Capacitance calculation of supercapacitors

Source: Capacitance Calculation of supercapacitors

Recently, I was busy designing some hardware circuits, which used super capacitors. The formula for the super capacitor given online is:

Where U1 is the initial voltage of the supercapacitor, the U2 is the lowest voltage of the supercapacitor (the lowest voltage the system can accept), and I is the period of the current, T is the entire discharge time of the U1 into U2. ^2 represents the square. To tell the truth, I was using this formula to design the super capacitance capacity, but the system did not work very well, so I have doubts about this formula, seriously suspected that it is counterfeit. So self-proof, want to do embedded friends will use, take to share with you.

The energy storage formula for the capacitor is:

C is the capacitance, and U is the voltage at both ends of the capacitor plate.

The energy emitted by the capacitance from the voltage U1 discharge to the voltage U2 is:

I current of T-second is maintained during this period. During this period the voltage change is a function of time:

Then the energy released is:

After accumulating the integral, the simplification is:

To solve this one-dimensional two-time equation:

You can get:

Consider the physical meaning, choose a larger value as the actual value, and thus become the formula:

Welcome friends to shoot bricks.

Capacitance calculation for supercapacitors (RPM)