Analog Integrated Circuit Device Data

16

Freescale Semiconductor

34845

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.

In order to calculate the Duty Cycle, the internal losses of

the MOSFET and Diode should be taken into consideration:

The average input current depends directly on the output

current when the internal switch is off.

Inductor

For calculating the Inductor, consider the losses of the

internal switch and winding resistance of the inductor:

It is important to look for an inductor rated at least for the

maximum input current:

Input Capacitor

The input capacitor should handle at least the following

RMS current.

Output Capacitor

For the output capacitor selection the transconductance

should be taken in consideration.

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.

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.

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.

The crossover frequency must be set much lower than the

location of the Right half plane zero:

The recommended values of these capacitors for an

acceptable performance of the system in different operating

conditions are Ccomp1=2.2nF and Ccomp2=56pF.

In order to improve the transient response of the boost a

resistor divider has been 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 is close to

Ω and 39kΩ.

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

D

–

+

–

+

-----------------------------------------------

=

–

1D

–

-------------

=

L

–

×

()

–

() D

×

–

r

×

×

------------------------------------------------------------------------------------------------------------------

=

IIN MAX

–

IIN AVG

–

VIN VOUT VIN

–

()

×

2L

×

FSW

×

VOUT

×

---------------------------------------------------------

+

=

IRMS C

IN

–

VIN VOUT VIN

–

()

×

2L

×

FSW

×

VOUT

×

---------------------------------------------------------

⎝⎠

⎜⎟

⎛⎞

0.3

×

=

COUT

RCOMP 5

×

GM

×

IOUT

×

L

×

1D

–

() VOUT

×

0.35

×

-------------------------------------------------------------------------------

=

ESRC

OUT

VOUT ΔVOUT

×

FSW

×

L

×

VOUT 1D

–

()

×

---------------------------------------------------------------------------

=

OUT

–

D

1D

–

-------------

×

=

fRHPZ

VOUT 1D

–

()

2

×

IOUT 2π

×

L

×

---------------------------------------------

=

5

---------------

=

CCOMP1

2

2

π fCROSS

×

COMP

R

×

----------------------------------------------------------------

=

CCOMP2

GM

6.28 FSW

×

-----------------------------

=