Modified buck converter for LED applications
Contents
1. VL VIN VLED EA lt il m AM00368 6 21 ky AN2928 Design equations for the modified buck converter Using Equation 1 it is possible to calculate an inductor current change during ton and torr time Equation 2 baer Vin Vici t L Vinen ton 0 Equation 3 ton torr 7 L LED lorr AlL ofr J Tat geo ton Al op inductor current change during toy time A Al op inductor current change during torr time A Vin input voltage V VLep LED load voltage V ton turn on time s torr turn off time s In CCM the inductor current change during ton and torr time is the same Equation 4 All on AIL off Using Equation 2 and Equation 3 it is possible to create following equations Equation 5 Vin Viep ton _ Vren torp L L Equation 6 Vin ton Vieo ton Ven torr Equation 7 Vin ton Viren tore ton Vep T The duty cycle for the modified buck topology also valid for a standard buck topology converter is calculated Equation 8 7 21 Design equations for the modified buck converter AN2928 2 2 8 21 Fixed off time network calculation The basic idea for this type of converter is to obtain a constant off time when the power MOSFET is turned off This design approach is quite simple and cost effective because the constant off time is easily set by the RC network Its calculation is described in this section The2. Ti AN2928 Yg Application note Modified buck converter for LED applications Introduction The use of high power LEDs in lighting applications is becoming increasingly popular due to rapid improvements in lighting efficiency longer life higher reliability and overall cost effectiveness Dimming functions are more easily implemented in LEDs and they are more robust and offer wider design flexibility compared to other light sources Applications suitable for the use of LEDs include lighting for streets stadiums fairs and exhibitions shops interiors as well as for decorative lighting outdoor wall lighting and consumer lighting such as lamps and ballasts Therefore LED use for lighting is likely to represent an increasingly large proportion of the lighting market in the future To assist engineers in their design approach the STEVAL ILL013V1 80 W offline PFC LED driver demonstration board has been developed This application note describes step by step all the principles and calculations used for a modified buck converter intended for high brightness LED applications The converter is designed as a constant current source to achieve the best lighting performance from the LEDs A modified buck topology was chosen because the power switch is connected to ground rather than the high side switch as in a standard buck topology so with this solution it is easier to control the switch The design uses a fixed off time FOT network
3. For a proper inductor core the calculated area product must be higher than the APyyin calculated in Equation 35 If the condition derived from Equation 38 is not fulfilled the designer must select a bigger inductor core Equation 38 APwin lt AP A simple way how to calculate the number of inductor turns is shown in Equation 39 since manufacturers also include the inductance factor A which depends on air gap in the product datasheets For example the ETD29 core with 1 mm gap and N27 ferrite material has an inductance factor of 124 nH ky AN2928 Design equations for the modified buck converter Equation 39 L N A A inductance factor H N inductor number of turns The number of turns for the inductor is Equation 40 L NAL After the number of turns is calculated it is also necessary to calculate the wire diameter The maximum power loss can be calculated using the maximum inductor temperature and core thermal resistance with the following equation Equation 41 P Tmax T4 MAX LOSS 7 Ro T T Pmax_Loss Maximum power loss in the inductor W Tmax maximum inductor temperature C Ry thermal resistance of the inductor core used C W for example thermal resistance for the E25 core used in the STEVAL ILL013V1 design is 40 C W The loss in the core is Equation 42 3 Poore Py W 10 Pcore loss in the inductor core W Py core loss defined in the datasheet mW g W core weight
4. is chosen based on its maximum stress voltage its maximum peak current and total power losses The power losses are lower for a larger duty cycle and vice versa because the diode is opened connected during off time Maximum voltage stress across the diode is equal to the input voltage Vy and therefore the power diode must be selected with some voltage margin For example if the input voltage is maximally 400 V then maximum repetitive peak reverse voltage Varn should be 450 V or higher Maximum peak diode current is selected in order to calculate the inductor size in Equation 20 Also in this case the power diode must be selected with some current margin Power losses are generally calculated with the following equation Equation 30 i Ploss p if ip D Up t dt 0 PLoss_p power diode losses W ip power diode current A Up power diode voltage V And assuming a constant voltage drop over the diode it is possible to approximately calculate the power losses on the diode switching losses are not included with the following equation Equation 31 Ploss p lavr p Ve lavR D Power diode average current A Ve power diode forward voltage for calculated average diode current V AN2928 Design equations for the modified buck converter 2 6 where the average diode current is shown in Figure 6 and can be calculated using Equation 32 Imax IMIN hun o 1 D MAS ta And finally the junctio
5. CI AP win minimum area product cm Ipeak inductor peak current A Iams inductor RMS current A Bmax saturation limited flux density T power ferrites like N27 or N67 have typically 0 3 T Equation 36 4 Cis Jak Cpe 10 Jmax maximum current density A cm That commonly used for natural convection cooling is 420 A cm Cr ratio of the total copper area to the window area The constant Cr gives an estimation of how effectively the wires are placed on the core For example if the input voltage of the modified buck converter is 400 V such as when a power factor preregulator is used then the wires must be well isolated and the ratio between the copper and window area is about 0 5 which in the end means that there is 50 of the wire on the inductor core The exact calculation using the equation listed here can be found in the user manual UM0670 see Section 3 Reference and related materials Once the minimum area product is calculated the designer should then select the right inductor core and ferrite material according to the higher AP value The AP value is calculated from the winding cross section and core cross section For example the ETD29 core with ferrite material N27 from EPCOS has a winding cross section of 97 mm and a core cross section of 71 mm Maximum flux density for the N27 is 0 3 T Equation 37 AP An AMIN Ay winding cross section mm Am n minimum core cross section mm
6. duty cycle is defined by the switching frequency and turn off time Equation 9 ton T t t De pe ten ite ie f switching frequency in CCM Hz T period in CCM s D duty cycle From Equation 8 and Equation 9 the turn off time can be calculated the switching frequency is selected Equation 10 V 1 f torr a Equation 11 1 D t VIN OFF f As stated above the modified buck converter uses a FOT network The off time is set by resistor R4 and capacitor C4 as shown in Figure 2 During the on time the gate voltage of the power MOSFET is high diode D is opened and the voltage at the ZCD pin is internally clamped at Vzcp clamp 5 7 V During the off time the gate voltage of the power MOSFET is low diode D is closed and the voltage at the ZCD pin decreases based on an exponential law Equation 12 aa Vzcp Vzcp clamp amp The voltage at the ZCD pin decreases until it reaches the internal triggering limit which causes switching to the turn on stage The trigger voltage for the L6562A is 0 7 V The time needed for the ZCD voltage to go from Vzcp clamp tO Vzcp TRIGGER defines the duration of the off time torr E Equation 13 VZCD CLAMP tore Ra Cg Inf A ZCD TRIGGER AN2928 Design equations for the modified buck converter Vzcp voltage on the ZCD pin of the L6562A V Vzcp_cLamp Clamp voltage on the ZCD pin of the L6562A V VZcCD_TRIGGER trigger voltage on the ZCD pin of the L6
7. operating in continuous conduction mode CCM rendering the overall solution simple and cost effective The modified buck converter described in this document can be used for lighting applications from low power and low voltage to high power and high voltage This allows designers to cover a wide range of different LED systems using a single topology Additionally in lighting applications where the input active power is higher than 25 W and a high power factor is required the high PF converter can be connected as the first stage before the modified BUCK converter The STEVAL ILL013V1 shows this design concept The STEVAL ILLO13V1 demonstration board is an 80 W offline dimmable LED driver with high power factor PF intended for 350 mA 700 mA and 1 ALEDs and is based on STMicroelectronics L6562A transition mode PFC controller The design is complaint with standard EN61000 3 2 limits for harmonic current emissions The order code is STEVAL ILLO013V1 and the complete design including schematic diagram bill of material calculations measurements etc is described in user manual UM0670 see Section 3 Reference and related materials March 2009 Rev 1 1 21 www st com Contents AN2928 Contents 1 Modified buck converter in constant current mode 4 2 Design equations for the modified buck converter 6 2 1 Basic equations for the modified buck converter 6 2 2 Fixed off time
8. 562A V Capacitor C4 can be selected and the resistor is easily calculated using Equation 14 or the inverse can be calculated with Equation 15 Equation 14 Ra 5 eae f 4 Equation 15 _ _ tore O4 z7 R4 Resistor Rs shown in Figure 2 is designed to limit the charge current flowing to capacitor C4 during the toy time and must be within the following range as described in application note AN1792 See Section 3 Reference and related materials Equation 16 Vap max Yzco cramp VF v v v NL Z R lt R GD MINT YZCD CLAMP F ZCD CLAMP 55 P4 E ae loop Max t ZCD CLAMP 4 Ve diode D forward voltage V typically 0 7 V Vzcp_cLamp Clamp voltage on the ZCD pin of L6562A V 5 7 V Vep_max output high maximum gate driver voltage V 15 V Vep_miIn Output high minimum gate driver voltage V 9 8 V Izcp max Maximum sink capability for the ZCD pin A 0 01 A If the toy time is very short light load or low output voltage then capacitor C4 cannot be quickly charged via resistor Rs Therefore it is recommended to connect capacitor Cz in parallel with resistor Rg The maximum size of capacitor C3 can be calculated with the following equation Equation 17 aan VZCD CLAMP A 1 GR naaa N Vap max Yzco clamp VP 9 21 Design equations for the modified buck converter AN2928 2 3 10 21 LED current calculation The preceding equations Equation 12 through 17 are used to calculate the
9. 8 Modified buck converter in constant current mode Figure 2 Modified buck converter topp time Vc VIN O ee e A FOT iFori I ae TD lt gt i 2 eea a Y lt i Rs ON tOFF toNtorF t i I FOT fixed off time c ee Rg aad Te Ra Pj ae AN AM00367 ky 5 21 Design equations for the modified buck converter AN2928 2 2 1 Figure 3 Design equations for the modified buck converter This section provides all the calculations required for a designer to develop an application with the modified buck converter working in FOT and CCM The equations are described step by step following an application design procedure First the basic equations for this type of converter are shown then the components for the torr time are calculated the proper power diode and power MOSFET is selected and finally the power inductor calculation is demonstrated Basic equations for the modified buck converter Figure 3 shows basic circuit stage during toy and torr time with indicated voltage and component references used in the equations The voltage across the inductor L is calculated using the following equation Equation 1 Viel a VL inductor voltage V L inductance H I inductor current A Modified buck converter theory of operation ton time tOFF time VLED D Don A LEDs R4 load
10. FOT network using resistors R4 and Rs and capacitors C3 and C4 At this point focus shifts to the power circuit because the output LED current and inductor must be calculated For the inductor current change the following equation is used Equation 18 Al IMax win 2 max lavr Al inductor LED current change A Imax Maximum LED inductor current A Imin Minimum LED inductor current A lavR average LED inductor current A Combining Equation 18 and Equation 3 considering the current change as an absolute value i e positive it is possible to derive Equation 19 V Aly LED ore SB Aya lage where torr is calculated using Equation 11 From Equation 11 and Equation 19 the equation for deriving the inductor size can be formulated maximum and average LED current is selected Equation 20 L Vp D _ Veep tore 2 max lay f 2 max lavn Sense resistor Rg can be easily calculated because the voltage threshold on the CS pin for the L6562A is 1 08 V and therefore the resistor size is following Equation 21 Re Ves _ 1 08 IMAX IMAX Vcs current sense threshold V Although the modified buck converter using the FOT network and working in CCM that is described here works as a constant current source a limitation is the current dependency on the output voltage number of LEDs To understand this limitation it is necessary to derive the average inductor current which is the LED current
11. ain current A lpp peak to peak current A difference between ax and win The real drain current waveform is given in Figure 5 As can be observed the signal is quite similar to the signal in Figure 4 except that there is no current during the off time stage lo 0 and the on and off times are reversed Therefore for real current Equation 24 is modified to become Equation 25 Square RMS drain current is calculated using the equation Equation 25 l 2 ic is 2 D Max miN 4 PPl p l2 g P RMS 2 12 AVR ON 12 lavr_on average current during toy time A see Figure 5 And finally it is possible to calculate the continuous conduction losses Equation 26 2 Poon rms Roscon Rpscon Static drain source on resistance for working MOSFET temperature 9 AN2928 Design equations for the modified buck converter Figure 5 Real drain MOSFET current gt The second part of the MOSFET losses is switching losses which depend on the on and off switching time drain MOSFET current drain source voltage and the switching frequency The switching time rise time and fall time is a function of the gate to drain Miller charge of the MOSFET Q gp the internal resistance of the driver the threshold voltage VgsctH and the minimum gate voltage which enables the current through the drain source of the MOSFET As the correct calculation of switching power losses is complex due to non linear behavior
12. from Equation 20 The result is shown in Equation 22 which provides the information listed AN2928 Design equations for the modified buck converter 2 4 Equation 22 Lool Veo D _ Vlen tore avR MAX 5 i MAX 9 Imax is constant and set by the resistor Rs torr is constant and set by the FOT network The average inductor LED current is independent of the input voltage The average inductor LED current depends slightly on the voltage across the LEDs i e number of LEDs and therefore the design shows the best results using a fixed number of LEDs A variable number of LEDs results in less current precision Power MOSFET calculation The power MOSFET is chosen based on maximum stress voltage maximum peak MOSFET current total power losses maximum allowed operating temperature and the driver capability of the L6562A Maximum stress voltage on the power MOSFET drain source voltage for this modified buck converter is equal to the input voltage The power MOSFET must be selected with some voltage margin For example if the input voltage is maximally 400 V then maximum drain source voltage should be 450 V or higher Maximum peak MOSFET current was selected in order to calculate the inductor size in Equation 20 Also in this case the power MOSFET must be chosen with some current margin Total power losses on the power MOSFET must be calculated due to the importance of designing a proper heat sink to avoid temperat
13. g for example the ETD29 has a weight of 28 g Maximum power loss in the wire is simply Equation 43 PWIRE Pmax LOSS PcorE Pwire maximum power loss in the wire W The maximum wire resistance derives from the following equation Equation 44 R PWIRE MAX WIRE 95 RMS Rmax wire Maximum wire resistance Q 17 21 Design equations for the modified buck converter AN2928 18 21 Winding resistance depends on the diameter and is defined using the following formula Equation 45 R wire resistance Q p resistivity of the copper Q cm 1 76 10 for temperature 25 C S conductor cross section area cm wire length cm In average length of turn cm d wire diameter cm The wire diameter is properly selected if the total wire resistance is lower than the maximum wire resistance Equation 46 R lt RMAX WIRE AN2928 Reference and related materials 3 Note Reference and related materials 5 STEVAL ILL013V1 80 W offline PFC and LED driver demonstration board with dimming based on the L6562A data brief AN1792 Design of fixed off time controlled PFC pre regulators with the L6562 application note L6562A Transition mode PFC controller datasheet AN1059 Design equations of high power factor Flyback converters based on the L6561 application note UM0670 80 W off line LED driver with PFC user manual The reference and related materials
14. he power MOSFET Q and the sensing resistor Capacitor C4 is charged via diode Do and resistor Rs since the transistor Q is open and its gate voltage is around 10 V During the toy time the load current increases and stops as soon as the voltage on the current sense resistor reaches the internal threshold on the CS pin of the L6562A The current sense of the L6562A is clamped at 1 08 V typ Figure 2 shows the torr time when the power MOSFET is switched off The inductor keeps the current flowing in the same direction and the circuit is closed through diode D4 The load current is decreasing and the minimum current is set by the fixed off time network torr time is always constant because capacitor C4 is discharged to the resistor R4 The voltage on capacitor C4 is connected to the ZCD zero current detector pin of the L6562A As soon as the capacitor is discharged and its voltage falls below 0 7 V the ZCD threshold the L6562A switches the power MOSFET again and the load current is increased This process repeats cycle by cycle as shown in the timing diagrams in Figure 1 and Figure 2 Modified buck converter ton time Ve YIN TT trek i a oad EJ tON L6562A COMP 4 L I FOT lt gt FOT TD ON toFF ton toFF t FOT fixed off time Q a K H HH 4 L Fixed off time network AM00366 4 21 AN292
15. listed above are available on the STMicroelectronics web site at www st com 19 21 Revision history AN2928 4 20 21 Revision history Table 1 Document revision history Date Revision Changes 24 Mar 2009 1 Initial release AN2928
16. n diode temperature without using the heat sink can be calculated from the following equation ambient temperature is chosen Equation 33 Ty Pross p Rthuc Rinca Ta Tj power diode junction temperature C Rinca Case to ambient thermal resistance C W for example the TO 220 package has a typical thermal resistance of 60 C W The calculated power diode junction temperature must be lower then maximum diode junction temperature T jyjax For proper design it is recommended to keep the junction temperature much lower than its maximum in order to avoid temperature stress on the power diode Equation 34 Ty lt Tymax Figure 6 Real power diode current Inductor calculation All components for the design are calculated but the final step in the design procedure still remains since it is necessary to calculate the inductor L The calculations that follow are valid for the inductor used in the STEVAL ILL013V1 demonstration board but for applications with for example lower voltages some standardized inductors for DC DC can also be used 15 21 Design equations for the modified buck converter AN2928 16 21 First the inductor core size must be selected for which it may be helpful to calculate the minimum area product using application parameters The minimum required core area product AP where the flux swing is limited by core saturation is Equation 35 4 L Ipeak IRMS AP MIN Bmax
17. network calculation 8 2 3 LED current calculation anaa aaa ee ene 10 2 4 Power MOSFET calculation eee ee eens 11 2 5 Power diode selection 0 0 cee ee ee ee ee eens 14 2 6 Inductor calculation ee ee ee eee 15 3 Reference and related materials 0 000 ce eee eee eee 19 4 REVISION history ies ad odeee ade sc ndew ened deeeeawn wank ener 20 2 21 ki AN2928 List of figures List of figures Figure 1 Modified buck converter toy tiMe ekk eee 4 Figure 2 Modified buck converter topp time 6 eee 5 Figure 3 Modified buck converter theory of operation 6 Figure4 Sawtooth sional 0 ce eee eee 12 Figure 5 Real drain MOSFET current sara kenaa akaaka TREE tenets 13 Figure 6 Real power diode current 00 eee 15 ky 3 21 Modified buck converter in constant current mode AN2928 Figure 1 Modified buck converter in constant current mode As stated in the introduction the aim of this application note is to describe a modified buck converter working in FOT and CCM The basic principle of the design using the L6562A controller is shown in Figure 1 and Figure 2 Figure 1 represents the stage when the power MOSFET Q is turned on As shown by the red arrow the current flows from the DC voltage input Vin through the load LEDs the inductor L t
18. of the switch it is not possible to obtain an exact equation for the calculation of switching losses Moreover the switching behavior is also influenced by the performance of the driver and layout design leakage inductance and parasitic capacitors To arrive at an estimation of the switching power losses Equation 27 can be used Equation 27 Vin Imax torr sw f Psw 2 torr_sw Switch off time s typically tens of ns For example switched off time measured on the STEVAL ILLO13V1 using the STP9NM50N power MOSFET 400 V input voltage is 120 ns Total power P_tor is lost in the power MOSFET and its heat sink so it is simple to calculate Equation 28 T ymax Ta P Tymax Maximum junction temperature C Ta ambient temperature C Rthuc junction to case thermal resistance C W Rthcu case to heat sink thermal resistance C W usually between 0 35 and 0 8 for the insulating washer Rina heat sink to ambient thermal resistance C W 13 21 Design equations for the modified buck converter AN2928 2 5 14 21 Finally if the heat sink and its thermal resistance is known it is possible to calculate maximum static drain source on resistance from Equation 26 Equation 27 and Equation 28 for easy power MOSFET selection Equation 29 Tamak Ta Vin Imax torr sw f Rpsvon lt 2 2 Ringe Rincon Rinna IRMS 2 IRs Power diode selection The power diode D from Figure 1
19. ure stress on the power MOSFET Basically total power losses on the power MOSFET occur through conduction losses depending on the Rps on switching losses and gate charge loss caused by charging up the gate capacitance and then discharging this capacitance to ground The gate charge loss is very small compared to the conduction and switching losses so it is not used for further calculations For total power MOSFET loss a valid equation is Equation 23 Prot Poon Psw Por total power losses on the power MOSFET W Pcon conduction losses on the power MOSFET W Psw switching losses on the power MOSFET W The power MOSFET conduction loss is represented by the continuous conduction current flowing through the MOSFET during the on time stage Therefore the power loss depends on its static drain source resistance Rpgon In order to calculate conduction loss properly it is necessary to calculate the drain current RMS value Figure 4 shows the sawtooth signal for which the RMS value was calculated in Equation 24 Note that in this case average current layp is defined as the average value of the sawtooth portion IMaxt min 2 11 21 Design equations for the modified buck converter AN2928 12 21 Figure 4 Sawtooth signal Equation 24 to T to DT to T 2 lams f Podst Pod f Poat D a D Imax lun lpp rus 7 Mz i DdtH i t dtj D Ip 1 D 5 2 to to t DT IRms root mean squared dr
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