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Concept Kit:PWM Buck Converter Average Model

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Concept Kit:PWM Buck Converter Average Model, 10JUN2011. This concept kit is PSpice Version by Bee Technologies.

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Concept Kit:PWM Buck Converter Average Model

  1. 1. PWM Controller Power Switches Filter & Load (Voltage Mode Control) U? U? PWM_CTRL BUCK_SW L VOUT 1 2 Vo- -+ PWM C + D 1/Vp Rload REF ESRVREF VP = 2.5 VREF = 1.23Concept Kit:PWM Buck ConverterAverage Model All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 1
  2. 2. Contents • Concept of Simulation • Buck Converter Circuit • Averaged Buck Switch Model • Buck Regulator Design Workflow 1. Setting PWM Controller’s Parameters. 2. Programming Output Voltage: Rupper, Rlower 3. Inductor Selection: L 4. Capacitor Selection: C, ESR 5. Stabilizing the Converter (Example) • Load Transient Response Simulation (Example) Appendix A. Type 2 Compensation Calculation using Excel B. Feedback Loop Compensators C. Simulation Index All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 2
  3. 3. Concept of SimulationBlock Diagram: PWM Controller Power Switches Filter & Load (Voltage Mode Control) Averaged Buck Parameter: VOUT Switch Model •L - + Parameter: •C • VP • ESR VREF • VREF • RloadModels: U? U? L PWM_CTRL BUCK_SW 1 2 Vo - C PWM D + Rload 1/Vp ESR REF VP = 2.5 VREF = 1.23 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 3
  4. 4. Buck Converter Circuit Power Switches Filter & Load U2 BUCK_SW L 1 2 Vo D C Vin Rload ESR 0 PWM Controller Type 2 Compensator C2 R2 C1 U3 Comp Rupper PWM_CTRL - FB d PWM + 1/Vp Rlower REF VP = 2.5 VREF = 1.23 0 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 4
  5. 5. Averaged Buck Switch Model iin U2 iout BUCK_SW + D + vin vout D - - • The Averaged Buck Switch Model represents relation between input and output of the switch that is controlled by duty cycle – d (value between 0 and 1). • Transfer function of the model is vout = d  vin • The current flow into the switch is iin = d  iout All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 5
  6. 6. Buck Regulator Design Workflow 1 Setting PWM Controller’s Parameters: VREF, VP 2 Setting Output Voltage: Rupper, Rlower 3 Inductor Selection: L 4 Capacitor Selection: C, ESR 5 Stabilizing the Converter: R2, C1, C2• Step1: Open the loop with LoL=1kH and CoL=1kF then inject an AC signal to generate Bode plot. (always default)• Step2: Set C1=1kF, C2=1fF, (always keep the default value) and R2= calculated value (Rupper//Rlower) as the initial values.• Step3: Select a crossover frequency (about 10kHz or fc < fosc/4). Then complete the table.• Step4: Read the Gain and Phase value at the crossover frequency (10kHz) from the Bode plot, Then put the values to the table• Step5: Select the phase margin at the fc ( > 45 ). Then change the K value until it gives the satisfied phase margin, for this example K=6 is chosen for Phase margin = 46.• Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again. 6 Load Transient Response Simulation All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 6
  7. 7. Buck Regulator Design Workflow U2 BUCK_SW 3 L 1 2 Vo D C Vin Rload ESR 4 0 5 Type 2 Compensator C2 R2 C1 2 U3 Comp Rupper PWM_CTRL - FB d PWM + 1/Vp Rlower REF 1 VP = 2.5 0 VREF = 1.23 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 7
  8. 8. 1 Setting PWM Controller’s Parameters U? vcomp PWM_CTRL • VREF, feedback reference voltage, value - FB is given by the datasheetd PWM • VP = (Error Amp. Gain  vFB ) / d + 1/Vp Error Amp. REF • vFB = vFBH – vFBL VP = 2.5 • d = dMAX – dMIN VREF = 1.23 • Error Amp. Gain is 100 (approximated)The PWM block is used to transfer the error voltage(between FB and REF) to be the duty cycle. where3.0V2.0V VP is the sawtooth peak voltage.SEL>> VP vFBH is maximum FB voltage where d = 0 0V V(osc) V(comp) vFBL is minimum FB voltage where d =1(100%) dMAX is maximum duty cycle, e.g. d = 0(0%) V(PWM) Duty cycle (d) is a value from 0 to 1 dMIN is minimum duty cycle, e.g. d =1(100%) Time If vFBH and vFBL are not provided, the default value, VP=2.5 could be used. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 8
  9. 9. 1 Setting PWM Controller’s Parameters (Example)  If the VP ( sawtooth signal amplitude ) does not informed by the datasheet, It can be approximated from the characteristics below. from vFBH VP = (Error Amp. Gain  vFB )/d vFB = •Error Amp. Gain = 100 (approximated) 25mV •from the graph on the left, vFB = 25mV (15m - (-10m)) vFBL d = 1 (100%) • d = 1 – 0 = 1 VP ≈ ( 100  25mV )/1 dMIN dMAX ≈ 2.5V LM2575: Feedback Voltage vs. Duty Cycle If vFBH and vFBL are not provided, the default value, VP=2.5 could be used. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 9
  10. 10. 2 Setting Output Voltage: Rupper, Rlower• Use the following formula to select the resistor values.  Rupper  VOUT  VREF1   Type 2 Compensator Vo  Rlower  C2 • Rlower can be between 1k and 5k. R2 C1 U3 Comp RupperExample PWM_CTRLGiven: VOUT = 5V - FB d VREF = 1.23 PWM + Rlower = 1k 1/Vp Rlower Error Amp. REFthen: Rupper = 3.065k VP = 2.5 VREF = 1.23 0 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 10
  11. 11. 3 Inductor Selection: L L1 2 Vo Inductor Value C • The output inductor value is selected to set the converter to work in CCM (Continuous Current Rload ESR Mode) or DCM (Discontinuous Current Mode). • Calculated by LCCM  VI , max VOUT  RL, min 2 fosc VI , max Where • LCCM is the inductor that make the converter to work in CCM. • VI,max is input maximum voltage • RL,min is load resistance at the minimum output current ( IOUT,min ) • fosc is switching frequency All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 11
  12. 12. 3 Inductor Selection: L (Example) L1 2 Vo Inductor Value C from ESR Rload LCCM  VI , max VOUT  RL, min 2 foscVI , max Given: • VI,max = 40V, VOUT = 5V • IOUT,min = 0.2A • RL,min = (VOUT / IOUT,min ) = 25 • fosc = 52kHz Then: • LCCM  210(uH), • L = 330(uH) is selected All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 12
  13. 13. 4 Capacitor Selection: C, ESR L 1 2 Vo Capacitor Value • The minimum allowable output capacitor value should C be determined by Rload ESR C  7,785  VI , max F VOUT  L( H) Where • VI, max is the maximum input voltage. • L (H) is the inductance calculated from previous step ( 3 ).• In addition, the output ripple voltage due to the capacitor ESR must be considered as the following equation. VO , RIPPLE ESR  IL , RIPPLE All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 13
  14. 14. 4 Capacitor Selection: C, ESR (Example) L1 2 Vo Capacitor Value From C C  7,785  VI , max F ESR Rload VOUT  L( H) and VO , RIPPLE ESR  IL , RIPPLE Given: • VI, max = 40 V • VOUT = 5 V • L (H) = 330 Then: • C  188 (F) In addition: • ESR  100m All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 14
  15. 15. 5 Stabilizing the Converter U2 BUCK_SW L H(s) 1 2 Vo D C Vin 12Vdc Rload ESR 0 Type 2 Compensator G(s)• Loop gain for this configuration is C2 R2 C1 Rupper GPWM T ( s)  H ( s)  G( s)  GPWM 3.066k U3 Comp PWM_CTRL - FB d PWM + 1/Vp Rlower REF 1.0k VP = 2.5 VREF = 1.23 0• The purpose of the compensator G(s) is to tailor the converter loop gain (frequency response) to make it stable when operated in closed-loop conditions. All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 15
  16. 16. 5 Stabilizing the Converter (Example) U2 LSpecification: BUCK_SW 1 330uH 2 VoVOUT = 5V D C 330uFVIN = 7 ~ 40V Vin Rload 12Vdc ESR 5ILOAD = 0.2 ~ 1A 100mPWM Controller: 0 G(s) Type 2 CompensatorVREF = 1.23V 1 C2VP = 2.5V e.g. Given values from National R2 C1fOSC = 52kHz Semiconductor Corp. IC: LM2575 RupperRlower = 1k, 2 U3 3.1k PWM_CTRLRupper = 3.1k, LOL - FBL = 330uH, 3 1kH d PWM +C = 330uF (ESR = 100m) 4 COL 1/Vp REF Rlower 1.0k 1kF VP = 2.5 0Task: 1Vac V3 VREF = 1.23 0Vdc• to find out the element of the Type 2 compensator ( R2, C1, 0 and C2 ) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 16
  17. 17. 5 Stabilizing the Converter (Example) The element of the Type 2 compensator ( R2, C1, and C2 ), that stabilize the converter, can be extracted by using Type 2 Compensator Calculator (Excel sheet) and open-loop simulation with the Average Switch Models (ac models). U2 L BUCK_SW 330uH 1 2 Vo D C 330uF Vin Rload 12Vdc ESR 5 100m 0 Step2 Set C1=1kF, C2=1fF, Type 2 Compensator and R2=calculated valueStep1 Open the loop with C2 1f (Rupper//Rlower) as theLoL=1kH and CoL=1kF then inject R2 C1 initial values.an AC signal to generate Bode 0.756k 1kplot. Rupper 3.1k U3 PWM_CTRL LOL - FB d PWM 1kH + 1/Vp Rlower COL 1k 1kF REF VP = 2.5 V3 VREF = 1.23 0 1Vac 0Vdc  C1=1kF is AC shorted, and C2 1fF is AC opened (or Error-Amp without compensator). 0 All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 17
  18. 18. 5 Stabilizing the Converter (Example)Type 2 Compensator Calculator Step3 Select a crossover frequency (about 10kHz or fc < fosc/4 ), forSwitching frequency, fosc : 52.00 kHz this example, 10kHz is selected.Cross-over frequency, fc Then complete the table.(<fosc/4) : 10.00 kHzRupper : 3.1 kOhm values from 2Rlower : 1 kOhmR2 (Rupper//Rlower) : 0.756 kOhm (automatically calculated) Calculated value ofPWM the Rupper//RlowerVref : 1.230 V values from 1Vp (Approximate) : 2.5 V All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 18
  19. 19. 5 Stabilizing the Converter (Example) Gain: T(s) = H(s)GPWM 80 40 Step4 Read the Gain and Phase value at the crossover frequency (10kHz) 0 (10.000K,-44.211) from the Bode plot, Then put the values -40 to the table. -80 DB(v(d))180d Phase  at fc Parameter extracted from simulation 90d (10.000K,65.068) Set: R2=R1, C1=1k, C2=1f Gain (PWM) at foc ( - or + ) : -44.211SEL>> 0d Phase (PWM) at foc : 65.068 100Hz 1.0KHz 10KHz 100KHz P(v(d)) Frequency Tip: To bring cursor to the fc = 10kHz type “ sfxv(10k) ” in Search Command. Cursor Search All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 19
  20. 20. 5 Stabilizing the Converter (Example) Step5 Select the phase margin at fcK-factor (Choose K and from the table) (> 45 ). Then change the K valueK 6 (start from K=2) until it gives the -199  (automatically calculated)phase margin, for this satisfied example K=6 is chosen for PhasePhase margin : 46 (automatically calculated) 46. margin =R2 : 122.780 kOhm (automatically calculated) As the result; R2,C1 : 0.778 nF (automatically calculated) C1, and C2 areC2 : 21.600 pF (automatically calculated) calculated.Remark: If K-factor fail to gives the satisfied phase margin, Increase the outputcapacitor C then try Step1 to Step5 again.  K Factor enable the circuit designer to choose a loop cross-over frequency and phase margin, and then determine the necessary component values to achieve these results. A very big K value (e.g. K > 100) acts like no compensator (C1 is shorted and C2 is opened). All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 20
  21. 21. 5 Stabilizing the Converter (Example)The element of the Type 2 compensator ( R2, C1, and C2 ) extraction can be completed by Type 2Compensator Calculator (Excel sheet) with the converter average models (ac models) and open-loopsimulation. U2 L BUCK_SW 330uH 1 2 Vo D C 330uF Vin Rload 12Vdc ESR 5 100m 0 The calculated values of the Type 2 Compensator C2 type 2 elements are, 21.6p R2=122.780k, C1=0.778nF, R2 122.780k C1 0.778n and C2=21.6pF. Rupper 3.1k U3 PWM_CTRL LOL - FB d PWM 1kH + 1/Vp Rlower COL 1k 1kF REF VP = 2.5 V3 VREF = 1.23 0 1Vac 0Vdc *Analysis directives: 0 .AC DEC 100 0.1 10MEG All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 21
  22. 22. 5 Stabilizing the Converter (Example) Gain and Phase responses after stabilizing 80 40 (9.778K,0.000) 0 -40 SEL>> Gain: T(s) = H(s) G(s)GPWM -100 DB(v(d)) 180d Phase  at fc 90d (9.778K,45.930) 0d 100Hz 1.0KHz 10KHz 100KHz P(v(d)) Frequency • Phase margin = 45.930 at the cross-over frequency - fc = 9.778kHz. Tip: To bring cursor to the cross-over point (gain = 0dB) type “ sfle(0) ” in Search Command. Cursor Search All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 22
  23. 23. Load Transient Response Simulation (Example)The converter, that have been stabilized, are connected with step-load to perform load transientresponse simulation. U2 L Load BUCK_SW 330uH 1 2 Vo D C 330uF I1 Vin Rload I1 = 0 20Vdc ESR 25 I2 = 0.8 100m TD = 10m TF = 25u TR = 20u PW = 0.43m PER = 1 0 Type 2 Compensator C2 21.6p 5V/2.5 = 0.2A step R2 C1 to 0.2+0.8=1.0A load 122.780k 0.778n Rupper 3.1k U3 PWM_CTRL - FB d PWM + 1/Vp Rlower REF 1k*Analysis directives: VP = 2.5 VREF = 1.23 0.TRAN 0 20ms 0 1u All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 23
  24. 24. Load Transient Response Simulation (Example) Simulation Measurement 5.2V 4.0A1 2 Output Voltage Change 5.1V 3.5A 5.0V 3.0A 4.9V 2.5A 4.8V 2.0A 4.7V 1.5A Load Current 4.6V 1.0A 4.5V 0.5A >> 4.4V 0A 9.9ms 10.1ms 10.3ms 10.5ms 10.7ms 10.9ms 1 V(vo) 2 I(load) Time • The simulation results are compared with the measurement data (National Semiconductor Corp. IC LM2575 datasheet). All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 24
  25. 25. A. Type 2 Compensation Calculation using Excel Switching frequency, fosc : 52.00 kHz Given spec, datasheet Cross-over frequency, fc (<fosc/4) : 10.00 kHz Input the chosen value ( about 10kHz or < fosc/4 ) Rupper : 3.1 kOhm Given spec, datasheet, or calculated Rlower : 1 kOhm Given spec, datasheet, or value: 1k-10k Ohm R2 (Rupper//Rlower) : 0.756 kOhm (automatically calculated) PWM Vref : 1.230 V Given spec, datasheet Vp (Approximate) : 2.5 V Given spec, or calculated, (or leave default 2.5V) Parameter extracted from simulation Set: R2=R2, C1=1k, C2=1f Gain (PWM) at foc ( - or + ) : -44.211 dB Read from simulation result Phase (PWM) at foc : 65.068  Read from simulation result K-factor (Choos K and  from the table) K 6 Input the chosen value (start from k=2)  -199  (automatically calculated) Phase margin : 46 (automatically calculated) Target value > 45 R2 : 122.780 kOhm (automatically calculated) C1 : 0.778 nF (automatically calculated) C2 : 21.60 pF (automatically calculated) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 25
  26. 26. B. Feedback Loop Compensators Type2 Compensator C2 Type 1 Compensator Type2a Compensator VOUT VOUT VOUT C1 R2 C1 R2 C1 Rupper Rupper Rupper PWM_CTRL PWM_CTRL PWM_CTRL - FB - FB - FBd d d PWM PWM PWM + + + 1/Vp Rlower 1/Vp Rlower 1/Vp Rlower REF REF REF 0 0 0 Type1 Compensator Type2 Compensator Type2a Compensator Type2b Compensator Type3 Compensator R2 C2 VOUT VOUT C1 R2 C1 C3 Rupper Rupper PWM_CTRL PWM_CTRL R3 - FB - FBd d PWM PWM + + Rlower 1/Vp Rlower 1/Vp REF REF 0 0 Type2b Compensator Type3 Compensator All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 26
  27. 27. C. Simulation IndexSimulations Folder name1. Stabilizing the Converter.................................................... ac2. Load Transient Response.................................................. steploadLibraries :1. ..¥bucksw.lib2. ..¥pwm_ctr.libTool :• Type 2 Compensator Calculator (Excel sheet) All Rights Reserved Copyright (C) Bee Technologies Corporation 2011 27

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