NCP3126 Datasheet, PDF (11/23 Pages) ON Semiconductor – 3 A Synchronous PWM Switching Converter

NCP3126
LP_{_DC} + I_RMS ² @ DCR ³
173 mW + 3.01 A² @ 19.1 mW
(eq. 11)
I_RMS
= Inductor RMS current
DCR
= Inductor DC resistance
LP_{CU_DC} = Inductor DC power dissipation
The core losses and AC copper losses will depend on the
geometry of the selected core, core material, and wire used.
Most vendors will provide the appropriate information to
make accurate calculations of the power dissipation at which
point the total inductor losses can be captured by the
equation below:
LP_tot + LP_{CU_DC} ) LP_{CU_AC} ) LP_Core ³
(eq. 12)
185 mW + 173 mW ) 0 mW ) 12 mW
LP_{CU_DC}
LP_{CU_AC}
LP_Core
= Inductor DC power dissipation
= Inductor AC power dissipation
= Inductor core power dissipation
Output Capacitor Selection
The important factors to consider when selecting an
output capacitor are DC voltage rating, ripple current rating,
output ripple voltage requirements, and transient response
requirements.
The output capacitor must be rated to handle the ripple
current at full load with proper derating. The RMS ratings
given in datasheets are generally for lower switching
frequency than used in switch mode power supplies, but a
multiplier is usually given for higher frequency operation.
The RMS current for the output capacitor can be calculated
below:
Co_RMS
+
I_OUT
@
ra
Ǹ₁₂
³
0.243
A
+
3
A
28%
Ǹ₁₂
(eq. 13)
Co_RMS
I_OUT
ra
= Output capacitor RMS current
= Output current
= Ripple current ratio
The maximum allowable output voltage ripple is a
combination of the ripple current selected, the output
capacitance selected, the Equivalent Series Inductance
(ESL), and Equivalent Series Resitance (ESR).
The main component of the ripple voltage is usually due
to the ESR of the output capacitor and the capacitance
selected, which can be calculated as shown in Equation 14:
ǒ Ǔ V_{ESR_C} + I_OUT * ra *
Co_ESR
)
8
*
1
F_SW *
C_OUT
³
(eq. 14)
ǒ 42.64 mV + 3 * 28% * 50 mW )
1
Ǔ
8 * 350 kHz * 470 mF
Co_ESR
C_OUT
F_SW
I_OUT
ra
= Output capacitor ESR
= Output capacitance
= Switching frequency
= Output current
= Ripple current ratio
The ESL of capacitors depends on the technology chosen,
but tends to range from 1 nH to 20 nH, where ceramic
capacitors have the lowest inductance and electrolytic
capacitors have the highest. The calculated contributing
voltage ripple from ESL is shown for the switch on and
switch off below:
V_ESLON
+
ESL
*
Ipp
D
*
F_SW
³
10 nH * 0.84 A * 350 kHz
15.27 mV +
27.5%
(eq. 15)
V_ESLOFF
+
ESL * Ipp * F_SW
(1 * D)
³
10 nH * 0.84 A * 350 kHz
5.79 mV +
ǒ_{1 * 27.5%} Ǔ
(eq. 16)
D
= Duty ratio
ESL
= Capacitor inductance
F_SW
= Switching frequency
Ipp
= Peak−to−peak current
The output capacitor is a basic component for the fast
response of the power supply. For the first few microseconds
of a load transient, the output capacitor supplies current to
the load. Once the regulator recognizes a load transient, it
adjusts the duty ratio, but the current slope is limited by the
inductor value.
During a load step transient, the output voltage initially
drops due to the current variation inside the capacitor and the
ESR (neglecting the effect of the ESL).
DV_OUT*ESR + I_TRAN Co_ESR ³ 100 mV + 2.0 50 mW
(eq. 17)
Co_ESR
= Output capacitor Equivalent Series
Resistance
I_TRAN
= Output transient current
DV_{OUT_ESR} = Voltage deviation of V_OUT due to the
effects of ESR
A minimum capacitor value is required to sustain the
current during the load transient without discharging it. The
voltage drop due to output capacitor discharge is given by
the following equation:
DV_OUT*DIS +
2
ǒ_ITRANǓ² _LOUT
³
D_MAX C_OUT ^ǒV_IN * V_OUT^Ǔ
ǒ_{2 A}Ǔ² _{6.8 mH} ^{(eq. 18)}
4.02 mV +
2
75%
470 mF
ǒ_{12 V * 3.3 V}Ǔ
C_OUT
D_MAX
I_TRAN
L_OUT
V_IN
V_OUT
DV_{OUT_DIS}
= Output capacitance
= Maximum duty ratio
= Output transient current
= Output inductor value
= Input voltage
= Output voltage
= Voltage deviation of V_OUT due to the
effects of capacitor discharge
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