power supplyswitch-mode-power-supplytransformer
I've been experimenting on Half Bridge converter and there is something that I can not understand. what is the purpose of the capacitance and extra winding in gate base driver? 
The extra winding is magnetically coupled with other winding of driver transformer.
Your circuit is a DC-restore gate drive scheme. The primary waveform gets AC-coupled and DC-restored on the secondary side.
Probe across the 4.7k resistor and you'll see what the MOSFET is seeing. (Also, 100nF is a little excessive for a MOSFET gate - go with 1 to 10nF to keep it real.) When you look at the gate, you should see that this scheme needs an active pull-down as there's no discharge path for the gate capacitance other than the resistor. Commonly a PNP transistor is used for this function.
(You may also need to damp/clamp the coupling capacitors depending on the amount of ringing you get.)
Assuming you only want the positive parts of the pulses, here's another configuration that's suitable for a half-bridge (symmetrical drive for each FET) - notice no coupling capacitors.
Yes. Any form of isolated or boost supply can provide the high-side gate voltage referenced to its source. Some ideas:
The main concern is level-shifting the control signal without killing your deadtime, introducing too much latency, or slowing down turn-on.
Obviously you need to be cautious of exceeding the Vgs during turn on/off of the floating supply also.
Some references:
http://www.vishay.com/docs/91421/appnote9.pdf
Is it safe to "top up" bootstrap capacitors using a charge pump?
http://www.ti.com/lit/an/slva444/slva444.pdf
https://www.fairchildsemi.com/application-notes/AN/AN-6076.pdf
Best Answer
The below circuit shows a quick simulation file concentrating on the power section only. The thing is to crank the power supply by forcing a self-relaxing activity through the extra winding you mention. An initial start-up current is given by \$R_2\$ which biases \$Q_1\$ at power-up. Given the presence of the speed-up winding and its polarity, this strengthens the biasing of \$Q_1\$ until its collector current no longer rises given the available base current. As \$\frac{d\phi}{dt}=0\$ in the transformer, the transistor blocks because the extra bias disappears. The polarity reverses on the speed-up winding, effectively blocking \$Q_1\$ and now biasing \$Q_2\$ until a new cycle repeats. Then I believe the TL494 will soon drive operations once the auxiliary supply is alive. The start-up sequence seems to be at low frequency and nicely oscillating considering the arbitrary values I put there. It should be enough to understand the role of this extra winding which blindly (there is no over current protection or over voltage protection in the sec. side either) ensures a self-relaxing start-up until the TL494 takes over. I have looked at the Czech site in which the owner gathered a lot of power supply schematics (nice collection!) and it was the way cheap ATX power supplies were designed a while ago. I however do not see the need for a self-relaxing circuit like this one when a 5-V USB auxiliary power supply is present in the silver box as this power supply starts first and then provides a \$V_{cc}\$to the control circuit. Nowadays, most ATX boxes uses a 2-SW forward converter with MOSFETs and a dedicated control section powered from a standby power supply.