The number of turns on the primary winding (N_P) of the transformer is determined by two design considerations:

1. The maximum flux density (B_MAX) must be kept below the saturation limit (B_SAT) of the chosen magnetic core under the highest peak magnetizing current (I_M+(MAX)) condition, the cross-sectional area (A_E) of the core, and highest core temperature. When I_FB = 0 A, such as during V_O soft-start or step-up load transient, the peak magnetizing current reaches I_M+(MAX), since V_CST = V_CST(MAX) in those conditions. I_M+(MAX) can be estimated based on the output power triggering an OPP fault (P_O(OPP)) with V_CST = V_CST(OPP1) at V_BULK(MIN).
   Equation 25.
   Equation 26.
2. 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 (I_M-), used to put into the Steinmetz equation for more accurate core loss estimation. For V_BULK ≥ N_PS(V_O+V_F), I_M- is calculated with V_BULK divided by the characteristic impedance of L_M and the lumped time-related switch-node capacitance (C_SW). I_M- is always a negative value. The expression of f_SW is derived based on the triangular approximation of the magnetizing current, which also considers the effect of I_M- 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 I_M- is a negative value and that ΔB is a peak-to-peak flux swing. Core loss is based on ½ of ΔB.