SNOSDL9 Data sheet

SNOSDL9B December 2024 – May 2026 LMG5126

PRODUCTION DATA

7.2.3.5 Inductor Selection L_m

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.
Verify that the falling slope of the inductor current is small enough to prevent sub-harmonic oscillation. A larger inductance value results in a smaller falling slope of the inductor current.
Place the RHPZ at a 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:

Equation 45.

V_{s l o p e} \times f_{s w} > \frac{V_{o u t_m a x} - V_{i n_m i n}}{2 \times L_{m}} \times R_{c s}

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:

Equation 46.

L_{m} > \frac{V_{o u t_m a x} - V_{i n_m i n}}{2 \times V_{s l o p e} \times f_{s w}} \times R_{c s}

Estimating R_cs = 2mΩ,:

Equation 47.

L_{m} > 1.9 µ H

The RHPZ frequency can be found as:

Equation 48.

ω_{R H P Z} = \frac{R_{o u t} \times {D'}^{2}}{L_{m_e q}}

Verify that the crossover frequency is lower than 1/5 of RHPZ frequency

Equation 49.

f_{c} < \frac{1}{5} \times \frac{ω_{R H P Z}}{2 π}

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

Equation 50.

L_{m} < 6.2 µ H

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:

Equation 51.

I_{i n_v i n m a x} = \frac{P_{o u t}}{V_{i n_m a x}} = 23.4 A

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:

Equation 52.

V_{i n_R R m a x} = V_{o u t_m a x} \times (1 - 0.33) = 30 V

Thus, use the maximum input voltage V_{in_max} to calculate the maximum ripple ratio.

For this example, a ripple ratio of 0.3, 30% of the input current is chosen. Knowing the switching frequency and the typical output voltage, the inductor value can be calculated as follows:

Equation 53.

L_{m} = \frac{V_{i n_m a x}}{I_{i n} \times R R} \times \frac{1}{f_{s w}} \times (1 - \frac{V_{i n_m a x}}{V_{o u t_m a x}}) = \frac{18 V}{23.4 A \times 0.3} \times \frac{1}{400 k H z} \times 0.6 = 3.8 µ H

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

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

Equation 54.

I_{p p} = \frac{V_{i n_t y p}}{L_{m}} \times \frac{1}{f_{s w}} \times (1 - \frac{V_{i n_t y p}}{V_{o u t}}) = 4.36 A

If a ferrite core inductor is selected, make sure the inductor does 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 leads 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:

Equation 55.

I_{p p_b i a s} = \frac{V_{i n_t y p}}{0.7 \times L_{m}} \times \frac{1}{f_{s w}} \times (1 - \frac{V_{i n_t y p}}{V_{o u t}}) = 6.8 A

7.2.3.5 Inductor Selection Lm

7.2.3.5 Inductor Selection L_m