FUNCTIONAL DEVICE OPERATION
COMPONENT CALCULATION
Compensating for boost operation:
R1
• L: A boost power stage can be designed to operate in
CCM for load currents above a certain level usually 5 to
15% of full load. The minimum value of inductor to
maintain CCM can be determined by using the following
procedure:
-----------------------
RB =
[Ω]
Vo
VREF
-------------
– 1
• Compensation network. (C1,C2,C3, R2, R3)
1. Define IOB as the minimum current to maintain CCM as
15% of full load:
For compensating a boost converter, 4 important
frequencies referring to the plant are:
1. Output LC filter cutoff frequency (FLC):
Vo(D)(1 – D)2T
[H]
------------------------------------------
≥
Lmin
2IOB
D′min
--------------------------
=
FLC
[Hz]
However the worst case condition for the boost power
stage is when the input voltage is equal to one half of the
output voltage, which results in the Maximum ΔIL, then:
2π
LCOUT
• Where D’min is the minimum off time percentage given
by:
Vo(T)
16IOB
[H]
---------------
≥
Lmin
Vinmin
• COUT: 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:
----------------------
=
D′min
Voutmax
2. Cutoff frequency due to capacitor ESR:
1
IomaxDmax
[Hz]
[Hz]
----------------------------------------
FESR =
[F]
----------------------------
≥
COUT
2π(COUT)ESR
FswΔVor
3. The right plane zero frequency:
• Where ΔVOr is the desired output voltage ripple.
(D′ )2RLOAD
• Now calculate the maximum allowed ESR to reach the
---------m-----i-n-------------------------
=
desired ΔVOr:
RHPZ
2πL
4. Crossover frequency (or bandwidth): select this
frequency as far away form the RHPZ as much as
ΔVor
--------------------------------------------
ESR ≤
possible:
Iomax
[Ω]
⎛
⎞
-----------------------
+ IOB
⎝
⎠
1 – Dmax
RHPZ
---------------
«
• R1 and RB:
[Hz]
FBW
6
These two resistors help to set the output voltage to the
desire value using a Vref=0.6V, select R1 between 10k and
100K and then calculate RB as follows:
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:
FPO = FBW
FZ1 = 0.9FLC
F22 = 1.1FLC
FSW
-----------
=
FP1 = FESR
F2P
2
34704
Analog Integrated Circuit Device Data
Freescale Semiconductor
43
FREESCALE [ Freescale ]
