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COMPONENTS CALCULATION
COMPONENTS CALCULATION
The following formulas are intended for the calculation of
R Comp × 5 × G M × Iout × L
( 1 – D ) × Vout × CSG
Vout + V D – Vin
Iin avg = -------------
Vout × Δ Vout × F SW × L
ESR Cout = ---------------------------------------------------------------
( Vin – V SW – ( Iin avg × rw ) ) × D
Iin avg × r × F SW
Irms Cout = Iout × -------------
= Iin avg + -------------------------------------------------
Iin max
all external components related with the Boost converter and
Network compensation.
In order to calculate a Duty Cycle, the internal losses of the
MOSFET and Diode should be taken into consideration.
D = ---------------------------------------------
Vout + V D – V SW
The average input current depends directly to the output
current when the internal switch is off.
Iout
1 – D
Inductor
For calculating the Inductor we should consider the losses
of the internal switch and winding resistance of the inductor.
L = ----------------------------------------------------------------------------------
It is important to look for an inductor rated at least for the
maximum input current.
Vin × ( Vout – Vin )
2 × L × F SW × Vout
Input Capacitor
CSG = A CSA × R Sense
Cout = --------------------------------------------------------------------
The output voltage ripple ( Δ V OUT ) depends on the ESR of
the Output capacitor, for a low output voltage ripple it is
recommended to use Ceramic capacitors that usually have
very low ESR. Since ceramic capacitor are expensive,
Electrolytic or Tantalum capacitors can be mixed with
ceramic capacitors to have a cheaper solution.
Vout × ( 1 – D )
The output capacitor should handle at least the following
RMS current.
Network Compensation
Since this Boost converter is current controlled, Type II
compensation is needed.
D
1 – D
I order to calculate the Network Compensation, first we
need to calculate all Boost Converter components.
For this type of compensations we need to push out the
Right Half Plane Zero to higher frequencies where it can’t
affect the overall loop significantly.
Vout × ( 1 – D )
f RHPZ = ----------------------------------------
The input capacitor should handle at least the following
RMS current.
2
Iout × 2 × π × L
The Crossover frequency must be set much lower than the
location of the Right half plane zero
Irms Cin = ? ? ? ? × 0.3
f Cross = ---------------
Vin × ( Vout – Vin )
------------------------------------------------
2 × L × F SW × Vout
Output Capacitor
For the output capacitor selection the internal current
sense gain (CSG) and the Transconductance should be
taken in consideration.
The CSG is the internal R SENSE times the current sense
amplifier gain (A CSA ).
f RHPZ
5
Since our system has a fixed Slope compensation set by
R SLOPE , R COMP should be fixed for all configurations.
R Comp = 5.6kohm
C COMP1 and C COMP2 should be calculated as follows:
34844
Analog Integrated Circuit Device Data
Freescale Semiconductor
55
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