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I want to design a single led to be powered by 4 garden-sized solar cells

You are using the very old transistor as a switch. It must be saturated when used as a switch. Its datasheet and the datasheet for almost all datasheets say that to be a saturated switch then the base current must be 1/10th the collector current. Your base current is way too low then some 2N2907 transistors barely turn on and will not even make the LEDs produce a very dim light.
To use less daytime current you should use a darlington transistor or Jfet and a higher resistor value feeding it.

A flat battery is called a Li-PO (Lithium-Polymer).
 
AK,
The drop down from high ohms to low occurs fairly rapidly as I do your dvm test. At about 6k in increasing light the leds start to dim but very quickly, if the light increases just a bit, the ohms drop further to 3k or less and leds are off. It happens in a blink. The simulation is pretty accurate for my setup. BTW, I use a discrete resistor to represent the CsD sensor in the simulator because of the idiosyncratic app I use that limits the low end manual potentiometer slider to 1%. Since on my sensor, that is 1% of 1 meg, or 10k, the simulation doesn’t work since I can’t slide the pot to my 6k threshold. Probably a way around that, but even though it doesn’t show a variable resistor, the app still has a slide you don’t see that lets me set ohms for each light sensor situation .

Audioguru,
You are right. Old transistor. I never throw anything away and the 2N2907 could be as old as 50 years when I started with my first EE job. This morning was dark and dreary. The patio led project jar light was strong past its 7 am normal off time. I watched it while eating breakfast and even though it was still dark and raining at 740am the dim morning light seemed to snap off the leds. One moment they were on and the next time I looked up from my plate, they were off. I’ll consider what you recommend, but it seems to work great. I’ll take voltage readings each day and report back here when I reach that low voltage limit I was warned about above. So far, about 55 hours over 5 nights, maybe >1600maH.

A note on effective light. Late last night, I noticed a cast of light on my 2nd floor bedroom ceiling coming from my contraption, strong enough to make hand-puppet movement in its shadow, all from three 8ma white leds.
Thanks.
 
A note to Martin about safety.
I found this website and am studying it about Li-Po charging.
So far I have charged my Li-Po with my accurate large power supply set at 4.20 v and only charge it while at my workbench.
E4-BDC3-ED-8833-4542-A814-7-BB44-AAA5-D26.png
 
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Three thoughts.

First. It is better if there is an individual resistor in series with each LED. Ultra-low cost products such as flashlights don't care about mismatches in Vf, but your circuit can have a problem if one LED fails open. The "right" way is to have all of each LEDs current through its own resistor, with no combined currents in one resistor as you have now.

Either way, the resistors set the maximum possible current. If you want an absolute max current per LED of, say, 25 mA, then replace the 10 ohm part with three.68 ohm resistors. A compromise is to keep the 10 ohm part in place, and cut traces to add an additional resistor for each LED. Besides, if you really want to run the LEDs at 20 mA each, 10 ohms is way too small.

Second. If you want a really long time between charging cycles, use two batteries in series and put the three LEDs in series. In this way, the max battery current is only 25 mA, and the voltage drop across a single 56 ohm resistor will be less than before, meaning less power in the resistor for the same power in the LEDs. Efficiency up, brightness matching optimized, current sharing guaranteed.

Third. Buy a small battery charger designed for your battery type and size. Those safety agency markings matter.

ak
 
When you are charging a lithium battery at 4.2V with a large power supply, what is limiting the current if the battery has a problem?
4.2V x a high current= high heating and an explosion. Lithium, titanium and magnesium are flammable.
 
AK,
I just now came to accept your admonition about the solar charged Li-Po or Li-Ion garden light being "waaaaaay" too expensive. So, I am shutting down any further design with such a system.
That means:
1. My present Li-Po garden light, dusk to dawn, may well last a week or more without any attached recharging ability. After it gets to 3.3v (a tedious process to check it daily) I will have to remove the battery and charge it elsewhere.
2. To put a large enough solar panel on the lithium battery garden light along with the necessary microprocessor safety circuits and limits would be ridiculous for each garden light.
3. I will not give up however. I will focus on my original goal of a cheap but better solar garden light that stores enough energy to make it from dusk to dawn consistently, even when a few stormy dark days string together. Regular rechargeable AA batteries probably.
4. And Audioguru's warnings are legitimate and I won't go there with unregulated lithium charging anymore.
txs.
 
To be clear, I wasn't saying it is a bad idea, just so expensive that not-enough people would to pay for it. IMO

Cruise around the Linear Technology and Maxim sites. They both make battery management chips that do not need micro's. Linear Tech and National make lotsa low voltage, low current comparators that can be a simple low-battery-voltage latch-off.

ak
 
April update:
Just to add to my former comments, I have a solution to my original goal of "I want an all-night solar light..."
Here it is:
a. I modified a $2 garden solar light to add a few hundred microhenries to the QX5252F circuitry and thereby reduced the mA draw from 45 mA to 12 mA, that amount chosen because that level of illumination was very sasifactory to me while reducing load mA. I soldered extender wires to place the LED about 2" lower.
b. Thus modified, the cheap solar light with 500 mAh NiCd battery will easily last till dawn and probably 2 or 3 days without solar charge.
d. Then I added my LI-Po battery LED with CdS sensor circuit to the bottom of the same glass jar, with the CdS sensor pointed to the solar light LED but also able to detect ambient light. The previous testing shows the Li-Po will last 7 nights (without recharging) before it hits 3.5 volts and drops off quickly.
e. Result is the Solar LED comes on at dusk and off at dawn. When the Solar LED is on, the Li-Po LED is forced off by the CdS sensor sensing the Solar LED being on. If the Solar LED fails for a lack of battery charge, the Li-Po LED can act as backup for up to 7 days. But, in actual use, I anticipate that lack of sun to be only occasional, and the Li-Po backup may in fact be available for 6 months or more before having to remove it for desktop charging.
f. By doing the above I have a dependable Solar light that meets my goals and I do not violate any safety concerns or expense with solar charging the Li-Po.
g. Costs: Old parts drawer Li-Po, CdS cell and inductor and transistor and resistor, plus Solar light, maybe $3 all together.
 
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