Datasheet

ESR OUT
R C
C5
R3
´
=
ZESR
ESR OUT
1
2 R C
¦ »
p ´ ´
P2
1
2 R3 C5
¦ =
p ´ ´
RHPZ
co2
3
¦
¦ =
SW
co1
5
¦
¦ =
Z
1
2 R3 C4
¦ =
p ´ ´
P
1
2 10M C4
¦ =
p ´ W ´
IN
OUT
OUT OUT SENSE
V
1.229 1
A Gea 10M R
V V R 2
= ´ ´ W ´ ´ ´
´
OUT
IN
RHPZ
OUT
2
R
V
2 L V
æ ö
¦ » ´
ç ÷
p´
è ø
OUT
OUT OUT
2
2 R C
¦ »
p ´ ´
TPS55340
www.ti.com SLVSBD4B –MAY 2012–REVISED OCTOBER 2012
The following equations summarize the loop equations for the TPS55340 configured as a CCM boost converter.
They include the power stage output pole (ƒ
OUT
) and the right-half-plane zero (ƒ
RHPZ
) of a boost converter
calculated with Equation 27 and Equation 28 respectively. When calculating ƒ
OUT
it is important to include the
derating of ceramic output capacitors. In the example with an estimated 10.2 µF capacitance, these frequencies
are calculated to 980 kHz and 22.1 kHz respectively. The DC gain (A) of the power stage is calculated with
Equation 27 and is 39.9 dB in this design. The compensation pole (ƒ
P
) and zero (ƒ
Z
) generated by R3, C4 and
internal transconductance amplifier are calculated with Equation 30 and Equation 31 respectively.
Most CCM boost converters will have a stable control loop if f
Z
is set slightly above ƒ
P
through proper sizing of
R3 and C4. A good starting point is C4 = 0.1 µF and R3 = 2kΩ. Increasing R3 or reducing C4 increases the
closed loop bandwidth, and therefore improves the transient response. Adjusting R3 and C4 in opposite direction
increases the phase and gain margin of the loop, which improves loop stability. It is generally recommended to
limit the bandwidth of the loop to the lower of either 1/5 of the switching frequency ƒ
SW
or 1/3 the RHPZ
frequency, ƒ
RHPZ
shown in Equation 28. The spreadsheet tool located in the TPS55340 product folder at
www.ti.com can also be used to aid in compensation design.
(27)
(28)
(29)
(30)
(31)
(32)
(33)
Where
C
OUT
is the equivalent output capacitor (C
OUT
=C8+C9+C10)
R
OUT
is the equivalent load resistance (V
OUT
/I
OUT
)
Gea is the error amplifier transconductance located in the ELECTRICAL CHARACTERISTICS table
R
SENSE
(15mΩ, typical) is the sense resistor in the current control loop
ƒ
co1
and ƒ
co2
are possible bandwith.
An additional capacitor from the COMP pin to GND (C5) can be used to place a high frequency pole in the
control loop. This is not always necessary with ceramic output capacitors. If a non-ceramic output capacitor is
used, there is an additional zero (f
ZESR
) in the control loop which can be calculated with Equation 35. The value
of C5 and the pole created by C5 can be calculated with Equation 36 and Equation 34 respectively. Finally if
more phase margin is needed, an additional zero (f
ZFF
) can be added by placing a capacitor (C
FF
) in parallel with
the top feedback resistor R1. It is recommended to place the zero at the target cross-over frequency or higher.
The feed forward capacitor also adds a pole at a higher frequency. The recommended value of C
FF
can be
calculated with Equation 37.
(34)
(35)
(36)
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