8.2.2.3 Transformer Turns Ratio, Inductance, Primary-Peak Current

The maximum primary-to-secondary turns ratio can be determined by the target maximum switching frequency at full load, the minimum input capacitor bulk voltage, and the estimated DCM resonant time.

First, determine the maximum duty cycle of the MOSFET based on the target maximum switching frequency, f_MAX, the secondary conduction duty cycle, D_MAGCC, and the DCM resonant period, t_R. For t_R, assume 2 µs (500-kHz resonant frequency), if you do not have an estimate from experience or previous designs. For the transition mode operation limit, the time interval from the end of the secondary current conduction to the first resonant valley of the V_DS voltage is ½ of the DCM resonant period, or 1 µs assuming 500 kHz. Actual designs vary. D_MAX can be determined using Equation 10.

Equation 10.

D_MAGCC is defined as the secondary diode conduction duty cycle during constant current, CC, operation. In the UCC28730, it is fixed internally at 0.432. Once D_MAX is known, the ideal turns ratio of the primary-to-secondary windings can be determined with the equation below. The total voltage on the secondary winding needs to be determined, which is the total of V_OCV, the secondary rectifier drop V_F, and cable compensation voltage V_OCBC, if used. For 5-V USB charger applications, for example, a turns ratio in the range of 13 to 15 is typically used.

Equation 11.

The actual turns ratio depends on the actual number of turns on each of the transformer windings. Choosing N_PS > N_PS(ideal) results in an output power limit lower than (V_OCV x I_OCC) when operating at V_IN(min), and line-frequency ripple may appear on V_OUT. Choosing N_PS < N_PS(ideal) allows full-power regulation down to V_IN(min), but increases conduction losses and the reverse voltage stress on the output rectifier.

Once the actual turns ratio is determined from a detailed transformer design, use this ratio for the following parameter calculations.

The UCC28730 constant-current regulation is achieved by maintaining a maximum D_MAGCC duty cycle of 0.432 at the maximum primary current setting. The transformer turns ratio and constant-current regulating factor determine the current-sense resistor, R_CS, for a regulated constant-current target, I_OCC. Actual implementation of R_CS may consist of multiple parallel resistors to meet power rating and accuracy requirements.

Because not all of the energy stored in the transformer is transferred to the secondary output, a transformer efficiency term, η_XFMR, is used to account for the core and winding loss ratio, leakage inductance loss ratio, and primary bias power ratio with respect to the rated output power. At full load, an overall transformer efficiency estimate of 0.91, for example, includes ~3% leakage inductance loss, ~5% core and winding loss, and ~1% bias power. Actual loss ratios may vary from this example.

Equation 12.

The primary-transformer inductance can be calculated using the standard energy storage equation for flyback transformers. Primary current, maximum switching frequency and output and transformer power losses are included in the equation below.

Initially, determine the transformer peak primary current, I_PP(max).

Peak-primary current is simply the maximum current-sense threshold divided by the current-sense resistance.

Equation 13.

Then, calculate the primary inductance of the transformer, L_P.

Equation 14.

The auxiliary winding to secondary winding turns ratio, N_AS, is determined by the lowest target operating output voltage in constant current regulation, the VDD turn-off threshold of the UCC28730, and the forward diode drops in the respective winding networks.

Equation 15.

There is additional energy supplied to VDD from the transformer leakage inductance energy which may allow a lower turns ratio to be used in many designs.