JAJSNP4 データシート

JAJSNP4A May 2023 – February 2024 TPS54KB20

PRODUCTION DATA

パッケージ・オプション

メカニカル・データ（パッケージ｜ピン）

RZR|16
- MPQF704A

サーマルパッド・メカニカル・データ

発注情報

jajsnp4a_oa

7.2.2.5 Choose the Output Capacitor

There are three considerations for selecting the value of the output capacitor:

Stability
Steady state output voltage ripple
Regulator transient response to a change load current

First, calculate the minimum output capacitance based on these three requirements. Equation 22 calculates the minimum capacitance to keep the LC double pole below the f_P(MAX) to meet stability requirements. This requirement helps to keep the LC double pole close to the internal zero. Equation 23 calculates the minimum capacitance to meet the steady state output voltage ripple requirement of 33mV. This calculation is for CCM operation and does not include the portion of the output voltage ripple caused by the ESR or ESL of the output capacitors.

Equation 22.

C_{O U T_S T A B I L I T Y} > {(\frac{1}{2 π \times f_{P (RAMP4)} \times (1 + {(\frac{V_{O U T}}{V_{I N (T Y P)}})}^{2})})}^{2} \times \frac{1}{L_{O U T}} = {(\frac{1}{2 π \times 20.3 k H z \times (1 + {(\frac{3.3 V}{12 V})}^{2})})}^{2} \times \frac{1}{0.47 μ H} = 113 μ F

Equation 23.

C_{O U T_R I P P L E} > \frac{I_{R I P P L E}}{8 \times V_{R I P P L E} \times f_{S W}} = \frac{7 A}{8 \times 33 m V \times 800 k H z} = 33 μ F

Equation 25 and Equation 26 calculate the minimum capacitance to meet the transient response requirement of 99mV with a 10A step. These equations calculate the necessary output capacitance to hold the output voltage steady while the inductor current ramps up or ramps down after a load step. Calculations determine only 418.5μF is needed to meet the transient response requirement. This calculation assumes instant load step.

Equation 24.

C_{O U T_U N D E R S H O O T} > \frac{L \times {I_{S T E P}}^{2} \times (\frac{V_{O U T}}{V_{I N} (m i n) \times f_{S W}} + t_{O F F_M I N} (m a x))}{2 \times V_{T R A N S} \times V_{O U T} \times (\frac{V_{I N} (m i n) - V_{O U T}}{V_{I N} (m i n) \times f_{S W}} - t_{O F F_M I N} (m a x))}

Equation 25.

C_{O U T_U N D E R S H O O T} > \frac{0.47 μ H \times {10 A}^{2} \times (\frac{3.3 V}{4.5 V \times 800 k H z} + 150 n s)}{2 \times 99 m V \times 3.3 V \times (\frac{4.5 V - 3.3 V}{4.5 V \times 800 k H z} - 150 n s)} = 418.5 μ F

Equation 26.

C_{O U T_O V E R S H O O T} > \frac{L \times {I_{S T E P}}^{2}}{2 \times V_{T R A N S} \times V_{O U T}} = \frac{0.47 μ H \times {10 A}^{2}}{2 \times 99 m V \times 3.3 V} = 71.9 μ F

The output capacitance needed to meet the undershoot requirement is the highest value, so this sets the required minimum output capacitance for this example. Stability requirements can also limit the maximum output capacitance. Equation 27 calculates the recommended maximum output capacitance. This calculation keeps the LC double pole above 1/100th the f_SW. Using more output capacitance is possible, but the stability must be checked through a bode plot or transient response measurement. The selected output capacitance is 7 × 22μF, 10V ceramic capacitors. When using ceramic capacitors, the capacitance must be derated due to DC and AC bias effects. The selected capacitors derate to 58% the nominal value giving an effective total capacitance of 89μF. Additionally, 2 × 220μF, 6.3V bulk capacitors are also selected, increasing the effective total output capacitance to 529μF. This effective capacitance meets the minimum and maximum requirements.

Equation 27.

C_{O U T_S T A B I L I T Y} < {(\frac{50}{π \times f_{S W}})}^{2} \times \frac{1}{L} = {(\frac{50}{π \times 800 k H z})}^{2} \times \frac{1}{0.47 μ H} = 842 μ F

This application uses all ceramic capacitors so the effects of ESR on the ripple and transient were ignored. If using non ceramic capacitors, as a starting point, the ESR must be below the values calculated in Equation 28 to meet the ripple requirement and Equation 29 to meet the transient requirement. For more accurate calculations or if using mixed output capacitors, the impedance of the output capacitors must be used to determine if the ripple and transient requirements can be met.

Equation 28.

R_{E S R_R I P P L E} < \frac{V_{R I P P L E}}{I_{R I P P L E}} = \frac{33 m V}{7 A} = 4.7 m Ω

Equation 29.

R_{E S R_T R A N S} < \frac{V_{T R A N S}}{I_{S T E P}} = \frac{99 m V}{10 A} = 9.9 m Ω