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 Submit Documentation Feedback Basic Calculation of a Boost Converter's Power Stage Copyright © 2009–2014, Texas Instruments Incorporated 1 Calculate the Maximum Switch Current 2 www.ti.com 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 SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Copyright © 2009–2014, Texas Instruments Incorporated Inductor Selection www.ti.com 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 SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Basic Calculation of a Boost Converter's Power Stage Copyright © 2009–2014, Texas Instruments Incorporated 3 Output Voltage Setting 5 www.ti.com 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 Basic Calculation of a Boost Converter's Power Stage SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Copyright © 2009–2014, Texas Instruments Incorporated Output Capacitor Selection www.ti.com 7 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 SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Basic Calculation of a Boost Converter's Power Stage Copyright © 2009–2014, Texas Instruments Incorporated 5 Equations to Calculate the Power Stage of a Boost Converter 8 www.ti.com 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) SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Copyright © 2009–2014, Texas Instruments Incorporated Equations to Calculate the Power Stage of a Boost Converter www.ti.com 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 SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Basic Calculation of a Boost Converter's Power Stage Copyright © 2009–2014, Texas Instruments Incorporated 7 References 9 www.ti.com 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 SLVA372C – November 2009 – Revised January 2014 Submit Documentation Feedback Copyright © 2009–2014, Texas Instruments Incorporated IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, enhancements, improvements and other changes to its semiconductor products and services per JESD46, latest issue, and to discontinue any product or service per JESD48, latest issue. Buyers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. 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