8.2.2.3 Determining the Duty Cycle

The input to output voltage conversion ratio of the TPS55330 is limited by the worst case maximum duty cycle of 89% and the minimum duty cycle which is determined by the minimum on-time of 77 ns and the switching frequency. The minimum duty cycle can be estimated with Equation 7. With a 600 kHz switching frequency the minimum duty cycle is 4%.

The duty cycle at which the converter operates is dependent on the mode in which the converter is running. If the converter is running in discontinuous conduction mode (DCM), where the inductor current ramps to zero at the end of each cycle, the duty cycle varies with changes of the load much more than it does when running in continuous conduction mode (CCM). In continuous conduction mode, where the inductor maintains a minimum dc current, the duty cycle is related primarily to the input and output voltages as computed in Equation 8. Assume a 0.5 V drop V_D across the Schottky rectifier. At the minimum input of 2.9 V, the duty cycle will be 47%. At the maximum input of 4.2 V, the duty cycle is 24%.

Equation 8.

At light loads the converter will operate in DCM. In this case the duty cycle is a function of the load, input and output voltages, inductance and switching frequency as computed in Equation 9. This can be calculated only after an inductance is chosen in the following section. While operating in DCM with very light load conditions the duty cycle demand will force the TPS55330 to operate with the minimum on time. The converter will then begin pulse skipping which can increase the output ripple.

Equation 9.

All converters using a diode as the freewheeling or catch component have a load current level at which they transit from discontinuous conduction mode to continuous conduction mode. This is the point where the inductor current just falls to zero during the off-time of the power switch. At higher load currents, the inductor current does not fall to zero and diode and switch current assume a trapezoidal wave shape as opposed to a triangular wave shape. The load current boundary between discontinuous conduction and continuous conduction can be found for a set of converter parameters as shown in Equation 10.

Equation 10.

For loads higher than the result of the Equation 10, the duty cycle is given by Equation 8. For loads less than the results of Equation 10, the duty cycle is given Equation 9. For Equation 7 through Equation 10, the variable definitions are as follows.

• V_OUT is the output voltage of the converter in V
• V_D is the forward conduction voltage drop across the rectifier or catch diode in V
• V_IN is the input voltage to the converter in V
• I_OUT is the output current of the converter in A
• L is the inductor value in H
• ƒ_SW is the switching frequency in Hz

Unless otherwise stated, the design equations that follow assume that the converter is running in continuous conduction mode, which typically results in a higher efficiency for the power levels of this converter.