I had not seen your schematic before - it did not show in the simple text editor I first used to view your document. It is a basic analog design. Perhaps a better way of characterizing the current source would be its impulse response - how it behaves in response to a step or pulse input. However, as Jack of all Trades pointed out, it is not very efficient - you are dissipating about 200-300 Watts in the transistors at higher current levels, which is enough energy to run two standard household incandescent lamps. That's why you can get away with using relatively large (10 Ohm) current sharing resistors - they are just taking some of the heat for the transistors.
That's why we recommend pulse width modulation. With this technique, the drive transistor(s) is turned on and off at a fixed frequency. The amount of on time is controlled by comparing the output with the control voltage (input waveform). (The "on" time is the output analog quantity, so no DAC is needed.) The big advantage of this is that instead of converting a lot of power into heat, you can store it in reactive elements (inductor and capacitor) and feed it to the LEDs when the transistor is off. Also, since you aren't heating the transistors so much, you can get by with a much smaller heat sink. To make it even more efficient, you can use power MOSFETs so you don't need as much transistor drive current and can obtain a much smaller voltage drop across the transistor than you would with a bipolar device.
Another reason for using a switched, fixed current level is that LED color varies with drive current. A fixed level gives you more predictable results.
However, as you surmise, a PWM circuit is more complex. The most common circuit uses a reference voltage in a ramp generator circuit. The feedback voltage (taken from the LC filtered output or a load current sense resistor) is compared with the ramp. If it exceeds the ramp voltage, the output drive is turned off.
Fortunately, since this circuit is so commonly used in modern switch mode power supplies, there are plenty of integrated circuits available with all of the really complicated stuff inside them. That's why I recommended you look at the data sheets and application notes for some of these - so you can see how they would be used. The most complicated part is the output drive design. Following is a list of some of the design considerations.
1. It appears that you want to vary the LED current with an input voltage waveform. That means your PWM ramp frequency (usually called switching frequency) needs to be at least twice the highest frequency component of the input waveform to avoid unwanted low frequency variations (the Nyquist criterion). Are you familiar with the Fourier transform? This is used to mathematically convert a waveform into a sum of sine-wave components. Square-waves, sawtooth waves, etc. have a lot of high-frequency content. In practice, you would pick an upper frequency limit that will permit the circuit to do the job you specify, and filter out any input frequency content over that (you're already doing that to some extent with the first-order RC filter at the input of your current source). There is nothing wrong with having your switching frequency much greater than the Nyquist minimum; that would give you a better resolution of the waveform and more stable operation. The trade-off is that circuit layout and EMI reduction become more critical.
2. Your switch-mode regulator IC needs to have an external voltage reference pin (your input goes there), otherwise you would have to use an extra PWM circuit to gate the output using a digital control input (this was what I meant by modulating a regulated maximum current). In other words, you would be looking for an adjustable switching regulator rather than a fixed voltage unit.
3. There are a number of output circuit design topologies. You can use one of the simplest, the "buck" configuration. In this design, the output transistor switches current into an output capacitor through an inductor in series with the transistor drain. The inductor bucks the change in current from the higher input voltage, provided the transistor on-cycle time is not too long.
You can use a regulator IC with a supply voltage less than the LED drive voltage, but then you need a level shifting circuit so you can connect your transistor drain circuit to the higher voltage power supply. This is also available as an integrated circuit called a "high side driver," for example, the International Rectifier IRS2117 or IRS2118. https://ec.irf.com/v6/en/US/adirect/ir;jsessionid=8D81CA35DFC0F4DEAFB221A491F20631?cmd=catSearchFrame&domSendTo=byID&domProductQueryName=IRS2117PBF
4. Study the IC manufacturer's recommendations for the output circuit design. In particular, proper consideration of the inductor flyback voltage and diode reverse recovery current is critical to prevent blowing your output transistor (I recommend using a fast-blow fuse in your prototype to protect the LEDs!) or unnecessarily wasting energy.
http://www.national.com/pf/LM/LM3423.html is a good example of the kind of circuit I'm talking about in "2." above. This IC is designed specifically for driving the type of LED you have, and is rated for up to 75 Volt input, so no high side driver is needed. Note that you would need a separate PWM converter to convert your input waveform to its pulse equivalent. If your waveform is digitally generated, you can skip the DAC and do the PWM generation in software. The serial control signal can then be connected directly to the nDIM input, using an optical isolator if necessary.
A note on selecting inductors and capacitors: make sure they are rated for the current! If you use a capacitor not rated for the high-frequency ripple current you will run, even though it may otherwise be the right size, it could overheat or even explode. I mention this point because it is sometimes neglected in textbooks.
That should cover the circuitry for now. The next topic is thermal and reliability considerations. You should not run right at the maximum current of 1.5 A - keep it down
to 1.2 A or less. The lifetime of a device goes down exponentially as
its temperature rises, more current generates more heat, and the LED is
less efficient at higher currents (see the data sheet graph of light
output vs. current). If you are running at maximum current, a voltage
surge could push you over the limit and destroy your expensive LED
collection. Also, some high-power LEDs have internal back-to-back zener diodes for protection against ESD or other over-voltage; raising the drive power to the limit only wastes energy in the zener diodes instead of providing more light. (I didn't see that in the K2 data sheet, but similar products from other vendors have them.)
Now, to address your biggest concern: heat. The data sheet for the K2 LED states that the thermal resistance is 9 degrees C per watt., meaning for every watt dissipated in the device, its internal temperature rises 9 degrees Celsius. If at 1 A, the voltage drop is 3.72 V (from the K2 data sheet), your device junction could be 33.5 degrees warmer than the point at which it is mounted to its heat sink, assuming all of the power is converted to heat. This is in addition to the thermal resistance of the heat sink and case.
If you get an LED already mounted to a star heat sink, this is an additional 4 °C/W (that's from the 13 °C/W value given for the star package). If you mount a bare LED directly to a circuit board with narrow traces, the additional thermal resistance is several tens of degrees per watt, so the LED will be much hotter than a star plate mounted part. (Each material between the heat generator and the ambient environment is an added thermal resistance in series. Moving air has a lower thermal resistance than still air, which is why fans are commonly part of the solution.)
The star plate offered by Phillips is probably the easiest way to make electrical connections and still take care of the heat. The thermal resistance measurement of 4 °C/W (13 °C/W total) assumes that there is free airflow on both sides of the star, so you would either need to arrange for that or attach the backs of the stars to a larger heat sink. Even so, your LED will still be hot to the touch.
If you don't want to use a lot of space between LEDs to dissipate the heat, consider mounting the LEDs on a ceramic-on-metal substrate (instead of a fiberglass PCB) attached to a finned or liquid-cooled heat sink. I don't know if you have the resources to make this. Since tooling costs are quite high, this technology is rarely used for prototyping or limited runs. If money is of no concern, you could try liquid nitrogen cooling .
The web page at http://www.national.com/analog/led/high_brightness has a number resources for your project, including more on the material I have discussed. I hope I haven't overwhelmed you with detail or insulted you with stuff you already know; I tried to cover the background without knowing how far you have progressed in studies. I look forward to your next post.
