Battery life calculation

Go To Last Post
11 posts / 0 new
Author
Message
#1
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Battery is 1000 mAh, Tiny44A in powerdown mode takes 5 uA current, after every 2 min it wakes up and sends data, current is 10 mA during 0.2 sec, after that it goes to powerdown mode. How can I calculate (theoretical) battery life, I got amazing 5 years, can it be correct.
Battery is lithium type (not rechargeable) what can be expected real life time.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

In a 2 minute period:
119.8s @ 5uA + 0.2s @ 10000uA = 599uAs + 2000uAs = 2600uAs = 0.00072mAh

In 5 years 5 x 366 x 24 x 30 = 1.4 million "2 minute periods"

So yes, in theory your cell might last 5 years.
You will have to see what the data sheet says about self-discharge or shelf life.

I bet that within your 5-year life, you will have humid or warm days that will affect the current.

You will also want to add extra features. So I suggest that you are realistic about the 'life'.

David.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Ok, thanks. System has already been running several months with button cell, I wondered if it never 'dies'.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

What's the requirement?

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

ana57,

To answer your question about calculating "theoretical battery life":

This is a classic Law of Conservation of Energy exercise. The well-established Law of Conservation of Energy states that energy can neither be created nor destroyed, it can only be transferred from one form to another.

In your case there is a certain quantity of "chemical energy" in the lithium battery which will be converted to electrical energy as the demand presents itself in the form of load current draw on the battery's terminals. Even though the specific dose of energy stored in the battery is held in the form of chemical bonds ( so called "chemical energy"), you can legitimately look at the battery as a vessel holding a certain fixed quantity of electrical energy. The most energy you can ever remove from this battery, slowly or quickly, is this fixed amount of energy. So, how much electrical energy is stored in your lithium battery?

Electrical energy is measured in Joules. One Joule is the energy converted to heat when 1 amp flows thru 1 Ohm for 1 second. Many beginners get Joules and Watts confused. Joules are a measure of energy, Watts are a measure of power. By definition Power is the transfer of energy per unit of time. In other words Watts = Joules per Second. See the distinction? There is no Law of Conservation of Power, but there is a Law of Conservation of Energy. In one sense Power is a derivative of Energy.

The colloquial use of the units of Watts and Kilo-Watts as indicators of energy adds to the confusion. We talk about a "2400 Watt Heater", but never a "2400 Joules per Second Heater".

In order to calculate the amount of energy in your battery, we need to perform some minor league mathematical gymnastics. But before we do that, let me state that the energy we are about to calculate is indeed, the "theoretical maximum"; however, lots of other factors come into play that will thwart attempts to take all of this energy from the battery.

Your battery is rated at 1000 maHr
, which is the numerical equivalent of 1 ampere-hour. Taken at face value this means your battery can deliver 1 amp for one hour at its rated terminal voltage (let's call that a steady 3.00 volts over the duration of any energy extraction period). So, in order to get a 1 amp draw on the battery to adhere to that 1 amp-hour rating, we need to connect a 3.0 Ohm Load to the battery. When we do that we have a current of one amp flowing thru the 3.0 Ohm resistor with 3.0 volts across its terminals. The power is easy to calculate here: either amps times volts (3 Watts) or I-squared times R = 1 x 1 x 30 (3 Watts).

3 Watts of power is the equivalent of 3 Joules of energy being delivered to the resistor each second. How many Joules is that in one hour (i.e. the "hour" in your 1 amp-hour rating)? That's simple, there's 3600 seconds in one hour, so the answer is 3600 seconds times 3 Watts = 10,800 Joules. That's your theoretical energy stored in the battery - 10,800 Joules. You can use those 10,800 Joules any way you like - by drawing 1 amp for one hour, or 1 milli-amp for 1000 hours, or 1 micro-amp for a million hours - but you'll only ever get a grand total of 10,800 Joules. The Law of Conservation of Energy - you can never beat it!

So your original question about "battery life", is a bit misleading. The primary parameter at play here is the amount of energy stored in the battery. The rate at which you "spend" that fixed amount of energy will determine the "life" of the battery. The question is equivalent to asking how many hours you will be able to drive your car with a full tank of gas.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Quote:
The question is equivalent to asking how many hours you will be able to drive your car with a full tank of gas.

You are correct but
I think I and David ended to correct (theortical) battery 'life' without joules.
I gave tank size (1000 mAh, not maHr), what is consumption in different driving situations (5 uA * 120 s + 10 mA * 0,2 s), so we can calculate (without calculating joules) how many hours I can drive with full tank.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

ana57,

You are correct but,

I was attmpting to point out that a battery is an energy storage device, it is not a maHr storage device.

Getting the correct numerical answer when solving an electrical problem is only part of the reward for the effort of analysing the problem. Understanding and manipulating the underlying physical principles and the interaction betwen those priciples, is more important in any analytical exercise.

One of Chuck's hard-learned Rules of Electrical Enginering:

You can be right more than one time in the same day for the wrong reason.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

I really do not understand your differentiation between Joules and mAH.

Surely a Joule is an watt-second ? ( or volt-ampere-second )

For a specific battery voltage: V you get VxA watts.
Likewise a battery (voltage V) with capacity in ampere-hours will be V x A x H or 3600xVxAxH Joules.

Since the voltage V is generally fixed by your application, you might just as well ignore the V in any comparison.

Yes, as far as I can see ana57's calculations are correct. You just have to apply a 'safety-margin'.

After all, you don't want your nuclear bomb to fail because the battery has run flat !

David.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

I promise to change battery after every 4 years so Chernobyl disaster wont happen in our new Olkiluoto nuclear plant :)

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

I would be happier with an annual maintenace replacement!

Designing 4 year service for a theoretical 5 year lifetime is a little risky. (especially if environmental conditions affect the lifetime)

David.

  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

david,

There is a huge fundamental & theoretical difference between Joules and maHr.

The joule is a measure of energy. Energy = Power x Time = volts x amps x seconds.

maHrs, or AmpHrs, are a measure of current multiplied by time. Show me a physics or EE text book where Energy = Amperes x Time.

MaH and AH are a calculational convenience, and a very handy one I agree.

But be careful in how you apply this convenience to an understanding of the underlying mechanisms at work in a battery.

The danger is that you'll take your conclusions from this relatively simple example, and try to apply them to a more complex problem where the assuptions about the implied equivalency of Joules and maH are not valid.

It's good to have the right answer, but it's even better to be right for the right reason.

Energy is one of those parameters we tend to play down a bit in the EE field. We are much more concerned with the amps, volt, ohms and seconds in our daily toils. Still all of these parameters and the laws that describe their relationships (Ohms Law, Kirchoffs Law, Nortons Law, etc) are all subservient to the Law of Conservation of Energy. A law of physics which is blatently scorned in newspaper advertizements for super-efficient Amish Space Heaters and ultra-high-MPH Chevy Volt automobiles.