Datasheet

( ) ( )
OUT
C
REF
MOD c EA
V
R
G gm V
f
=
´ ´
( )
( )
( )
( )
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 ´ ´
TPS54160 , TPS54160A
www.ti.com SLVSB56C –MAY 2012–REVISED FEBRUARY 2014
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 selects a crossover frequency which will determine the bandwidth of the control loop. The
crossover frequency must be located at a frequency at least five times higher than the modulator pole. The
crossover frequency must also be selected so that the available gain of the error amplifier at the crossover
frequency is high enough to allow for proper compensation.
Equation 47 is used to calculate the maximum crossover frequency when the ESR zero is located at a frequency
that is higher than the desired crossover 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 crossover frequency, ƒ
C
, has been selected, the gain of the modulator at the crossover frequency is
calculated. The gain of the modulator at the crossover frequency is calculated using Equation 47 .
(47)
For the example problem, the gain of the modulator at the crossover frequency is 0.542. Next, the compensation
components are calculated. A resistor in series with a capacitor is used to create a compensating zero. A
capacitor in parallel to these two components forms the compensating pole. However, calculating the values of
these components varies depending on if the ESR zero is located above or below the crossover frequency. For
ceramic or low ESR tantalum output capacitors, the zero will usually be located above the crossover frequency.
For aluminum electrolytic and tantalum capacitors, the modulator zero is usually located lower in frequency than
the crossover frequency. For cases where the modulator zero is higher than the crossover frequency (ceramic
capacitors).
(48)
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