34704_09 Datasheet, PDF (38/49 Pages) Freescale Semiconductor, Inc – Multiple Channel DC-DC Power Management IC

FUNCTIONAL DEVICE OPERATION
COMPONENT CALCULATION
1. Output LC filter cutoff frequency (F_LC):
F_LC = ------------1-------------
[Hz]
2π _LCOUT
2. Cutoff frequency due to capacitor ESR:
F_ESR = _2----π----₍--C----_O----_U^1----_T---₎--E----S----R--
[Hz]
3. Crossover frequency (or bandwidth):
F_BW
=
F----_S---W---
10
[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_Z1 = 0.9F_LC
F₂₂ = 1.1F_LC
F_P1 = F_ESR
F_2P
=
F----_S---W---
2
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
38
Analog Integrated Circuit Device Data
Freescale Semiconductor