# Computing stuff tied to the physical world

## Supercap discharge – part 2

In Hardware on Apr 23, 2012 at 00:01

Yesterday, I charged a 0.47F 5.5V supercap to 5.1V and kept charging it for 24 hours to reduce the leakage current.

Actually, I lowered it to 5.01V in the last hour – there’s a slight memory effect, so right after lowering the voltage actually rises when power is disconnected.

Next step is to measure the supercap’s self-discharge time from 5.00V to 1.84V (i.e. 36.8% of 5V) – that’ll give the time constant of the RC circuit (the real capacitance, in parallel with an imaginary internal current leakage resistor). Note that this is not the same as the ESR of a cap, which is about charge & discharge current losses.

Ok, let’s disconnect the power supply and track the voltage readings in high-impedance mode. It is 10:17 here, and the voltage has just dropped to 5.00V – with the power supply removed.

Time passes. Unfortunately, waiting for the voltage to drop to 1.84V (i.e. 36.8% of 5V) would take a bit long, so let’s throw some math at this and come up with a quicker way to measure leakage current:

• for T = R x C, we need to measure a drop to 36.8% (i.e. a factor 0.368) of the original voltage
• since the charge decay curve is exponential, we can estimate when 0.5 T will happen
• this turns out to be the square root of 0.368, i.e. a factor of 0.607
• so with a drop to 0.607 x 5V = 3.033V, we know 0.5 x T
• let’s repeat that trick one more time, to get at 0.25 x T
• my trusty on-screen calculator tells me that the square root of 0.607 is 0.779
• so if we wait for a drop to 0.779 x 5V = 3.894V, we’ll know 0.25 x T
• four times that duration, and we have T, the RC time constant we’re after

Good. That means I only need to wait for the supercap charge to drop by roughly 1V i.s.o. over 3V.

More time passes. It’s now 0:26 after midnight, and the voltage has dropped to 3.98V – i.e. not yet the 3.894V we need to reach, but hey, let’s call it a day anyway.

That’s over 14 hours total, i.e. over 50,000 seconds = 0.25 x T, so the calculation now becomes:

• 200000s = R x 0.47F
• R = 200000 / 0.47 ≈ 425 kΩ
• so at 5V, the internal discharge current is 5V / 425kΩ ≈ 12 µA

Hmmm…. that amount of leakage is three orders of magnitude higher than with a 47 µF electrolytic cap, but it might still be usable as power source for a JeeNode or JeeNode Micro. Here’s my reasoning:

• suppose the JN/JNµ draws 12 µA on average – a tough target, but it should be feasible
• then we’re effectively draining the supercap twice as fast as its self-discharge
• it looks like the supercap can hold a charge down to 1.8V for 56 hours on its own
• note that 1.8V is too low for RFM12B use, but the microcontroller would still work
• with the added load from the JN/JNµ, this halves to 28 hours, i.e. slightly over a day
• so the challenge will be to fully recharge the supercap to 5V at least once a day

A solar cell might just do it – assuming it’s large enough to overcome a dark and cloudy winter day. And the good news is that supercaps can charge up very fast, so a short period of bright light could be enough.

UpdateThere’s a lot more to supercaps than this…

As suggested by @jpc in a comment yesterday, I had a look at some documentation from Panasonic, in particular Part 2. And sure enough, they show that a supercap can be modeled as a whole set of capacitors in parallel, each with their own – often substantial – series resistance. It takes a while to “reach them” with charge, so to speak. Which explains why a long charge time increases the charge and voltage:

And which also explains why the supercap tends to drop quickly at first:

Having seen the discharge tail off much more than expected (i.e. flatten out and retain voltage), I can confirm that a supercap behaves considerably differently from a plain electrolytic capacitor.

The good news, is that for our intended purpose, this might actually work out quite well: a solar cell, keeping the supercap charged up fairly well most of the time, with just night-time JeeNode activity to drain the charge a bit, and occasional dark days, expecially in wintertime.

Update #2 – Three days have passed, and the voltage is still 3.23V, so T will be over 6 days, and the corresponding discharge rate even lower than estimated above. Bit of a puzzle – the discharge tails off considerably, apparently. Which is good news in fact, because that leaves more charge for a JeeNode to use. I’m ending this experiment for now: real-world testing with a JeeNode sending packets will be more useful.

To be continued…

1. Thanks for the posts about supercaps. I too am looking to play around with a solar powered WSN node (I’m using Synapse Wireless nodes). My idea was a floating, solar powered pool temp sensor that reports every 10-30 minutes (even at night). I’m in a great spot for solar (Phoenix, AZ), but heat is an issue. I figured a supercap would be a better solution than a battery backup due to the heat build up inside my waterproof case. Yes, I suppose I could heat sink something since the pool water won’t be 48C, but that adds complexity.

At any rate, I thought I’d mention a DC boost controller chip I found via http://www.ambientsensors.com/ :

It’s meant to harvest energy from super low voltage sources. I was thinking I should use such a chip so even when the solar panel was in the shade, I could still charge the supercap. Then again, perhaps your proposed solar cell, diode, supercap solution would work better. I don’t know what I should choose. I guess to be more confident I either have to break down and do the circuit analysis (I’m not a circuit guy, but a ASIC designer) or buy a bunch of components and play around.

I’ll be eagerly awaiting your next posts where you explore your solar supercap node more.

2. Hello,

I don’t know about the power supply, but the HP multimeter, like (probably) all HP bench instruments, has an HPIB bus, which could be a nice project to get connected to the PC. Then you could run these experiments in full automated mode, not needing to wait, fully repeatable! As far as I remember from a long time ago, this was a rather simple protocol…

• This is indeed my plan – power supply, frequency generator, multimeter, and oscilloscope all have a control bus (at least one of RS232/USB/GPIB), and with the same SCPI protocol as far as I checked it. Big project, waiting in the wings.

3. Would it make sense to use a buck-boost converter instead of the stock LDO to address the RFM12B low-voltage issue? Something like the Linear LTC3531: http://www.linear.com/product/LTC3531 .

4. Another in a long line of intreguing and educational posts! I have recently been looking at SeeedStudio LiPo Rider Pro/Lithium Ion polymer battery/solar cell combination, to power my outside/garder JeeNode’s. Although that will work, this solution would defintely reduce the overall size of the enclosures (not to mention price of the project). I look forward to the next installment of this topic.

5. Glad y’all like it, but please be patient as it will take at least a week to follow up on these supercap experiments – got some other posts lined up…

6. Seems fair to me, as you are doing all of the work. If it works out it might make a nice alternate power supply, much like the AA Power Board. I was just wondering what size solar panel you envision might be needed to keep the supercap up and running?

• Thx. As for size: check the weblog in two days, for something “quite” small… (not sure yet whether it’ll work)

7. FWIW, my latest estimate for self-discharge is under 5 µA. I’ve pulled the plug on this part of the experiment, I need my workbench and my instruments back :)

8. I’m loving this series of posts. I have a handful of 1F supercaps that I had tried using to power a jeenode with a 2.2V 100mA solar panel through the AA board. My tests results were incredibly disappointing, as I could only get a small number of transmits out of the setup once I removed the solar panel. I assumed the “high self discharge rate” was a several orders of magnitude higher, I was almost certainly not charging the capacitor to anywhere near its capacity.

I’m looking forward to you getting back to this and working your nanojoule magic to show how viable a setup this is. Seeing the error of my ways I’ll swap the NiCd battery for one of those 1F supercaps in my 8MHz outdoor solar transmitter and have some additional numbers by the time you get back to it.

9. I’m using a set of ultracaps for quite some time to power a wireless sensor node (that reports the light level in my garden to steer the windows blinds. It is not a jeenode though, but a custom PIC design. My experience is that the system works fine for the first few months, but after that the capacity of the ultracap detoriates until the point that you cannot bridge a single night on a fully charged ultracap. The fact that the node is outside of course does mean the cap temperature fluctuates quite a bit. This does not help in prolonging the lifespan of the cap. I have linked to the project name with my website link, there is more info there.

• Thanks for sharing this very valuable info (with very nice graphs on the page you link to!).

Hm… lifetime is something I haven’t heard much about until now. Good to know – I’ll probably keep a couple of alternatives on the back-burner. Evidently, finding a good solution which lasts several years is important, otherwise we might as well just use a couple of AA batteries…

10. I’ve been playing around with a similar supercap (Cooper Bussmann KR-5R5H474-R) for a miniature rocket altimeter I’m creating. I’ve found the following site helpful for estimating discharge times: http://www.circuits.dk/calculator_capacitor_discharge.htm I use an LDO (TI TPS71533) in my application to keep the max voltage to 3.3V and then the regulator tracks the capacitor discharge down to my brown-out voltage level (2.7V) where I stop operating. If I wanted to get every last coulomb of charge out of the capacitor, I would boost it with something like Linear’s LTC3525-3.3. I haven’t tried that option for my application, but that boost regulator would still provide 3.3V with a capacitor discharged to 1V.

11. Since the µA count, don’t forget the blocking diode for the solar panel – unfortunately reverse leakage is not negligible with a conventional diode…