increase at capacitor core(deg.)②The life estimation formula based on Guaranteed life
(when rated ripple current is superimposed at uppercategory temperature) is derived as follows bymodifying formula (4).

)

T̶
0ーT
L ＝ Lr × 2 10)))

T0ーΔTΔ̶
10×K………(5)Where Lr : Guaranteed life
(Life at the upper category temperature
with the rated ripple current [h])ΔT0 : Temperature increase at capacitor core,at the upper category temperature (deg.)③Life estimation formula considering ambient temperature and ripple current is derived as follows by usingequation (3) to transform equation (5) into equations
forⅠ, Ⅰ0, ΔT0.

))) )

Ⅰ 2
ΔT0T̶
0ーT
1ー ̶ × ̶Ⅰ
0
10 ……(6)10L ＝ Lr × 2×K

WhereⅠ0 : Rated ripple current at the upper categorytemperature (Arms)
Ⅰ : Applied ripple current (Arms)
Use below ΔT0 value at each category highest
temperature when calculating life expectancy usingequation (5) or (6).

Since it is actually difficult to measure the temperature
increase at the capacitor core, the following table isprovided for conversion from the surface temperature
increase to the core temperature increase.
Table 2-1
Case diameter

to 10

12.5 to 16

18

Core / Surface

1.1

1.2

1.25

①The life estimation formula that considers ambient
temperature and temperature rise due to ripple isderived as follows by modifying formula (1).

NOTE : ‌Design, Specifications are subject to change without notice.
It is recommended that you shall obtain technical specifications
from ELNA to ensure that the component is suitable for your use.

Aluminum
Electrolytic Capacitors

85: 10deg
105 to 135 : 5deg
150
: 3degPolymer hybrid type aluminum
Electrolytic Capacitors

105
125
135150: 15deg: 10deg: 10deg: 5deg

The life expectancy formula shall in principle beapplied to the temperature range between the ambient
temperature of +40℃ and upper category temperature.
(Temperature conditions below +40℃ are uniformly
treated as +40°C.)
The expected life time shall be about fifteen years atmaximum as a guide in terms of deterioration of thesealant. Also, please note that the calculation results
calculated by the above formulas (4), (5), and (6) are
not guaranteed values.
CAT.No.2023/2024E

L＝

TECHNICAL NOTEALUMINUM ELECTROLYTICCAPACITORS

2-2 Practical Examples of Life Expectancy

By using the life estimation formula (6), the capacitor's
guaranteed time Lr (category upper limit temperature T0,rated ripple current Ⅰ0 ) can be converted to operating time
L under actual usage conditions (temperature T, ripple
current Ⅰ).
When considering whether a certain capacitor can beapplied to a mission profile (a combination of multiple
conditions of temperature, current, and operating time) thatassumes actual use, calculate L for each profile condition
using formula (6), and it can be assumed that the capacitor
is applicable for profile conditions if the ratio of the total
value of actual operating time Lc to the total value of L (lifeconsumption rate Let) is within 100%.
(Since the calculation result is not a guaranteed value,please make a decision after thorough testing regarding
profile application.)[Calculation example]
Calculate whether the RKC series 80V1600μF (Data A) isapplicable to the mission profile (Data B).
Data A (Basic sample data)
Item: 80V 1600μF φ18 x 40L RKC series
T0＝ 135°C∆T0＝ 5deg＝ 3.82Arms at 135°C，100kHz
Ⅰ0
Lr(Guarantee ＝ 2000hours at 135°Ctime)
Data B (Mission profile)

Condition1

T(Ambienttemperature)

Ⅰ(Ripple currentat 100kHz)

Lc(Operatingtime)

120°C

3.00Arms

3000h

80°C

Condition2

Condition340°C

2.00Arms

5000h

0.00Arms

123400h[Condition2]
Calculate L2 (120℃, 3.00Arms) by using
T0=135℃, Ⅰ0=3.82Arms, Lr=2000h, ∆T0=5degC

L2 = 2000×[2] = 6461[h]{1-(3.00/3.82)2}×(5/10){(135-120)/10}×2Life consumption rate L et2 of actual operating time L c2(=3000h) against L2 is calculated as,

Let2 = 100×( Lc2/ L2 ) = 100×(3000/6461) = 46.4[％][Condition3]
Calculate L3 (40℃, 0.00Arms) by using
T0=135℃, Ⅰ0=3.82Arms, Lr=2000h, ∆T0=5degC

L3 = 2000×[2= 2048000[h]{(135-40)/10}{1-(0.00/3.82)2}×(5/10)

×2]Life consumption rate L et3 of actual operating time L c3(=123400h) against L3 is calculated as,

Let3 = 100×( Lc3/ L3 ) = 100×(123400/2048000)= 6.03[％]
Therefore, the total value Let_all of the life consumption rateof each profile is calculated as follows.

Let̲all = Let1+ Let2+ Let3 = 4.30[％]+46.4[％]+6.03[％]= 56.8[％]Therefore, since it is less than 100%, RKC series 80V1600μF
is presumed to be applicable to this profile.

[Condition1]
Calculate L1 (80℃, 2.00Arms) by using
T0=135℃, Ⅰ0=3.82Arms, Lr=2000h, ∆T0=5degCL1 = 2000×[2= 116400[h]{(135-80)/10}{1-(2.00/3.82)2}×(5/10)

×2]Life consumption rate L et1 of actual operating time L c1(=5000h) against L1 is calculated as,

Let1 = 100×(Lc1/ L1 ) = 100×(5000/116400)= 4.30[％]NOTE : ‌Design, Specifications are subject to change without notice.
It is recommended that you shall obtain technical specifications
from ELNA to ensure that the component is suitable for your use.

CAT.No.2023/2024E

TECHNICAL NOTETECHNICALNOTEALUMINUM ELECTROLYTIC
ALUMINUM ELECTROLYTICCAPACITORSCAPACITORS3 To calculate Balance when connecting inseries

3-1 Circuit layout
Circuit for connecting two capacitors (C1, C2) in series
and equivalent circuit can be illustrated as below figure.
Formula to calculate a balance resistance RB of below
figure is shown as follows.

®

If a＝0.8, 400(V)×2×0.8＝640(V) as an impressedvoltage.
If b＝2, R2＝b R1＝426(kΩ), LC＝0.94(mA).
Balance resistance RB will be.
RB ≦ 2×2×213(kΩ)(1−0.8)＝852(kΩ)(2×0.8)×2−1

4 Regarding Recovery Voltage
C1RB

R1RB

V1V

C2RBR2RB

V2Following are the preconditions of the circuit.
(V1＜V2)② V shall be a times V0×2. V＝2aV0(a＜1)③ R2 shall equal R1×b.
(b＜1) (1)① V2 shall be the rated voltage (＝V0).

3-2 Formulas to calculate [RB]3-2-1 Following formula can be established frombalanced condition.
V1

1 ＋ 1
＝ V2
R1RB

1 ＋ 1R2RB(2)

3-2-2 Following formula can be established frompreconditions.
(3)V2 ≦ V0V1 ＝ V − V2(4)＝2aV0 − V2(4’)
3-2-3 Put formulas (1), (3) and (4’) in formula (2).
bR1 ＋ RB
R1 ＋ RB＝V2R1 x RB
bR1 x RB
2abV0(R1＋RB)＝V2 {b(R1＋RB)＋bR1＋RB}
2ab(R1＋RB) ≦ 2bR1＋(1＋b)RB
Accordingly, balance resistance R
shall be thefollowing formula.
(2aV0−V2)RB≦2bR1(1−a)(2a−1) x b−1(5)• After charging and then discharging the aluminumelectrolytic capacitor, and further causing short-circuit
to the terminals and leave them alone, the voltage
between the two terminals will rise again after someinterval. Voltage caused in such case is called recovery
voltage. Following is the process that causes thisphenomenon :• When the voltage is impressed on a dielectric,
electrical transformation will be caused inside thedielectric due to dielectric action, and electrification
will occur in positive-negative opposite to the voltage
impressed on the surface of the dielectric. Thisphenomenon is called polarization action.
• After the voltage is impressed with this polarization
action, and if the terminals are discharged till theterminal voltage reaches 0 and are left open for a while,
an electric potential will arise between the two terminals
and thus causes recovery voltage.
• Recovery voltage comes to a peak around 10 to 20
days after the two terminals are left open, and thengradually declines. Recovery voltage has a tendency to
become bigger as the component (stand-alone basetype) becomes bigger.
• If the two terminals are short-circuited after therecovery voltage is generated, a spark may scare theworkers working in the assembly line, and may put lowvoltage driven components (CPU, memory, etc.) in
danger of being destroyed. Measures to prevent this isto discharge the accumulated electric charge withresistor of about 100 to 1kΩ before using, or ship out
by making the terminals in short-circuit condition bycovering them with an aluminum foil at the production
stage. Please consult us for adequate procedures.

3-3 Calculation Example
Calculate the value of the balance resistance in thecase of connecting two 400V 470µF ( LC standard
value : 1.88mA) capacitors in series.
R1 ＝400(V)＝213(kΩ)1.88(mA)NOTE : ‌Design, Specifications are subject to change without notice.
It is recommended that you shall obtain technical specifications
from ELNA to ensure that the component is suitable for your use.

CAT.No.2023/2024E

TECHNICAL NOTE

5 Electrode Foil Development Technology

5-1 Corrosion inhibition of cathode foil
Inactive treatment is implemented to ensure long life byinhibiting natural corrosion of the cathode foil. Fig. 3-1
shows its effects with values of the polarization
resistance inversely proportional to the corrosion rateusing the AC impedance method (FRA). This indicatesthat the cathode foil used in the High reliability capacitors
has the polarization resistance higher than that of theconventional capacitors owing to corrosion inhibition.

5104103102ReferenceFig. 3-15-2 Sealing material permeability of electrolyte
To ensure long life, a low permeable lactone solvent forthe sealing material is used as the main solvent of theelectrolyte of the High reliability capacitor. Fig. 3-2 shows
the test results on the permeability obtained by changing the weight of the capacitors produced with different
types of electrolytes at a high temperature.
; High reliability capacitors; Amidic solvent

100100101020001000
Time (h)Fig.. 3-35-4 Long-time stability of electrolyte
The electrolyte used in the High reliability capacitor is stable with low initial resistivity and small secularchanges at a high temperature. Fig. 3-4 showschange in resistivity at 105°C.

1000

5-5 Dielectric formation voltage and leakage current
characteristics of anode foil
To increase the operating life by controlling the gas
generation inside capacitor because of 1.5 to 2 times
the rated voltage, while that of the previous capacitor
is about 1.3 times the rated voltage.
100

2000

1010.1Time (h)1Fig.. 3-2

NOTE : ‌Design, Specifications are subject to change without notice.
It is recommended that you shall obtain technical specifications
from ELNA to ensure that the component is suitable for your use.

1.5

2

2.5

Voltage ratio

Fig. 3-5

5-6 Lowered ESR of Electrode Foil
To reduce the ESR of electrolytic capacitor, we have
improved our chemical conversion technology foranode foil to develop lower ESR electrode foil comparedto the conventional product as shown in Fig. 3-6; High reliability capacitors

10ESR Index

5-3 Airtightness of sealing material
Since the electrolyte is stable for hours, the key element
for capacitor’s life is the sealing material. By optimizing
the crosslinking density of the sealing material polymer,
the sealing material of the High reliability capacitor attains
its long life with electrolyte permeability less than that of
the conventional capacitors.
Fig. 3-3 shows the test results on the airtightness ofthe sealing material obtained by changing the weightof the capacitors at a high temperature, producing
capacitors with the conventional sealing material andimproved one both containing the electrolyte used in
the High reliability capacitor.

2000

Fig. 3-4LC (µA)
1000

100

Time (h)101; Reference

2000; Lactonic product

0; Reference; High reliability capacitors

High reliability capacitors

Exponent of weight changes; High reliability capacitors

Exponent of resistivity

Resistance (W)(Ω)
10TECHNICAL NOTEALUMINUM ELECTROLYTIC
ALUMINUM ELECTROLYTICCAPACITORSCAPACITORS

Exponent of weight changes®

; Reference

0.50205080105Fig. 3-6 ESR Index of Anode Foil

CAT.No.2023/2024E