TPS40200-Q1_16 Datasheet, PDF (23/40 Pages) Texas Instruments – Wide-Input-Range Nonsynchronous Voltage-Mode Controller

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TPS40200-Q1
SLUS739F – SEPTEMBER 2006 – REVISED JANUARY 2016
L_MIN is calculated using Equation 17.
L_MIN
=
V_IN í V_OUT
I_PEAK
× t_ON
=
32
µH
where
• V_IN = 16 V
• V_OUT = 3.3 V
• I_PEAK = 0.25 A
• t_ON = 0.686 μs
1 3.3 V
´
• t_ON is given by 300 kHz 16 V
(17)
The inductor used in the circuit, L1, is the closest standard value of 33 μH. This is the minimum inductance that
can be used in the converter to deliver the minimum current while maintaining continuous conduction.
8.2.1.2.4 Output Capacitance
In order to satisfy the output voltage overshoot and undershoot specifications, there must be enough output
capacitance to keep the output voltage within the specified voltage limits during load current steps.
In a situation where a full load of 2.5 A within the specified voltage limits is suddenly removed, the output
capacitor must absorb energy stored in the output inductor. This condition may be described by realizing that the
energy in the stored in the inductor must be suddenly absorbed by the output capacitance. This energy
relationship is written using Equation 18.
[ ( )] ¹
2
´
L
O^IO
2
1
£´
2
C_O
V_OS ² - V_O ²
where
• V_OS = allowed overshoot voltage above the output voltage
• L_O = inductance
• I_O = output current
• C_O = output capacitance
• V_O = output voltage
(18)
In this application, the worst-case load step is 2.25 A, and the allowed overshoot is 100 mV. With a 33-μH output
inductor, this implies an output capacitance of 249 μF for a 3.3-V output and 165 μF for a 5-V output.
When the load increases from minimum to full load, the output capacitor must deliver current to the load. The
worst case is for a minimum on time that occurs at 16 V_IN, 3.3 V_OUT, and minimum load. This corresponds to an
off time of (1 – 0.2) times the period 3.3 μs and is the worst-case time before the inductor can start supplying
current. This situation may be represented using Equation 19.
DV_O
<
DI_O
´
t _OFFMAX
C_O
where
• ΔV_O = undershoot specification of 60 mV
• ΔI_O = load current step
• t_OFFMAX = maximum off time
(19)
This condition produces a requirement of 100 μF for the output capacitance. The larger of these two
requirements becomes the minimum value of output capacitance. In the schematic, an output capacitor of 220 µF
(C12) in parallel with 1 µF (C11) is shown. This is from the EVM to balance both 3.3-V and 5-V output use cases.
For fixed voltage output, modify the C11 and C12 values per the equations.
The ripple current develops a voltage across the ESR of the output capacitance, so another requirement on this
component is that ESR be small relative to the ripple voltage specification.
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