# Simple Test for Cell Phone Battery

#### MrAl

Joined Jun 17, 2014
11,250
Hello,

Recently i had a cell phone battery swell up so i had to replace it. I noticed there was something wrong with the battery that's the only reason i checked it. Since then however, i have looked into this matter a bit more and found that it is not too hard to measure the Ampere Hour capacity of the battery without having to take the battery out for a test. You just need a USB tester that measures at least current or ampere hours.

First, the state of charge curve vs time is not linear as you probably already know. So to test the battery given some relatively small amount of time requires a correlation between the battery curve and the charge current and time. Doing this we can estimate the health of the battery.

The change in state of charge i selected for example was 10 percent. That is, when the phone battery goes up by 10 percent anywhere on the curve. When the battery is being charged, the SOC goes up by 10 percent and by measuring the charge current and time we can estimate the battery health. I like to go by percent because the phone displays this information in the settings/battery section on the phone.

The formula is simple (this is only for a normal charge where the current decreases over time):
t=AhCapacity/ChargeCurrent*SOCfactor (in hours)

The SOCfactor is related to the span in percent change.
For example, for SOC=40 to 50 percent the SOCfactor is 0.1 but for
SOC=70 to 80 percent the SOCfactor is 0.2 which means it takes twice as long to raise the SOC by 10 percent.

So for example if the phone charges up from 40 to 50 percent in 1 hour at a charge current of 300ma then the Ah capacity of the battery must be 3000mAh. If it was charging from 70 to 80 percent however then that would take twice as long to accomplish. This is for the normal non linear charge curve only.

If the current is constant over the entire charge time of 10 percent charge then the formula is very simple:
t=AhCapacity/ChargeCurrent/10

So if the AhCapacity is 3000 and the charge current is 300ma then the time to charge by 10 percent is
t=3000/300/10
which comes out to 1 hour. So you can work this out for the Ampere Hour capacity after measuring the time, current, and noting a 10 percent rise on the phone in the settings/battery section.
Some of those little USB testers measure Ampere Hours so you can just multiply by 10 to get the capacity of the battery.

The most important point though is that if it charges from 40 to 50 percent in 1 hour at 300ma when it is new and 6 months later it charges from 40 to 50 percent in 1/2 hour then the capacity must have went down by 1/2. It may be good to check the battery and probably get a new one.

If anyone wants to add to this feel free. Perhaps any tests you have done.

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#### MrAl

Joined Jun 17, 2014
11,250
I just tested my cell phone battery using this simple idea.
The formula is simple:
AhCapacity=100*MmAh/(p2-p1)

where MmAh is the measured milliampere hour input to the phone, p1 is percent before charging, p2 is percent after charging is halted, assuming the input current is constant.
p1=63 percent
p2=81 percent
MmAh=362 mAh

and from the formula i get:
AhCapacity=2011 mAh

The label on the battery says 1900mAh so this is close enough.
In fact, letting it go to 82 percent i get 1979 mAh.
I figure this is close enough even if the phone itself draws some current during the charge so not all of the input current goes to the battery charging process. There's also the charge efficiency which is not factored in which would lower the actual capacity somewhat.

It's probably better to go by only 10 percent though so it is easier to test next time too. I just did not watch the phone close enough to catch it in time for 73 percent. The current does have to be constant though over the entire charge period.
Ultimately the rating will go down over time so i just have to check it now and then.

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#### Rich2

Joined Mar 3, 2014
254
Sterling work! I must check mine when I get round to it

#### MrAl

Joined Jun 17, 2014
11,250
Sterling work! I must check mine when I get round to it
Oh yes it helps to know if the battery is getting too bad which could be dangerous as i have read. Mine was swelled up so i was lucky i caught it before anything bad happened.

Oh BTW it is much easier if you have one of those little USB testers that plugs right into the USB port and the charge cable plugs right into that and it gives you an Ampere Hour reading. It is a little harder with a tester that just measures current. I had the old type and just recently got the new type (that measures Ah too) and it is a lot easier because i dont really have to watch the time of the entire charge.

#### Rich2

Joined Mar 3, 2014
254
Oh yes it helps to know if the battery is getting too bad which could be dangerous as i have read. Mine was swelled up so i was lucky i caught it before anything bad happened.

Oh BTW it is much easier if you have one of those little USB testers that plugs right into the USB port and the charge cable plugs right into that and it gives you an Ampere Hour reading. It is a little harder with a tester that just measures current. I had the old type and just recently got the new type (that measures Ah too) and it is a lot easier because i dont really have to watch the time of the entire charge.
Yes got one, it's got an LED display switching between voltage and current and branded "charge doctor"

#### MrAl

Joined Jun 17, 2014
11,250
Yes got one, it's got an LED display switching between voltage and current and branded "charge doctor"
Oh ok that's great. You will just have to keep track of the time too then.
Charging for 1 hour at 400ma results in a total charge of 400mAh,
charging for 2 hours at 400ma results in a total charge of 800mAh,
etc.

#### MrAl

Joined Jun 17, 2014
11,250
Hello again,

Unfortunately i ran into an anomaly i can not yet explain.
The next test i did was with 623ma charge current and the MmAh was 333mAh.
The span was only 11 percent though (60 to 71 percent) so that would put the battery capacity at about 3027mAh which can not be right.
I used the phone in between for a couple minutes but nothing that would cause an error of 1000mAh. There must be something about charging the phone at a higher current. Maybe not all of the charge goes to charging the battery some is lost in some inefficiency at the higher current.

I'll have to look into this further at some point, but in the mean time i can still use all this data for future comparative testing.

#### KeepItSimpleStupid

Joined Mar 4, 2014
5,088

#### jpanhalt

Joined Jan 18, 2008
11,087
What you find will vary with the original state of charge and when during the charge cycle you take your measurements. I have had the unfortunate need this past week to review a lot of "modern" datasheets for BMS/chargers designed for mobile devices.

They all use a multi-step step charge curve that involves: 1) Low-current conditioning; 2) Fast charge ; and 3) Constant voltage final charge. Simple enough, except because of the small packages used for the linear-regulating IC's operating at 500 mA to 1 A, heat is a problem. Thermal shut-down of the IC is not treated as a error so much as just part of the designed charge cycle. Here's an example from TI (BQ2409x series):

In other words, it is expected that the charger will go into thermal shut-down one or more times during charging. You will find similar data for TI BQ21040 series, MAX1811 and Microchip's MCP7383x/y devices.. I have been reviewing devices in SOT-23(5 or 6), SSOP-like packages (small leaded packages). BGA and leadless packages have the same heat issue.

If you measure during the conditioning period at the very start you may get erroneous results. That period can be adjusted by the designer, but it is usually 10% of the estimated charge time, and it is only included when the initial battery voltage is below a threshold (also adjustable). Also, using a wall wart supply versus a powered UBS source may give different shut-downs as the former is often a slightly higher voltage.

#### MrAl

Joined Jun 17, 2014
11,250
What you find will vary with the original state of charge and when during the charge cycle you take your measurements. I have had the unfortunate need this past week to review a lot of "modern" datasheets for BMS/chargers designed for mobile devices.

They all use a multi-step step charge curve that involves: 1) Low-current conditioning; 2) Fast charge ; and 3) Constant voltage final charge. Simple enough, except because of the small packages used for the linear-regulating IC's operating at 500 mA to 1 A, heat is a problem. Thermal shut-down of the IC is not treated as a error so much as just part of the designed charge cycle. Here's an example from TI (BQ2409x series):

View attachment 198281
In other words, it is expected that the charger will go into thermal shut-down one or more times during charging. You will find similar data for TI BQ21040 series, MAX1811 and Microchip's MCP7383x/y devices.. I have been reviewing devices in SOT-23(5 or 6), SSOP-like packages (small leaded packages). BGA and leadless packages have the same heat issue.

If you measure during the conditioning period at the very start you may get erroneous results. That period can be adjusted by the designer, but it is usually 10% of the estimated charge time, and it is only included when the initial battery voltage is below a threshold (also adjustable). Also, using a wall wart supply versus a powered UBS source may give different shut-downs as the former is often a slightly higher voltage.
Hi,

Well the only thing that really changed here is the charging current.
I started from the same percent as before almost.
The thing is there is 1000mAh missing somewhere when before it was very close to expected.

Yes the charge regimen is normallycurved, but if the current is constant then it's not curved. I keep a close eye on the current and it stays within a couple milliamperes for all of these tests i do. This last one just had higher current, but that never changed as it would if the chip went into thermal limit or for any other current limit mechanism. Constant current says it is still in the more or less linear part of the charge cycle and it is more or less proceeding without any interruptions.
Remember i am measuring both total charge (mAh) and current (ma). 1000mAh is a lot of extra charge.

Any other ideas welcome too.

#### MrAl

Joined Jun 17, 2014
11,250
Hello again,

I did another test but after i hooked it up i fell asleep and so it charged all the way up to 100 percent.
The calculation this time came out to 1850mAh. That's not unreasonable but it is different from the others. It surely reached the nonlinear portion of the charge cycle too and the formula doesnt really apply unless you also apply the SOC factor which i mentioned originally.

#### MrAl

Joined Jun 17, 2014
11,250
Hello again,

Did another lower current test this time from 60 percent to 100 percent. This test result was 2200mAh.
This means it is going to vary a bit depending on what portion of the battery is being charged and what the charge current is. However, i believe a bad battery will test really low.

I am tempted to put the old battery back in and test with that, but it's a risk because the battery is already swollen. So i wont be able to do that. The way i found out the battery was bad or at least suspected it was bad was because the charge current never dropped below the max for that USB source and that was 445ma. When charged it drops very low to something like 1ma but the bad battery never allowed that to happen.
I should have tested the old battery better when i had it in there i guess.
Well maybe this battery will go bad prematurely (ha ha) and i will get the chance to do a better test soon.

#### MrAl

Joined Jun 17, 2014
11,250
Hello again,

Getting consistent results using the charge current of 445ma.
This time 58 percent to 88 percent gave me a cell capacity of 2167mAh.
That's good enough.
Also, noting the percentage fall over time when the phone is sleeping (screen off but phone still turned on) tells me the phone is drawing about 8.3ma when not being used but still turned on.

So i think i have enough data now to be able to judge the health of this battery over time without having to remove the battery. This will be even more valuable if i move to a phone with a non removable battery and a lot of manu's are moving toward non removable batteries which really bites. The claim is they can make them thinner.

#### MrAl

Joined Jun 17, 2014
11,250
Hello again,

This is just a small update.

I found again that charging over a wider range of percentage (as reported by the phone itself) provides for a more realistic measurement of the capacity of the cell phone battery. When new it has its maximum rating and that goes down over time so it is good to check now and then.

The simple formula i am using now is:
Rating=m/pcd
where
m is the measured milliampere hour rating as measured over time during a charge, and
pcd is the fractional percent difference (for example charging from 80 percent to 100 percent pcd=0.20)_.

To make it even a little more straightforward:
Ratring=100*m/(100-pc)
where
m is the measured milliampere hour rating over the percentage from pc to 100 percent.
So if m=300 and pc=90, then the Rating comes out to 3000mAh.

I found that the closer the percentage is to 100 percent at the start of the charge the higher the calculated milliampere hour charge comes out to.
For example, on my phone charging from 70 percent to 100 percent the Rating comes out to around 3000mAh, but charging from just 95 percent to 100 percent results in a Rating of 4460mAh. That's quite a difference, and knowing the manufacturers rating i know it is closer to 3000mAh. So the measurement over a wider spread is more accurate.
It may not matter that much if you measure over the same range each time, but it seems better if you measure over a wider range each time.

There is also a higher level of error over a small range because the cell phone only reports percentages in integer form like 90, 82, etc., and never 82.4 or 91.1 or like that. So over a shrt range the error is higher because of the phones internal roudning.

Today i measured 223mAh over 95 to 100 percent and thus the rating came out far too high.
The round off error means a range of Rating is 4054 to 4956 and that is almost 1000mAh difference JUST because of the phones round off error in the display of the percentage.

Normally i measure over a wider range anyway but i thought i would mention this.
It's a good idea to test this now and then and compare with previous measurements on the same phone.

Oh BTW, the easiest way to measure the milliampere hour rating is to use an inline measuring device that you reset to zero at the start of the charge and then just read off the milliampere hours at the end of the charge. That makes it a lot easier to measure that. They are available all over the web such as at Amazon and are very reasonably priced. It may be a good idea to get two so you have a backup, and compare readings, and always use the same one each time unless they read very close to the same. You can plug them in in tandem to see if they both read the same for a given charge cycle. The connectors are standard male and female USB "A" type.

Good luck.