LTC3124_15 Datasheet, PDF (20/28 Pages) Linear Technology – 15V, 5A 2-Phase Synchronous Step-Up DC/DC Converter with Output Disconnect

LTC3124
APPLICATIONS INFORMATION
Decide how much phase margin (Φ_m) is desired. Greater
phase margin can offer more stability while lower phase mar-
gin can yield faster transient response. Typically, Φ_m ≈ 60°
is optimal for minimizing transient response time while
allowing sufficient margin to account for component
variability. Φ₁ is the phase boost of Z1, P2, and P5 while
Φ₂ is the phase boost of Z4 and P4. Select Φ₁ and Φ₂
such that:
Φ₁ + Φ₂ = Φ_m + tan^−
1

ƒ_C
Z3


and
Φ₁
≤
74° ;
Φ₂
≤


2
•
tan^−1
V_OUT
1.2V


−
90°
where V_OUT is in V and ƒ_C and Z3 are in kHz.
Setting Z1, P5, Z4, and P4 such that
Z1=
ƒ_C
a₁
,
P5
=
ƒ_C
a₁, Z4 =
ƒ_C
a₂
,
P4
=
ƒ_C
a₂
allows a₁ and a₂ to be determined using Φ₁ and Φ₂
a₁ =
tan²


Φ₁
+
2
90°


,
a₂
=
tan²


Φ₂
+ 90°
2 ^
The compensation will force the converter gain G_BOOST
to unity at ƒ_C by using the following expression for C_C:
C_C
=
10³
• g_ma • R2 • G_ƒC (a₁
2π • ƒ_C • (R1+ R2)
− 1)
a₁
a_{2 pF}
(g_ma in µS, ƒ_C in kHz, G_ƒC in V/V)
Once C_C is calculated, R_C and C_F are determined by:
R_C
=
10⁶ •
2π • ƒ_C
a₁
• C_C
kΩ
(ƒ_C
in
kHz,
C_C
in
pF)
C_F
=
C_C
a₁ − 1
A method for improving the converter’s transient response
uses a small feedforward series network of a capacitor and
a resistor across the top resistor of the feedback divider
(from V_OUT to FB). This adds a phase-lead zero and pole to
the transfer function of the converter. The values of these
phase lead components are given by the expressions:
R_PL
=
R1−
a₂
•


R1• R2
R1+ R2


a₂ − 1
kΩ
and
C_PL
=
10⁶ (a₂ −
2π • ƒ_C
1)(R1+ R2)
• R1² a₂
pF
where R1, R2, and R_PL are in kΩ and ƒ_C is in kHz.
Note that selecting Φ₂ = 0° forces a₂ = 1, and so the
converter will have Type II compensation and therefore
no feedforward: R_PL is open (infinite impedance) and C_PL
= 0pF. If a₂ = 0.833 • V_OUT (its maximum), feedforward is
maximized; R_PL = 0 and C_PL is maximized for this com-
pensation method.
Once the compensation values have been calculated, ob-
taining a converter bode plot is strongly recommended to
verify calculations and adjust values as required.
Using the circuit in Figure 8 as an example, Table 4 shows
the parameters used to generate the Bode plot shown in
Figure 9.
Table 4. Bode Plot Parameters
PARAMETER
VALUE
V_IN
V_OUT
R_L
C_OUT at No Bias
C_OUT at 12V Bias
R_ESR
LA, LB
5
12
8
22 × 2
14 × 2
2.5
4.7
f_SWITCH
R1
1
1020
R2
113
g_ma
100
R_O
10
g_mp
3.4
η
90
R_C
84.5
C_C
680
C_F
56
R_PL
Open
C_PL
0
UNITS
V
V
Ω
µF
µF
mΩ
µH
MHz
kΩ
kΩ
µS
MΩ
S
%
kΩ
pF
pF
kΩ
pF
COMMENT
App Specific
App Specific
App Specific
App Specific
App Specific
App Specific
App Specific
Adjustable
Adjustable
Adjustable
Fixed
Fixed
Fixed
App Specific
Adjustable
Adjustable
Adjustable
Optional
Optional
3124f
20
For more information www.linear.com/LTC3124