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ZHCSSP5D January 2009 – September 2023 TPS54332

PRODUCTION DATA

8.2.2.7 Capacitor Selection

The important design factors for the output capacitor are DC voltage rating, ripple current rating, and equivalent series resistance (ESR). The DC voltage and ripple current ratings cannot be exceeded. The ESR is important because along with the inductor current it determines the amount of output ripple voltage. The actual value of the output capacitor is not critical, but some practical limits do exist. Consider the relationship between the desired closed-loop crossover frequency of the design and LC corner frequency of the output filter. In general, keeping the closed-loop crossover frequency at less than 1/5 of the switching frequency is desirable. With high-switching frequencies such as the 1 MHz frequency of this design, internal circuit limitations of the TPS54332 limit the practical maximum crossover frequency to about 75 kHz. In general, the closed-loop crossover frequency must be higher than the corner frequency determined by the load impedance and the output capacitor. This limits the minimum capacitor value for the output filter to:

Equation 12.

C_{O_M I N} = \frac{1}{2 \times π \times R_{O} \times F_{C O_M A X}}

Where R_O is the output load impedance (V_O/I_O) and f_CO is the desired crossover frequency. For a desired maximum crossover of 75 kHz the minimum value for the output capacitor is around 3.2 μF. This can not satisfy the output ripple voltage requirement. The output ripple voltage consists of two components; the voltage change due to the charge and discharge of the output filter capacitance and the voltage change due to the ripple current times the ESR of the output filter capacitor. The output ripple voltage can be estimated by:

Equation 13.

V_{O P P} = I_{L P P} \times (\frac{(D - 0.5)}{4 \times F_{S W} \times C_{O}} + R_{E S R})

Where C_O is the total effective output capacitance.

The maximum ESR of the output capacitor can be determined from the amount of allowable output ripple as specified in the initial design parameters. The contribution to the output ripple voltage due to ESR is the inductor ripple current times the ESR of the output filter, so the maximum specified ESR as listed in the capacitor data sheet is given by Equation 14.

Equation 14.

{E S R}_{M A X} = \frac{V_{O P P M A X}}{I_{L P P}} - \frac{(D - 0.5)}{4 \times F_{S W} \times C_{O}}

Where V_OPPMAX is the desired maximum peak-to-peak output ripple. The maximum RMS ripple current in the output capacitor is given by Equation 15.

Equation 15.

I_{C O U T (R M S)} = \frac{1}{\sqrt{12}} \times (\frac{V_{O U T} \times (V_{I N (M A X)} - V_{O U T})}{V_{I N (M A X)} \times L_{O U T} \times F_{S W} \times N_{C}})

The minimum switching frequency must be used in the above equations (derated by a factor of 0.8). For this design example, two 47-μF ceramic output capacitors are chosen for C2 and C3. These are rated at 10 V with a maximum ESR of 3 mΩ and a ripple current rating in excess of 3 A. The calculated total RMS ripple current is 300 mA (150 mA each) and the total ESR required is 20 mΩ or less. These output capacitors exceed the requirements by a wide margin and result in a reliable, high-performance design. Note that the actual capacitance in circuit can be less than the catalog value when the output is operating at the desired output of 2.5 V. 10-V rated capacitors are used to minimize the this reduction in capacitance due to dc voltage on the output. The selected output capacitor must be rated for a voltage greater than the desired output voltage plus ½ the ripple voltage. Any derating amount must also be included. Other capacitor types work well with the TPS54332, depending on the needs of the application.