Watt-hours vs mAh and Simple Run Times
(Warning, technical jargon ahead!)
Most of us are accustomed to seeing batteries rated in milliampere-hours (mAh),
a measure of how much current they can provide over time. A rating of
1600 mAh means that the battery should theoretically be able to supply 1600
milliamps (mA) for one hour, or 160 milliamps for ten hours, etc. The best NiMH
AA cells today carry ratings of 1700 to 1800 mAh.
It turns out though, that mAh is really only part of the story. What we really
care about is how much total energy a battery can deliver. Energy is
measured in Watt-hours, the product of voltage and current over time, or volts
times amperes, measured over hours. (A milliamp is 1/1000 of an ampere.) To
measure total energy, we need to measure the voltage and current moment by moment
throughout the battery's discharge, multiply the two values together, and total
up all the individual readings. This sounds like a lot of hassle, and it would
be, were it not for automated data collection, and always-handy spreadsheet
software.
Still, I'd hoped I would be able to avoid the tedium of explicitly calculating
energy capacity for every test run. I expected that overall run times in my
simple test setup (see below) would be a pretty good measure of total energy,
saving me from the hassle of running all the data through a spreadsheet. I was
quite surprised to discover that total run time was actually only an approximate
indicator of energy capacity: When I ran the numbers, I discovered that some
batteries that ran shorter periods of time actually delivered more energy
than ones with shorter run times. Even more surprising, I found that even the
measured mAh capacities of the batteries didn't correlate perfectly with total
energy capacity.
This is pretty significant because it means that the usual battery-testing
practice of just hooking a resistor across a battery pack and timing how long
it takes the pack to run down won't give a very accurate representation of how
well the batteries will do powering a digital camera.
Fortunately, because my little test system measured voltage (and thereby current)
continuously throughout the discharge process, I could accurately compute total
watt-hours with just a little spreadsheet work.
The point of all this is that run times with a resistive load and even actual
mAh measurements don't tell the full story: Watt-Hours are the real McCoy.
Further Fallacies of mAh
There's a lot of gamesmanship with mAh ratings, but even the standard way of
measuring mAh gives wildly optimistic values when compared to what the batteries
actually deliver in typical digicam usage. The problem is that digicams gobble
power in big gulps, while battery-testing standards measure power delivered
in small sips. Batteries are much less efficient when driving heavy loads than
light ones. Thus, even if a manufacturer tests and reports their batteries'
capacities truthfully according to the accepted standard, the resulting numbers
may have little to do with how well the batteries perform in real-world digicam
usage.
Because of this load-dependent behavior, I set up my battery test system to
run the batteries under loads closer to those seen in typical digicams. As a
result, the mAh capacities I measured are generally quite a bit lower than the
manufacturer's claims, but do give a much better idea of how the batteries will
do when plugged into an average digicam.
 Test
Methodology (Nerdly Details)
Obviously, I couldn't stand around for an hour or more at a time, watching
each set of batteries run down, let alone make constant voltage/power measurements
on them as they discharged. (Well, I could, but updates to anything else
on the IR site would come to a standstill.) My solution was to cobble together
a little MSD (Mad Scientist's Device) battery discharge tester, using a Basic
Stamp microcontroller, a Linear Tech A/D chip, a relay to connect or disconnect
the batteries from the load, a couple of big power resistors (to serve as the
load itself), and a few other components. The whole mess is as appears at right.
Not beautiful (I'm a master of understatement), but it worked just fine for
what I wanted.
Note, added 3/1/2002: Well, not quite "just
fine" - Months into my testing, I discovered that one or more of the contacts
on the breadboard socket had fatigued over time, with the result that the load
resistance increased by a few tenths of an ohm. Worse, the resistance varied
whenever I jiggled the load resistors. Argh! I soldered all the high-current
connections, with the exception of those between the batteries and battery holder,
and those I clamped to reduce resistance and improve consistency. The result
was much less variation between runs, but also the need to retest all
the batteries I'd previously run through the apparatus. Yeesh, what a pain.
(A word to the wise for anyone else contemplating such testing: DON'T trust
the contacts in these little breadboard sockets over time for anything requiring
more than milliamps of current!)
I tested batteries in sets of four, as they're most commonly used in digicams.
I used a total load resistance of about 5 ohms, providing peak discharge currents
of a bit under an amp (1000 milliamps), equivalent to a fairly power-hungry
digicam running with its LCD turned on in capture mode. This isn't an absolute
worst-case test, but should be pretty representative of what batteries will
encounter with real-world digicams (as opposed to the sort of gentle discharge
curves used by manufacturers when setting the mAh ratings). For the techies
out there, this is a discharge rate of about 0.6C for 1600 mAh cells, as compared
to the 0.1C discharge rate used to determine the normal mAh rating of batteries.
The system starts up with the relay open, and no current flowing. I plug the
batteries into the holder and press the reset button for the Basic Stamp, which
starts the test program running. The program closes the relay, connecting the
load resistor across the battery pack, and measures the battery voltage. When
the voltage has been measured (to 12-bit accuracy, with a full-scale range of
about 5.5 volts) the Basic Stamp goes to "sleep", waking up one minute
later for the next reading. This cycle continues until the voltage from the
battery pack drops below 4.0 volts, at which point the Stamp stops the test
by opening the relay contacts again, disconnecting the load. (Update note,
added 7/11/2002: The original test setup used the "sleep" function
of the Basic Stamp to generate the delay between samples. This proved to be
very temperature dependent, to the extent that minor changes in room
temperature could affect the test accuracy. I subsequently added a little crystal
oscillator and divider chain to the test setup, giving very accurate
timing. All of the results shown here were collected using crystal-controlled
timing, with the Stamp sampling the voltage every 30 seconds (instead of every
minute) to further improve accuracy.)
The Stamp then goes into a wait loop, watching for keyboard input. I set the
terminal program on my laptop (the "host" computer for the Stamp)
to capture data to a disk file, and then type "go" on the keyboard,
to tell the Stamp to play back all the data values it's collected.
After I've collected a batch of test results, I run them through an Excel spreadsheet
that calculates the total energy delivered, actual mAh, etc. (This is one of
the most tedious parts of the testing, as I haven't bothered to write a Visual
Basic program to automate the data reduction.)
In the end, a lot of very interesting data spills out the other end of the
process, with some lesser-rated batteries performing better than higher-rated
ones, mAh not correlating well with total energy, and charging parameters making
a huge difference in attainable battery capacity.
Controlling the Variables (or not)
I found out right away that it was easy for results to vary as much as 50%
between runs, depending on the charger used, the charge time, and probably the
phase of the moon. I settled on a protocol that involved charging the batteries
for a minimum of 5 hours in the Maha C204 chargers (which brings them pretty
nearly to full capacity), and then popping them in very low-rate trickle chargers
for at least 10 hours more. (To be sure the batteries are fully "topped
off," I now always let them sit in the trickle charger overnight or longer.)
This protocol seemed to reduce cycle-to-cycle performance variations to a minimum,
although there were still individual runs that'd be as much as 7-10% off the
best performance a pack could muster. I attributed the underperforming runs
to incomplete charging, and so only accepted the runs that fell within a 3-5%
window as being truly indicative of ultimate energy capacity. (The point of
this testing was to determine the actual energy capacity of the batteries, not
the effectiveness of a particular charging protocol.)
I'm pretty sure I could have come up with absolutely consistent results if
I'd nailed down *all* the variables, but frankly I have too much else to do
to justify spending the time doing that. The problem is that there's a huge
range of possible variables. (time from discharge to subsequent recharge, charging
duration, current profile during recharge cycle, temperature profile during
recharge cycle, time between rapid charge termination (when the batteries were
switched to the trickle-charge topping-off/maintenance current) and subsequent
discharge testing, temperature during discharge, etc.) Trying to control for
all of these parameters would be enormously time-consuming, and quite likely
yield little more in the way of information, other than reducing the variations
between test cycles. - I'm pretty confident that my approach of averaging the
results of the best test runs for each set of batteries, and then averaging
results for at least two different sets of each model of batteries gives a pretty
good indication of ultimate performance. (Note: Run to run consistency improved
quite a bit once I soldered the high-current connections, and clamped the batteries
in their holder to reduce contact resistance I now routinely get repeatability
of 1-2% from run to run with the same cells.)
The Importance of the Charger (!)
One of the most interesting things I found was that the right (or wrong) charger
can make a difference of nearly 2x in the results! The worst chargers (in terms
of completeness-of-charge) produced "charged" batteries with only
half the stored energy of ones charged with the best chargers. Interestingly
though, the best overall results were obtained by combining the worst fast-charger
with an inexpensive trickle-charger for topping-of and charge maintenance. -
This combination was also the gentlest on the batteries. (Stay tuned for a detailed
overview of battery chargers as I can get to it. For now, you can just take
as given that the Maha C204 charger was among the most consistent I tested,
and charged the batteries to close to their maximum capacity every time. To
insure that the batteries were *totally* topped-off, I always gave each set
at least an overnight trickle charge as well though..) The Lightning 4000 charger
sold by RipVan100 was also very good - It was more gentle during the charge
cycle, but took longer to charge the cells than the C-204, and didn't charge
them quite as fully as the 204, even if left overnight. The difference
in charged capacity was rather slight though.)
Grains of Salt
For all the effort I've invested in testing batteries, my results still need
to be taken with several grains of salt.
First, my purely resistive test load is a bit easier for batteries to handle
than the constant-power loads that most digicams present. As batteries discharge
in a digicam (and their terminal voltage drops), the camera draws proportionately
more current from them. This is a bit harder on batteries than the sort of load
I used in my testing. Thus, Your Mileage May Vary when comparing my results
here with actual digicam usage. (Not by much though, I don't think.)
A second factor is that, as just noted above, battery performance is very
dependent on the charger used. - Having the best batteries in the world won't
do you a whit of good if you've got a lousy charger. To avoid seeing charger-dependent
variation, I standardized on the most reliable high-performing combination I
found, a Maha C204 followed by a long, low-rate trickle charge in a Maha 2A4,
or a homebuilt trickle charger with similar characteristics. You may see very
different performance than I measured here if you're using a charger that doesn't
charge the batteries as completely as the C204/2A4 combination. (The C204 does
a pretty good job by itself, without a subsequent trickle charge, about as good
as any fast charger I've seen that doesn't burn the batteries up in the process.)
Finally, even with a consistent charging protocol, I still found a 3-5% variation
between runs. (Note, this variation dropped to less than 1% after I soldered
all the high-current connections and applied a clamp to the battery holder to
reduce contact resistance.) Since the top-performing batteries are separated
by less than one percent in their total-energy numbers, closely-ranked batteries
should really be considered as equivalent to each other).
Conclusions - Battery Best Buys & Cautions
OK, so what's the bottom line? Well, the table near the top of this article
shows all the pertinent data so I'll just comment briefly on the results here.
Energizer has edged the competition in this round, with their 2300 mAh cells, although longtime champion Powerex isn't too far behind with their own 2300 mAh offering. Now that I've cranked up the tester again though, I've got a number of even higher-rated cells currently under test. Stay tuned, I hope to have another update fairly soon. (At least, quicker than the year-plus this latest update took me to get around to!)
It continues to be the case that taking one step down in capacity may yield great economy: Depending on where you buy your batteries, you can often get more bang for the buck from lower-rated cells, which may sell for significantly lower prices. (Note too though, that there are some cheap brands of cells that just aren't worth it regardless. (IMHO) - Taking an example from the earlier days of this test, the Powerizer 1800s tested worse than Sanyo industrial 1600 cells from RipVan100.) Bottom line, battery cost isn't terribly relevant for digicam usage: Spending another $4-5 for a set of batteries for your $800 digital camera (or even your $200 one) makes sense if it'll net you an extra 5-7% in run time, charge after charge. - One missed picture would easily erase any benefit the cheaper batteries might have.
The final discovery came as no surprise at all: In digicam usage, even so-called "high capacity" disposable alkaline cells are pretty worthless. (Although a number of recent digital camera models do sip power pretty sparingly, at least compared to most older models.) You could easily spend the equivalent of a set of high-capacity NiMH rechargeables and good-quality charger in just a few weeks of use with disposable alkaline batteries.
Special Thanks: Thomas Distributing
In conclusion, a special note of thanks needs to go to Thomas Distributing,
who generously provided most of the (literally hundreds of) batteries and chargers
used in my testing. Thomas Distributing has about the widest range of power
solutions for digital cameras I've seen anywhere on the web, and at some of
the most competitive prices. If you have a digicam and need batteries (who doesn't?),
you really owe it to yourself to pay them a visit, at http://www.thomas-distributing.com/!
For those interested, here's a link to the Powerex website,
for more information on their NiMH
batteries.
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