Hi Welcome to the Eev Blog an Electronics Engineering Video blog of interest to anyone involved in electronics design. I'm your host Dave Jones Hi. There's one very misunderstood aspect of electronics, and that's the Humble battery. or, more precisely, battery capacity.

How much energy does one of these things hold? How much current can you get out of it for How long? How long can you power your device for? How do you do the calculations? Well, it's a very good question, and a lot of people don't know the finer details of it. So I Thought we'd have a tutorial on battery capacity now. I'm sure everyone's familiar with a standard double a rechargeable battery and look at the number on it 2300 and I'm sure you're familiar with that figure. You know 2300 milliamp hours, 2800 milliamp hours And you think that's the capacity of the battery measured in milliamp hours? Well, is it? Well, not really.

There's a lot more to it. That figure is very nominal figure. It's borderline. So what is the capacity of a battery? Well, the battery capacity is the ability of a battery to supply a constant current or a constant amount of energy into a load for a given amount of time.

Simple as that. So, how do you characterize battery capacity? Well, You can do it in two different ways. There's two ways to specify it. The first and probably the most common is you've probably seen it amp hours or milliamp hours that specified ah or maah, as the case may be.

Now, this isn't strictly the correct way to specify battery capacity because it makes some assumptions. It assumes that, uh, it's it. It ignores, totally ignores the voltage change in the battery, and it assumes that you've got a constant current load and not all loads are like that, which we'll go into. But basically the capacity.

Let's say a battery is rated for one amp hour here. Well, that means it can deliver one amp for one hour, or it can deliver 0.1 amps for 10 hours and so forth and so forth as you go as you drop in current. Usually that's the upper limit sorry, one amp hour battery. You might be able to draw two amp hours from it, but the performance the capacity is going to be much less.

And the second way to define battery capacity is in what's called Watt hours or W H and you can get milliwatt hours and stuff like that as well. Same for milliamp hours up here. Now this is the true, the only true way to measure the actual capacity of the battery because you're actually measuring the true amount of energy in there because it takes into account the current and the voltage Watts V times I Ohm's law, right? So um, it doesn't make any assumptions at all. it's the true capacity and it's the same thing for milliamp hours up here.

What if you're if it's specified if you've got a one watt hour battery, it means it can deliver one watt for one hour or 0.1 Watts for 10 hours and so forth. And once again, you can go higher than that. A one watt hour battery. You might be able to draw two Watts for half an hour, but probably not.

It's usually going to be less than that. So measuring in milliamp hours capacity millionaire Powers is only valid if you assume that the battery voltage is constant. Now let's take a look at this. It all comes down to What's called the discharge curve or the discharge characteristic curve of a battery.

Now, there's lots of different batteries out there. lots of different Technologies and the curves. The characteristic curves will all be different shapes, but they will all have a characteristic curve. No battery is perfect.

Now take the case of an ideal battery. Okay, what a discharge curve is is the battery voltage on the y-axis in volts. In this case, 1.5 Volts For you know, a double A a standard single cell. Um, alkaline cell everyone's familiar with versus time on the x-axis Now, an ideal battery in this case is the one in red.

It will start out at 1.5 volts and it will stay at one point 5 volts for all of the time that you are discharging, pairing your product, Then all of a sudden just die and drop straight off. That's called a brick wall response. An ideal brick wall response. No battery will even ever come close to giving you that it'll have a characteristic curve, which is this green line down here.

and it'll start out at say 1.5 It'll drop fairly quickly, it might flatten out and all go a bit, that will just drop at a linear rate for a while and then curve off right at the end. And that's the True Performance. Now, as you'll see with this laptop battery, its capacity is rated in milliamp hours and also in Watt hours as well. What does that mean? What's the difference? Well, there's not really much difference in this term in for this actual application because what they do to calculate the Watt hours is they just take a nominal voltage figure they don't actually take into account.

they they just choose is a nominal figure in the middle of the curve. Here, somewhere they don't actually take into account the full change in voltage usually anyway, so there's not much difference. But what hours is technically a better way to rate battery capacity. Or it's also the way that they actually rate the different Technologies Alkaline Nickel Metal Hydride Lithium Ion Lithium Polymer All that sort of stuff.

It's um, the capacity of those type of batteries and those battery technologies is rated in uh, what hours per something? So it's Watt hours per kilogram of battery material. So just how much energy is in your humble double? A or AAA Battery Well, it might surprise you. In fact, it might surprise you a lot now because we're talking what hours? What out? That's energy. So we can also talk joules as well.

It's a direct relationship now. One Jewel here here equals one what second, not watt hour. So uh, to get your energy in joules, you have to multiply your watt hour figure by 3600 because it's 3600 seconds in an hour. So if you do that and you look at a double, a triple A and a double A battery, your AAA Battery 1.4 Watt hours.

Maybe you know it varies a lot as we'll go into. um, and that's equivalent to about 5 000 odd joules are thereabouts. a double A battery 2.5 Watt hours roughly. or nine thousand joules.

Okay, don't even mention your huge uh D cell battery or something like that. These tiny little batteries. Now to give you an idea of what many, many thousands of joules can do, you may have seen this video before my friend. Doug Ford and I blew up, blew the out of a multimeter with 400 joules.

Let's try 400. A battery has over 10 times that amount of energy in it. It's incredible. So why can't you, uh, blow up a multimeter into flames and make it explode with AAA Battery Well, it all comes down to the internal resistance.

so internal resistance of a battery limits its capability to get the energy out of it and to do some serious damage. Even though there's a massive amount of energy stored in the chemicals in these batteries. A humble AAA or double A battery. A massive amount of energy.

You can actually extract it. If you actually extracted the energy out of this and stored it in a massive big capacitor bank at large voltages with very low ESR and it's able to dump that energy, then you can well and truly blow a multimeter or something else to dust with. AAA Battery It's amazing. So how do you actually measure the capacity of the battery? Well, if you look at the discharge curve again, that's the green one.

here. The capacity of any battery is the total area under that curve, and you know, and you may know that the area under the curve is an integral. So if you know how to do your integrals and you've got the actual data, you can do an integral of it. but we won't do that the other.

um, the easier way to actually do it. The more traditional method is to log the voltage and the current from the battery for a given load. so it must be at a given load, and then you measure the voltage and the current at regular intervals all the way along, and then you can calculate from that the total watt hour capacity of the battery and that's how it's traditionally done. What actually is the difference between the watt hour capacity and the amp hour capacity? Is there any major practical difference in practice? Well, the answer series.

Not often. That's why a lot of batteries will be specified in Amp hour capacity and their discharge will be assumed to be a constant current load. Now, the reason for this is fairly simple. Now, we've already mentioned that the true capacity of a battery is measured in Watt hours and it's the total area under the curve under the green discharge curve there which makes sense.

But if you want to make the if you want to measure the or specify the Amp hour capacity of a battery, then you just assume a nominal voltage like that across there, you know it might be 1.2 volts or something like that now. Uh, and for a nominal uh, constant current load as well. Now what happens in that case? when you make those assumptions, you're actually measuring this area in here, which you normally shouldn't be. Okay, so there's going to be some extra capacity there, but you're not measuring this one up here so they can kind of sort out cancel each other out in terms of area.

So that's why the constant current uh, amp hour capacity at a certain constant current load might often be similar to the watt hour capacity or the true capacity of the battery. So what sort of things can affect battery capacity? It turns out there's quite a lot of things that can actually affect it. Number one, and we'll go through all these in detail later. But number one, The cutoff voltage that you choose to use in your circuit Or the product.

You've got Number two: The temperature of the battery. Not just the ambient temperature, but we'll go into that, the discharge current, or the discharge power, or whatever you determine the discharge rate. The shelf life of the battery will affect it as well. If it's a two-year-old battery, it will have lost some of its initial capacity and then you've got the self discharge as well.

Some batteries are a lot better than others self discharge and that's tied into shelf life there as well. So let's look at these. Okay, now let's take a look at some real data sheets. I've got an Energizer double A Here, it's an alkaline double a standard Energizer You know it, you've used it.

And let's take a look at the effect of the cutout voltage on your actual product. So if you're actually designing a product and let's actually take a look at the discharge, A typical discharge curve right here. Now, if you're actually designing a product, here is here is the voltage of the battery. Now, if you design your product to cut out at, say, or give you a low battery warning error at say 1.1 volts here, then Bingo Look at all this capacity under the curve here that you're throwing away.

You're just pissing away all of that battery capacity. Now it gets even worse if you do 1.2 look at 1.2 volts. If you set it to cut out at that, you're wasting half of your battery capacity. It's crazy.

So a well-designed product will have as low a cutout voltage as possible, and for an alkaline, that's about 0.8 volts. A superbly designed product will operate all the way down to 0.8 volts per cell. So when you're actually designing your circuit to work off double A or AAA alkaline cells or primary cells. These are the voltages that you should design your product to work down to.

Ideally, if you want to use the most capacity inside this battery that you can, then this is what you should do for a single cell. 0.8 volts as I said, because that just drops off like a brick wall down at 0.8 volts there. So, but a two cell design normally three volts 1.6 volts is there is what you want it to work down to. three cell and four cell and nominal six volt system.

3.2 volts down to and a six cell system or your standard nine volt. uh, battery like this. Ideally your product should work down to 4.8 volts and this is why in my product reviews you will see that I actually measure the uh, the cut out voltage of the battery. So if a multimeter is working from this nine volt battery and it's cut out voltage is you know 6.5 or 7 volts as some of them are or even higher then they're just pissing away a ton of capacity in the battery.

It's crazy. Don't do it. Now one of the big things that affects batteries, particularly alkaline cells, is the temperature. Not just the ambient temperature, but the temperature of the cell as well.

and in particular low, uh temperatures. Now this is the Energizer L91. It's a double A but it's one of these Lithium. It's a lithium ion disulfide battery and you've probably seen it.

You've probably heard how great they are and how they work it at low temperatures and how they work at higher discharge currents and all that. But they've actually got some, uh, some? Well, they've got some charts down here for the temperature and let's take a look at them where they compare the this Lithium to a standard uh, alkaline cell. Now these dark bars here represent the Lithium battery and these ones and the other one there represents the alkaline. And as you can see, this is at cold temperature here zero degrees C and this is at room temperature 21 degrees C Over here.

Now as you can see at room temperature at this different discharge currents, you can see how the Lithium totally outperforms the alkaline cell. But the interesting thing to note is that notice the level of the alkaline cells here here here and here. Now that's at room temperature 21 degrees. Once you take them down to zero degrees, look, they're really dropped.

They've more than halved so you're losing a lot of Your Capacity especially at the high discharge temperatures. Now, that's pretty obvious when you take a look at the reason for it. Pretty obvious if you take a look at a temperature curve here. basically the series resistance in the cell versus temperature on the X-axis Here this is positive temperature This is 40 degrees up here and minus 40 degrees down here.

you'll see that as the temperature decreases, the series resistance in the cell increases. so you're going to lose capacity due to your IR increasing. And of course, the discharge current affects the capacity greatly as well. Now as you can see, we've got the capacity of the battery in milliamp hours up here from zero to three thousand and different discharge currents 25 milliamps up to 500 milliamps.

As you can see at 25, uh, 25 milliamps, quite low discharge current for a double A battery, it's capacitally. its capacity is a nominal, say 2 800 milliamp hours and that's the figure that you'll typically hear about. But hey, if you go to 500 milliamps in, the capacity is look, it's only about 1200 milliamp hours a big difference. And if you take a look at shelf life here, then you can see that after it's got after seven years from the data manufacture at 21 degrees C, it's only going to have 80 percent of its initial capacity.

Now that those figures aren't often true, it depends on the actual manuf, the manufacturing quality of this particular batch of it. You can't always rely on that figure strictly, so take it with a grain of salt. Now comes the big reason why batteries have the discharge characteristic curve that they do, and why it's not ideal like that. it's because of the internal resistance of the battery.

Now, the internal resistance or the IR are sometimes called the ESR of the battery. The equivalent series resistance is actually made up of two different types of resistances in series. One is the electrical resistance and that's like the internal metal contacts and things like that internal to the construction of the battery and the other part is the ion. What's called the ionic resistance or the electrochemical reaction inside the battery and that's uh to do with the electrolyte.

you know the conductivity of the electrolyte, the surface area of the electrode, and polarization, and that sort of stuff. and this one acts much slower than the electrical resistance. The electrical resistance will actually um will always be there, bang straight on, but the ionic resistance has a bit of lag so it will only show up under Um under pulse conditions. Now as you can see, this is Uh, the data sheet for a CR2032 coin cell battery which you're all familiar with and it just happens so happens to have a pulse characteristic graph like this.

which actually Uh is the method used to measure these two different types of resistances down here. and you can actually see when you apply a pulse like this. This is the battery voltage in volts up here and this is time over here. and as you can see, if you apply a pulse bang here then it drops down suddenly and that part there.

The very steep part is the electrical resistance down here which works straight away. Okay, it's always there and then the ionic. Then after some time the ionic resistance will kick in and and go like that. It'll take some time, but it'll eventually settle down to a fixed value and the total IR that you see in the graphs here.

here's a graph of the IR versus the Um versus the characteristic Uh. Characteristic Discharge Curve Uh, you'll see that the IR is just one particular value, which they'll actually specify up here in the data sheet. There it is typical: IR will start out at 10 ohms and increase to 40 ohms at the end of its life. Now what I love about this particular discharge characteristic graph is it shows beautifully.

It's Splendid how the IR increases at the same rate as the characteristic discharge curve decreases now. I've actually made a transparency of this look Okay, now it's no coincidence that if we flip that over, look what happens. It matches the discharge characteristic curve almost exactly. Magic, huh? And of course, when you're talking about battery capacity, the load type is all important.

Now there are three different types of loads, and you might see these three types. In fact, you might see all three types on a particular data sheet for a battery. Now, the most common is the constant current load type. Now the second type is the constant resistance type and as it says, it's a resistance.

So to test that, they literally put you know a 10 ohm or 100 ohm resistor across the battery and that's it. Well, most circuits aren't going to be constant resistance. are they really? You know they're going to actually be constant current. Or the third type which is constant power.

Now, this is probably the most, uh, accurate one for most circuits. You're going to actually design most products, which is why the watt hour capacity. Because what hours is power? Okay, what his power. So the constant power graph might be more important for you.

If you've got a DC to DC converter circuit driving driving your particular circuit, then you probably might want to look at the constant power graph instead of the constant current or constant resistance characteristic graphs. And in a previous blog I've showed how you can design a simple dummy load that can actually do all three of these in one. It's just got an Op-amp A Fat and a load resistor down here. and by hooking the in my example in the previous blog I Just hooked this up to a voltage source of pot and that just worked as a constant current load.

But if you hook up if you feed this back, if you feed the voltage back to a micro controller and you actually control the input if you feed via a DAC. So if you use an intelligent micro in there, you can actually by doing some simple Ohm's law calculations on the Fly and actually changing this as the thing discharges, you can generate a constant resistance or a constant power in this load. So this is a pretty handy way to measure battery capacity. and there's actually a fourth type of load as well.

and that is the pulse load. And the pulse load can actually apply to any three of these types. and it just means that they'll typically have If this is, uh, say current up here, then they might actually pulse it like this. They might have a steady low current down here and pulse it to a high current periodically.

and as you can see, a good data sheet will actually have constant power performance curves and will also have constant current performance curves. And down here. it's got these what they call industry standard tests and they're based on Old You know, transistor radio kind of things and they're actually constant resistance tests in this case, 43 ohms for four hours per day and stuff like that. They give service hours so you need to pick the performance graph that you think is acceptable.

Uh, for for the particular type of load that your product is going to represent. So how do you calculate the battery life of your particular product? Well, as I said, you've got to pick the type of load which is typical of your product: Constant current, constant power, constant resistance, Whatever. Maybe a combination. Maybe it's got some pulse stuff as well, but generally speaking, it's actually pretty darn hard to get a really accurate uh estimate of the battery life for your product based on just the Uh characteristic Curves in the data sheet.

Really, if you're serious about it, there is no substitute for actually measuring the actual battery life in your actual product, and often that is just what you have to do. You simply don't have enough data available to actually make a true calculation. so you've just got to suck it and see. I mean sometimes you can just you know.

Rules of thumb, ballpark stuff. You know, if a batteries you know 2 000 milliamp hours and you know it's going to roughly or 50 milliamps plus minus 25 Something like that, you can assume it's constant current and you can just well do the simple figures and calculate it's going to have X amount of life. And typically those ballpark figures are usually pretty good. You might drop it down by you know, 30 or calculate it, and then drop it back by 30.

but really, it's just a guess Now, of course, sometimes it's okay to just go near enough. and well, my circuit's got a DC to DC converter and it's delivering a constant power into my product. And because the efficiency curve is is doesn't drop off too much, you can say that there's a constant input power from the battery as well. And well, every everything's hunky-dory and you can get some reasonably accurate ballpark measurements from that so it it's not bad engineering at all to just wet the finger and go eh near enough in the ballpark, especially for first order calculations just for product viability and general comparison.

Work estimations are great. So there you have it. Let's go through a quick summary or a cheat sheet of what battery capacity is all about. Now number one, it's all about the battery cutoff voltage.

There's absolutely no point specifying the capacity of a battery if you don't know what the cut off. If you don't specify or know what the cutoff voltage is, it's crazy. Second, if you increase the current or increase the load Uh current then you decrease the overall capacity of the battery due to IR. If you decrease the temperature, you decrease the capacity and remember that's the temperature of the cell, not necessarily the ambient temperature because the cell can heat up due to IR down here.

Now you've got to know your low type. Constant current, constant power, constant resistance. Choose the one that's most appropriate for your particular product when you're dealing with the grass. And if you're serious, use Watt Hour plus Constant power Because true Watt hour that is the true capacity of the battery.

Milliamp hours is a bit of a guesstimate. Okay, and the really the only way to measure true capacity and battery life in your particular product is to actually measure it in your circuit. Do some real world tests, and IR is everything. It's all about the internal resistance of the battery.

and that means power wasted in your product. Just pissed away because you've got this excess current if you try and draw too much current from a you know, a double A battery. If you try and draw two amps out of this thing, or four amps or 5 amps, it's just not gonna do it because of the internal resistance. It's going to heat up, it's going to have a short life, and your characteristic curves aren't worth squat.

Now, No talk about battery capacity would be complete without mentioning a rather obscure law, which not very often used. A lot of people wouldn't have even heard of it, but you may come across it's worth mentioning briefly to Kurt's law, and it basically is the reduction in capacity at higher currents, as we've seen and discussed in the characteristic curves and all the rest of it. Okay, and it's actually a more complex, formal and this is a simplified version, but this is most commonly used Basically, T equals C on I to the power of K where K is constant, which is actually an empirical measured value for the battery. 1.0 being ideal 1.2 might be typical something like that for a battery.

T is the discharge time, theoretical capacity and the discharge current. So as you can see the um, the actual uh, the discharge time goes down If if K actually goes up the constant so your nominal, you know one amp hour battery might drop to you know, 0.8 amp hours or something like that. Look it up if you want to know more foreign.