34704_09 Datasheet, PDF (42/49 Pages) Freescale Semiconductor, Inc – Multiple Channel DC-DC Power Management IC

FUNCTIONAL DEVICE OPERATION
COMPONENT CALCULATION
RB = _{1----.-5----–-----V0---.--9o----–-----0---.-9--R1}
[Ω]
NOTE: RB is not grounded, instead is connected to
VREF7 pin (VREF7=1.5V) which provide a positive voltage to
assure a positive voltage at the FB7 pin.
• Compensation network. (C1,C2,C3, R2, R3)
For compensating a buck converter, 4 important
frequencies referring to the plant are:
• Output LC filter cutoff frequency (F_LC):
F_LC = ------D-----^′--^m----ⁱ-ⁿ-------
[Hz]
2π _LCOUT
Where D’_min is the minimum off time percentage given by:
D′_min
=
----V-----i--n---^m----ⁱ--ⁿ----
Vout_max
• Cutoff frequency due to capacitor ESR:
F_ESR
=
------------------1-------------------
2π(C_OUT)ESR
[Hz]
• The right plane zero frequency:
RHP_Z
=
-⁽--D-----^′-^m----ⁱ--ⁿ---⁾--²---R----^L---^O----^A----^D-
D • 2πL
[Hz]
• Crossover frequency (or bandwidth): select this
frequency as far away form the RHP_Z as much as
possible:
F_B
W
«
R-----H-----P---_Z-
6
[Hz]
The Type 3 external compensation network will be in
charge of canceling some of these poles and zeros to
achieve stability in the system. The following poles and
zeroes frequencies are provided by the type 3 compensation:
F_PO = F_BW
F_P1 = F_ESR
F_Z1 = 0.9F_LC
F_2P
=
F----_S---W---
2
F₂₂ = 1.1F_LC
The passive components associated to these frequencies are calculated with the following formulas.
C1
=
-V-----i--n---^m----ⁱ--ⁿ-
V_RAMP
⎛
⎜
⎝
D-----′^--_m^1----_i^--_n^{--2-⎠⎟⎞}
⎛
⎝
-2---_π---₍---F---_P-1--_O----R-----1---_{)⎠⎞}
C2
=
⎛
⎝
2----π^---(^---F---1_Z^----₂^--R-----1---)^{-⎠⎞}
R2
=
⎛
⎝
2----π^---(^---F---1_Z^----₁^--C-----1---)^{-⎠⎞}
R3
=
⎛
⎝
-2---_π---₍---F---1_P---₁---C-----2---_{)⎠⎞}
C3
=
⎛
⎝
2----π^---(^---F---1_P^---₂^{---R-----2---})^⎠⎞
On the 34704 V_RAMP is half of 1.2V since each operation mode spends only half the ramp.
34704
42
Analog Integrated Circuit Device Data
Freescale Semiconductor