Hi Cobotrox,
I have experienced what you describe. The DRV8800 should be able to do up to 2.8A but the problem is that massive cooling is needed to reach currents close to or above the 2.0A mark. Lets do a mental experiment with its maximum of 2.8A. You can then use the same equations to understand the 2.0A current level. Or you can use this spreadsheet and change the current value on the second column.
http://www.avayan.com/images/RobotTalk/DRV8800PowerDissipationCalculator.xls As you may imagine, the power dissipation inside this device is in the order of 2.8A * 2.8A * (.48+.35) = 6.5W (for the lowest expected RDSON) to 2.8 * 2.8 * (0.85+0.7) = 12.15W for the largest RDSON. The problem is that you may start with the low RDSON when you first power up your load, but as the die heats up, RDSON increases. Hence, I expect to see the device power dissipation being closer to the 12W than to the 6W.
This is a problem because the thermal impedance of the AE-DC1 is fairly poor. The board is small, it only has two layers (with 1 oz copper density) and the bottom layer is not as well designed as my subsequent designs. So lets assume my thermal impedance is something like 35C/W (which is almost wishful thinking). At 12W, we are dealing with a temperature rise of 420C, which is of course a preposterous magnitude as the die is programmed to thermally shutdown at around 175C. Hence, if ambient is about 25C, all we have is 150C termperature rise available, not 420C.
Say you wanted to run at th e 2.8A current and obtain a temperature rise of 150C. We would need a thermal impedance of 12.5C/W. This is VERY hard to obtain! Most likely you would need a very big board, 4 or more layers with 2 ounces of copper and possibly a heat sink on top (or even on bottom!) of the device. Air flow or even water cooling would also help. You can do the math and determine what kind of thermal impedance you would need to get for other lower currents.
The AE-DC1 was superseded by the AE-DualC3A which is a better board in terms of routing, but do not be confused. Still this is a good platform to play with DC motors and subject them to high current for only quite finite amounts of time. In order to obtain a truly continuous DC current output at those high levels, you would need very agressive thermal management considerations.
Have in mind this is not the DRV8800's fault. The truth is the device can do and will do the 2.8A it claims. The problem is that the cost needed to take it there may not be cost effective. I have been telling myself to work on a water cooled project, but have not brought me to do so. I am certain these little devices can be greatly enhanced with some kind of a water cooled contraption. The problem is that the chip may be 3 bucks, but the water cooler system may be that a few dozen times. So I feel pressed to ask "What's the point!?" Sure, it would be a cool idea (eh, literally!) but would just render the cheapness of the DRV8800 a moot point.
Hope the info helps!
Avayan