# PSUs 101: A Detailed Look Into Power Supplies

## Current Ripple Measurement On A Cap

Current ripple is one of the most important factors for measuring a cap's lifetime. Below, we will show you an example of how you can measure the current ripple on a bulk cap used in the APFC converter. We'll assume that the voltage ripple of a bulk cap is 5Vpp and that the ESR of this cap is 0.5Ω. To keep things simple, we will also make the assumption that ESR is kept constant (because ESR is frequency-dependent). We have to first convert the Vpp value to Vrms (Vrms = Vpp × 1/  √2= Vpp × 0.7071), so in our case we have:

(3)             Vrms = 5V × 0.7071 = 3.5355 Vrms

All we have to do now is use Ohm's law (I = V/R) and find the rms ripple current through the cap since we already know its ESR.

(4)             3.5355 Vrms / 0.5Ω = 7.071A

The above ripple current value is pretty high and will apply huge stress to the bulk cap. By using the equation P = I2 × R, we find that 25W (7.0712 × 0.5Ω) of power has to be dissipated, so the bulk cap will get very hot after a while. In this case, we need a very powerful cooling fan (which means increased noise levels) to help the bulk cap keep its temperature at acceptable levels. The most effective solution to restrict ripple current is to reduce ripple voltage and select a bulk capacitor with the proper ESR value.

## Electrolytic Cap Life Calculation

Having a way to easily calculate a cap's lifetime is very important. Here is the basic equation that we will use.

(5)                 L2 = L1 x (Vr/Vo) x 2x

In the above equation where:    x = (Tm-(Ta+ΔT))/10

Ta  represents the ambient temperature.
Tis the max rated temperature of the capacitor.
ΔT  is the temperature rise of the capacitor due to ripple current.
Vr  is the maximum voltage rating of the capacitor.
Vis the operating voltage of the capacitor.
L1  indicates the load life rating of the capacitor (provided by its manufacturer).
L2  is the calculated lifetime of the capacitor under the current operating conditions.

What is APFC?

APFC stands for active power correction factor and an APFC converter shapes the current waveform to make it match the voltage waveform. It also makes the PSU compatible with a wide range of voltage inputs.

Now, let's say that we have an electrolytic bulk cap with a 2000-hour load life rating, 420V max voltage rating and 105 °C max temperature rating. If we use this capacitor inside an APFC converter where the DC bus is around 380VDC, assuming that its internal temperature will be kept at 50 °C while the temperature rise of the cap due to ripple current will be 10 °C, its estimated lifetime will be calculated by the following equation:

(6)            L2 = 2000 x (420/380) x 24.5 ≈ 50,019 hours

If we assume that the ambient temperature is 40 °C, then we have the following:

(7)            L2 = 2000 x (420/380) x 25.5 ≈ 100,037 hours

The above example clearly shows that 10 °C difference in the operating temperature of an electrolytic capacitor can double or cut in half its estimated lifetime. In addition, caps with 105 °C rating have four times the life compared with similar specification caps that have an 85 °C temperature rating.