Datasheet

f
C
+
f
SW
4
(Hertz)
BIAS
O
0.7 R1
R
V 0.7
´
= W
-
f
Z
+
1
2p ESR C
O
(Hz)
f
LC
+
1
2p L C
O
Ǹ
(Hz)
( )
( )
( )
IN min IN min
MOD
MOD dB
RAMP RAMP
V V
A or A 20 log
V V
æ ö æ ö
ç ÷ ç ÷
= = ´
ç ÷ ç ÷
è ø è ø
D +
V
O
V
IN
+
V
C
V
S
or
V
O
V
C
+
V
IN
V
S
TPS40060
TPS40061
www.ti.com SLUS543F –DECEMBER 2002–REVISED JUNE 2013
Duty cycle, D, varies from 0 to 1 as the control voltage, V
C
, varies from the minimum ramp voltage to the
maximum ramp voltage, V
S
. Also, for a synchronous buck converter, D = V
O
/ V
IN
. To get the control voltage to
output voltage modulator gain in terms of the input voltage and ramp voltage,
(19)
With the voltage feedforward function, the ramp slope is proportional to the input voltage. Therefore, the
moderator DC gain is independent of the change of input voltage. For the TPS40060 and TPS40061 the
modulator dc gain is shown in Equation 20, with V
IN(min)
as the minimum input voltage required to cause the ramp
excursion to reach the maximum ramp amplitude of V
RAMP
.
(20)
Calculate the Poles and Zeros
For a buck converter using voltage mode control there is a double pole due to the output L-C
O
. The double pole
is located at the frequency calculated in Equation 21.
(21)
There is also a zero created by the output capacitance, C
O
, and its associated ESR. The ESR zero is located at
the frequency calculated in Equation 22.
(22)
Calculate the value of R
BIAS
to set the output voltage, V
O
.
(23)
The maximum crossover frequency (0 dB loop gain) is set by Equation 24.
(24)
Typically, f
C
is selected to be close to the midpoint between the L-C
O
double pole and the ESR zero. At this
frequency, the control to output gain has a –2 slope (-40 dB/decade), while the Type III topology has a +1 slope
(20 dB/decade), resulting in an overall closed loop –1 slope (–20 dB/decade). Figure 9 shows the modulator
gain, L-C filter, output capacitor ESR zero, and the resulting response to be compensated.
A Type III topology, shown in Figure 10, has two zero-pole pairs in addition to a pole at the origin. The gain and
phase boost of a Type III topology is shown in Figure 11. The two zeros are used to compensate the L-C
O
double pole and provide phase boost. The double pole is used to compensate for the ESR zero and provide
controlled gain roll-off. In many cases the second pole can be eliminated and the amplifier's gain roll-off used to
roll-off the overall gain at higher frequencies.
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