@Zzaimon seems to have gotten it right. To expand:
The usual timing for the FETs would be A and D turn on and off simultaneously, with B and C switching simultaneously while A,D are off. And
vice versa.
from figure 3
The "new" approach has the controller chip modifying the switching times.
Notice that A,D are not switching simultaneously, and neither are B,C.
from figure 4.
In this case FET 'D' switches off before FET 'A' does; and the added inductor in the primary reduces the ringing frequency in the primary circuit.
The ringing frequency is chosen so that the voltage waveform at the FET 'D' Drain (FET 'C' Source) terminal is at its positive peak (the supply voltage) when FET 'C' is switched On. Since there is zero voltage across FET 'C' there is no turn-on loss.
And with 'C' On, FET 'A' is now turned Off.
(Whew!)
Now the Primary circuit is still in its first ringing cycle. Since 'C' is On, the right end of the primary is held at supply voltage and the ringing causes the left end of the Primary to be relatively Negative. At some point the left end of the primary is at the Negative supply voltage. When this occurs there is no voltage across FET 'B', so it is now turned on with zero turn-on loss.
Synopsis:
Starting with FETs 'A' and 'D' on, primary current flowing.
D turns Off
When the ringing voltage rises to the supply voltage, turn On 'C'
Turn Off 'A'
With ringing voltage at Negative supply, Turn On 'B'
Primary polarity switching is now complete.
That's how you get Zero Voltage Switching (ZVS) with an H-bridge power supply.
Rather clever, thanks for the thread.
Cheers,
Tom
p.s. All of this was taken from the TI App Note with a few details skipped... and fewer words to wade thru.