Datasheet

( )
SENSE CO O
Gain = 20 log 2 R F C + 3- ´ ´ ´ ´p
( )
P1 Z P
F = 1/ 2 R Cp´ ´ ´
( )
Z1 Z Z
F = 1/ 2 R Cp´ ´ ´
( )
PO OA Z
F = 1/ 2 R Cp´ ´ ´
ggm REF
DC
O
V V
G =
V
´
( )
LPP
OUT RMS
1
I = × I
12
TPS54231
SLUS851C –OCTOBER 2008–REVISED JULY 2012 www.ti.com
R
ESR
= Equivalent series resistance of the output capacitors
The peak-to-peak output voltage ripple consists of two terms. The first term is due to the ac ripple current (I
LPP
)
charging and discharging the output capacitance in each switching cycle and the second term is due to the ac
ripple current in the ESR of the output capacitor. These two terms maybe out of phase and may add or subtract
depending on the duty cycle. The required capacitance and ESR of the output filter capacitor must be chosen to
meet the allowable output ripple voltage requirement as specified in the initial design parameters.
The maximum RMS ripple current in the output capacitor is given by Equation 14
(14)
For this design example, two 47-μF ceramic output capacitors are chosen for C8 and C9. These are TDK
C3216X5R0J476M, rated at 6.3 V with a maximum ESR of 2 mΩ and a ripple current rating in excess of 3 A. The
calculated total RMS ripple current is 184 mA ( 92 mA each) and the maximum total ESR required is 56 mΩ.
These output capacitors exceed 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 at the desired output of 3.3 V The selected output capacitor must be rated for a voltage
greater than the desired output voltage plus ½ the ripple voltage. Any derating amount must also be included.
Other capacitor types work well with the TPS54231, depending on the needs of the application.
COMPENSATION COMPONENTS
The external compensation used with the TPS54231 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 ceramic X5R
dielectric output capacitors, but other types are supported.
A Type II compensation scheme is recommended for the TPS54231. 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 required compensation components are a resistor R
Z
) in series with a capacitor R
Z
) from
COMP to ground and a capacitor C
P
) in parallel with R
Z
and C
Z
from COMP to ground.
The dc gain is approximated by Equation 15:
(15)
Where:
V
ggm
= 800
V
REF
= 0.8 V
The low-frequency pole is determined by Equation 16:
(16)
The mid-frequency zero is determined by Equation 17:
(17)
And, the mid-frequency pole is given by Equation 18:
(18)
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 TPS54231it is recommended that the
maximum closed loop crossover frequency be not greater than 25 kHz. Next, the required gain and phase boost
of the crossover network needs to be calculated. By definition, the gain of the compensation network must be the
inverse of the gain of the modulator and output filter. For this design example, where the ESR zero is much
higher than the closed loop crossover frequency, the gain of the modulator and output filter can be approximated
by Equation 19:
(19)
14 Copyright © 2008–2012, Texas Instruments Incorporated