Datasheet

LTC3816
25
3816f
applicaTions inForMaTion
LC Filter
The external inductor and output capacitor combination
causes a second order LC roll-off at the output with 180°
of phase shift. At higher frequencies, the reactance of the
output capacitor approaches its ESR, and the roll-off due to
the capacitor stops, leaving –20dB/decade and 90° of phase
shift. Beyond the ESR zero, the ceramic capacitor creates a
high frequency pole. The LC filter transfer function, poles
and zero locations are given by the following equations:
A
V
V
sR C
s L C SR C
LC
OUT
SW
ESR BULK
L OUT L OUT
= ≈
+
+ +
( )
1
1
1
2
•
•
11
1
2
+
=
sR
C C
C
f
L C
ESR
BULK CER
OUT
LC DOUBLE POLE
L OU
•
( _ )
π
TT
ESR ZERO
ESR BULK
CER POLE
ESR
f
R C
f
R
C
( )
( )
• •
•
=
=
1
2
1
2
π
π
BBULK CER
OUT
C
C
•
where:
R
L
includes DCR, sense resistance, PCB trace resistance
and the turn-on resistance of the power MOSFET.
L
L
includes the inductor inductance, PCB trace induc-
tance and sense resistor ESL.
C
OUT
= C
BULK
+ C
CER
AITC and Differential Amplifiers
With the sense resistor configuration, the AITC and the
differential amplifiers add a double zero and a pole in the
vicinity of the feedback loop crossover frequency, f
C
, and
multiple poles at higher frequencies. The simplified low
frequency transfer function from the regulator output node
to the SERVO pin, as shown in Figure 14a, is given by the
following equation:
V
V
sA s B
sR C
SERVO
OUT
SR SR
ESR BULK
≈
+ +
+
1
1
2
( ) ( )
•
where:
A
(SR)
= R
ESR
• C
BULK
+ A
G(SR)
• R
SEN
• C
OUT
B
(SR)
= A
G(SR)
• R
SEN
• R
ESR
• C
BULK
• C
CER
Similarly, for the DCR configuration with NTC compen-
sation, the simplified low frequency transfer function is
given by:
V
V
sA s B
sR C
SERVO
OUT
DCR DCR
ESR BULK
≈
+ +
+
1
1
2
( ) ( )
•
where:
A
(DCR)
= R
ESR
• C
BULK
+ A
G(DCR)
• R
DCR
• C
OUT
B
(DCR)
= A
G(DCRN)
• R
DCR
• R
ESR
• C
BULK
• C
CER
Note that with either the sense resistor or the DCR current
sense configuration, the AVP circuitry introduces a pole at
the same location as the LC lowpass filter ESR zero. This
cancels the increase in gain and phase caused by the ESR
zero. Fortunately, the zero in the AVP transfer function is
typically within the closed-loop bandwidth and provides a
beneficial phase boost at the crossover frequency.
Error Amplifier
The error amplifier provides most of the low frequency
loop gain and servos the switcher output voltage to the
VID DAC potential minus the AVP droop. After selecting
the inductor, the output capacitor and the AVP component
values, the control loop is compensated by tailoring the
frequency response of the error amplifier. A typical LTC3816
application uses Type 3 compensation to frequency com-
pensate the feedback loop. Figure 14a and Figure 14b
show the LTC3816 error amplifier Type 3 configuration.
The transfer function of this amplifier is given by the fol-
lowing equation:
V
V
sR C sR C
sR C C
COMP
SERVO
C C FF
C C
=
+
( )
+
( )
+
( )
+
–
• •1 1 1
1 1
1
ssR
C C
C C
C
C C
C C
•
1
1
+






The error amplifier component values can be obtained
using the following guidelines.