Q2 should have emitter to Q1 emitter and collector grounded.
The transistors are configured as emitter followers.
They have a gain of 1 (and a voltage drop for base to emitter of about 0.6V when on).
But, each transistor has a current gain equal to its Beta or Hfe.
This is typically in the 50 to 300 range depending on devices used.
Input drive sources are often limited in the drive current that they can provide.
The transistors act as "current amplifiers".
For a Beta of say 100, for every 1 mA of input drive they can provide 100 mA of drive to the FET gate.
The result is that the FET gate capacitance is much more rapidly charged or discharged during switching.
This greatly reduces switching times and so decreases switching losses.
Rgate serves two purposes.
- It sets an upper limit on the gate drive current to prevent extremely fast switching with increased EM radiation.
- It provides damping of any gate voltage oscillations which are prone to occur during switching.