LTC3442 Datasheet, PDF (15/20 Pages) Linear Integrated Systems – Micropower Synchronous Buck-Boost DC/DC Converter with Automatic Burst Mode Operation

LTC3442
APPLICATIO S I FOR ATIO
where f = switching frequency in MHz. Therefore fre-
quency selection is a compromise between the optimal
efficiency and the smallest solution size.
Closing the Feedback Loop
The LTC3442 incorporates voltage mode PWM control.
The control to output gain varies with operation region
(buck, boost, buck/boost), but is usually no greater than
15. The output filter exhibits a double pole response, as
given by:
f_{FILTER—POLE} = _{2 • π •}
1
L • C_OUT ^Hz
(in buck mode)
f_{FILTER—POLE} =
2
•
V_OUT
•
V_IN
π•
L • C_OUT ^Hz
(in boost mode)
where L is in henries and C_OUT is in farads.
The output filter zero is given by:
f_{FILTER—ZERO} =
2
•
π
•
1
R_ESR
•
C_OUT
Hz
where R_ESR is the equivalent series resistance of the
output cap.
A troublesome feature in boost mode is the right-half
plane zero (RHP), given by:
2
f_RHPZ =
V_IN
2 • π • I_OUT • L • V_OUT
Hz
The loop gain is typically rolled off before the RHP zero
frequency.
A simple Type I compensation network can be incorpo-
rated to stabilize the loop, but at a cost of reduced
bandwidth and slower transient response. To ensure
proper phase margin using Type I compensation, the loop
must be crossed over a decade before the LC double pole.
The unity-gain frequency of the error amplifier with the
Type I compensation is given by:
ERROR
AMP
1.22V
FB
12
V_C
C_P1
11
V_OUT
R1
R2
3442 F07
Figure 7. Error Amplifier with Type I Compensation
f_UG
=
2
•
π
1
• R1•
Hz
C_P1
referring to Figure 7.
Most applications demand an improved transient response
to allow a smaller output filter capacitor. To achieve a
higher bandwidth, Type III compensation is required,
providing two zeros to compensate for the double-pole
response of the output filter. Referring to Figure 8, the
location of the poles and zeros are given by:
f_POLE1
≅
2
•
π
•
1
32e³
•
R1•
Hz
CP1
(which is extremely close to DC)
f_ZERO1
=
2
•
π
1
• R_Z
•
Hz
C_P1
f_ZERO2
=
2
•
π
•
1
R1•
Hz
C_Z1
f_POLE2
=
2
•
π
1
• R_Z
•
C_P2
Hz
where resistance is in ohms and capacitance is in farads.
V_OUT
ERROR
AMP
1.22V
FB
12
R1
C_Z1
V_C
R_Z ^CP1
R2
11
C_P2
3442 F08
Figure 8. Error Amplifier with Type III Compensation
3442f
15