Is Vf the thing labeled "Forward Voltage" on page 5 of the spec sheet for royal blue here?
http://www.cree.com/products/pdf/XLampXP-E.pdf
It says forward voltage is 3.5 at 1000mA, and 3.2 at 350 mA. Is forward voltage linear? So at 675mA, the forward voltage or Vf would be 3.35?
Yeah, Vf is forward voltage and is typically listed in datasheets. For the LEDs we're using it is usually between 3 and 3.5v. On a large scale it's extremely non-linear but in the region we're talking about you can kinda assume it is linear. The only real catch is that it's a very "loose" spec in that the tolerance is poor. So you want to give some headroom above the calculated Vf in case they all trend high. The typical "industrial" style DC power supplies most people are using have a trimpot on them to tweak the exact voltage so most people don't get bent out of shape trying to figure out the exact Vf, since you can just tweak the power supply if it's not exactly what you expected. This is way more of a potential issue with the CAT4101 chips, since they're linear, and dissipate the extra power as heat. The LM3409 is a switching regulator, and is reasonably efficient over a much wider range.
In your example, your extra 1.5v is handled by resistors and dissipated as heat right?
Kinda not.
At a very high level, these LEDs need a constant current power supply. The way we achieve this is by providing more power than we need (via the DC power supply) then putting some sort of regulator between the power supply and the LEDs to "chop" the power down to what we want.
There are two basic kinds of circuits that typically are used - passive and active. Passive circuits are "dumb" in that they don't react to conditions. Resistors are passive. You can drive an HPLED with a carefully chosen resistor, just like you do with a tiny little "normal" LED, but the drive current will change with temperature and other fluctuations, and it's inefficient, so it's almost never done. The resistor works by turning the extra power into heat. You use basic math to guess at the resistor's size, then trim it to get the exact current you want under a given set of conditions. In the end, the resistor is just turning a static amount of power into heat.
An active circuit can react to changes in the environment (temperature is the big one) to keep the current constant no matter what. There are two kinds of active regulator circuits - linear and switching. A linear regulator is kind of like a smart resistor. It still does nothing but turn extra power into heat, but it has a feedback mechanism that allows it to adjust to conditions to keep the current stable. When using a linear regulator, efficiency is basically the difference between Vin and Vout, so you want to keep the DC power supply's voltage close to what you actually need in the LED strings, with the caveat that most regs have a minimum difference (for the CAT4101 it is half a volt).
A switching regulator works by turning the current on and off very rapidly, then smoothing the chopped-up current into a constant current at the correct level. The smoothing is usually via a diode and inductor on the output. The losses (and hence efficiency) are mostly related to the switching action itself, plus some small losses in the passives (inductor, diode, etc) not to the difference between input and output voltage. There is no linear relationship between Vin-Vout and efficiency. Switching regs are generally efficient over a wide range of conditions.
The CAT4101 and LM3409 are very typical examples of a linear design vs. a switching design.
Dwzm - very interested in the lm3409 drivers. I just finished reading the thread but still not 100% sure what I need. I'll shoot you a pm.
Saw your email, I will shoot you a note back.
Nate is there a maximum amount of voltage you can use through a power supply? I mean you couldnt run a 110v driver could you?
In theory, more or less there is no limit. However, there are some very serious safety concerns with high voltage DC, and there are diminishing returns as voltages get bigger. Plus, it starts to get really hard to design drivers for higher voltages because your choices for components get really hard. If you read the recent pages in the DIY driver thread you'll see that even for 48v, component selection starts to get really hard for the diode, inductor, and mosFET used by the LM3409 design.