Here is the simulation of the final optimized version. This simulation matches measured values accurately.
https://tinyurl.com/Schematics-WS2811-CCR
Based on real-life measurements the average sinking current of WS2811 is around 16.5ma (not 18.5 as indicated in the datasheet). In an outside circuit with series resistor value of 610 ohms allowing 20ma, voltage drop of WS2811 to ground was measured at 0.62v with Iws=16.5ma.
In the main circuit approximate average hfe=Ic/Ib=50, Ie/Ib=49 with Vbe=0.7
Rc=6.2 ohm 2W, Rb=1k 1/4W, Re(r)=9.1 ohm 2W, Re(g)=1 ohm 1/4W, Re(b)=1 ohm 1/4W. The selected resistors are more common resistors which are readily available.
There are a few simple relationships that hold true in this circuit. One can modify resistors as long as certain balance is maintained.
1- Ib=Ie/(1+hfe) (set LED current and then calculate Ib, Ie=I-led)
2- Ic=Ie-Ib
3- Iws=16.5=Irb+Ib (with Ie=300ma, Ib=6ma and Irb=10.5ma)
4- Vrb=Vbe+Vre+Vf (note that this relationship is independent of Vcc, for Vbe at or near saturation =0.7)
5- Vb(min)=0.65
6- For the batch of 10W Common Anode RGB used, average Vf for red, grn, blu were 6.85, 9.3, 9.54 respectively at their individually set I-led (305,293,289).
7- Vce needs to be at or above 0.3v and preferably below 1.4v to keep the transistors from overheating. (TO-92 Package)
8- With Vb-min at 0.65 and Vbe of 0.7 then Ve>=1.35 and Vc>=0.95. To tailor the circuit to your specific currents, decide on individual LED currents for color balancing near 300ma, pick a starting voltage for Vb above 0.65 volts, calculate individual Ib=Ie/50 and Irb=16.5-Ib, set Ve=Vb+0.7, Vc=Ve-0.4, and then calculate resistors (Rb, Rc, Re) based on Vb, Ve, Vc, Irb, Ie, Ic. Side note: With everything biased and fixed, Vce changes with WS2811 current sink (0-16.5ma).
9- Once bias has been achieved Vcc cannot be increased more than 1v or transistors will overheat and will be destroyed for long exposure to this voltage. Vcc can range between 11.8 to 12.6v (Ideal Vcc is about 12.2v). The beauty of this circuit is that it is a constant current and constant voltage. If Vf increases due to overheating, Vrb is increased, Irb is increased and the transistor's Ib is pinched to maintain 16.5ma for Iws. This causes the LED current and voltage to drop, keeping the LED at a constant current. Similarly small drop in Vf causes the reverse effect, increasing LED current to compensate. The circuit will maintain a constant current for Vcc between 11.6 and 13v. For long run of wires between pixels, It is recommended that Vcc is set between 12.2v to 12.6V to avoid noticeable dimming of pixels since voltage drop of 30 feet run of wiring is about 0.6v).
10- LED currents were intentionally selected as such to produce a slightly warmer white with good color mixing for yellow, Magenta, and Aqua-Teal. Power Diss. of Transistors are less than 250mw with no need for any heat-sinks as long as Vce is kept in check (<1.5v).
2N4403: TO-92, Vbe(on)=0.6, Vbe(sat)=0.7, Vce(on)=0.3, Vce(sat)=0.6, Ic(max)=600ma, Pd(max)=625mw
Op-amp, NPN, Voltage reference and Resistor below it represent the constant current sinking of WS2811. With a simple modification this circuit can be used as a dumb constant current driver for high power RGB. Remove WS2811 from the circuit and replace it with a Quad op-amp with a simple voltage divider to produce individual voltage references for the op-amps.
Added resistors to achieve the appropriate bias increases power consumption by only 3.4%. This extra power consumption is mostly compensated by running the LED's at their optimum currents below their maximum ratings, increasing life of LED's. Total circuit current consumption including WS2811 overhead is about 1A per RGB pixel which translates to an approximately 12W in power consumption per pixel. The pcb board is small enough to easily fit inside the metal casing of power LED (1-inch x 2.25-inch). Total part cost including pcb is about $1.50 which meets the original set requirements of this post. The ultimate goal of this project is to utilize a low cost interface to convert a "Dumb" 10W RGB Pixel into an "Intelligent" Pixel while providing the Pixel with a constant current. This allows the user to control a large number of High Power pixels by setting individual brightness and colors, utilizing some of the more common SPI and PC based controllers available on the market.