ADP1823 Datasheet, PDF (21/32 Pages) Analog Devices – Dual, Interleaved, Step-Down DC-to-DC Controller with Tracking

ADP1823
Select RTOP between 1 kΩ and 10 kΩ. A good starting value is
2 kΩ.
Next, calculate RBOT as
R_BOT
=
V_FB R_TOP
V_OUT − V_FB
(35)
R _BOT
=
0.6 V × R_TOP
V_OUT − 0.6 V
(36)
Note that if ratiometric tracking is used, substitute the actual FB
voltage for the 0.6 V term used in Equation 36.
Calculate the compensator gain needed at crossover to achieve
0 dB total system gain:
A_T = A_MOD + A_FILTER + A_COMP
(37)
0 dB = A_MOD + A_FILTER + A_COMP
(38)
A_COMP = 0 dB − A_MOD − A_FILTER
(39)
Calculate the value of RZ to achieve that gain:
A_COMP
= 20 × log_{⎜⎜⎝⎛}
R_Z
R_TOP
⎟⎟⎠⎞
(40)
⎜⎛ ^ACOMP ⎟⎞
R_Z = R_TOP × 10 ^{⎝ 20 âŽ} 
(41)
Calculate the integrator cap value to place the compensation
zero at the desired frequency:
C_I
=
2π
1
R_Z
f_Z
(42)
Calculate the capacitor value for the high frequency pole:
C_HF
=
2π
1
R_Z
f_P
(43)
Type III Compensator
G
(dB)
–1 _SLOPE
+1 ^SLOPE
–1 _SLOPE
–90°
PHASE
f_Z
f_P
–270°
C_HF
R_FF C_FF
R_Z
C_I
FROM
V_OUT
R_TOP
R_BOT
EA
VREF
COMP
TO PWM
VRAMP
0V
Figure 28. Type III Compensation
K
=
⎜⎜⎝⎛
tan⎜⎛
⎝
φ_B
2
+
45
⎟⎞
⎠
⎟⎟⎠⎞
2
(44)
and
f_Z
=
f_CO
K
(45)
and
fP = fCO √K
(46)
Select RTOP between 1 kΩ and 10 kΩ. A good starting point is
2 kΩ.
Next, calculate RBOT as
R_BOT
=
V_FB R_TOP
V_OUT − V_FB
(47)
R _BOT
= ^{0.6 V × RTOP}
V_OUT − 0.6 V
(48)
Note that if ratiometric tracking is used, substitute the actual FB
voltage for the 0.6 V term in Equation 48.
Calculate the feedforward capacitor to produce the first
compensator zero:
C_FF
=
2π
1
R_TOP
f_Z
(49)
Calculate the resistor of the feedforward network to provide the
first high frequency compensator pole:
R_FF
=
2π
1
C_FF
f_P
(50)
Calculate the impedance of the feedforward network at the
crossover frequency, as this is required to set the gain of the
compensator:
Z _FF
=¹
2π C_FF f_CO
+ R_FF
(51)
Calculate the compensator gain needed at crossover to achieve
0 dB total system gain:
AT = AMOD + AFILTER + ACOMP
(52)
0 dB = AMOD + AFILTER + ACOMP
(53)
ACOMP = 0 dB − AMOD − AFILTER
(54)
Calculate the value of RZ to achieve that gain:
A_COMP
=
20 ×
log_{⎜⎜⎝⎛}
R_Z
R_TOP || Z_FF
⎟⎟⎠⎞
(55)
( ) ^{⎜⎛ ACOMP ⎟⎞}
R_Z = R_TOP || Z_FF × 10^{⎝ 20 âŽ} 
(56)
Calculate the integrator cap value to place the compensation
zero at the desired frequency:
C_I
=
2π
1
R_Z
f_Z
(57)
Rev. A | Page 21 of 32