Looking at the Add tek data sheet for the amc 7135 sot-89 it says that the current consumed at the Vdd pin is 200 micro amps or .2 mA. This is for each chip on the board, so a 1.4 A 4- chip board would need .8 mA (.0008A)and an 8x 7135 board would need 1.6 mA shared between all of the Vdd pins on the board. It also says that the sot-89 package, which is the one commonly seen on drivers, can handle ~ 700 mW or ~ 2V excess at 350mA output.
This equates to a max of about 5.3 V at the output for a single led with a Vf of 3.3V. This is all speculation on my part so far but for a board to drive 4 xpg from a 4-cell Li-ion:
4 x 4.2 = 16.8 V
4 x 3.3 = 13.2 V or 3.6 V excess. To get the excess within spec of the chips, I would need to lower the hot battery voltage by 1.6 V. 1.6 V / 1.4 A = ~1.1 ohms and 1.6 x 1.4 = 2.24W equals the power consumed in the resistor. Note, this is power that would otherwise have to be burned off by the 7135 chips, so it is no more wasted than it would be otherwise.
On the processor side of the circuit, the input voltage would need to be lowered from 16.8 down under 6V or a total of 10.8 V. So 10.8V / .0008A = 13.5 k ohms and the wattage would be 10.8V x .0008A = 9mW, not a problem for a 1/10 W surface mount resistor.
So what happens when the battery level drops to ~ 3.7V per cell or 14.8V?
14.8V - 13.2V = 1.6V and we no longer need the 1.1 ohm resistor. A fuel guage on the battery would be helpfull in determining when to switch out the resistor.
For the processor, 14.8V - 10.8 V = 4V and the driver is still within spec. At about 13.5 Vm, the voltage to the processor would drop to 2.7V and possibly shut off. In reality, under load, Vbatt would drop immediatly and such a high value resistor might not be necessary. If under load Vbatt was only 4V per cell or 16V total, then the resistor would be: 10V / .0008A or 12.5 kohms and the input voltage to the processor would drop to 2.7V when cell voltage was at 12.7V or ~3.2V per cell. At this point the leds are already begining to be underdriven. This happens whether cells are in series or parallel. The ideal would be to have the leds begin to dim and have the resistance set to kill the lights nearer to the low voltage cutoff of the cells ~3V.
The push behind this idea is that for bike lights, which often have the lamp in one location, the switch by your thumb, and the cells in a third location, having wires with several amps running though them(as is needed for parallel circuits) is not the best solution. Having your light all in one body would solve this at the expense of having to take one hand off the bars to switch modes; not for me on rocky singletrack.