Basic Calculation of a Boost Converter's Power Stage

Application Report
SLVA372C – November 2009 – Revised January 2014
Basic Calculation of a Boost Converter's Power Stage
Brigitte Hauke
......................................................................................... Low Power DC/DC Application
ABSTRACT
This application note gives the equations to calculate the power stage of a boost converter built with an IC
with integrated switch and operating in continuous conduction mode. It is not intended to give details on
the functionality of a boost converter (see Reference 1) or how to compensate a converter. See the
references at the end of this document if more detail is needed.
For the equations without description, See section 8.
1
Basic Configuration of a Boost Converter
Figure 1 shows the basic configuration of a boost converter where the switch is integrated in the used IC.
Often lower power converters have the diode replaced by a second switch integrated into the converter. If
this is the case, all equations in this document apply besides the power dissipation equation of the diode.
IIN
VIN
CIN
D
L
SW
IOUT
COUT
VOUT
Figure 1. Boost Converter Power Stage
1.1
Necessary Parameters of the Power Stage
The following four parameters are needed to calculate the power stage:
1. Input Voltage Range: VIN(min) and VIN(max)
2. Nominal Output Voltage: VOUT
3. Maximum Output Current: IOUT(max)
4. Integrated Circuit used to build the boost converter. This is necessary, because some parameters for
the calculations have to be taken out of the data sheet.
If these parameters are known the calculation of the power stage can take place.
SLVA372C – November 2009 – Revised January 2014
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1
Calculate the Maximum Switch Current
2
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Calculate the Maximum Switch Current
The first step to calculate the switch current is to determine the duty cycle, D, for the minimum input
voltage. The minimum input voltage is used because this leads to the maximum switch current.
VIN(min) ´ η
D=1 VOUT
(1)
VIN(min) = minimum input voltage
VOUT = desired output voltage
η = efficiency of the converter, e.g. estimated 80%
The efficiency is added to the duty cycle calculation, because the converter has to deliver also the energy
dissipated. This calculation gives a more realistic duty cycle than just the equation without the efficiency
factor.
Either an estimated factor, e.g. 80% (which is not unrealistic for a boost converter worst case efficiency),
can be used or see the Typical Characteristics section of the selected converter's data sheet
( Reference 3 and 4).
The next step to calculate the maximum switch current is to determine the inductor ripple current. In the
converters data sheet normally a specific inductor or a range of inductors is named to use with the IC. So
either use the recommended inductor value to calculate the ripple current, an inductor value in the middle
of the recommended range or, if none is given in the data sheet, the one calculated in the Inductor
Selection section of this application note.
ΔIL =
VIN(min) ´ D
fS ´ L
(2)
VIN(min) = minimum input voltage
D = duty cycle calculated in Equation 1
fS = minimum switching frequency of the converter
L = selected inductor value
Now it has to be determined if the selected IC can deliver the maximum output current.
ΔIL ö
æ
IMAXOUT = ç ILIM(min) ´ (1- D)
2 ÷ø
è
(3)
ILIM(min) = minimum value of the current limit of the integrated switch (given in the data sheet)
ΔIL = inductor ripple current calculated in Equation 2
D = duty cycle calculated in Equation 1
If the calculated value for the maximum output current of the selected IC, IMAXOUT, is below the systems
required maximum output current, another IC with a higher switch current limit has to be used.
Only if the calculate value for IMAXOUT is just a little smaller than the needed one, it is possible to use the
selected IC with an inductor with higher inductance if it is still in the recommended range. A higher
inductance reduces the ripple current and therefore increases the maximum output current with the
selected IC.
If the calculated value is above the maximum output current of the application, the maximum switch
current in the system is calculated:
IOUT(max)
ΔI
ISW(max) = L +
2
1- D
(4)
ΔIL = inductor ripple current calculated in Equation 2
IOUT(max) = maximum output current necessary in the application
D = duty cycle calculated in Equation 1
This is the peak current, the inductor, the integrated switch(es) and the external diode has to withstand.
2
Basic Calculation of a Boost Converter's Power Stage
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Inductor Selection
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3
Inductor Selection
Often data sheets give a range of recommended inductor values. If this is the case, it is recommended to
choose an inductor from this range. The higher the inductor value, the higher is the maximum output
current because of the reduced ripple current.
The lower the inductor value, the smaller is the solution size. Note that the inductor must always have a
higher current rating than the maximum current given in Equation 4 because the current increases with
decreasing inductance.
For parts where no inductor range is given, the following equation is a good estimation for the right
inductor:
L=
VIN × (VOUT - VIN )
ΔIL ´ fS ´ VOUT
(5)
VIN = typical input voltage
VOUT = desired output voltage
fS = minimum switching frequency of the converter
ΔIL = estimated inductor ripple current, see below
The inductor ripple current cannot be calculated with Equation 1 because the inductor is not known. A
good estimation for the inductor ripple current is 20% to 40% of the output current.
V
ΔIL = (0.2 to 0.4) ´ IOUT(max) ´ OUT
VIN
(6)
ΔIL = estimated inductor ripple current
IOUT(max) = maximum output current necessary in the application
4
Rectifier Diode Selection
To reduce losses, Schottky diodes should be used. The forward current rating needed is equal to the
maximum output current:
IF = IOUT(m ax)
(7)
IF = average forward current of the rectifier diode
IOUT(max) = maximum output current necessary in the application
Schottky diodes have a much higher peak current rating than average rating. Therefore the higher peak
current in the system is not a problem.
The other parameter that has to be checked is the power dissipation of the diode. It has to handle:
PD = IF ´ VF
(8)
IF = average forward current of the rectifier diode
VF = forward voltage of the rectifier diode
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Output Voltage Setting
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Output Voltage Setting
Almost all converters set the output voltage with a resistive divider network (which is integrated if they are
fixed output voltage converters).
With the given feedback voltage, VFB, and feedback bias current, IFB, the voltage divider can be calculated.
VOUT
IR1/2
R1
IFB
VFB
R2
Figure 2. Resistive Divider for Setting the Output Voltage
The current through the resistive divider shall be at least 100 times as big as the feedback bias current:
IR 1/2 ³ 100 ´ IFB
(9)
IR1/2 = current through the resistive divider to GND
IFB = feedback bias current from data sheet
This adds less than 1% inaccuracy to the voltage measurement. The current can also be a lot higher. The
only disadvantage of smaller resistor values is a higher power loss in the resistive divider, but the
accuracy will be a little increased.
With the above assumption, the resistors are calculated as follows:
V
R2 = FB
IR1/2
æV
ö
R1 = R2 ´ ç OUT - 1÷
è VFB
ø
(10)
(11)
R1,R2 = resistive divider, see Figure 2.
VFB = feedback voltage from the data sheet
IR1/2 = current through the resistive divider to GND, calculated in Equation 9
VOUT = desired output voltage
6
Input Capacitor Selection
The minimum value for the input capacitor is normally given in the data sheet. This minimum value is
necessary to stabilize the input voltage due to the peak current requirement of a switching power supply.
the best practice is to use low equivalent series resistance (ESR) ceramic capacitors. The dielectric
material should be X5R or better. Otherwise, the capacitor cane lose much of its capacitance due to DC
bias or temperature (see references 7 and 8).
The value can be increased if the input voltage is noisy.
4
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Output Capacitor Selection
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Output Capacitor Selection
Best practice is to use low ESR capacitors to minimize the ripple on the output voltage. Ceramic
capacitors are a good choice if the dielectric material is X5R or better (see reference 7 and 8).
If the converter has external compensation, any capacitor value above the recommended minimum in the
data sheet can be used, but the compensation has to be adjusted for the used output capacitance.
With internally compensated converters, the recommended inductor and capacitor values should be used
or the recommendations in the data sheet for adjusting the output capacitors to the application should be
followed for the ratio of L × C.
With external compensation, the following equations can be used to adjust the output capacitor values for
a desired output voltage ripple:
IOUT(max) ´ D
COUT(min) =
fS ´ ΔVOUT
(12)
COUT(min) = minimum output capacitance
IOUT(max) = maximum output current of the application
D = duty cycle calculated with Equation 1
fS = minimum switching frequency of the converter
ΔVOUT = desired output voltage ripple
The ESR of the output capacitor adds some more ripple, given with the equation:
æ IOUT(max) ΔIL ö
ΔVOUT(ESR) = ESR ´ ç
+
÷
2 ø
è 1- D
(13)
ΔVOUT(ESR) = additional output voltage ripple due to capacitors ESR
ESR = equivalent series resistance of the used output capacitor
IOUT(max) = maximum output current of the application
D = duty cycle calculated with Equation 1
ΔIL = inductor ripple current from Equation 2 or Equation 6
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Equations to Calculate the Power Stage of a Boost Converter
8
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Equations to Calculate the Power Stage of a Boost Converter
Maximum Duty Cycle: D = 1 -
VIN(min) ´ η
VO UT
(14)
VIN(min) = minimum input voltage
VOUT = desired output voltage
η = efficiency of the converter, e.g. estimated 85%
VIN(min) ´ D
Inductor Ripple Current: ΔIL =
fS ´ L
(15)
VIN(min) = minimum input voltage
D = duty cycle calculated in Equation 14
fS = minimum switching frequency of the converter
L = selected inductor value
æ
ΔIL ö
Maxim um output current of the selected IC: IMAXOUT = ç ILIM(min) ÷ ´ (1 - D)
2 ø
è
(16)
ILIM(min) = minimum value of the current limit of the integrated witch (given in the data sheet)
ΔIL = inductor ripple current calculated in Equation 15
D = duty cycle calculated in Equation 14
IOUT(max)
ΔI
Application specific maximum switch current: ISW (max) = L +
2
1- D
(17)
ΔIL = inductor ripple current calculated in Equation 15
IOUT(max) = maximum output current necessary in the application
D = duty cycle calculated in Equation 14
VIN × (VOUT - VIN )
Inductor Calculation: L =
ΔIL ´ fS ´ VOUT
(18)
VIN = typical input voltage
VOUT = desired output voltage
fS = minimum switching frequency of the converter
ΔIL= estimated inductor ripple current, see Equation 19
Inductor Ripple Current Estimation: ΔIL = (0.2 to 0.4) ´ IOUT(max) ´
VOUT
VIN
(19)
ΔIL = estimated inductor ripple current
IOUT(max) = maximum output current necessary in the application
Average Forward Current of Rectifier Diode: IF = IOUT(max)
(20)
IOUT(max) = maximum output current necessary in the application
Power Dissipation in Rectifier Diode: PD = IF ´ VF
(21)
IF = average forward current of the rectifier diode
VF = forward voltage of the rectifier diode
Current Through Resistive Divider Newtwork for Output Voltage Setting: IR1/2 ³ 100 ´ IFB
(22)
IFB = feedback bias current from data sheet
Value of Resistor Between FB Pin and GND: R 2 =
6
Basic Calculation of a Boost Converter's Power Stage
VFB
IR1/2
(23)
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Equations to Calculate the Power Stage of a Boost Converter
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æV
ö
Value of Resistor Between FB Pin and VOUT : R1 = R2 ´ ç OUT - 1÷
è VFB
ø
(24)
VFB = feedback voltage from the data sheet
IR1/2 = current through the resistive divider to GND, calculated in Equation 22
VOUT = desired output voltage
IOUT(max) ´ D
Minimum Output Capacitance, if not given in the data sheet: COUT(min) =
fS ´ ΔVOUT
(25)
IOUT(max) = maximum output current of the application
D = duty cycle calculated in Equation 14
fS = minimum switching frequency of the converter
ΔVOUT = desired output voltage ripple
æ IOUT(max) ΔIL ö
Additional Output Voltage Ripple due to ESR : ΔVOUT(ESR) = ESR ´ ç
+
÷
2 ø
è 1- D
(26)
ESR = equivalent series resistance of the used output capacitor
IOUT(max) = maximum output current of the application
D = duty cycle calculated in Equation 14
ΔIL = inductor ripple current from Equation 15 or Equation 19
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7
References
9
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References
1.
2.
3.
4.
5.
6.
7.
Understanding Boost Power Stages in Switchmode Power Supplies (SLVA061)
Voltage Mode Boost Converter Small Signal Control Loop Analysis Using the TPS61030 (SLVA274)
Data sheet of TPS65148 (SLVS904)
Data sheet of TPS65130 and TPS65131 (SLVS493)
Robert W. Erickson: Fundamentals of Power Electronics, Kluwer Academic Publishers, 1997
Mohan/Underland/Robbins: Power Electronics, John Wiley & Sons Inc., Second Edition, 1995
Improve Your Designs with Large Capacitance Value Multi-Layer Ceramic Chip (MLCC) Capacitors by
George M. Harayda, Akira Omi, and Axel Yamamoto, Panasonic
8. Comparison of Multilayer Ceramic and Tantalum Capacitors by Jeffrey Cain, Ph.D., AVX Corporation
Spacer
Revision History
Changes from B Revision (July 2010) to C Revision ..................................................................................................... Page
•
Changed VIN to VOUT in Figure 2
........................................................................................................
4
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from A Revision (April 2010) to B Revision .................................................................................................... Page
•
•
Changed IOUT(max) x (1–D) To: IOUT(max) x D in Equation 12
Changed IOUT(max) x (1–D) To: IOUT(max) x D in Equation 25
............................................................................
............................................................................
5
7
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from Original (November 2009) to A Revision ................................................................................................ Page
•
•
Added VOUT/VIN (Typical) to Equation 6 ................................................................................................ 3
added VOUT/VIN (Typical) to Equation 19 ............................................................................................... 6
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
8
Revision History
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