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Sunday, September 26, 2010

Low Power Series : Battery Life Calculation

Battery has become the key source of energy in the Emerging Low Power Devices. It's important to note that the capacity is a limitation for batteries, so they need to be used wisely.
To help in this regard we would like to share our Battery Life Calculation Technique that we have used successfully in many of our projects.

# First of all let's start with the basics of identifying some of the key characteristics of any system that is battery driven:

- Cycle Time: t(p)
This is a unit time between any two subsequent wake-up(or Active Mode) or sleep(or Low Power Mode) timings of any battery driven device. This is also known as Operation Cycle.

- Sleep Time: t(sleep)
This is the total time within one operation cycle time of a battery powered device, where it consumes the least amount of energy( in terms of electric current ).

- Active Time: t(act)
This is the total amount of time within one operation cycle time of the battery device where it consume energy
more than it does in Sleep Time t(sleep)

Hence, t(p) = t(act) + t(sleep)

# Next, would be to determine the Operation Cycle:
We know that for every specific operation the device performs some tasks and then go back to Low Power mode. The rate at which this switching is performed determines the battery life and is also required to determine the Cycle Time t(p).

Let's take an example of a thermometer that needs to perform temperature measurement every hour in a Day
and for rest of the time it remains in low power mode.

So, Rate of Therm. Operation (in days) = 1/24 day

Since, there are 24 hours in a day and it needs to perform the measurements on an hourly basis.
Also expressing of the rate can't be directly in days , as it makes things difficult for embedded guys who deals
with Milli-seconds. Let us now convert the above mentioned rate in terms of milliseconds.

Rate of Therm. Operation (in mS) = (1/24)*24*60*60*1000 mS = 3600000 mS

Now, if you closely observe this rate is nothing but the Operation Cycle since it's exactly the distance between the two subsequent Measurements.

Thus, have been able to find our first parameter Cycle Time t(p) = 3600000 mS

# Next job is to find the Active Time t(act):
This is the time taken by the battery device to do it's intended function. It is important to note that this
time can be subdivided into multiple tasks on the basis of device current consumption.
Shown below is the current verses time graph for a typical battery powered device.

The time and current values of all these tasks are used to find the Energy Time Product(express in mAmS ) which can then be multiplied to voltage to obtain Energy Capacity(expressed in mAH ). To explain this we would take two examples - one from our prior Thermometer example and, another from a more complex embedded device example.

Let us consider that our Hourly thermometer needs to operate for 10mS
and would consume an estimate of 10mA

Then, Active state time t(act) = 10mS
Active State Energy Time product for Thermometer = 10mA * 10mS = 100mAmS 

Let us consider the Active time graph of the more complex embedded device.

Here we would like to tabulate the values in order to find individual Energy Time Products and the total Active Time t(act) Shown below is the graph depicting the same.

Time(mS) Current(mA)
1 5
2 2
3 3
4 1
5 1
6 2
7 1
8 1
9 2
10 3
11 3
12 1
13 1
14 2
15 5
16 6
17 2
18 1
19 1
20 2

# Next would be the Sleep Time t(sleep):
This is the time in which the battery powered device consume the least amount of power in terms of current drawn. In general the device would try to remain in this state for the maximum of the Operating Cycle in order to minimize the power consumption. However the actual power consumed by the battery
powered device can't be zero unless batteries are taken out. So this small consumption is what would again contribute to battery life. To explain this let's see the above two examples.

Let us consider that our Hourly thermometer would consume 10uA of current in it's low power mode or sleep mode.

Thus, Sleep time t(sleep) = t(p) - t(act) = 3600000 - 10 = 3599990mS
Sleep Sate Energy Time Product for Thermometer = 0.01mA * 3599990mS = 35999.9 mAmS

For the complex embedded device we would modify the the table to grab the various consumption levels into different tasks. The new table with a column for the Energy Time Product added.

The Next parts would be covered Later, Hope that this would provide some useful information on the Low Power Calculations. Let me know your feedback on this.

Warm Regards,

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