By coincidence I was looking for a bycycle dynamo operated LED lamp. White LEDs require about 3.6V, but because the supply varies from the speed you cycle (6V max, AC) I had to put a bunch of electronics in there for it anyway. Furthermore I wished high effiency, I don't want to be cycling for a resistor converting my power into heat.. So I started looking.
Also note that if you get a 1.4V battery, if you drain it, the voltage will slowly drop to about 1V. At 0.8V it's completely dead. You may want to consider to have a working product at 1.2V or 1.1V for example, also if you want to support rechargeable batteries.
For that you really need a DC/DC converter to boost a voltage up. The LT1932 is probably even more suitable for your purpose. It converts a low voltage to a constant current (which you need for a LED). It's a bit expensive (because 1) it's linear technologies, 2) you're trying to do something low-voltage), but it is able to drive a single LED from 1V. It also has a SHDN pin so you can control it:
It can drive several white LEDs (they require over 3V drop each) from 2V input. This figure shows 4 white LEDs, so that's why it needs 2.7V minimal. I don't know how it will behave if you put only 1 LED in there, but I think it will work just fine.
All you need for this driver is shown there. Rset sets the current through the LEDs(in the datasheet is probably a table). It drives the LEDs in this example with 15mA. And as said, LEDs are controlled by current not by voltage. The resistor you normally use only sets a 'fixed' current (for a certain voltage you apply on the system). This regulator is set to a certain current with the resistor Rset, and then you're done. If you put another LED in series, it will adjust the voltage so the current stays the same. Ofcourse, this has limits, but you won't reach that I suppose.
There are more of these IC's and are quite handy. You probably find more examples that are cheaper, but might not be able to work from 1V.
Is it be correct to say that the CSR = ESR + external resistor = 1.3 + 0.5 = 1.8 ohms?
According to a footnote in the datasheet, "CSR(compensation series resistance) refers to the total series resistance, including the equivalent series resistance (ESR) of the capacitor, any series resistance added externally, and PWB trace resistance to CO."
In most cases, the trace resistance will be small enough that you can ignore it, and your formula would be correct enough.
Now I would much rather use a ceramic cap, which from what I've read, has an ESR in the milliohms.
Remember that a ceramic cap in the 10 - 15 uF range is going to be fairly large, which can cause reliability issues (due to mismatched CTE between the cap and board).
It looks like a CSR of 0.1 to 2 ohms would be sufficient.
Notice, comparing figs 28 and 29, that the required CSR changes depending on the capacitor value.
And your capacitor value will change depending on voltage and temperature. But 1-3 Ohms total resistance seems to be okay for any capacitance value.
If I use a ceramic cap instead of the tantalum, and if I add an external resistance of say 1 ohm would this yield proper operation?
Based on the above, this should work. Be sure that your capacitor will have 10 uF or so minimum value over all operating conditions.
Best Answer
That positive passive resistance you have in your box is very 'pure'. Low noise, wide bandwidth, very low reactive components (depending on construction), floating with respect to ground, and very robust against transient high voltages and currents, without clipping or croaking.
You can rig up an opamp or two, with power followers, that can force the current pulled and pushed into/out of a pair of nodes to be proportional to a scale factor of their differential voltage, and that scale factor can be positive or negative, and controllable by a pot.
However, that circuit will have limited bandwidth, add noise, will have stray impedances to ground, and will clip for small overloads and will die with large overloads, depending on how conservatively you design it.
Were I to try such a thing, my biggest problem would be deciding on a specification. I'd start off with a capacity of 1v and 1amp, then think again and it would grow to until it was too large to build.
What can you do with good low Rdson FETs for switches, you could manage mOhms? But it will still be non-zero, and positive.