8.2.2.4 Transformer Turns-Ratio, Inductance, Primary Peak Current

The target maximum switching frequency at full-load, the minimum input-capacitor bulk voltage, and the estimated DCM resonant time determine the maximum primary-to-secondary turns-ratio of the transformer.

Initially determine the maximum-available total duty-cycle of the on-time and secondary conduction time based on the target switching frequency, f_MAX, and DCM resonant time. For DCM resonant frequency, assume 500 kHz if an estimate from previous designs is not available. At the transition-mode operation limit of DCM, the interval required from the end of secondary current conduction to the first valley of the V_DS voltage is ½ of the DCM resonant period (t_R), or 1 µs assuming 500 kHz resonant frequency. The maximum allowable MOSFET on-time D_MAX is determined using Equation 12.

Equation 12.

When D_MAX is known, the maximum primary-to-secondary turns-ratio is determined with Equation 13. D_MAGCC is defined as the secondary-diode conduction duty-cycle during CC operation and is fixed internally by the UCC28740 at 0.425. The total voltage on the secondary winding must be determined, which is the sum of V_OCV, V_F, and V_OCBC. For the 5-V USB-charger applications, a turns ratio range of 13 to 15 is typically used.

Equation 13.

A higher turns-ratio generally improves efficiency, but may limit operation at low input voltage. Transformer design iterations are generally necessary to evaluate system-level performance trade-offs. When the optimum turns-ratio N_PS is determined from a detailed transformer design, use this ratio for the following parameters.

The UCC28740 constant-current regulation is achieved by maintaining D_MAGCC at the maximum primary peak current setting. The product of D_MAGCC and V_CST(max) defines a CC-regulating voltage factor V_CCR which is used with N_PS to determine the current-sense resistor value necessary to achieve the regulated CC target, I_OCC (see Equation 14).

Because a small portion of the energy stored in the transformer does not transfer to the output, a transformer-efficiency term is included in the R_CS equation. This efficiency number includes the core and winding losses, the leakage-inductance ratio, and a bias-power to maximum-output-power ratio. An overall-transformer efficiency of 0.91 is a good estimate based on 3.5% leakage inductance, 5% core & winding loss, and 0.5% bias power, for example. Adjust these estimates as appropriate based on each specific application.

Equation 14.

The primary transformer inductance is calculated using the standard energy storage equation for flyback transformers. Primary current, maximum switching frequency, output voltage and current targets, and transformer power losses are included in Equation 16.

First, determine the transformer primary peak current using Equation 15. Peak primary current is the maximum current-sense threshold divided by the current-sense resistance.

Equation 15.

Equation 16.

N_AS is determined by the lowest target operating output voltage while in constant-current regulation and by the VDD UVLO turnoff threshold of the UCC28740. Additional energy is supplied to VDD from the transformer leakage-inductance which allows a lower turns ratio to be used in many designs.

Equation 17.