Re: AA alkaline battery discharge curve

Hi Mike.

This is a very interesting question! There is a lot of great information about primary (non-recharchable) batteries at the Duracell technical bulletin page. Alkaline Manganese Dioxide (commonly called alkaline batteries) are known for their high capacity and long shelf life when compared to their conventional Zinc-Carbon counterparts. Alkalines are good candidates for long life operation.

Battery capacity is commonly expressed in Ampere-hours (Ah) or milliamp-hours (mAh). A "AA" alkaline battery like the Duracell MN1500, yields a nominal capacity of 2850 mAh. That means that if you draw 100 mA from this battery, it will last approximately 28.5 hours. This is far from the "magic equation" you are looking for because how a battery is drained is crucial to determining how long it will last. Even a "dead" battery will deliver some power. Duracell defines end of life as a terminal voltage of 0.8 volts, that's more than half of the initial terminal voltage.

There are a several ways to draw power from a battery: constant resistance, constant current, and constant power. Perfectly constant resistance circuits are not as common as one might think, even the resistance of a flashlight bulb varies with voltage. This means that the life of the battery is not a simple linear relationship because battery voltage and current draw will vary as the battery is drained. There are a few graphs that can be used to estimate battey life of a constant resistance circuit at the Duracell site. Constant current circuits are not very common, but battery life can be simply calculated by dividing the battery capacity by the current draw. Constant power circuits are the best way to get the most energy out of a battery. Constant power draw is usually accomplished by introducing a high efficiency DC-DC converter or switching regulator. Linear Technologies sells a number of simple, inexpensive devices for just this purpose. Using such a device, you can extend the life of a battery well beyond the reported 0.8 volt limit. Predicting life of a constant power system is not trivial and depends on the design of the switching regulator. One way to determine battery life in this case is to draw high power and measure the lifetime. From that measurement you can determine the total energy (power times time) capacity of your battery-regulator combination. You can then estimate life by dividing the total energy by the actual power draw.

Now for your specific circuit! You can determine the type of load presented to the battery by measuring the current as a function of supply voltage. I will assume that the circuit you describe appears as a constant current to the battery. In general, digital circuits do not behave as a constant current, but we can estimate the life using the average current draw. For a Duracell MN1500, the lifetime is slightly more that 4000 hours if we use an average current draw of 0.71 mA. This assumes your circuit will work down to 0.8 volts per cell, which is not the case. If your circuit will only work down to 1.05 volts/cell, we can interpolate the difference. 1.05 volts is roughly 30% more than the 0.8 volt limit, so the total lifetime will be roughly 30% less than 4000 hours or 2800 hours.

The above estimate assumes battery terminal voltage is linear with time, which is not necessarily the case here, but it's probably not far off the mark. If you need a more accurate estimate, drain a single cell down to 1.05 volts using a small resistor, say 100 Ohms. To find the lifetime of your circuit, multiply the 100 Ohm lifetime by the ratio of the resistance of your circuit to 100 Ohms.

If long lifetime what you are looking for, I would suggest adding a low voltage, high efficiency switchmode regulator to your circuit. This way, you can extend the usefulness of the batteries well below 1.05 volts/cell.

If you have any further questions, feel free to contact me at madhu@madhu.com