How to calculate iPhone battery capacity?

Taking the iPhone lithium-ion battery as an example, discuss how to calculate the battery capacity of a mobile phone? And theoretical knowledge related to lithium batteries.

1. iPhone lithium-ion battery

I recently found that my iPhone XS charges very slowly and the battery is not durable. As I turned on the battery health in the settings, I found that the maximum battery capacity of the phone was only 81%. It has been used for two and a half years so far. Why does the battery capacity drop? What is the cell phone capacity of the iPhone XS battery? Marking of battery capacity m A h mAhWhat does$m$$A$$h\; mean?$A series of questions followed. The picture below shows the battery health:

2. Lithium battery capacity

I need to find the phone capacity of the iPhone XS battery. ^{However, the introduction of power and battery 1} on Apple's official website did not list the battery capacity of the iPhone, which surprised me. Instead, Apple describes the iPhone's battery capacity in terms of how long a specific function (video, audio) is used. This is more friendly to consumers who are not very technically savvy in terms of their understanding of iPhone battery capacity. The power supply and battery are introduced as follows:

Later, out of the idea of ​​replacing the battery, I searched for a mobile phone battery that could replace the iPhone XS on Taobao. After some searching, I found that the merchant only listed the battery parameters of the iPhone 6P on the details page, so I got the following picture ² of the battery capacity of the iPhone 6P :

2.1 Calculation of battery capacity

In the iPhone 6P battery capacity picture, we focus on the rated capacity, standard voltage and charging limit voltage. We often come into contact with the battery capacity unit of rated capacity mAh, which is also a selling point advocated by major domestic mobile phone manufacturers. The rated capacity of 3100mAh means that the battery can work for 1h with a discharge current output of 3100mA. However, low-power devices such as mobile phones often do not work with the maximum discharge current, but select and run various required modules with low current to achieve long-term work. The standard voltage is the output voltage when the battery is working. The charging limit voltage is the battery electrolyte withstand voltage.

2.1.1 Battery output current

^{We reversely} deduce the usage time of iPhone 6P specific functions (video, audio) given by Apple’s official website , and we can get the output current of the battery when the iPhone 6P is working with the corresponding functions.

• Video playback, up to 14 hours ³ , output current:
  $$i=3100mAh/14h=221mA$$
• Audio playback, up to 80 hours ³ , output current:
  $$i=3100mAh/80h=38mA\_$$

From the calculation results, it is found that the battery output current of the iPhone 6P is 7 times greater when playing video than when playing audio, and it can be seen that the heating phenomenon will be more serious. This is consistent with our daily use experience.

2.1.2 Battery capacity conversion

In the battery picture, we find 3100mAh followed by 11.84 Wh, which is another battery capacity mark. We know that the calculation formula of power is: $P=U\ast I$ , the corresponding unit formula is:$W=V\ast A=V\ast mA\ast 1000$ . Then we can also get$The\; Wh$ unit formula is:
$$Wh=V\ast Ah=V\ast mAh\ast 1000$$

Put the battery standard voltage 3.82V and rated capacity 3100mAh (ie: 3.1Ah) into the formula, get:
$$x=3.82V\ast 3.1Ah=11.84Wh$$

In fact, both mAh and Wh can be considered as battery capacity. Since the battery is in the normal working process, ideally the standard voltage will not change, but only the current will change. Therefore, we use the change of current mAh to judge the change of battery capacity.

In the end, we all want to have a high-capacity battery so we can reduce charging anxiety when we're out and about. In order to increase the battery capacity, based on $Wh=mAh\ast V$ , we can increase$V$ or$mAh$ , thus increasing the battery capacity$Wh$ . But unfortunately, want to increase the operating voltage$V$ is very difficult because the upper limit of the lithium battery electrolyte withstand voltage is^4.5V. If the charging voltage is higher than 4.5V, the battery will be damaged. Therefore, the charging limit voltage 4.35v in the iPhone 6P battery capacity picture can be understood as the electrolyte withstand voltage of the battery. From a theoretical point of view, it is difficult to further improve the battery electrolyte withstand voltage. Therefore, in the actual battery production process, mainly by increasing$mAhto$ increase battery capacity$.$Such as various m A h mAhsold on Taobao$18650\; battery\; packwith\; mAh$$capacity$ .

How to increase $mAh$ , this needs to be explored from the working principle of the battery$.$

3. Working principle of lithium battery

As an excellent energy storage device, lithium-ion batteries are mainly composed of four parts: positive electrode material, negative electrode material, electrolyte, and separator . Among them, the positive and negative electrode materials can ensure the reversible intercalation and extraction of lithium ions in it , so as to achieve the purpose of storing and releasing energy. The electrolyte should have high lithium ion conductivity and extremely low electronic conductivity to ensure that lithium ions can conduct rapidly in the electrolyte and reduce self-discharge. The separator is in the middle of the positive and negative electrode materials, avoiding the short circuit of the battery due to direct contact between the two electrodes, and has good wettability to the electrolyte, which can form a migration channel for lithium ions. ⁵

The basic working principle of a rechargeable Li-ion battery ⁵ is shown in the figure:

When charging, Li+ comes out of the positive electrode of lithium cobaltate, and is embedded in graphite through the electrolyte and diaphragm. The electrons pass through the external circuit from the positive electrode to the negative electrode and are accompanied by the oxidation of Co3+ in the positive electrode material. The concentration of lithium ions in the positive electrode material decreases and the lithium ions in the negative electrode material Concentration rises. The discharge process is just the opposite. Li+ spontaneously escapes from the negative electrode, passes through the electrolyte and separator, and is embedded in the positive electrode material. Electrons reach the positive electrode from the external circuit and trigger the reduction of high-priced cobalt. ⁵

In the process of battery charging and discharging, there must be loss of positive electrode material, negative electrode material, electrolyte and separator. What is the relationship between the loss of these materials and the number of charge and discharge times? Discuss below.

4. Lithium battery working loss

Qian Dongpei et ^al6 conducted an experimental study on the relationship between lithium battery material loss and charge-discharge times in the lithium-ion battery capacity decay diagnosis method, and obtained the relationship between battery capacity and charge-discharge times Figure 6 is as ^follows :

In Figure (a), as the number of charge and discharge cycles (Cycle) of the lithium battery increases, the battery capacity (Capacity) gradually decays. After 200 cycles, the battery capacity has decayed to less than 80% of the initial capacity, and the rate of capacity decay gradually increases in the later period. . During the cycle charge and discharge process, the results of battery capacity decay and internal component decay are shown in Figure (b). As the number of cycles increases, the battery capacity decreases linearly at the initial stage of aging, but its decay speed is significantly accelerated after 100 cycles. $Q_{PE}$、$Q_{}$、$Q_{LI}$Significantly attenuated, where $Q_{LI}$Give $Q_{PE}$After the first 100 times of stable decay, it is similar to the battery capacity and presents an exponential rapid decay; $Q_{}$The approximately linear stable decay over the full cycle indicates that PE is more easily lost during cycling than NE active materials in Li-ion batteries. At the end of the battery cycle, the accelerated capacity decay is closely related to the loss of the battery's positive electrode active material and the loss of the battery's available lithium ions. ⁶

In this paper, the internal resistance changes of two batteries A and B after cyclic charging and discharging are also experimentally studied. The change of internal resistance of batteries A and B during cycle charging and discharging is as shown in Figure ⁶ :

It can be seen from the figure that the internal resistance of batteries A and B gradually increases during the cycle and is clearly divided into two stages, and the growth rate of internal resistance suddenly accelerates in the later stage of the cycle.

5. Conclusion and summary

This paper studies the cause of the loss of lithium-ion battery capacity of iPhone mobile phones from the principle level, and finds that the decline in lithium battery capacity mainly comes from the loss of internal electrode materials and electrolytes caused by battery cycle charging and discharging . At the same time, this paper presents the understanding of the battery capacity of mobile phones in the market, discusses the understanding and calculation methods of battery capacity mAh, and introduces the conversion formula of mAh and Wh.

6. References

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1. https://www.apple.com.cn/iphone-13/specs/#footnote-12 ↩︎

2. https://detail.tmall.com/item.htm？spm=a230r.1.14.16.51cd770fC1iZXf&id=653520372792&ns=1&abbucket=1&skuId=4941606031622 ↩︎

3. https://www.apple.com.cn/iphone/compare/?modelList=iphone13promax,iphone13pro,iphone6plus ↩︎ ↩︎ ↩︎

4. Zhang Jin. The development process and trend of mobile phone batteries[J]. Science and Technology Wind, 2015(23): 45. DOI: 10.19392/j.cnki.1671-7341.2015.23.038. ↩︎

5. Xiao Han, Chengkun Zhang, Hualong Wu, Youzhang Huang, Qingshui Xie, Laishen Wang, Dongliang Peng. Working Principle and Key Materials of Lithium-ion Batteries[J]. Metal Functional Materials, 2021,28(02):37-58.DOI:10.13228/ j.boyuan.issn1005-8192.20210001. ↩︎ ↩︎ ↩︎

6. Qian Dongpei, Jiang Jiongting, Yang Yueping, Wang Jiongeng, Dong Dong, Liu Shuangyu, Xu Junjie, Wang Danni.Diagnostic method for capacity fading of lithium-ion batteries[J].Journal of Materials Science and Engineering,2022,40(03):406-411.DOI:10.14136 /j.cnki.issn1673-2812.2022.03.006. ↩︎ ↩︎ ↩︎ ↩︎