Table 2. Design Parameters

8.2.2.1 Output Voltage Set-Point

The output voltage of LMR14050-Q1 is externally adjustable using a resistor divider network. The divider network is comprised of top feedback resistor R_FBT and bottom feedback resistor R_FBB. Equation 7 is used to determine the output voltage:

Equation 7.

Choose the value of R_FBT to be 100 kΩ. With the desired output voltage set to 5 V and the V_FB = 0.75 V, the R_FBB value can then be calculated using Equation 7. The formula yields to a value 17.65 kΩ. Choose the closest available value of 17.8 kΩ for R_FBB.

8.2.2.2 Switching Frequency

For desired frequency, use Equation 8 to calculate the required value for R_T.

Equation 8.

For 300 kHz, the calculated R_T is 86.57 kΩ and standard value 86.6 kΩ can be used to set the switching frequency at 300 kHz.

8.2.2.3 Output Inductor Selection

The most critical parameters for the inductor are the inductance, saturation current and the RMS current. The inductance is based on the desired peak-to-peak ripple current Δi_L. Since the ripple current increases with the input voltage, the maximum input voltage is always used to calculate the minimum inductance L_MIN. Use Equation 10 to calculate the minimum value of the output inductor. K_IND is a coefficient that represents the amount of inductor ripple current relative to the maximum output current. A reasonable value of K_IND should be 20%-40%. During an instantaneous short or over current operation event, the RMS and peak inductor current can be high. The inductor current rating should be higher than current limit.

Equation 9.

Equation 10.

In general, it is preferable to choose lower inductance in switching power supplies, because it usually corresponds to faster transient response, smaller DCR, and reduced size for more compact designs. But too low of an inductance can generate too large of an inductor current ripple such that over current protection at the full load could be falsely triggered. It also generates more conduction loss since the RMS current is slightly higher. Larger inductor current ripple also implies larger output voltage ripple with same output capacitors. With peak current mode control, it is not recommended to have too small of an inductor current ripple. A larger peak current ripple improves the comparator signal to noise ratio.

For this design example, choose K_IND = 0.4, the minimum inductor value is calculated to be 7.17 µH, and a nearest standard value is chosen: 8.2 µH. A standard 8.2 μH ferrite inductor with a capability of 6 A RMS current and 9 A saturation current can be used.

8.2.2.4 Output Capacitor Selection

The output capacitor(s), C_OUT, should be chosen with care since it directly affects the steady state output voltage ripple, loop stability and the voltage over/undershoot during load current transients.

The output ripple is essentially composed of two parts. One is caused by the inductor current ripple going through the Equivalent Series Resistance (ESR) of the output capacitors:

Equation 11.

The other is caused by the inductor current ripple charging and discharging the output capacitors:

Equation 12.

The two components in the voltage ripple are not in phase, so the actual peak-to-peak ripple is smaller than the sum of two peaks.

Output capacitance is usually limited by transient performance specifications if the system requires tight voltage regulation with presence of large current steps and fast slew rate. When a fast large load increase happens, output capacitors provide the required charge before the inductor current can slew up to the appropriate level. The regulator’s control loop usually needs three or more clock cycles to respond to the output voltage droop. The output capacitance must be large enough to supply the current difference for three clock cycles to maintain the output voltage within the specified range. Equation 13 shows the minimum output capacitance needed for specified output undershoot. When a sudden large load decrease happens, the output capacitors absorb energy stored in the inductor. The catch diode can’t sink current so the energy stored in the inductor results in an output voltage overshoot. Equation 14 calculates the minimum capacitance required to keep the voltage overshoot within a specified range.

Equation 13.

Equation 14.

where

• K_IND = Ripple ratio of the inductor ripple current (Δi_L / I_OUT)
• I_OL = Low level output current during load transient
• I_OH = High level output current during load transient
• V_US = Target output voltage undershoot
• V_OS = Target output voltage overshoot

For this design example, the target output ripple is 50 mV. Presuppose ΔV_{OUT_ESR} = ΔV_{OUT_C} = 50 mV, and chose K_IND = 0.4. Equation 11 yields ESR no larger than 25 mΩ and Equation 12 yields C_OUT no smaller than 33.3 μF. For the target over/undershoot range of this design, V_US = V_OS = 5% × V_OUT = 250 mV. The C_OUT can be calculated to be no smaller than 180 μF and 79.2 μF by Equation 13 and Equation 14 respectively. In summary, the most stringent criteria for the output capacitor is 180 μF. Four 47 μF, 16 V, X7R ceramic capacitors with 5 mΩ ESR are used in parallel .

8.2.2.5 Schottky Diode Selection

The breakdown voltage rating of the diode is preferred to be 25% higher than the maximum input voltage. The current rating for the diode should be equal to the maximum output current for best reliability in most applications. In cases where the input voltage is much greater than the output voltage the average diode current is lower. In this case it is possible to use a diode with a lower average current rating, approximately (1-D) × I_OUT however the peak current rating should be higher than the maximum load current. A 5 A to 7 A rated diode is a good starting point.

8.2.2.6 Input Capacitor Selection

The LMR14050-Q1 device requires high frequency input decoupling capacitor(s) and a bulk input capacitor, depending on the application. The typical recommended value for the high frequency decoupling capacitor is 4.7 μF to 10 μF. A high-quality ceramic capacitor type X5R or X7R with sufficiency voltage rating is recommended. To compensate the derating of ceramic capacitors, a voltage rating of twice the maximum input voltage is recommended. Additionally, some bulk capacitance can be required, especially if the LMR14050-Q1 circuit is not located within approximately 5 cm from the input voltage source. This capacitor is used to provide damping to the voltage spike due to the lead inductance of the cable or the trace. For this design, two 2.2 μF, X7R ceramic capacitors rated for 100 V are used. A 0.1 μF for high-frequency filtering and place it as close as possible to the device pins.

8.2.2.7 Bootstrap Capacitor Selection

Every LMR14050-Q1 design requires a bootstrap capacitor (C_BOOT). The recommended capacitor is 0.1 μF and rated 16 V or higher. The bootstrap capacitor is located between the SW pin and the BOOT pin. The bootstrap capacitor must be a high-quality ceramic type with an X7R or X5R grade dielectric for temperature stability.

8.2.2.8 Soft-start Capacitor Selection

Use Equation 15 in order to calculate the soft-start capacitor value:

Equation 15.

where

• C_SS = Soft-start capacitor value
• I_SS = Soft-start charging current (3 μA)
• t_SS = Desired soft-start time

For the desired soft-start time of 5 ms and soft-start charging current of 3.0 μA, Equation 15 yields a soft-start capacitor value of 20 nF, a standard 22 nF ceramic capacitor is used.

For design with LMR14050-Q1 in WSON package, the maximum value of C_SS is 4.7 nF.