Vo will also be exactly 0 or 5 volts since the arduino output will sink the tiny current flowing through the resistor when it's LOW (0 volts)

It's quite possible that your 10000 cycle loop takes less than a millisecond to execute

How about using a super capacitor instead of a battery? As far as I know their capacity is more linearly proportional to their voltage than a lithium battery so they don't require a specific voltage to be charged. I could just buy a 4+ volt super cap, and simply use 1 diode to stop reverse current draw back through the solar panel. The watch will run fine anywhere from about 2.5-5v anyway. I just discharged a 3600uF capacitor from 4v at ~6mA/s for 1 second to simulate the watch while active, and it was at 2.2v afterwards. So really a super cap with over 4mF of capacitance should work; at least until it gets recharged. I could get something like this (http://www.digikey.ca/product-detail/en/EEC-S0HD334V/P11065-ND/300481) for way cheaper than the cheapest 4+ volt battery.

Yes, I'm following those charging recommendations. It's too bad the battery requires such a precise voltage. Maybe I can cheat and take it up to 3.5 or even 4v at low current? I'd rather not though, and of course it says right there that I shouldn't.

@dhenry Like I said, the solar panel will be under artificial light for about 12 hours in a day. I planning on using a monocrystalline cell (http://www.digikey.ca/product-detail/en/KXOB22-01X8/KXOB22-01X8-ND/2754274) so it should work inside just fine. My only gripe is that the cell is expensive. There's also this one (http://www.digikey.ca/product-detail/en/CPC1824N/CLA290-ND/1485717) which is much cheaper, but I don't know if it will provide enough current. Either way, I need to figure out a charging circuit.

I'm using a 3.0v ML1220 (http://www.digikey.ca/product-detail/en/ML-1220%2FF1AN/P295-ND/447504) lithium battery that I had laying around. It's sort of overkill I think. Even If the watch pulls 1mA (which is about 1000 times what it should when left alone) it should still get through the night if fully charged. I'm not entirely sure about charging though. I'm going to use a 4v solar panel (don't actually have it yet so I can't check voltage under load and different light intensity). Initially I was going to drop the voltage with diodes so that even in max. light I would only get 3.1v after the diodes, but then I can't charge the battery unless the panel is putting out it's max voltage. My second idea was to use a 3.3v switching regulator and series diode on the output to drop the voltage a bit, but I'm not sure which regulator to pick. Does this one look OK? (http://semicon.njr.co.jp/eng/PDF/NJU7261series_E.pdf). It says it's a step-up but the input voltage can be higher than the output so I'm guessing it can work as a step-down. What do I need other than a 100uH inductor and decoupling caps? Could I use a 3v regulator and skip the diode? The datasheet doesn't mention reverse current draw when Vin < Vout which is why I thought of using 3.3v + diode. Will these regulators even work at 20uA input? My latest idea was to use a comparator to compare solar panel voltage and battery voltage and somehow switch in 0, 1, or 2 series diodes to drop the voltage form solar panel to battery. Not sure how I would implement that though. Sorry for the eruption of questions, I've pondering all of this for a quite a while and appreciate any input

they gloss over it with little clear info .

They're not the only ones.

@HazardsMind That's not the easiast thing to do when the current draw changes every 2ms.  But, yes, I have already wired it together and the average current draw that my multimeter gives me seems to be reasonable.

@CrossRoads Yes, even at 250uA with the 25% duty cycle it's running at, it's comparable to an LED watch that I bought. It's amazing what LEDs can do. What would say is a reasonable charging time? I sit in a classrooms for 7 hours a day and at my desk for at least a few hours. With a small, low quality panel at my (not so) well lit desk I get a minimum of 20uA.

Anyway, It was supposed to be more of a check that my math was correct (hence the title), rather than finding other methods to check current consumption.

I'm building a solar powered LED watch and I'm trying to calculate how much current the display will draw so that I can find out what kind solar panel I need. The display is a 4 digit, 7 segment display.

This is what I have so far:

LED current should be ~500uA or more preferably.
At any given time, when looking at the watch there will be ~16/28 segments lit.
The watch will be checked 50 max. in a day (random figure I found online, can't be bothered to actually count.  )
The display will be on for 3 seconds when checking the time.
Only one digit will be displayed at a time. Each digit will be on for 2ms before switching to the next digit, with no dead time in between digits and/or wrap-arounds (last digit back to first digit)

Since ~16 segments will be displayed, this means that on average 4 LEDs are on at any time. 16 segmets/4 digits = 4 segments.

4 LEDs for 3 seconds is the same as 12 LED's for 1 second.
12 LEDs * 500uA = 6000uA/s
6000uA/s * 50 times a day = 300000uA/s = ~83 uA/h

Assuming the watch can charge for 12 hours a day.

83uA/h = ~7 uA/12h
so the solar panel will need to provide at least 7uA continuously for 12 hours. And if I want each LED to get 1mA then the solar panel will need to provide at least 14uA for 12 hours.

Does any of this sound correct? And yes, I know I'm not taking into account active and sleeping MCU current draw, charging circuitry losses, etc.

Its been faster for me too, recently

Not exactly related, but does anyone know the major differences between tje atmega8 and the atmega88? The only difference I've found so far (although I haven't looked much) is that the 88 has pin change interupts on every pin, wheras the m8 doesn't.

Definitely, want the higher PWM frequencies with this mode, perhaps 10kHz or higher, or there will be lots of
copper losses from high AC currents.

Can you elaborate on this? I always thought that the higher the frequency, the worse the losses because of the skin effect. Or are you talking about something else?

I remember using that site sometime before. Completely forgot it existed though.

It seems to work, albeit very slowly, again. I guess I shouldn't be working on electronics in the middle of the night!

Is it down again or it just me? the main page loads but not the product index.

Again, this isn't a regular 3.7v lipo, and I'm not exactly charging it using conventional methods. I just checked digikey and they have pretty cheap step up converters( http://semicon.njr.co.jp/eng/PDF/NJU7261series_E.pdf ). This one seems to do what I need, 3v output. I have a question though. In the equivelent schematic it shows a voltage divider to get an output voltage reference for the comparator. I don't see any info on the datasheet about reverse current draw though. Does anyone know the typical reverse current draw for one of these, if input voltage is too low?