As portable devices become more capable, powerful and smaller, people expect them to have more features, perform better, and replace the functionality of multiple devices. However, while embedded performance has skyrocketed, battery performance has stayed relatively the same. This has forced developers and engineers to be much more conscious of power consumption.
The Simple Case
When discussing battery life and power consumption, average current draw is king. If certain electronics in a device draw a large amount of current, battery life can only be improved to a certain extent. There is no way to magically get more energy. The best case scenario is that a device’s battery life will follow this formula (Battery Life = Battery Capacity / Average Current Draw). This looks something like Battery Life = 300mAh / 1.2 mA = 250 hours. However, this assumes that the current draw is around the same level that the battery was rated for and that the current draw is constant. In almost all situations, this will not be the case.
In an ideal world this formula would always hold true, however the focus of this article will be all the cases in which this isn’t true and how to get as close as we can to this ideal state.
Battery Ratings and Battery Life Calculations
Any battery can be thought of as a voltage source in line with a resistor. This resistor is referred to as the internal resistance of the battery. At the beginning of its life, a battery has a small internal resistance and can supply large amounts of current with little drop in voltage. However, as the battery is depleted, this internal resistance increases to the point where drawing current from the battery reduces its voltage below a devices operating voltage. This means the battery is unable to power the device and is considered “dead”. The internal resistance of a battery tends to stay relatively constant for the beginning of its life and then increases rapidly. Therefore, measuring the behavior of a battery’s internal resistance over time is fundamental to the study a battery’s life or “relative capacity”.
When looking at a typical datasheet for a battery, there will some key points of information. The first will simply be the voltage and rated capacity of the battery. This is typically how people will reference the battery (e.g. 3 .0V 240mAh). It is important to note that this capacity should also have a resistance and end of life voltage listed with it to specify the conditions it was tested under (e.g. 240 mAh to 2.0 volts, Rated at 15K ohms at 21°C). A typical drain current may also be used in place of the resistance (0.19mA). Additionally, there may be one or more charts detailing the battery test showing a plot of battery voltage versus time under specific draw down conditions.
If there was a device with the same current draw characteristics as one of these tests, calculating its battery life would be as simple as looking at which point on the graph the voltage drops below the devices minimum operating voltage.
Using the battery sheet referenced earlier if we had a CR2032 battery powering a device with a constant resistance of 15K ohms and a minimum operating voltage of 2.4 V, it would have a battery life of 1200 hours.
In an ideal world one would know the exact current profile of a device and there would be a draw down graph for that profile and the devices battery. However, both are unlikely for anything beyond a very simple device. Therefore, it is important to be able to estimate battery life based on a standard graph or capacity rating, as well as know how different conditions affect battery life.
Effects on the Relative Capacity of a Battery
We now know that fundamental to the calculation of a device’s battery life is the change in the battery's internal resistance over time. So in order for us to estimate the device's battery life or the relative capacity of our battery, we need to know how different current draws affect our batteries internal resistance.
We will start with our best case scenario and go from there. In the best case we are drawing a very small constant current similar to the conditions the battery is rated under. Under these conditions we will get the entire capacity rated by the battery. So now let’s change some things.
This is the simplest case. If a device operates at a different minimum voltage than the standard rating we simply shift our end point along the rating curve (Lower voltage = longer life, higher voltage = shorter life). It’s also important to remember the quick decay in the battery voltage curve. o a change between 2V end of life and 2.1V end of life on a 3V battery will have very little effect on battery life since the resistance at this point is drastically increasing. However, if a device has an end of life voltage of 2.9 V on a 3V battery its battery life will be much shorter since it is not taking advantage of a large portion of the battery curve.
In this case the device is still drawing a constant current, but at a different level from the rated conditions. One might think that there is a purely linear relationship between current draw and battery life (e.g. Life = capacity/current), but this is NOT the case. The higher the current draw from the battery the quicker the internal resistance increases. So a 300mAh battery supplying 1 mA may last 300 hours, but when supplying 5mA will only last 50 hours which is less than expected (300/5 = 60 hours).
The last case would be if a device did not draw a constant current, but rather changed based on its active state. For example it may draw 9 mA for 1 second and then 1mA for 9 seconds. In this case, the average current draw will end up being 2mA over any extended period of time. However, this device will have a shorter battery life than a device drawing a constant 2mA. This is because the short period of time during which there is a high current (9mA) has a lasting impact on the resistance of the battery.
In any complex design it is likely for all of these conditions to apply. It is important to note that each has a compound effect on the final battery life and needs to be considered individually. So if a higher voltage decreases your batteries relative capacity by 5%, and a different current draw decreases it by 10%, and a variable current decreases it by 20%, our resulting device will only have a battery capacity equal to (.95x.9x.8 = .68) 68% of the rated capacity.
In summary, batteries are fairly complex things and behave differently in all sorts of conditions. Therefore, calculating battery life is not a matter of simply dividing the battery capacity by a devices average current draw. In this article we talked generally about how batteries are rated and the effects of different conditions on the battery. If you're interested, there are tons of other great resources and studies on this topic that can be found through a simple Google search. Specifically DMC used the two studies below on the CR2032 coin cell detailing behavior under high pulse draw conditions.
Coin cells and peak current draw
High pulse drain impact on CR2032 coin cell battery capacity
In part 2 we will take a look at how this all applies to a specific device.
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