34704_11 Datasheet, PDF (46/54 Pages) Freescale Semiconductor, Inc – Multiple Channel DC-DC Power Management IC

FUNCTIONAL DEVICE OPERATION
COMPONENT CALCULATION
V_RRM ≥ Vin – Vo
• L: The minimum value of inductor to maintain CCM can be
determined by using the following procedure:
L_min
≥
--^–----^V----^o----^T----
2Io_max
⎛
⎝
-_V----_o---^V--_–--ⁱ--ⁿ-_V--^m--_i--_nⁱ--ⁿ-_m----_i--_n-_⎠⎞
2
[H]
• C_OUT: The three elements of output capacitor that
contribute to its impedance and output voltage ripple are
the ESR, the ESL and the capacitance C. The minimum
capacitor value is approximately:
• 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
C_OUT
≥
I_---o_{---m----a---x---}D_{-----m----a---x}
F_SWΔVo_r
[F]
• Where ΔVO_r is the desired output voltage ripple.
• Now calculate the maximum allowed ESR to reach the
desired.
E
S
R
≤
-------------------^Δ----^V----^o----^r------------------
⎛
⎝
-----^I--^o---^m-----^a---^x-----
1 – D_max
+
1^---I--O–^----B-D^{---⎠⎞}
[Ω]
• 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:
• R1 and RB: These two resistors help to set the output
voltage to the desire value using a V_FB7=0.6V, select R1
between 10 k and 150 K and then calculate RB as follows:
RB = ₁----_.-₅-----_–-----^0V---^.--_o9----_–-----₀----_.-₉--R1
[Ω]
NOTE: RB is not grounded, instead is connected to
VREF7 pin (VREF7=1.5 V) 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:
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
34704
46
Analog Integrated Circuit Device Data
Freescale Semiconductor