Does high frequency transformer design vary based on type of switch used for inverter
There are quite a few considerations in transformer design, but one of the main ones is the requirement to keep the transformer out of saturation.  In traditional transformer applications where an ac signal is applied and an ac signal is the result, the transformer input must have no DC component to prevent the core from saturating; in switched mode power supplies, a push-pull circuit is the one that comes to mind where the primary side is always powered.  The primary windings must have exactly the same number of turns, and the duty cycle must be exactly 50% to keep the DC bias from affecting the transformer performance.  In most other topologies, the transformer is really an inductor that is charged by the primary and discharged into the secondary so that both the input and output are not continuous.  In these cases, the transformer's inductance must be controlled, either by means of a gap in the core or by using a core material that performs the same function as gapping.