5.1 Inductor Selection

Values for inductance, peak, and RMS currents are required to select the output inductor. The input and output voltages and the inductance value determine the peak-to-peak inductor ripple current. Generally, higher inductance values are used with higher input voltages. Larger peak-to-peak ripple currents will increase the power dissipation in the inductor and MOSFETs. Larger output ripple currents will also require more output capacitance to smooth out the larger ripple current. Smaller peak-to-peak ripple currents require a larger inductance value and, therefore, a larger and more expensive inductor. A good compromise between size, loss, and cost is to set the inductor ripple current to be equal to 20% of the maximum output current. The inductance value is calculated by the equation below:

$L = \frac{V_{OUT} \times \left(V_{IN\left(MAX\right)} - V_{OUT}\right)}{V_{IN\left(MAX\right)} \times f_{SW} \times 20\% \times I_{OUT\left(MAX\right)}}$

Where:

f_SW = Switching frequency, 300kHz.

20% = The ratio of AC ripple current to DC output current.

V_IN(MAX) = The maximum power stage input voltage.

The peak-to-peak inductor current ripple is:

$∆I_{L\left(PP\right)} = \frac{V_{OUT} \times \left(V_{IN\left(MAX\right)} - V_{OUT}\right)}{V_{IN\left(MAX\right)} \times f_{SW} \times L}$

The peak inductor current is equal to the average output current plus one half of the peak-to-peak inductor current ripple.

$I_{L\left(PK\right)} = I_{OUT\left(MAX\right)} + 0.5 \times ∆I_{L\left(PP\right)}$

The RMS inductor current is used to calculate the I²R losses in the inductor.

$I_{L\left(RMS\right)} = \sqrt{{I_{OUT\left(MAX\right)}}^2 + \frac{∆{I_{L\left(PP\right)}}^2}{12}}$

Maximizing efficiency requires the proper selection of core material and minimizing the winding resistance. The high frequency operation of the MIC26400 requires the use of ferrite materials for all but the most cost sensitive applications. Lower cost iron powder cores may be used but the increase in core loss will reduce the efficiency of the power supply. This is especially noticeable at low output power. The winding resistance decreases efficiency at the higher output current levels. The winding resistance must be minimized, although this usually comes at the expense of a larger inductor. The power dissipated in the inductor is equal to the sum of the core and copper losses. At higher output loads, the core losses are usually insignificant and can be ignored. At lower output currents, the core losses can be a significant contributor. Core loss information is usually available from the magnetics vendor. Copper loss in the inductor is calculated by the equation below:

$P_{INDUCTOR\left(CU\right)} = {I_{L\left(RMS\right)}}^2 \times R_{WINDING}$

The resistance of the copper wire, R_WINDING, increases with temperature. The value of the winding resistance used should be at the operating temperature.

$R_{WINDING\left(HT\right)} = R_{WINDING\left(20°C\right)} \times \left(1 + 0.0042 \times \left(T_H - T_{20°C}\right)\right)$

Where:

T_H = Temperature of the wire under full load.

T_20°C = Ambient temperature.

R_{WINDING(20°C)} = Room temperature winding resistance (usually specified by the manufacturer).