UCC28780: Data sheet & MathCad worksheet equation question

Hello Gerrit,

Thank you for scrutizing our equations. Explaining how we derived them keeps us sharp.

As you noticed, the datasheet equation (30) is the same as the worksheet equation for i.pk(Vin,Vo,Io). To avoid all the function parenthesis, let’s rearrange the terms of (30) such that we’ll arrive at Po(fl)/eta = 1/2Lmfsw( Im+^2 – Im-^2). This is the form that you were looking for, but it has both peaks of Im in place of the usual I-squared factor.

The reason for this is that the input power (Po/eta) is the net average energy transferred to the output plus losses each switching cycle, and this consists of the total positive energy built up during the on-time minus the “negative energy” needed to ring the switched node to zero (for ZVS). The negative energy (to coin a convenient term) is larger at high line where sufficient negative magnetizing current must be built-up to force the post-demagnetization resonant ring all the way to 0V, and lower at low line where natural resonance achieves ZVS without additional forcing. With the UCC28780 ACF controller, the energy to build up the negative current peak (Im-) is “borrowed” at the end of the demag time (by extending the clamp Fet on-time) from the charge stored on the clamp capacitor. This borrowed charge is replenished during the next primary on-time (by extending the main Fet on-time) and building up a higher positive peak (Im+) than would normally be needed with a simpler flyback scheme. Because energy grows with I^2, Im+ needs to grow only a little bit from a high peak to a slightly higher peak to cover the energy represented by the low-amplitude negative peak.

In the Mathcad worksheet, the amount of Im- is calculated per the conditional equation about 3 eqn’s above the i.pk equation, right next to the diagram you cited. Because the Im- current needed to ring the resonance from a particular voltage level to another is an independent factor (not dependent on power throughput), we can use it to find Im+ peak at any Vin and Vo and Po level. Essentially, equation (30) is derived from an energy balance equation, and the “positive” energy has to increase a little to accommodate the “negative” energy which is not delivered to the load, but used to force ZVS from high bulk voltage and low reflected voltage. That is why Im- is squared and added to the “usual” flyback equation to find Im+. The transformer flux change (which influences core loss) is subject to the same situation, requiring determination of the full span from Im- to Im+ peaks.

Regards,
Ulrich