The number of turns on the primary winding (NP) of the transformer is determined by two design considerations:
- The maximum flux density (BMAX) must be kept below the saturation limit (BSAT) of the chosen magnetic core under the highest peak magnetizing current (IM+(MAX)) condition, the cross-sectional area (AE) of the core, and highest core temperature. When IFB = 0 A, such as during VO soft-start or step-up load transient, the peak magnetizing current reaches IM+(MAX), since VCST = VCST(MAX) in those conditions. IM+(MAX) can be estimated based on the output power triggering an OPP fault (PO(OPP)) with VCST = VCST(OPP1) at VBULK(MIN).
Equation 25. Equation 26. - The AC flux density (ΔB) affects the core loss of the transformer. For a transition-mode ZVS flyback, the core loss is usually highest at high line, since the switching frequency is highest, duty cycle is smallest, and peak-to-peak magnetizing current swing is greatest for a given load condition. The following equation is the ΔB calculation including the contribution of negative magnetizing current (IM-), used to put into the Steinmetz equation for more accurate core loss estimation. For VBULK ≥ NPS(VO+VF), IM- is calculated with VBULK divided by the characteristic impedance of LM and the lumped time-related switch-node capacitance (CSW). IM- is always a negative value. The expression of fSW is derived based on the triangular approximation of the magnetizing current, which also considers the effect of IM- over wide DC or AC input line conditions.
Equation 27. Equation 28. Equation 29. Equation 30. Equation 31. Equation 32.
For the ΔB calculation, remember that IM- is a negative value and that ΔB is a peak-to-peak flux swing. Core loss is based on ½ of ΔB.