Determine Average Current Consumption of Low Power Intermittent Device

Introduction

Out of curiosity I wanted to know how long the batteries might last in my remote temperature sensor. It takes two AA cells in series but it's little help placing an ammeter in line and watching the display because the power is consumed in bursts. Every couple of minutes the device switches on its 433 Mhz transmitter for a few seconds then returns to a quiescent state of just keeping time until the next transmission.

I needed a means to aggregate the overall current consumption over a period of hours to get an average. I did this by powering the device from a Super Capacitor and calculating the effective average current from the capacitor's voltage drop over the hours.

Clearly this cannot yield an entirely accurate result because the Capacitor suffers some internal leakage and loses charge each time the voltmeter is connected to get a reading. But the results obtained are sufficiently accurate for my purposes of deciding how long the normal batteries might last.

Supplies

Device under test (in my case a remote temperature sensor)
Voltmeter (a digital multimeter is perfect)
Super Capacitor (I used a 4 Farad 5.5V one)
Clock (to note when readings are taken)
croc-clip leads.

Step 1: Check Equipment

Make sure the Super Capacitor holds its charge sufficiently.

Using the two AA cells (assuming they are fully charged) connect them to the SuperCap to bring it up to the 3 Volts. Disconnect. Measure the SuperCap voltage to check it says 3 Volts (or nearly) and note the voltage and time. Disconnect the voltmeter. Wait a few hours. Measure the SuperCap voltage again to check if it is seriously leaking. Hopefully it will have hardly changed. My 4 Farad SuperCap still had half its initial voltage after a month!

Incidentally, my experience with SuperCaps suggests that the larger the capacitance, the quicker they leak away their voltage. My 100 Farad capacitor loses half its voltage in less than a day.

Step 2: Take Measurements

Connect the powered up SuperCap to the device under test and measure the initial voltage, remembering to note also the time.

Leave the device to run from the SuperCap and check the voltage every few hours. Once the voltage has dropped by, say, 25 percent (between half and one volt drop for my 3 Volt device) note the voltage and time again.

Don't assume that running for longer will be better because if the voltage drops too low the device may stop functioning.

Step 3: Do the Math

For an ideal (theoretically perfect) capacitor the discharge through a load is expressed by the BLUE formula shown.

Where:

Vc = Final capacitor voltage
Vs = Intitial capacitor voltage
e = the mathematical constant roughly 2.718
t = the time in seconds
R = the load resistance
C = the Capacitance

All we have to do is calculate R from the above. Then knowing the effective resistance and average supplied voltage we can get the average current consumption. That's not easy unless you are an advanced mathematician. To make it easier, we first rearrange that formula as per the BLACK-&-WHITE version where R is the subject.

(* means multiply and ln() means natural logarithm of what's in the brackets.)

Doing Mathematics is annoying and prone to error so I made a spreadsheet to do the heavy lifting.

You will see from my spreadsheet that I first used a known load resistor to check the accuracy of this approach. My worst case was less that 10 percent error. Not too bad.

Step 4: Download the Spreadsheet for Your Own Experiments

You can download my spreadsheet and put your own values into the columns when conducting your own experiments.

Conclusion

This method of determining average current consumption is adequate for most practical purposes.

As you'll see from the spreadsheet, my remote temperature sensor appeared to consume about 85 micro Amp. If I simply assume that's 100 micro Amp it means the 2000 mAh batteries in the device should last 20,000 hours - a couple of years. Which is what I wanted to know.