TPS54061 Datasheet, PDF (25/36 Pages) Texas Instruments – Wide Input 60V, 200mA Synchronous Step-Down DC-DC Converter with Low IQ

TPS54061
www.ti.com
SLVSBB7A – MAY 2012 – REVISED MAY 2012
Closing the Feedback Loop
The method presented here is easy to calculate and includes the effect of the slope compensation that is internal
to the TPS54061. This method assumes the crossover frequency is between the modulator pole and the ESR
zero and the ESR zero is at least 10 times greater than the modulator pole. Once the output components are
determined, use the equations below to close the feedback loop. A current mode controlled power supply
operating in DCM has a transfer function which includes an ESR zero and pole as shown in Equation 40. To
calculate the current mode power stage gain, first calculate, Kdcm, the DCM gain, and Fm, the modulator gain,
using Equation 41 and Equation 42. Kdcm and Fm are 32.4 and 0.475 respectively. The location of the pole and
ESR zero are calculated using Equation 43 and Equation 44 . The pole and zero are 491 Hz and 2.8 MHz,
respectively. Use the lower value of Equation 45 and Equation 46 as a starting point for the crossover frequency.
Equation 45 is the geometric mean of the power stage pole and the esr zero and Equation 46 is the mean of
power stage pole and the switching frequency. The crossover frequency is chosen as 5 kHz from Equation 46.
To determine the compensation resistor, R_COMP, use Equation 47. Assume the power stage transconductance,
gmps, is 1.0 A/V. The output voltage, V_O, reference voltage, V_REF, and amplifier transconductance, gmea, are
5.0 V, 0.8 V and 108 µA/V, respectively. R_COMP is calculated to be 38.3 kΩ; use the nearest standard value of
35.7 kΩ. Use Equation 48 to set the compensation zero to equalthe modulator pole frequency. Equation 48
yields 290 nF for compensating capacitor C_COMP, and a 330 nF is used. Use the larger value of Equation 49 or
Equation 50 to calculate the C_POLE, which sets the compensation pole. Equation 50 yields 178 pF standard value
of 220 pF is selected.
1+
s
Gdcm(s)
»
Fm ´ Kdcm ´
1+
2´p
´ f_ZERO
s
2 ´ p ´ f_POLE
(40)
2
Kdcm = ´
( ) V_OUT ´ V_IN - V_OUT
D1
æ
ö
V_IN ´
ç
ç_{2 +}
ç
Rdc
÷
÷
V_{OUT ÷}
- V_OUT
çè
I_O ^÷ø
(41)
Fm =
gmps
æ
ç
è
V_IN
L_O
- V_OUT
´ f_sw
ö
÷
+
ø
0.380
(42)
f_POLE (Hz) =
V_OUT
I_O
1
´ C_O ´ 2 ´ p
æ
ç
2
-
´ç
ç
çè
1
-
V_OUT ö
V_IN
÷
÷
V_{OUT ÷}
V_IN ^÷ø
(43)
f_ZERO (Hz) =
R_C
´
1
C_O ´
2
´
p
(44)
( ) f_CO1(Hz) = f_ZERO ´ f_POLE ^0.5
(45)
( ) f_CO2 (Hz) = f_SW ´ f_POLE ^0.5
(46)
R_COMP
=
¦_co
x
V_OUT
Kdcm ´ Fm ´ ¦_POLE V_REF ´ gmea
(47)
C_COMP
=
2
´
p
´
1
R_COMP ´
Kdcm
´
Fm
(48)
C_POLE1
=
R_C ´ C_O
R_COMP
(49)
1
C_POLE2 = _{RCOMP ´ fSW ´ p}
(50)
Copyright © 2012, Texas Instruments Incorporated
Product Folder Link(s): TPS54061
Submit Documentation Feedback
25