Need help understanding fast LED driver
The capacitor in the RC circuit effectively bypasses the resistor for a short time to provide a "gulp" of current for the device. The setup is reminiscent of a boot strap. Lets take the faster shunt driver as an example. To keep D3 off Q3 is on and diverting current away from D3. This sets up a voltage drop across R7 which is stored in C2. When Q3 turns off the point of C2 which was sitting at ground gets lifted to 5V causing the charge stored in it to push into D3. This push makes available a short burst of current helping to turn on D3 faster.