Electronic – arduino – Connecting arduino and separate power supply grounds

It's a good idea in general to keep the power for your logic and power devices separated. Motors for instance will generate a lot of noise on your power, and to some extent this may pass straight through the voltage regulator, polluting the microcontroller's \$V_{DD}\$.

One way to keep power supplies separated is feed them via a diode from the common power source. Place a buffer capacitor after the diode, sized for the expected load.

If the LEDs are controlled statically this should be less of a problem than for motors.

Simply power the LED driver (i.e., its VCC pin) with a battery (or other higher-current-capable source), since the Arduino pins are only capable of sourcing 50 mA.

1. First of all, you won't even need a transistor, if you use a battery as I mentioned above. But to answer your question, if you were using a transistor: while there is lag, lag won't be significant enough to affect your application here.

2. And secondly, the TLC5940 is a constant-current driver, so you're fine. A constant current source/sink is exactly that -- it ensures a constant current flows independent of power supply fluctuations/other conditions. Thus your LEDs will light up with constant brightness.

Finally, a clarification regarding PWM with the TLC5940: You don't use PWM of the Arduino pin to directly create PWM on the TLC5940 I/O pins; that's NOT how it works. Instead, the TLC5940 uses serial communication with Arduino -- so you would send it instructions from the Arduino (via SPI or bit-banging, for example; see this TLC5940 Arduino library), and the TLC5940 reads those instructions and performs PWM on the desired I/O pins as instructed.