The life of the power supply is determined by the shortest life of the components, and in general, the shortest life components may be aluminum electrolytic capacitors. The gradual evaporation of the electrolyte inside the aluminum electrolytic capacitor will cause all the characteristics of the capacitor to slowly degrade over time. The internal heating of the capacitor and the influence of surrounding heating components will accelerate this process. Although this process is slow, it will inevitably occur and ultimately determines the life of the capacitor.

It can be seen from the capacitor data sheet that the general rated life (Lo) is 2000~5000H. This life is obtained when the capacitor is working at the highest rated temperature (TR) with a typical value of 105℃ and working with a low frequency current (typically 120Hz) , The effective value of the current is equal to its ripple current rating IR.

When the ripple current IR flows through the capacitor, it will produce a certain optimal temperature rise between the shell and the surrounding environment, and the shell and the capacitor core, and the two temperature rises are often the same. The optimal temperature rise is 5°C for a 105°C capacitor and 10°C for a 85°C capacitor. Therefore, if a capacitor with a rated value of 105°C is placed in an environment of 105°C and the rated ripple current IR flows, the accurate value of its core temperature is 115°C. In other words, the so-called capacitor lifetime LO, for example 5000H, refers to the lifetime when its core temperature is maintained at 115°C.
The rule of thumb for doubling the lifespan is: for every 10°C drop in the core temperature, the lifespan doubles. However, the user cannot accurately estimate the life by measuring the core temperature, so the following equation is used to estimate the life L.

L=LO*2^(TR-TAMB)/10*2^(△To-△Tx)/5);
Capacitor rated life
Capacitor rated operating temperature
Ambient temperature around capacitor
Capacitor shell temperature
The optimal temperature rise between the shell and the core (105°C capacitor is 5°C)
Temperature rise from actual shell to core

It can be seen from the above equation that the lifespan doubles for every 10°C drop in the ambient temperature. If the actual temperature rise from the shell to the core exceeds the optimal temperature rise, the lifespan is halved every 5°C above the optimal value. The amount of heat generated by a capacitor is proportional to the square of the effective value of the current flowing through the capacitor, so the actual temperature rise can be estimated with the following equation:
△Tx=△To*（IA/IR）^2；
Actual effective value；
Rated effective value
In practical applications, the TAMB in the above formula can be replaced by TCACE due to the heating of adjacent components. This can provide a safety margin of 5°C when using a 105°C capacitor. The practical equation is:
L=LO*2^(TR-TCASE)/10*2^(△To-△Tx)/5);
For example：
470uF/16 capacitor, the maximum rated current in the specification is 0.68A@105℃, and the longest life is 2000H. The actual point temperature measured shell temperature data is 55.3℃, and the measured ripple current is 0.36A;
L= Lo*2^((105-55.3)/10)*2^((5-△Tx)/5)；
△Tx=5*（0.36/0.68）^2=1.4℃;
L=2000*2^4.97*2^0.72≈103250（Hours）=11.786（Years）；