Zaphappy
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Saturation is only o/k when its a part of a normal oscillation cycle, where it will instantly turn itself off and then repeat the cycle.You will want to prevent saturation and monitor current and core temp.
But do those allow for control of the frequency as the OP wants?There are better ways to drive this with a PWM chip for flyback converter that will work better.
Every linear IC company makes them.
http://www.richtek.com/selection-guide/en/selection-flyback.html
[url]https://www.richtek.com/Design%20Support/Technical%20Document/AN017 more detailed design
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