UCC28780: Value and format of KRES term in equation 23 of UCC28780 datasheet

Hello Robert,

Thank you for your interest in the UCC28780 ACF controller. 

Yes, you are correct; KRES should be entered into equation 23 as 0.05 or 0.06. 

As the text mentions, KRES represents a duty cycle associated with the resonant portion of the overall switching cycle period at the end of the demagnetization time.  This is the interval when the switched-node voltage "resonates" from the reflected output voltage down to zero.  I put the term "resonates" in quotes because although the behavior is that of resonating with the magnetizing inductance, the switched-node capacitance is highly non-linear and so the "resonant" waveform is quite distorted.  It starts out shallow, then drops steeply, then flattens out near zero as the node capacitance is high then low then high again depending on the voltages across both MOSFETs.  This is most pronounced with Si MOSFETs, but also happens with GaN MOSFETs. 

Nevertheless, the timing of this behavior can be approximated as from an equivalent lumped capacitance resonating with Lm, and it is a significant portion of the total switching period.  Significant enough to justify including its own duty-cycle adjustment term in the equation to calculate Lm (Eqn 23).  Here, we take the inverse of the targeted minimum switching frequency fsw(min), which is the maximum switching period, and modify it subtract off the resonant portion (e.g. (1-Kres)) to use the remaining (ton +toff) time in the standard equation for finding Lm in classic Transition Mode (or Critical Conduction Mode) operation.

I would add that the Kres range of 0.05 to 0.06 is a good estimate for minimum switching frequencies in the 150kHz to 300kHz range.  For designs targeting 300-500kHz minimum, 0.07-0.10 may be a better estimate, because the resonant interval begins to be come a larger portion of the overall period.  Also, I emphasize that these are estimates because the actual Lm and Coss are unknown until the design is constructed and tested, but a reasonable estimate gets you closer to your targets and is better than nothing.  Finally, I might add that the resonant transition time from High to Low is estimated, but the transition time from Low to High is neglected because the high peak current usually forces this interval to be extremely short.  Short enough to be neglected to help simplify the calculations.   

Regards,
Ulrich