SLVSHR7 Data sheet

SLVSHR7 August 2024 TPSM8287A12M , TPSM8287A15M

PRODUCTION DATA

9.3.2.4 Selecting the Output Capacitors

If the converter remains in regulation, the minimum required output capacitance is given by:

Equation 46.

C_{O U T (m i n) (r e g)} = (\frac{τ \times (1 + g_{m} \times R_{Comp1})}{2 \times π \times \frac{L}{Nɸ} \times {BW}_{τ}}) (1 + \sqrt{{T O L}_{τ}^{2} + {T O L}_{I N D}^{2} + {T O L}_{f S W}^{2}})

Equation 47.

C_{O U T (m i n) (r e g)} = (\frac{12.5 \times 10^{- 6} \times (1 + 1.5 \times 10^{- 3} \times 2000)}{2 \times π \times \frac{100 \times 10^{- 9}}{4} \times 400 \times 10^{3}}) (1 + \sqrt{{30 %}^{2} + {20 %}^{2} + {10 %}^{2}}) = 1166 μ F

If the converter loop saturates, the minimum output capacitance is given by:

Equation 48.

C_{O U T (m i n) (s a t)} = \frac{1}{∆ V_{O U T}} (\frac{L \times {∆ I_{OUT(max)}}^{2}}{2 \times V_{O U T} \times Nɸ} - \frac{∆ I_{OUT(step)} \times t_{t}}{2}) (1 + {T O L}_{I N D})

Equation 49.

C_{O U T (m i n) (s a t)} = \frac{1}{15 \times 10^{- 3}} (\frac{100 \times 10^{- 9} \times {30.5}^{2}}{2 \times 0.6 \times 4} - \frac{30.0 \times 1 \times 10^{- 6}}{2}) (1 + 20 %) = 345 μ F

In this case, choose C_OUT(min) = 1166µF as the larger of the two values for the output capacitance.

Table 9-3 lists the output capacitors chosen. 2 × 47µF capacitors are placed close to each of the four modules, giving a minimum effective capacitance of about 27µF each. Five 220µF capacitors and five 47µF are placed near the load to approximate the total decoupling capacitance required by a typical load. Each of the 220µF capacitors yield about 138µF of effective capacitance. Together, the 1041µF of effective capacitance is very close to the required minimum value calculated above. For further calculations, use C_OUT = 1041µF.

Equation 50 checks that most of the output capacitance is placed at the load. If the ratio is less than 1, increase the capacitance at the load or place the device, output capacitance, and load next to each other such that there is no separation between the output capacitances.

Equation 50.

\frac{C_{LOAD}}{2 {\times C}_{OUT}} > 1

Equation 51.

\frac{5 \times 27 \times 10^{- 6} + 5 \times 138 \times 10^{- 6}}{2 \times (4 \times 2 \times 27 \times 10^{- 6})} > 1

= True

Equation 52 calculates the output voltage ripple, based on the effective output capacitance value.

Equation 52.

V_{O U T (p - p)} = \frac{I_{L (PP)}}{8 \times C_{OUT} \times f_{s w}}

Equation 53.

V_{O U T (p - p)} = \frac{0.9}{8 \times 1041 \times 10^{- 6} \times 1.5 \times 10^{6}} = 0.072 m V

The ripple is slightly higher in the application due to the ESR and ESL in the output capacitors and the application board parasitics.