Datasheet

TPS54110−Q1
SLVS837 − JULY 2008
www.ti.com
10
where K is the frequency multiplier for the spread between
f
LC
and f
CO
. K should be between 5 and 15, typically 10 for
one decade of difference.
For a desired crossover of 60 kHz, K=10 and a 6.8 µH
inductor, the minimum value for the output capacitor is
100 µF. The selected output capacitor must be rated for a
voltage greater than the desired output voltage plus one
half the ripple voltage. Any derating factors must also be
included. The maximum RMS ripple current in the output
capacitor is given by equation 8:
I
COUT(RMS)
+
1
12
Ǹ
ȧ
ȡ
Ȣ
V
OUT
ǒ
V
IN(MAX)
–V
OUT
Ǔ
V
IN(MAX)
L
OUT
F
SW
N
C
ȧ
ȣ
Ȥ
(8)
where N
C
is the number of output capacitors in parallel.
The maximum ESR of the output capacitor is determined
by the allowable output ripple specified in the initial design
parameters. The output ripple voltage 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 9:
ESR
MAX
+ N
C
ǒ
V
IN(MAX)
L
OUT
F
SW
0.8
V
OUT
ǒ
V
IN(MAX)
–V
OUT
Ǔ
Ǔ
DV
p–p(MAX)
(9)
For this design example, a single 100 µF output capacitor
is chosen for C2. The calculated RMS ripple current is
80 mA and the maximum ESR required is 87 mΩ. An
example of a suitable capacitor is the Sanyo Poscap
6TPC100M, rated at 6.3 V with a maximum ESR of 45
milliohms and a ripple-current rating of 1.7 A.
Other capacitor types work well with the TPS54110,
depending on the requirements of the application.
COMPENSATION COMPONENTS
The external compensation used with the TPS54110
allows for a wide range of output-filter configurations. A
large range of capacitor values and dielectric types are
supported. The design example uses type 3 compensation
consisting of R1, R3, R5, C6, C7 and C8. Additionally, R2
and R1 form a voltage-divider network that sets the output
voltage. These component reference designators are the
same as those used in the SWIFT Designer Software.
There are a number of different ways to design a
compensation network. This procedure outlines a
relatively simple procedure that produces good results
with most output filter combinations. Use the SWIFT
Designer Software for designs with unusually high
closed-loop crossover frequencies; with low-value,
low-ESR output capacitors such as ceramics; or if you are
unsure about the design procedure.
A number of considerations apply when designing
compensation networks for the TPS54110. The
compensated error-amplifier gain must not be limited by
the open-loop amplifier gain characteristics and must not
produce excessive gain at the switching frequency. Also,
the closed-loop crossover frequency must be set less than
one-fifth of the switching frequency, and the phase margin
at crossover must be greater than 45 degrees. The general
procedure outlined here meets these requirements
without going into great detail about the theory of loop
compensation.
First, calculate the output filter LC corner frequency using
equation 10:
ƒ
LC
+
1
2p L
OUT
C
OUT
Ǹ
For the design example, f
LC
= 6103 Hz.
Choose a closed-loop crossover frequency greater than
f
LC
and less than one-fifth of the switching frequency. Also,
keep the crossover frequency below 100 kHz, as the error
amplifier may not provide the desired gain at higher
frequencies. The 60-kHz crossover frequency chosen for
this design provides comparatively wide loop bandwidth
while still allowing adequate phase boost to ensure
stability.
Next, the values for the compensation components that
set the poles and zeros of the compensation network are
calculated. Assuming an R1 value > than R5 and a C6
value > C7, the pole and zero locations are given by
equations 11 through 14:
ƒ
Z1
+
1
2pR3C6
ƒ
Z2
+
1
2pR1C8
ƒ
P1
+
1
2pR5C8
ƒ
P2
+
1
2pR3C7
Additionally there is a pole at the origin, which has unity
gain at a frequency:
ƒ
INT
+
1
2pR1C6
This pole is used to set the overall gain of the compensated
error amplifier and determines the closed loop crossover
frequency. Since R1 is given as 10 kΩ and the crossover
frequency is selected as 60 kHz, the desired f
INT
is
calculated from equation 16:
ƒ
INT
+
10
*0.74
ƒ
CO
2
And the value for C6 is given by equation 17:
(10)
(11)
(12)
(13)
(14)
(15)
(16)