Factors affecting battery capacity and measurement solutions

With the advent of mobile phones, rechargeable batteries and their associated charge level indicators have become an integral part of our information society. They are as important to us as the fuel indicator in our cars has been for the past 100 years, with one difference: drivers cannot tolerate an inaccurate fuel indicator, while mobile phone users expect a highly accurate, high-resolution charge level indicator.

After many technical problems were solved, lithium-ion batteries did not begin mass production until 1997. Because they offer the highest energy density (volume and weight), they are widely used in a variety of systems from mobile phones to electric vehicles. Lithium batteries have some key characteristics that affect the amount of power they can hold, and battery packs must contain various safety mechanisms to prevent the batteries from being overcharged, deeply discharged, or reversely connected. Because lithium is very reactive and potentially explosive, lithium batteries must not be exposed to high temperatures. The anode of a lithium-ion battery is composed of carbide, the cathode is composed of metal oxide, and lithium is added in a way that minimizes the damage to the lattice, a process called implantation. Metallic lithium reacts strongly with water, so lithium batteries use non-liquid organic lithium salts as electrolytes. When a lithium battery is charged, lithium atoms ionize at the cathode and are transferred to the anode through the electrolyte.

Battery capacity

The most important parameter of a battery (besides voltage) is capacity, which is measured in milliampere-hours (mAh) and is defined as the maximum amount of charge that a battery can provide. The capacity is defined by the manufacturer as the value of a battery under specific discharge conditions, but the capacity will change after the battery leaves the factory. Battery capacity is related to battery temperature (Figure 1). The top curve shows the process of constant current and constant voltage charging of a lithium battery at different temperatures. From this curve, it can be seen that the battery can be charged with about 20% more power at higher temperatures compared to the charging data at -20°C. The two curves below Figure 1 show that the battery is more affected by temperature when it is discharged. These curves show the remaining capacity of a fully charged battery when it is discharged to the cutoff point of 2.5V at two different discharge currents. From these two curves, it can be seen that the remaining capacity of the battery is related to the discharge current and temperature. At a given temperature and discharge rate, the lithium battery capacity that can be obtained is the difference between the top curve and the corresponding curve below. Therefore, when discharging at low temperatures or high currents, the capacity that a lithium battery can provide will be greatly reduced. When discharging at low temperatures or high currents, the battery has a large remaining capacity and can be discharged at a smaller current at the same temperature.

Due to impurities in the electrolyte, there are undesirable chemical reactions inside the battery, resulting in power loss. Typical self-discharge rates of common battery types at room temperature are shown in Table 1. The speed of chemical reactions is affected by temperature, so self-discharge is temperature-dependent. For different types of batteries, self-discharge can be modeled by a parallel resistor that consumes leakage current.

The capacity of a battery decreases as the number of charge and discharge cycles increases. This change is quantified as the service life, which is the number of times a battery can be charged and discharged before its capacity drops to 80% of its initial capacity. The service life of a typical lithium battery is 300 to 500 charge/discharge cycles. The life of a lithium battery is also affected by time. Regardless of whether it is used or not, its capacity begins to gradually decrease after leaving the factory. At 25°C, this effect can cause a fully charged battery to lose 20% of its capacity per year; at 40°C, it loses 35%. For batteries that are not fully charged, this aging process is slower: at 25°C, a battery with 40% remaining capacity loses about 4% of its capacity per year.

The battery data sheet specifies the discharge characteristic curve under certain conditions, and one of the factors that affects the battery voltage is the load current. However, the load current cannot be modeled by a simple source resistance because this resistance depends on other parameters, such as battery age and charge level. Rechargeable lithium batteries exhibit a very flat discharge curve compared to primary cells. System developers prefer this feature because the voltage provided by the battery remains roughly constant. However, as the battery discharges, the battery voltage has almost no correlation with the remaining charge.

Simple does not mean "shortcut"

To determine the available charge in a battery, a simple sensing method is first required. The sensing circuit consumes only a small amount of power and allows the user to infer the charge level from the battery voltage (ideally). However, sensing the battery voltage can provide unreliable results because there is no clear relationship between voltage and charge. In addition, the battery voltage depends on temperature and dynamic discharge effects (a slight increase in terminal voltage when the load current is reduced). Therefore, it is difficult for a simple voltage sensing scheme to ensure that the charge level is better than 25%. The relative level of charge, usually called the state of charge (SOC), is the ratio of the remaining charge to the battery capacity. Determining this parameter requires monitoring the amount of charge flowing in and out - a so-called "coulomb counting" method. In practice, coulomb counting is achieved by accumulating the current flowing into and out of the battery. When measuring this current with a high-resolution ADC, it is usually necessary to use a small resistor in series with the battery anode.

Since it is impossible to determine the functional relationship between the battery SOC and some of the parameters mentioned above, the battery capacity has to be determined empirically. There is currently no detailed analytical model (with sufficient accuracy) to calculate the capacity under specific operating conditions (such as temperature, number of charges, current, etc.). Theoretical models are only applicable to certain conditions. In order to obtain relative charging levels, these models are used for specific conditions and calibrated as a whole. In order to achieve a sufficiently high power measurement accuracy, the model parameters must be continuously calibrated - using the so-called power "learning" method, combined with a coulomb meter, this method can achieve a power measurement accuracy of within a few percentage points. Power measurement solution

Modern integrated circuits can determine the SOC of rechargeable batteries of varying types, configurations, and applications. These chips achieve high accuracy despite consuming a small amount of supply current (60mA in active mode and 1mA in sleep mode). Fuel gauge chips are classified into three categories (Table 2). Because lithium batteries are the preferred choice for most applications, examples of fuel gauge circuits for lithium-ion and lithium-polymer batteries are shown here.

Coulomb counters, also known as battery monitors, are used to measure, count, and convert battery parameters, including power, temperature, voltage, number of charges, and time of use. Coulomb counters cannot measure variables and are not yet intelligent. The DS2762 in this category includes a high-precision 25mΩ current-sense resistor, and can also monitor temperature, battery voltage, and current, and communicate via the 1-Wire bus, allowing the microcontroller in the battery pack or host system to read all data. A flexible, low-cost system can be formed, but it requires considerable background knowledge and development work, and development costs can be reduced through software, models, and support provided by IC suppliers.

Another approach is to use a fuel gauge to count coulombs. This fully integrated solution can run fuel gauging with a learning algorithm and perform all the necessary measurements. Smart batteries often use fuel gauges for automatic monitoring. Using an integrated fuel gauge requires less development work and helps shorten time to market. The DS2780 is a fully integrated fuel gauge that allows the host to read the SOC through the 1-Wire bus and provides the necessary safety protection circuits for lithium batteries.

Another option is to use a programmable fuel gauge that includes a microcontroller, which provides considerable flexibility. For example, the MAX1781

, which integrates RISC core, E2PROM and RAM. Developers can implement battery modeling, fuel gauge programming and necessary measurements. Simple and accurate SOC indication can be achieved through the internal LED driver.

in conclusion

Fuel gauging for rechargeable batteries is a complex task due to the influence of multiple interrelated parameters. Simple measurements do not provide accurate results and are only suitable for some unimportant applications. By using off-the-shelf fuel gauge chips, high-precision and reliable fuel gauging can be achieved.