8.2.2.5 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.

Initially determine the maximum available total duty cycle of the on time and secondary conduction time based on target switching frequency and DCM resonant time. For DCM resonant time, assume 500 kHz if you do not have an estimate from previous designs. For the transition mode operation limit, the period required from the end of secondary current conduction to the first valley of the V_DS voltage is ½ of the DCM resonant period, or 1 µs assuming 500-kHz resonant frequency. D_MAX can be determined using Equation 10.

Equation 10.

Once D_MAX is known, the maximum turns ratio of the primary to secondary can be determined with the equation below. D_MAGCC is defined as the secondary diode conduction duty cycle when load current reaches a specified limit operation. It is set internally by the UCC28742 at 0.475. The total voltage on the secondary winding needs to be determined; which is the sum of V_OCV and the secondary rectifier V_F.

Equation 11.

N_PS is determined also with other design factors such as voltage and current ratings of primary MOSFET, secondary rectifier diode, as well as secondary MOSFET if synchronous rectifier is used. Once an optimum turns-ratio is determined from a detailed transformer design, use this ratio for the following parameters.

The UCC28742 controller constant current limit is achieved by maintaining D_MAGCC = 0.475 at the maximum primary current setting. The transformer turns ratio and current limit determine the current sense resistor for a target constant current limit.

Since not all of the energy stored in the transformer is transferred to the secondary, a transformer efficiency term is included. This efficiency number includes the core and winding losses, leakage inductance ratio, and bias power ratio to rated output power. A bias power can be initially estimated at 0.1% to 0.5% rated power depending on power rating. An overall transformer efficiency of 94.5% is a good estimation of assuming 2% leakage inductance, 3% core and winding loss, and 0.5% bias power.

R_CS is used to program the primary-peak current with Equation 12:

Equation 12.

The primary transformer inductance can be calculated using the standard energy storage equation for flyback transformers. Primary current, maximum switching frequency, output and transformer efficiency are included in Equation 14.

Initially the transformer primary current should be determined. Primary current is simply the maximum current sense threshold divided by the current sense resistance.

Equation 13.

Equation 14.

The primary inductance L_P in Equation 14 also needs to consider primary MOSFET minimum turn on time as described in Transformer Parameter Verification.

The auxiliary winding to secondary winding transformer turns-ratio (N_AS) is determined by the lowest target operating output voltage V_OVL at current limit and above the VDD_(off) of the UCC28742. The output voltage reaches V_OVL when output current reaches its limit I_OCC; V_OVL is determined by I_OCC and the expected minimum load resistance R_LOAD at I_OCC, i.e., V_OVL = I_OCC x R_LOAD. Note that V_OVL can only be maintained within typical 120ms, and after that time, the output voltage will enter the cycle of shutdown and auto-start retry, as described in Constant Current Limit and Delayed Shutdown, and shown in Figure 14 and Figure 15. There is additional energy supplied to VDD from the transformer leakage inductance energy which may allow a slightly lower turns-ratio to be used in a design. The N_AS is then determined by the below equation.

Equation 15.