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Simpler SMPS schematic for ac-dc converter with planar transformer (high frequency switching)

I found two planar transformers that I want to use in an ac-dc converter.

750341145 and MTPL-2516.

Universal input: 90-265 Vrms AC

Output: 12VDC, 1A

Primary winding of transformers will see bridge rectified pulse DC.

I noticed that while traditional transformers can have high primary inductance (700-900uH), planar ones would have half that values, therefore they'd require much higher MOSFET switching frequencies.

UCC28742 can drive MOSFET switching at maximum 105Khz. Similar case with UCC28740DR which is what WEbench tool suggests when I try to simulate a necessary circuit. Webench doesn't account for a planar transformer, which may require higher than 200Khz of frequency.

Does it mean I have to use an SMPS controller such as UCC28780? The latter requires complex circuits (here's schematic), whilst I want small & simple schematics, such as the one that's offered by UCC28742.

Is it possible to have simpler SMPS circuit with UCC28780? Without having to use all of its pins, no ZVS/active clamp. I'd be fine with efficiency 75-80%, just want a small & simple circuit to go with a planar transformer. Is there another offline switch IC that'd be used then?