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TYPICAL APPLICATIONS
COMPONENTS CALCULATION
COMPONENTS CALCULATION
The following formulas are intended for the calculation of
all external components related with the boost converter and
network compensation.
= I OUT × -------------
In order to calculate the Duty Cycle, the internal losses of
the MOSFET and Diode should be taken into consideration:
I RMS – C
OUT
D
1 – D
V OUT + V D – V IN
D = -----------------------------------------------
V OUT + V D – V SW
I IN – AVG = -------------
( V IN – V SW – ( I IN – AVG × R INDUCTOR ) ) × D
I IN – AVG × r × F SW
V OUT × ( 1 – D )
I OUT × 2 π × L
2 × L × F SW × V OUT
f CROSS = ---------------
The average input current depends directly on the output
current when the internal switch is off.
I OUT
1 – D
Inductor
For calculating the Inductor, 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:
V IN × ( V OUT – V IN )
I IN – MAX = I IN – AVG + ---------------------------------------------------------
Input Capacitor
The input capacitor should handle at least the following
RMS current.
Note that before calculating the network compensation, all
boost converter components need to be known.
For this type of compensation it is recommended to push
out the Right Half Plane Zero to higher frequencies where it
will not significantly affect the overall loop.
2
f RHPZ = ---------------------------------------------
The crossover frequency must be set much lower than the
location of the Right half plane zero:
f RHPZ
5
Since our system has a fixed slope compensation, R COMP
? V IN × ( V OUT – V IN ) ?
? 2 × L × F SW × V OUT ?
I RMS – C
IN
= ? --------------------------------------------------------- ? × 0.3
should be fixed for all configurations, i.e. R COMP = 2 Kohm
C COMP1 and C COMP2 should be calculated as follows:
C COMP1 = -------------------------------------------------------------
π × f CROSS × COMP
( 1 – D ) × V OUT × 0.35
V OUT × Δ V OUT × F SW × L
ESR C
V OUT × ( 1 – D )
6.28 × F SW
Output Capacitor
For the output capacitor selection the transconductance
should be taken in consideration.
R COMP × 5 × G M × I OUT × L
C OUT = -------------------------------------------------------------------------------
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 have a very low
ESR. Since ceramic capacitor are costly, electrolytic or
tantalum capacitors can be mixed with ceramic capacitors for
a less expensive solution.
= ---------------------------------------------------------------------------
OUT
The output capacitor should at least handle the following
RMS current.
Network Compensation
Since this Boost converter is current controlled, a Type II
compensation is needed.
2
R
2 GM
C COMP2 = -----------------------------
The recommended values of these capacitors for an
acceptable performance of the system in different operating
conditions are Ccomp1=33nF and Ccomp2=220pF.
In order to improve the transient response of the boost a
resistor network can be implemented from the PWM pin to
ground with a connection to the compensation network. This
configuration should inject a 1V signal to the COMP pin and
the equivalent Thevenin resistance of the divider should be
close to R COMP , (i.e. for 2k COMP resistor, R COMP = 3.3k and
R SHUNT = 10k. See Figure 10 , Figure 11 and Figure 12 for
implementation guidelines.
If a faster transient response is needed, a higher voltage
(e.g. 1.3V) should be injected to the COMP pin; so the
resistor divider should be modified accordingly but keeping
the equivalent Thevenin resistance of the divider close to
R COMP .
34845
Analog Integrated Circuit Device Data
18
Freescale Semiconductor
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