20Oct 2014

Samsung recently announced their new Note 4 with a claim that it charges from zero to 50% in thirty-ish minutes. What is thirty-ish? Is it 31 or 39?  Motorola also announced that their newest Moto X will provide 6 hours of mixed use after only 15 minutes of charge. Mixed use, as Motorola defines it, includes a mix of actual use time as well as standby for an average user. Hmmm….this is not very specific! Let’s see if we can decipher some of these claims in this post and shed more light on what these handsets are accomplishing.

Let’s establish a few fundamentals that relate charge current, and consequently electrical power, with charge time. I will try to keep it simple enough for many readers to understand. 

First, we need to establish the C-rate. It should be fairly intuitive that more electrical current and power from the AC wall adapter into the battery should mean faster charging. To read the rating of your AC wall adapter, look at the fine print on the adapter itself and it will tell you the wattage (e.g., 5 Watts) and the output current (e.g., 1 A at 5 V). In this particular case, the charging current is about 1 A. This charging current should be measured relative to the capacity of the battery to establish charge time. For example, a charging current of 1 A will charge a 1,000-mAh battery far faster than it will charge a 3,000-mAh battery. So we define a new relative measure called the C-rate: It is the charging current divided by the capacity of the battery. So if the charging current is 1 A and the battery capacity is 1 Ah (1,000 mAh), then the C-rate is 1 A/1 Ah = 1 C. If the charging current is 1 A but the battery capacity is 3 Ah (3,000 mAh), the the C-rate is 1 / 3 = 0.33 C. The higher the C-rate, the faster the charging. So let’s take an example of a real-life smartphone: the iPhone 5S. Its AC wall adapter has an output rating of 1 A at 5 V (which you can read between the prongs of the little adapter cube). Its battery is rated at 1.55 Ah (1,550 mAh). You can’t see this unless you open your phone back cover; alternatively, you can google the capacity of the phone. So, the C-rate of an iPhone 5S is 1/1.55 = 0.65 C. So far, this should be fairly straightforward.

Second, let’s convert C-rate into charge times. This conversion table makes it quite easy.

Approximate charge times for a lithium-ion battery for particular charging C-rates.

So one can see that the higher the C-rate, the faster the charging. The numbers may vary a little from battery to battery, but these figures give you a fairly reasonable estimate.

Now, let’s go back to the Note 4 and see if we can decipher its claims. Samsung claims zero to 50% in  thirty-ish minutes. From the table, we see that 30 minutes would be equivalent to 1 C, but 39 minutes would be closer to 0.75 C. Given that the published capacity of the Note 4 is 3,200 mAh, the range of charging current would be 2.4 A up to 3.2 A. The corresponding AC wall adapter wattage rating would be in the range of 12 W up to 16 W. I have not seen yet an AC adapter for the Note 4, but if you have one, you can confirm the wattage and the charging current, and consequently the charge time.

For the Moto X, the claim is more tricky. The Moto X has a published capacity of 2,300 mAh. Motorola’s website claims that this capacity should last the average user up to 24 hours of mixed used. Therefore, if a 15-minute charge gives the user 6 hours of mixed used, one can estimate that this quick charge provides 6 / 24 = 25% battery capacity, or consequently, it will take 30 minutes to get to 50%. Based on the table above, this corresponds to 1 C or a charging current of 2.3 A, and a wall adapter rated at or near 12 W.