Datasheet

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LOAD C OUT ESR
PS
MOD c
C OUT LOAD ESR
gm R 2 C R 1
G
2 C R R 1
f
f
f
´ ´ p ´ ´ ´ +
=
p ´ ´ ´ + +
( ) ( )
C min P mod
5f f³ ´
( )
SW
C max
5
f
f £
( )
C max
OUT
51442
V
f £
( )
( )
P mod
C max
OUT
2100
V
f
f £
( )
Z mod
ESR OUT
1
2 R C
f =
´ p ´ ´
( )
( )
OUT max
P mod
OUT OUT
I
2 V C
f =
´ p ´ ´
TPS54140
www.ti.com SLVS889B –OCTOBER 2008–REVISED SEPTEMBER 2013
To compensate the TPS54140 using this method, first calculate the modulator pole and zero using the following
equations:
where
• I
OUT(max)
is the maximum output current
• C
OUT
is the output capacitance
• V
OUT
is the nominal output voltage (41)
(42)
For the example design, the modulator pole is located at 1.5 kHz and the ESR zero is located at 338 kHz.
Next, the designer needs to select a crossover frequency which will determine the bandwidth of the control loop.
The cross over frequency must be located at a frequency at least five times higher than the modulator pole. The
cross over frequency must also be selected so that the available gain of the error amplifier at the cross over
frequency is high enough to allow for proper compensation.
Equation 47 is used to calculate the maximum cross over frequency when the ESR zero is located at a frequency
that is higher than the desired cross over frequency. This will usually be the case for ceramic or low ESR
tantalum capacitors. Aluminum Electrolytic and Tantalum capacitors will typically produce a modulator zero at a
low frequency due to their high ESR.
The example application is using a low ESR ceramic capacitor with 10mΩ of ESR making the zero at 338 kHz.
This value is much higher than typical crossover frequencies so the maximum crossover frequency is calculated
using both Equation 43 and Equation 46.
Using Equation 46 gives a minimum crossover frequency of 7.6 kHz and Equation 43 gives a maximum
crossover frequency of 45.3 kHz.
A crossover frequency of 45 kHz is arbitrarily selected from this range.
For ceramic capacitors use Equation 43:
(43)
For tantalum or aluminum capacitors use Equation 44:
(44)
For all cases use Equation 45 and Equation 46:
(45)
(46)
Once a cross over frequency, ƒc, has been selected, the gain of the modulator at the cross over frequency is
calculated. The gain of the modulator at the cross over frequency is calculated using Equation 47 .
(47)
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