8.2.1.2 Inductor Selection

The duty cycle (D) can be approximated quickly using the ratio of output voltage (V_O) to input voltage (V_IN):

Equation 12.

The catch diode (D1) forward voltage drop and the voltage drop across the internal NMOS must be included to calculate a more accurate duty cycle. Calculate D by using the following formula:

Equation 13.

V_SW can be approximated by:

The diode forward drop (V_D) can range from 0.3V to 0.7V depending on the quality of the diode. The lower V_D is, the higher the operating efficiency of the converter.

The inductor value determines the output ripple current. Lower inductor values decrease the size of the inductor, but increase the output ripple current. An increase in the inductor value will decrease the output ripple current. The ratio of ripple current (Δi_L) to output current (I_O) is optimized when it is set between 0.3 and 0.4 at 1 A. The ratio r is defined as:

Equation 15.

One must also ensure that the minimum current limit (1.2 A) is not exceeded, so the peak current in the inductor must be calculated. The peak current (I_LPK) in the inductor is calculated by:

If r = 0.5 at an output of 1 A, the peak current in the inductor will be 1.25 A. The minimum verified current limit over all operating conditions is 1.2 A. One can either reduce r to 0.4 resulting in a 1.2-A peak current, or make the engineering judgement that 50 mA over will be safe enough with a 1.7-A typical current limit and 6 sigma limits. When the designed maximum output current is reduced, the ratio r can be increased. At a current of 0.1 A, r can be made as high as 0.9. The ripple ratio can be increased at lighter loads because the net ripple is actually quite low, and if r remains constant the inductor value can be made quite large. An equation empirically developed for the maximum ripple ratio at any current below 2 A is:

Note that this is just a guideline.

The LMR12010 operates at frequencies allowing the use of ceramic output capacitors without compromising transient response. Ceramic capacitors allow higher inductor ripple without significantly increasing output ripple. See the Output Capacitor for more details on calculating output voltage ripple.

Now that the ripple current or ripple ratio is determined, the inductance is calculated by:

Equation 18.

where

• f_s is the switching frequency
• I_O is the output current

When selecting an inductor, make sure that it is capable of supporting the peak output current without saturating. Inductor saturation will result in a sudden reduction in inductance and prevent the regulator from operating correctly. Because of the speed of the internal current limit, the peak current of the inductor need only be specified for the required maximum output current. For example, if the designed maximum output current is 0.5 A and the peak current is 0.7 A, then the inductor should be specified with a saturation current limit of >0.7 A. There is no need to specify the saturation or peak current of the inductor at the 1.7-A typical switch current limit. The difference in inductor size is a factor of 5. Because of the operating frequency of the LMR12010, ferrite based inductors are preferred to minimize core losses. This presents little restriction since the variety of ferrite based inductors is huge. Lastly, inductors with lower series resistance (DCR) provide better operating efficiency. For recommended inductors see example circuits.