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Updated: 2022-10-13

Or how to recharge the battery of your smartphone up to, let say, 90% by using a cheap constant voltage power adapter and so prolonging the life of your smartphone.

As many on the Internet suggest, fully recharging the Li-ion battery of your smartphone is not the best way to prolong its life. The suggested optimal top re-charge level varies between 85% and 90% depending on the author. Here I'll assume 90% as the top recharge level for my Xiaomi Redmi 10. Since the device comes with only a cheap constant voltage power adapter, the only way to stop the recharge to a specific level is by timing the recharge time. The problem is, how much time it will require to re-charge if I start from a given lower level?

By monitoring the time it takes to reach 90% of the full charge starting from different lower levels, I first collected all the data and I drawn a time-vs-level curve. From that heuristic curve, I then created the following model for the power adapter and battery set:

Although very simplistic, this model demonstrated to work perfectly. The power adapter provides a constant tension v_{0} of about 5 V. The battery is modeled as an ideal capacitor C with an internal resistance R_{i} which might include the output resistance of the power adapter as well. From that model, and after some calculations, I obtained the following analytic formula for the recharge time from a given level r_{1} to a given level r_{2}:

t_{R}= C R_{i}log((1 - r_{1}) / (1 - r_{2}))

The value for the time constant CR_{i} must be found experimentally from the data collected; in my case its value is 31 minutes. So for example, having to recharge the battery from r_{1}=55%=0.55 up to r_{2}=90%=0.90, the required recharge time is 47 minutes. The following chart, drawn by using the formula above, perfectly matches the heuristic data and then confirms the validity of the model:

From the model, the charging current could also be calculated with these formulas:

i(t) = v_{o}/R_{i}e^{-t/(CRi)}

i(r) = v_{o}/R_{i}(1 - r)

being t=0 the time when the re-charge started, and r the current charge level. Finally, the power dissipated over the internal resistance of the battery could also be calculated:

P(t) = R_{i}i(t)^{2}

P(r) = R_{i}i(r)^{2}

By assuming the internal resistance of my battery be R_{i} = 1 Ω, the charts of the current and dissipated power can also be drawn as functions of the elapsed time or as function of the current charge level:

Why all this could be useful:

1. Prolong the life of the battery avoiding overheating during the re-charge process.

2. Monitor the performances of the battery over time: the faster it charges, the less charge it holds.

3. If the charge left is below say 40%, then the re-charging process should proceed by steps no longer than 5 minutes, leaving the battery to cool down between each step; these steps should be repeated up to around 50%; from there on the charge can proceed normally up to 90% without the risk of overheating the battery.

4. Avoid leaving the left charge to drop below 50% before recharging; this implies to recharge the phone every 2 or 3 days, depending on the usage.

5. Do not leave the phone on charge permanently; instead, use the chart or the formula above to determine the expected recharge time to reach 90%; set an alarm clock to signal the end of the process.

Umberto Salsi |
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