A week on one charge: power budgets for calm devices

Estimating battery life is mostly arithmetic, and it is arithmetic worth doing before anyone draws a circuit board. A power budget tells you whether a device can last a day, a week or a month, and which part is eating the difference. When we sketched the Humanly Phone and the Humanly Slate, the budgets decided more of the design than the drawings did.

This post walks through the method we use. The worked examples at the end are estimates on paper, not measurements, and real hardware always does something you did not plan for. But a budget that is 30% wrong is still far more useful than no budget.

mAh is not energy

Batteries are sold in milliamp hours, which measures charge, not energy. A 2,000 mAh cell can supply 2,000 mA for an hour, or 20 mA for a hundred hours, in theory. To compare devices that run at different voltages, or to add up parts that run from different supply rails, you want watt hours:

Wh = mAh × nominal voltage / 1000
2,000 mAh × 3.85 V / 1000 = 7.7 Wh

Lithium-ion and lithium-polymer cells usually have a nominal voltage around 3.6 to 3.87 V. The difference sounds small, but if you compare a 3.6 V cell with a 3.87 V cell of the same mAh, the second holds about 7% more energy.

Then take some of it away. You will not get the rated capacity in practice. Regulators lose a little on every conversion, cells lose capacity in the cold and as they age, and most devices shut down before the cell is truly empty to protect it. We plan on using 80 to 85% of the label, and we are happier when the budget still works at 70%.

Average current is the whole game

A device is almost never doing one thing. It is asleep, then awake for a moment, then asleep again. The number that matters is the average current over a long period, and the simplest way to get it is a duty cycle:

I_avg = I_active × d + I_sleep × (1 - d)

active: 40 mA for 2% of the time    = 0.80 mA
sleep:  0.05 mA for 98% of the time = 0.049 mA
average                              ≈ 0.85 mA

300 mAh / 0.85 mA ≈ 350 hours ≈ 14 days

Two things jump out of that calculation. First, the active current is large but brief, so the 2% matters more than the 40 mA. Halve the time awake and you nearly double the battery life. Second, sleep current is small but constant. At 0.05 mA it barely registers. At 0.5 mA it would add half again to the total, and the device would last under ten days instead of two weeks.

That second point is where most real projects go wrong. Sleep current is made of things nobody thinks about: a pull-up resistor on a line that is held low, a sensor that was never told to power down, a voltage regulator with a high quiescent current, a status LED. A single small LED at 1 mA uses more than an entire well-behaved microcontroller asleep. The cheapest battery improvement is usually a careful look at what is still switched on at 3 a.m.

Where the energy goes

Across the devices we think about, the same five buckets cover almost everything.

Standby and sleep. The floor. For a phone this includes the cellular modem staying registered with the network, which wakes periodically to listen for incoming calls and data. The network sets much of that schedule, so standby on a phone varies with coverage in a way you cannot fully control. Weak signal means more transmit power and more retries.

Display. This depends entirely on the technology. An LCD backlight draws roughly the same power whatever is on screen. An AMOLED panel draws power per lit pixel, so a mostly black interface is genuinely cheaper than a white one. E-ink draws power only while the image changes and holds it for free afterwards, which is why a reader can show a page all night without cost. Memory-in-pixel LCDs, common in simple watches, sit in between, with very low power for a static image.

Processor. Modern chips are efficient when busy and even better when idle, so the goal is to finish work quickly and go back to sleep. Background tasks are the enemy here, not heavy tasks. One app that wakes the processor every few seconds costs more over a day than a minute of hard work.

Radios. Transmitting is expensive, and so is keeping a connection alive. Cellular calls and GPS directions are among the most power-hungry things a phone does. Wi-Fi is cheaper per byte but costs something to associate and stay connected. Bluetooth LE was designed for small, infrequent bursts and is very cheap when used that way. A radio that is off costs nothing, which is the simplest optimisation there is.

Light and sensors. A front light on an e-reader can easily use as much energy as the screen and processor combined. On a watch, an optical heart-rate sensor that samples often is one of the larger costs. Both are worth giving the user a direct control over.

Three worked budgets

Here is how the three devices in the chart come out. Each budget is for one ordinary day. All figures are our estimates, in Wh per day, and rounded.

A calm phone

Battery	About 2,000 mAh at 3.85 V, 7.7 Wh
Standby	1.0 Wh: modem registered all day, a dark interface asleep
Display	0.3 Wh: about an hour on, mostly black AMOLED
Processor	0.5 Wh: short bursts, no background apps
Radios	0.8 Wh: half an hour of calls, twenty minutes of turn-by-turn directions
Total	About 2.6 Wh per day, so roughly three days on paper

These day counts use the full label capacity. Take off the 15 to 20% you should not count on, allow for weak signal and an ageing cell, and three days on paper becomes two to three in real life. The standby line is the one to watch, and it is largely set by the network. The display line is small only because the interface is dark and there is nothing to scroll.

An e-ink slate

Battery	About 1,500 mAh at 3.8 V, 5.7 Wh
Sleep	0.01 Wh: deep sleep between sessions
Display	0.01 Wh: about sixty page turns in an hour of reading
Processor	0.05 Wh: laying out pages, awake only around each turn
Radios	0.02 Wh: a few minutes of Wi-Fi a day, then off
Front light	0.06 Wh: an hour at a moderate level
Total	About 0.15 Wh per day, so around five weeks on paper

The interesting number is the light. It is the largest single line, larger than the screen by a wide margin. Read in daylight with the light off and the daily total drops by about 40%. Leave Wi-Fi connected all day instead of a few minutes, and it becomes the largest line instead.

A simple watch

Battery	About 300 mAh at 3.85 V, 1.15 Wh
Sleep	0.03 Wh: clock and motion sensor always on
Display	0.02 Wh: a memory-in-pixel screen, always visible
Processor	0.03 Wh: wrist raises, notifications, step counting
Radios	0.02 Wh: Bluetooth LE sync with a phone a few times an hour
Sensors	0.04 Wh: heart rate sampled every few minutes
Total	About 0.14 Wh per day, so about eight days on paper

A week on one charge is possible, but only just, and only because the display is the right kind. Swap in a bright colour screen that stays on and the display line alone could exceed the whole budget above. Sample heart rate every few seconds instead of every few minutes and the sensor line grows several times.

Measuring instead of guessing

A budget on paper is a hypothesis. Once there is hardware, measure it. For small devices, a dedicated power profiler that sits between the battery and the board will show current over time, and you can see each wake, each radio burst and the sleep floor between them. A USB power meter is fine for rough numbers on anything that charges over USB. For finer work, a small shunt resistor and an oscilloscope still do the job.

Measure each state separately, then compare with the budget. The places where they disagree are where the design has a surprise in it. In our experience the surprise is almost always in sleep, and it is almost always something that was left on.

The last habit worth building is to write the budget down next to the feature list. When someone suggests syncing every minute instead of every hour, the budget turns the argument into a number. It is much easier to say no to 0.3 Wh a day than to an idea.