TPS54232
www.ti.com ........................................................................................................................................................................................... SLVS876–NOVEMBER 2008
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 13
D -0.5
VOPPMAX
(
)
4 ´ FSW ´ CO
ESRmax
=
-
ILPP
(13)
Where VOPPMAX is the desired maximum peak-to-peak output ripple. The maximum RMS ripple current in the
output capacitor is given by Equation 14.
æ
ç
ö
÷
VOUT × V
- VOUT
(
)
× LOUT × FSW × NC
IN(MAX)
1
ICOUT(RMS)
=
×
ç
÷
V
12
IN(MAX)
è
ø
(14)
For this design example, a single 22-µF ceramic output capacitor is chosen for C6. It is rated at 10 V with a
maximum ESR of 5 mΩ and a ripple current rating in excess of 3 A. The calculated total RMS ripple current is
182 mA and the maximum total ESR required is 51mΩ. This output capacitor exceeds the requirements by a
wide margin and will result in a reliable, high-performance design. it is important to note that the actual
capacitance in circuit may be less than the catalog value when the output is operating near the rated voltage for
the capacitor. The selected output capacitor must be rated for a voltage greater than the desired output voltage
plus ½ the ripple voltage but in this example a 10 V capacitor is used so that the effective capacitance will
remain close to the stated value of 22-µF. Other capacitor types work well with the TPS54232, depending on the
needs of the application.
COMPENSATION COMPONENTS
The external compensation used with the TPS54232 allows for a wide range of output filter configurations. A
large range of capacitor values and types of dielectric are supported. The design example uses a ceramic X5R
dielectric output capacitor, but other types are supported.
A Type II compensation scheme is recommended for the TPS54232. The compensation components are chosen
to set the desired closed loop cross over frequency and phase margin for output filter components. The type II
compensation has the following characteristics; a dc gain component, a low frequency pole, and a mid frequency
zero / pole pair.
The dc gain is determined by Equation 15:
Vggm ´ VREF
GDC
=
VO
(15)
Where:
Vggm = 800
VREF = 0.8 V
The low-frequency pole is determined by Equation 16:
VPO = 1/ 2 ´ p ´ R
(
´CZ
)
OO
(16)
(17)
(18)
The mid-frequency zero is determined by Equation 17:
FZ1 = 1/ 2 ´ p ´ R ´CZ
(
)
Z
And, the mid-frequency pole is given by Equation 18:
= 1/ 2 ´ p ´ R ´CP
F
(
)
P1
Z
The first step is to choose the closed loop crossover frequency. In general, the closed-loop crossover frequency
should be less than 1/8 of the minimum operating frequency, but for the TPS54232 it is recommended that the
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