Three main parameters are considered when selecting the inductance value: inductor current ripple ratio (RR), falling slope of the inductor current and the RHPZ frequency of the control loop.

• The inductor current ripple ratio is selected to balance the winding loss and core loss of the inductor. As the ripple current increases the core loss increases and the copper loss decreases.
• The falling slope of the inductor current should be small enough to prevent sub-harmonic oscillation. A larger inductance value results in a smaller falling slope of the inductor current.
• The RHPZ should be placed at high frequency, allowing a higher crossover frequency of the control loop. As the inductance value decrease the RHPZ frequency increases.

According to peak current mode control theory, the slope of the slope compensation ramp must be greater than half of the sensed inductor current falling slope to prevent subharmonic oscillation at high duty cycle, that is:

where

• V_slope is a 48mV peak (at 100% duty cycle) slope compensation ramp at the input of the current sense amplifier.

The lower limit of the inductance can be found as:

It can be estimated R_cs=1.5mΩ, it can be found:

The RHPZ frequency can be found as:

The crossover frequency should be lower than 1/5 of RHPZ frequency :

Assume a crossover frequency of 1kHz is desired, the upper limit of the inductance can be found as:

The inductor ripple current is typically set between 30% and 70% of the full load current, known as a good compromise between core loss and winding loss of the inductor.

Per phase input current can be calculated as:

In continuous conduction mode (CCM) operation, the maximum ripple ratio occurs at a duty cycle of 33%. The input voltage that result in a maximum ripple ratio can be found as:

Thus, the maximum input voltage V_{in_max} should be used to calculate the maximum ripple ratio.

For this example, a ripple ratio of 0.4, 40% of the input current was chosen. Knowing the switching frequency and the typical output voltage, the inductor value can be calculated as follows:

The closest standard value of 3.3 μH was chosen for L_m.

The inductor ripple current at typical input voltage can be calculated as:

If a ferrite core inductor is selected, make sure the inductor will not saturate at peak current limit. The inductance of a ferrite core inductor is almost constant until saturation. Ferrite core has low core loss with a big size.

For powder core inductor, the inductance decreases slowly with increased DC current. This will lead to higher ripple current at high inductor current. For this example, the inductance drops to 70% at peak current limit compared to 0A. The current ripple at peak current limit can be found as: