Datasheet

LTC3785
14
3785fc
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
OUT
2
V
IN
, Boost Mode
The output filter exhibits a double-pole response and is
given by:
f
FILTER _POLE
=
1
2 • π • L •C
OUT
where C
OUT
is the output filter capacitor.
The output filter zero is given by:
f
FILTER _ ZERO
=
1
2 • π •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
=
V
IN
2
2 • π •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
=
1
2 • π •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
=
1
2 • π •R
Z
•C
P1
f
ZERO2
=
1
2 • π •R1•C
Z1
f
POLE2
≈
1
2 • π •R
Z
•C
P2
Figure 5. Error Amplifier with Type I Compensation
–
+
FB
ERROR
AMP
1.225V
3785 F05
R1
R2
V
C
V
OUT
C
P1
Figure 6. Error Amplifier with Type III Compensation
–
+
FB
ERROR
AMP
1.225V
3785 F06
R1 C
Z1
R2
V
C
R
Z
V
OUT
C
P1
C
P2