LTC3785_15 Datasheet, PDF (14/20 Pages) Linear Technology – 10V, High Efficiency, Synchronous, No RSENSE Buck-Boost Controller

LTC3785
applications information
Closing the Feedback Loop
The LTC3785 incorporates voltage mode control. The
control to output gain is given by:
G_BUCK = 1.6 • V_IN, Buck Mode
G_BOOST
=
1.6
• V_OUT2
V_IN
,
Boost
Mode
The output filter exhibits a double-pole response and is
given by:
f_{FILTER _ POLE} = _{2 • π •}
1
L • C_OUT
where C_OUT is the output filter capacitor.
The output filter zero is given by:
f_FILTER
_
ZERO
=
2
•
π
1
• R_ESR
•
C_OUT
where R_ESR is the capacitor equivalent series resistance.
A troublesome feature in boost mode is the right half plane
zero (RHP), and is given by:
f_RHPZ
=
2
•
π
V_IN2
•I_OUT •L
•
V_OUT
The loop gain is typically rolled off before the RHP zero
frequency.
A simple Type I compensation network (Figure 5) can be
incorporated to stabilize the loop but at a cost of reduced
bandwidth and slower transient response. To ensure proper
phase margin, the loop must cross over almost a decade
before the L-C double pole.
The unity gain frequency of the error amplifier with the
Type I compensation is given by:
f_UG
=
2
•
π
•
1
R1•
C_P1
Most applications demand an improved transient response
to allow a smaller output filter capacitor. To achieve a higher
bandwidth, Type III compensation is required as shown
in Figure 6. Two zeros are required to compensate for the
double pole response.
f_POLE1 ≈
1
2 • π • 32e3 • C_P1 •R1
(a
very
low
frequency)
f_ZERO1 =
2
•
π
1
•R_Z
•
C_P1
f_ZERO2
=
2
•
π
•
1
R1•
C_Z1
f_POLE2
≈
2
•
π
1
•R_Z
•
C_P2
ERROR
AMP
1.225V
FB
V_OUT
R1
V_C ^CP1
R2
3785 F05
Figure 5. Error Amplifier with Type I Compensation
ERROR
AMP
1.225V
FB
V_OUT
R1
C_Z1
V_C
R_Z
C_P1
R2
C_P2
3785 F06
Figure 6. Error Amplifier with Type III Compensation
3785fc
14