From previous section, it has been determined that the transformer chosen must have a V-t product of 15 Vμs. However, before searching the manufacturer web sites for a suitable transformer, the user still needs to know its minimum turns ratio that allows the push-pull converter to operate flawlessly over the specified current and temperature range. This minimum transformation ratio is expressed through the ratio of minimum secondary to minimum primary voltage multiplied by a correction factor that takes the transformer’s typical efficiency of 97% into account:

V_S-min must be large enough to allow for a maximum voltage drop, V_F-max, across the rectifier diode and still provide sufficient input voltage for the regulator to remain in regulation. From the Section 9.2.2.2 section, this minimum input voltage is known and by adding V_F-max gives the minimum secondary voltage with:

Figure 9-5 Establishing the Required Minimum Turns Ratio Through N_min = 1.03 × V_S-min / V_P-min

Then calculating the available minimum primary voltage, V_P-min, involves subtracting the maximum possible drain-source voltage of the device, V_DS-max, from the minimum converter input voltage V_IN-min:

V_DS-max however, is the product of the maximum R_DS(on) and I_D values for a given supply specified in the data sheet:

Then inserting Equation 16 into Equation 15 yields:

and inserting Equation 17 and Equation 14 into Equation 13 provides the minimum turns ration with:

Examples are given on the calculation method. One is for the fixed input case without duty cycle control. Tthe other is for the wide-ranging input, with or without duty cycle control.

Example of Fixed Input:

For a fixed 24 V V_IN to 15 V_OUT converter using the rectifier diode PMEG200G20ELRX and the LM317A LDO, the data sheet values taken for a load current of 500mA and a maximum temperature of 85°C are V_F-max = 0.5 V,
V_DO-max = 0.7 V, and V_O-max = 15.15 V.

Then assuming that the converter input voltage is taken from a 24V regulated supply with a maximum ±2% accuracy makes V_IN-min = 23.52 V. Finally the maximum values for drain-source resistance and drain current at 24 V are taken from the data sheet with R_DS-max = 1 Ω and I_D-max = 0.5 A.

Inserting the values above into the Equation above yields a minimum turns ratio of:

Example of Wide-Ranging Input:

• Wide-Ranging Input without Duty-Cycle Control

For converter designs with wide-input range but no duty cycle control, the turns ratio needs to take the minimum input voltage into consideration.

Assuming the same diode and LDO are used, the calculation, so V_F-max = 0.5 V, V_DO-max = 0.7 V, and V_O-max = 15.15 V.

The input range from 18 V up to 30 V makes V_IN-min = 18 V. The input range from 18 V up to 30 V with 24 V typical makes V_IN-min = 18 V. Substituting the same R_DS-max = 1 Ω and I_D-max = 0.5 A into the Equation above yields to a minimum turns ratio of:

• Wide-Ranging Input with Duty-Cycle Control

For converter designs with wide-input range, the duty cycle feature is useful to compensate input variaton. But care must be taken to make sure that high turns ratios don’t lead to primary currents that exceed the specified current limits of the device.

Assuming the same diode and LDO are used, so V_F-max = 0.5 V, V_DO-max = 0.7 V, and V_O-max = 15.15 V.

It's recommends the use to set the DC=25% at typical V_IN-typ = 24 V. Substituting the same R_DS-max = 1 Ω and I_D-max = 0.5 A into the Equation above yields to a minimum turns ratio of: