The turns ratio and primary inductance of the transformer will be determined based on the target specifications of the converter. In order to calculate the maximum allowable turns ratio, a duty cycle limit must be selected for the design. Even though DCL will be connected to AVSS to impose a 50% duty cycle limit from the controller to ensure there is no overlap of the primary switching outputs, a maximum duty cycle of approximately 35% is targeted for the design in order to provide sufficient margin to the controller limit. This is due to the fact that the actual duty cycle is greater than calculated duty cycle when accounting for the converter efficiency, and to allow for duty cycle increases during load transient events. Equation 31 provides the formulate needed to calculate the maximum turns ratio for this design.

V_SR is estimated to be 0.5 V for the application and D_LIM is 35% duty cycle limit that was selected. N_{PS_MAX} is calculated using the values in Equation 32.

A value of 2.5 is selected for the turns ratio for the design.

In order to design for the primary inductance of the transformer, the magnetizing current must be selected. The value of the magnetizing current is a trade-off between transformer size and efficiency, with larger magnetizing current leading to a smaller size due to lower required inductance, but also leading to lower efficiency. A magnetizing current equal to 6% of the output current was initially targeted for this design. With this value, the primary inductance can be calculated using Equation 36. The minimum duty cycle expected is needed for this calculation can be determined using Equation 34, where the estimated efficiency η for the converter used in the calculation is 85%.

Though the calculated value of L_P is 33 μH, it may often be challenging to find the exact primary inductance value needed for the transformer design. As such, an inductance of 40 μH was used in the actual design.

The following equations detail the how to calculate transformer primary and secondary currents that are critical for proper design of the transformer. These equations are useful for defining the physical structure of the transformer. Note that these are ideal equations, and the final design should be optimized depending on the application.

Equation 39.

Equation 40.

Equation 41.

Equation 42.

Equation 43.

Equation 44.

Equation 45.

Equation 46.

Equation 47.

Equation 48.

Equation 49.

Equation 50.

Equation 53.

Equation 54.