KVoltage (Effects of applying voltage to life):
Miniature and large sized aluminum electrolytic capacitors for popular applications, such as surface mount types, radial lead types, snap-in types and block types, have little voltage effect on their life. Other factors like temperature and ripple current determine the life in comparison with voltage, as long as the capacitors are used at voltages and temperatures within the specifications prescribed in the catalog. Consequently, KVoltage = 1 is used for these capacitors. 350V and higher screw-mount terminal types of capacitors for custom-made power electronics applications allow the lifetime to extend by applying low voltage, relating to the characteristics of their aluminum oxide layer. For Kvoltage values of the screw-monut products, please contact our company or sales agents.
KRipple (Effects of ripple current to life):
Aluminum electrolytic capacitors have higher tanδ than any other types of capacitors; therefore, the ripple current gives aluminum electrolytic capacitors higher internal heat. Be sure to check the rated ripple current which is specified in the catalog for assuring the life. The ripple current through the capacitor produces heat by dissipating power from the capacitor. This leads to temperature increase. Internal heating produced
by ripple current can be expressed by:
W = (IRipple)2 * RESR + V * I Leakage
Where:
W = Internal power los
IRipple = R.M.S. Ripple current
RESR = Internal resistance (ESR) at ripple frequency
V = Applied voltage
ILeakage = Leakage current
Leakage current may be 5 to 10 times higher than the values measured
at 20℃, but compared with IRipple, the leakage current value is very small
and negligible. Thus, the above equation can be simplified:
W = (IRipple)2 * RESR
The following equation gives the internal heat rise; it's heat rise to stable
condition. (It is necessary to input several factors):
(IRipple)2 * RESR = β * A * △T
Where:
β = Heat transfer constant
A = Surface area of can case
A = (π/4) * D * (D + 4L)
Where:
D = Can case diameter
L = Can case length
△T = An increase in core temperature by internal heating
due to ripple current
(△T = Core temperature - Ambient temperature)
From the above equation, internal temperature rise (△T) produced by
ripple current is given by:
△T = (IRipple)2 * RESR / (β * A)
When the ripple frequency is 120Hz, RESR at 120Hz is expressed by
RESR = tanδ / (ω * C)
△T = (IRipple)2 * tanδ / (β * A * ω * C)
Where:
tanδ = 120Hz value
ω = 2π * f = 2π * 120Hz
C = 120Hz capacitance value
As above equation, △T varies with frequency of ripple, frequency and temperature dependent ESR and application on dependent β (even ripple current is constant). We really recommend that customers measure △T with a thermocouple at the actual operating conditions of the application in lieu of using the above equation. (Another approximation of △T will be stated later.) As mentioned in the paragraph of Ktemp, aluminum electrolytic capacitors will slowly increase in tanδ and ESR during their service life. The application without ripple current has no influence on the life of the capacitor even though the ESR will increase during life. In other words, the application with ripple current makes △T increase; furthermore, a △T increase results in ESR increase. The ESR increase then makes △T increase. It is a chain reaction. Theoretically, the ripple current acceleration term (KRipple) cannot be simply expressed like the ambient temperature acceleration term (KTemp). Practically, the ripple current acceleration term (KRipple) can be approximately expressed by an equation using a △T initially measured. The following table shows the ripple current acceleration term (KRipple) for each capacitor design group. Note that a △T over a certain maximum limit may over-heat the capacitor, though the lifetime estimation will not give you practical lifetime. For instance, the following shows a guide limit of △T at each ambient temperature for 105℃ maximum rated products. Approximation of △T
Estimation of the lifetime requires two temperature measurements; first obtain △T by actually measuring the core temperature, inserting the thermocouple inside the operating capacitor and secondary, the ambient temperature. A more convenient way to get the △T is to convert the surface temperature of the capacitor case and the ambient temperature by using a coefficient specified for each case diameter as
tu following:
△T = KC * (TS - TX)
Where:
KC = Coefficient from table below
TS = Surface temperature (℃) of capacitor can case
TX = Ambient termperature (℃)
No air flow conditions
Also, you can roughly estimate a △T by using the following equation
without measurement.
△T = △TO * (IX / IO)2
Where:
△TO = 5℃ for 105℃ maximum rated capacitors
IO = Rated ripple current (ARMS); If its frequency is different
from operating ripple current IX, it needs converting
by using a frequency multiplier prescribed in the
catalog.
IX = Operating ripple current (ARMS) actually flowing into a
capacitor
Like switching power supplies, if the operating ripple current consists
of commercial frequency element and switching frequency element(s),
an internal power loss is expressed by the following equation:
W = (If1)2 * ESRf1 + (If2)2 * ESRf2 + --------- + (Ifn)2 * ESRfn
Where:
W = Internal power loss
If1 ---- Ifn = Ripple currents at every frequencies f1 ---- fn
ESRf1 ---- ESRfn = ESR's at every frequencies f1 ---- fn