8.2.2.2.3 Primary Turns (N_P)

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

1. The maximum flux density (B_MAX) must be kept below the saturation limit (B_SAT) of the magnetic core under the highest peak magnetizing current (I_M+(MAX)) condition, a given cross-section area (A_E) of the core geometry, and highest core temperature. When I_FB = 0 A, such as 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 calculated based on the output power triggering an OPP fault (P_O(OPP)) with V_CST = V_CST(OPP1) at V_BULK(MIN). After N_P is chosen, N_S can be calculated through N_PS.
Equation 24.
Equation 25.
2. The AC flux density (ΔB) affects the core loss of a transformer. For a transition-mode active clamp flyback, the core loss at high line is usually highest, since the switching frequency is highest and duty cycle is smallest 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). The expression of f_SW is derived based on the triangular approximation of the magnetizing current, which also considers I_M- effect over wide AC line condition.
Equation 26.
Equation 27.
Equation 28.
Equation 29.
Equation 30.
Equation 31.