The datasheet states that the minimum duty cycle in buck mode is 20% (8.5 Electrical Characteristics.)
Let's say that the TPS63020 has a large supercap/ultracap on the output, and the circuit is being powered on for the first time in a while (the supercap is discharged to ~0V). +4V is applied to the input of the TPS63020 and the converter starts up. Since the output voltage is very low, the average inductor current setpoint is limited to somewhere around 400ma by the soft start circuit (9.4.1 Softstart and Short Circuit Protection.) The inductor current quickly ramps up and the converter is operating in CCM. Once the average inductor current exceeds the 400ma setpoint, the duty cycle will need to be decreased significantly below 20%, since Vout is still very near 0V, so either:
1. The duty cycle will be limited to 20% minimum and the average inductor current will increase without limit (quickly exceeding the 4A switch ratings), or
2. The duty cycle will be significantly below 20% until the capacitor voltage ramps up to ~0.8V -> M(D) = 0.2. If the voltage on the supercap is 50mV, M(D) = 1/80 D ~ 1.25%. Assuming a constant current of 400mA, it will take ~2s to charge the supercap to 0.8V, and during this time the duty cycle must be less than the minimum specified in the datasheet.
So which of these scenarios will happen?
Thank you!