LTC3816_15 Datasheet, PDF (25/44 Pages) Linear Technology – Single-Phase Wide VIN Range DC/DC Controller for Intel IMVP-6/IMVP-6.5 CPUs

LTC3816
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:
( ) ^ALC
=
V_OUT
V_SW
≈
1+ sR_ESR • C_BULK
s²L_LC_OUT + SR_LC_OUT + 1
•
1+
sR_ESR
1
C_BULK • C_CER
C_OUT
f_{LC(DOUBLE _POLE)} = _2π
1
L_LC_OUT
f_ESR(ZERO)
=
2π
•
1
R_ESR
•
C_BULK
f_CER(POLE)
=
2π
• R_ESR
1
C_BULK • C_CER
C_OUT
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_SERVO
V_OUT
≈
1+ sA_(SR) + s²B_(SR)
1+ sR_ESR • C_BULK
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_{SERVO ≈} ^{1+ sA}_(DCR) ^{+ s2B}_(DCR)
V_OUT
1+ sR_ESR • C_BULK
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_COMP
( ) ^VSERVO
=
–
1+ sR_C • C_C 1+ sR1• C_FF
sR1
C_C + C_C1


1+
sR_C
C_C
C_C
• C_C1
+ C_C1


The error amplifier component values can be obtained
using the following guidelines.
3816f
25