Generally speaking, the lifespan of aluminum electrolytic capacitors is greatly affected by the ambient temperature, and its lifespan can be calculated using the following formula.
Where L: lifetime at temperature T
L0: Lifespan at temperature T0. Compared to temperature, the impact of step-down operation on capacitor lifespan is minimal and negligible. 2-2. Calculation of lifespan considering ripple current The superimposed ripple current causes heat generation due to the internal equivalent series resistance (ESR), which affects the lifespan of the capacitor. The heat generated can be calculated by the following formula: P=I2R………………..(2) I: Ripple current (Arms) R: Equivalent series resistance (Ω) Temperature rise caused by heat generation Where, △T: Temperature rise at the center of the capacitor (°C) I: Ripple current (Arms) R: ESR (Ω) A: Surface area of the capacitor (cm2) H: Heat dissipation coefficient (1.5~2.0x10-3W/cm2x°C) The above formula (3) shows that the temperature rise of the capacitor is directly proportional to the square of the ripple current and the equivalent series resistance ESR, and inversely proportional to the surface area of the capacitor. Therefore, the magnitude of the ripple current determines the amount of heat generated and affects its lifespan. The type of capacitor and the conditions of use affect the magnitude of △T. Generally, △T<5°C. The following figure shows the measurement of temperature rise caused by ripple current. Test results: (1). Lifetime formula considering ambient temperature and ripple current Wherein, Ld: lifetime under DC operating voltage (K=2, within the allowable range of ripple current) (K=4, when the ripple current range is exceeded) T0: maximum operating temperature T: operating temperature △T: center temperature rise (2) When the capacitor operates at the rated ripple current and upper limit temperature, the lifetime of the capacitor can be obtained by converting equation (4) as follows: Wherein, Lr: lifetime (h) at rated ripple current and maximum operating temperature △T0: allowable temperature rise of the capacitor center at the maximum operating temperature. (3) Considering ripple current and ambient temperature, the following formula can be obtained from equation (5): Wherein, I0: rated ripple current (Arms) at the maximum operating temperature I: superimposed ripple current (Arms) Since it is difficult to directly measure the internal temperature rise of the capacitor, the following table lists the conversion relationship between surface temperature and internal core temperature. Diameter ~10 12.5~16 18 22 25 30 35 Center/Surface 1.1 1.2 1.25 1.3 1.4 1.6 1.65 The lifespan calculation formula is, in principle, applicable to an ambient temperature range of +40℃ to the maximum operating temperature. However, due to factors such as the aging of sealing materials, the actual calculated lifespan is generally a maximum of 15 years. (Table 2-1 Lifespan Calculation Curve)
