8.2.3.5.1 Inductor Selection

Use Equation 8 to calculate the minimum value of the output inductor (L_MIN).

Equation 8.

Where:

K_IND is a coefficient that represents the amount of inductor ripple current relative to the maximum output current.

In general, the value of K_IND is at the discretion of the designer; however, the following guidelines may be used. For designs using low-ESR output capacitors, such as ceramics, a value as high as K_IND = 0.3 can be used. When using higher ESR output capacitors, K_IND = 0.2 yields better results.

For this design example, use K_IND = 0.3. The minimum inductor value is calculated as 13.7 μH. For this design, a close standard value of 15 μH was selected for L_MIN.

For the output filter inductor, the RMS current and saturation current ratings must not be exceeded. Use Equation 9 to calculate the RMS inductor current (I_L(RMS)).

Equation 9.

Use Equation 10 to calculate the peak inductor current (I_L(PK)).

Equation 10.

Smaller or larger inductor values can be used depending on the amount of ripple current the designer wants to allow so long as the other design requirements are met. Larger value inductors have lower AC current and result in lower output voltage ripple. Smaller inductor values increase AC current and output voltage ripple.

8.2.3.5.2 Output Capacitor Selection

Consider three primary factors when selecting the value of the output capacitor. The output capacitor determines the modulator pole, the output voltage ripple, and how the regulator responds to a large change in load current. The output capacitance must be selected based on the more stringent of these three criteria.

The desired response to a large change in the load current is the first criterion. The output capacitor must supply the load with current when the regulator cannot. This situation occurs if the desired hold-up times are present for the regulator. In this case, the output capacitor must hold the output voltage above a certain level for a specified amount of time after the input power is removed. The regulator is also temporarily unable to supply sufficient output current if a large, fast increase occurs affecting the current requirements of the load, such as a transition from no load to full load. The regulator usually requires two or more clock cycles for the control loop to notice the change in load current and output voltage and to adjust the duty cycle to react to the change. The output capacitor must be sized to supply the extra current to the load until the control loop responds to the load change. The output capacitance must be large enough to supply the difference in current for 2 clock cycles while only allowing a tolerable amount of drop in the output voltage. Use Equation 11 to calculate the minimum required output capacitance.

Equation 11.

where

• ∆I_OUT is the change in output current
• ƒ_SW is the switching frequency of the regulator
• ∆V_{(OUT )}b is the allowable change in the output voltage

For this example, the transient load response is specified as a 5% change in the output voltage, V_OUT, for a load step of 1.5 A. For this example, ΔI_OUT = 1.5 A and ΔV_OUT = 0.05 × 5 = 0.25 V. Using these values results in a minimum capacitance of 24 μF. This value does not consider the ESR of the output capacitor in the output voltage change. For ceramic capacitors, the ESR is usually small enough to ignore in this calculation.

Equation 12 calculates the minimum output capacitance required to meet the output voltage ripple specification. In this case, the maximum output voltage ripple is 30 mV. Under this requirement, Equation 12 yields 4.56 μF.

Equation 12.

where

• ƒ_SW is the switching frequency
• V_(OUTripple) is the maximum allowable output voltage ripple
• I_(ripple) is the inductor ripple current

Use Equation 13 to calculate the maximum ESR an output capacitor can have to meet the output-voltage ripple specification. Equation 13 indicates the ESR should be less than 54.8 mΩ. In this case, the ESR of the ceramic capacitor is much smaller than 54.8 mΩ.

Equation 13.

The output capacitor can affect the crossover frequency ƒ_o. Considering to the loop stability and effect of the internal parasitic parameters, choose the crossover frequency less than 40 kHz without considering the feed forward capacitor. A simple estimation for the crossover frequency without feed forward capacitor C6 is shown in Equation 14, assuming C_OUT has small ESR.

Equation 14.

Additional capacitance deratings for aging, temperature, and DC bias should be considered which increases this minimum value. For this example, two 22-uF 25-V, X7R ceramic capacitors are used. Capacitors generally have limits to the amount of ripple current they can handle without failing or producing excess heat. An output capacitor that can support the inductor ripple current must be specified. Some capacitor data sheets specify the RMS value of the maximum ripple current. Use Equation 15 to calculate the RMS ripple current that the output capacitor must support. For this application, Equation 15 yields 79 mA for each capacitor.

Equation 15.

8.2.3.5.3 Feed-Forward Capacitor

The TPS54202 is internally compensated and the internal compensation network is composed of two capacitors and one resister shown on the block diagram. Depending on the V_OUT, if the output capacitor C_OUT is dominated by low ESR (ceramic types) capacitors, it could result in low phase margin. To improve the phase boost an external feedforward capacitor C6 can be added in parallel with R2. C6 is chosen such that phase margin is boosted at the crossover frequency.

Equation 16 for C6 was tested:

Equation 16.

For this design, C6 = 75 pF. C6 is not needed when C_OUT has high ESR, and C6 calculated from Equation 16 should be reduced with medium ESR. Table 2 can be used as a starting point.