LTC3785 Datasheet, PDF (14/20 Pages) Linear Technology – 10V, High Effi ciency, Synchronous, No RSENSE Buck-Boost Controller

LTC3785
APPLICATIO S I FOR ATIO
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.
ERROR
AMP
1.225V
FB
V_OUT
R1
V_C ^CP1
R2
3785 F05
Figure 5. Error Amplifier with Type I Compensation
The unity gain frequency of the error amplifier with the
type 1 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 ≈
2•π
1
• 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
C_Z1
V_C
R_Z
C_P1
R2
C_P2
3785 F06
Figure 6. Error Amplifier with Type III Compensation
EFFICIENCY CONSIDERATIONS
The percentage efficiency of a switching regulator is
equal to the output power divided by the input power
times 100%.
It is often useful to analyze individual losses to determine
what is limiting the efficiency and which change would
produce the most improvement. Although all dissipative
elements in circuits produce losses, four main sources
account for most of the losses in LTC3785 application
circuits:
3785f
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