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  1. 1. Everything you ever wanted to know about Buck Converter Design for LED Lighting - unless you are writing a book Woody Smith -Design Geek LINE-IN PART 1: ANALOG CONTROLLERS 1
  2. 2. 2 Index Agenda and goals pages 5,6,7 LED drivers first thoughts and spec’s pages 8-14 Basic Buck Theory pages 15-19 a) current mode page 20-158 1) First order models pages 21-36 2) Averaged models pages 37-46 3) more accurate models pages 47-158 a)intro pages48-57 b)block diagram CPM transfer functions pages 58-64 c) Tymerski model and transfer func’s pages 65-67 d) Effect of current feedback on Q pages 68 e) Low Q approx and transfer functions pages 69-77 f)example design pages 78-81
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  5. 5. AGENDA AND GOALS 1.)Develop a complete design procedure for advanced controller buck converters for LED Drivers Systems •Focusing on: •Overall power efficiency of the lighting assembly •LED operating efficacy (lumen output per watt of input power) •Thermal management of the LEDs and their driver circuit •AC power factor correction (PFC) for the driver circuitry •AC harmonics generation (distortion) •Meeting EMI restrictions •Whether or not dimming is required •LED driver reliability and service life (to match that of the LEDs) •Circuit protection devices needed •Electronics space efficiency (assembly size) •Cost/competitive position 5
  6. 6. AGENDA AND GOALS Design Approach 1.)Matlab/LTpice macro simulation to handle the majority of the design tasks --Combined with an Excel spreadsheet for spec and equations ---Showing the strengths of each controller Current Mode 1.)Peak, Average, OCPM V2 mode Sliding Mode COT 1.)Fixed on time 2.)Fixed off time Sigma Delta 2.) Comparison of the various architectures Decision based on the overall system spec 3.) final design in Spectre/Hspice 6
  7. 7. AGENDA and GOALS Design Criteria •LED operating efficacy (lumen output per watt of input power) •Overall power efficiency of the lighting assembly •Thermal management of the LEDs and their driver circuit • only 10-25% of the power is converted to Lumens!! •AC power factor correction (PFC) for the driver circuitry •AC harmonics generation (distortion) •Meeting EMI restrictions •Whether or not dimming is required •LED driver reliability and service life (to match that of the LEDs) •Circuit protection devices needed •Electronics space efficiency (assembly size) •Cost/competitive position -From an EDN article by Jim Young, ON Semiconductor, and Usha Patel, Littelfuse, Inc. - October 8, 2012 7
  8. 8. First some thoughts on a possible new direction for LED Lighting 8
  9. 9. AC dimmer Optional LED Microcontroller AC Control (I2C, PWM, Analog) Voltage, current, frequency, Harmonics, etc. Monitor Temperature, Brightness, Monitor GWSnet Interface BACnet Bus Smart Light - Rethink Customized for building communication medium Gateway Power supply built into the socket RF Interface 9
  10. 10. AC dimmer Optional LED Microcontroller AC Control (I2C, PWM, Analog) Voltage, current, frequency, Harmonics, etc. Monitor Temperature, Brightness, Monitor BACnet Interface BACnet Bus Smart Light – Rethink 2 Customized for building communication medium Gateway Power supply built into the socket RF Interface SMPSPFC Optional 10
  11. 11. The following is a primer for a top-level down design methodology. It emphasizes behavioral modeling and design oriented analysis(to borrow a phrase from Middlebrook). Our goal is to shorten the design cycle and increase physical insight. -Chip and board 11
  12. 12. First Steps • What’s your key specs? • Rank and review them in comparison to existing designs • Build an Excel spreadsheet and project timeline • Review this with your team • Revise and review again • Build a complete system level behavioral model-Matlab and spice • Check all spec’s! • Revise your Excel spreadsheet and timeline • Verify your resource needs • List all assumptions • Make sure your Timeline has “guard bands.” TORA, TORA, TORA! 12
  13. 13. Strawman Spec • 90% efficiency • 50,000 hr. lifetime with greater than 70% of the original luminosity • 100W equivalent • Assume 100 lm/W for Leds and 15lm/W for Incandescent -6’ish X advantage • Assume Iout=700mA • Vled(700mA) ~ 3.2v (phosphorous coated blue for white’ish light ) • 100W/6*700mA÷3.2≤8 leds required • Thermal temp≤ 125°C • 10-100% dimming Triac based • Triac bleeder ~20mA • Class B EMI spec 13
  14. 14. 1. Tmax =125C 2. Tmin= -25C 3. PFC= .9 4. Power eff=.85% min 5. 10-100% dimming 6. Front edge, triac dimmers 7. 20mA bleeder current 8. Vin =100-140V 9. Iout=500mA ±10ma 10.Vout= 30-32V 11.Inductor ripple=20-40% 12.vout-ripple=? 13.50k hr lifetime 14.Driver dimensions less than 2x3x5mm-working on it 15. driver cost ≤ $1.50 in 100k lots 16. internal OTP, OVP OCP 1. OTP at 125±5 2. OVP at input (MOV fuse- typically at 200V) 3. OCP-TBD 17. class C EN6001 18.UL approved Specification list 14
  15. 15. Ok, let’s get down to it. Let’s start with peak mode Buck theory ………let’s start with some solid insights from Abraham Pressman and follow it with a few(hundred) slides from: U. of Colorado, ECEN 5807 Great stuff with a solid balance between theory, design and ……math. 15
  16. 16. From A. Pressman, Switching Mode Power Supply , pp 177-178 Fig. 5.5a Fig. 5.5b Fig. 5.5c 16
  17. 17. From A. Pressman, Switching Mode Power Supply , p 178 KEY POINTS!! 17
  18. 18. From A. Pressman, Switching Mode Power Supply , p 179 18
  19. 19. Time to start the work of understanding the theory and math of Buck Converters 19
  20. 20. A pretty standard CPM buck 20
  21. 21. 21
  22. 22. Look at Ltspice sims 22
  23. 23. What’s the optimal ramp Size? 23
  24. 24. Pertubation is dying, but what are you losing? 24
  25. 25. 25
  26. 26. 1st Order models work For small bandwidth systems Download the Fairchild: fan4810_http://www.fairchildsemi.com/products/analo g/fan4810designtools.xls A wonderful tool for it’s purpose. Use it to explore the design space. Read the appnotes and enjoy the wonderful design process, but with your eyes wide open for it’s limitations 26
  27. 27. Read the appnotes; look at pfc setup, check the EMI filtering There is a ton of things to be learned here-dissect it!! 27
  28. 28. This a useful large signal, quasi- linearized model w/o averaging or small signal considerations. ic iL 28
  29. 29. Play with the ramps, the compensation. Observe the simplicity of the switch structure 29
  30. 30. 1st order model’s limitations foster a need for a more advanced approach. • Start with the large signal models and average them over the duty cycle phases • Good, but not yet high frequency aware or sensitive to sampling effects • or linear • Now let’s add State Space matrix formulation and add small signal perturbations and linearize • Excellent, but still not complete • Time to include sampling-Ridley and gang to the rescue. But which model? 30
  31. 31. 31
  32. 32. Ah, the small signal perturbation 32
  33. 33. 33
  34. 34. Positive effects on noise and Vin sensitivity too 34
  35. 35. 35
  36. 36. LOOP Even if D is always less than .5(for any setup) use a ramp. CPM means faster response, lower noise, max-current control on startup 36
  37. 37. 37
  38. 38. 38
  39. 39. 39
  40. 40. 40
  41. 41. 41
  42. 42. Erickson Textbook 42
  43. 43. Tan model Study this closely 43
  44. 44. 44
  45. 45. 45
  46. 46. Starting with either state space equations or the Tymerski-Vorperian models you will arrive at this schematic. The only remaining question.: how to model sampling effects? 46
  47. 47. 47
  48. 48. 48
  49. 49. 49
  50. 50. 50
  51. 51. 51
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  55. 55. 55
  56. 56. ∞ Or At least greater than one 56
  57. 57. 57
  58. 58. 58
  59. 59. 59
  60. 60. Ignore this for the moment How cool is this equation. Look how Fm (ie, comp ramp)influences both loops. Later we will add loop compensation, loop delay, and sampling effects and it gets really interesting. 60
  61. 61. 61
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  63. 63. 63
  64. 64. 64
  65. 65. 65
  66. 66. 66
  67. 67. 67
  68. 68. Study this carefully 68
  69. 69. Erickson Book 69
  70. 70. You’ll want to derive this 70
  71. 71. Compare to first-order approximation of the sampled-data control-to-current model hfs s sT sT c L sssT e esi si s s                1 1 )/(1 1 1 11 1 1 )(ˆ )(ˆ )/( 1 )/( 1   s ssT s s e s      s a s hf f m m DD f f 2 221 1 1 1      Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at Model (4) is consistent with the sampled-data small-signal model 71
  72. 72. A quick aside on 2nd order transfer function roots 72
  73. 73. 73
  74. 74. Wow, Q< 1 gain is pretty nicely behaved and the phase variation is getting smooth 74
  75. 75. At low Q the poles are separate but interact depending on their frequency separation(a decade of frequeny to really separate them phase-wise. Gain-wise decades of separation removes most interaction) 75
  76. 76. 76
  77. 77. 77
  78. 78. Approx iL= ic 78
  79. 79. Compare to first-order approximation of the high-frequency sampled-data control-to-current model hfs s sT sT c L sssT e esi si s s                1 1 )/(1 1 1 11 1 1 )(ˆ )(ˆ )/( 1 )/( 1   s ssT s s e s    kHz32 221 1 1 1 2         ss a s hf ff m m DD f f Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at 32k vs.39kHz~20% with Ma=M2. play with Ma. I grew up using Ma=( .5-.75) x M2, but is that opt? 79
  80. 80. 2nd-order approximation in the small-signal averaged model Except Fm 80
  81. 81. Example • CPM buck converter: Vg = 10V, L = 5 mH, C = 75 mF, D = 0.5, V = 5 V, I = 20 A, R = V/I = 0.25 W, fs = 100 kHz • Inductor current slopes: m1 = (Vg – V)/L = 1 A/ms m2 = V/L = 1 A/ms A/V25.0 2 '  L TDD F s g D = 0.5: CPM controller is stable for any compensation ramp, ma/m2 > 0 Select: ma/m2 = Ma/M2 = 1, Ma = 1 A/ms 1/A1.0 1 2 1 21     s a m TMM M F 81
  82. 82. Example (cont.) kHz2.8 1 2 1  LC fo  1 L C RQ 47.047.0 1 1     Q L VRCF R VF QQ gm gm ckHz3.1851  o gm oc f R VF ff kHz4.81  ccp fQf kHz39/2  cchfp Qfff Duty-cycle control Peak current-mode control (CPM) 82
  83. 83. 83
  84. 84. 84
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  86. 86. Repeating the obvious about these models • Averaged models depend on small variations on all variables • Particularly duty cycle • It works well for DCM too, but only if key control variables are well controlled • Peak current mode wants small ∆IL to minimize switching uncertainty; minimum peak to average error(always check this at low current levels) • Low peak/average means low distortion but big inductors • Leading to shallow current ramps and more noise sensitivity at low vin • Why? Low vin shallow ramps and the same level of switching noise (comparator switching spikes(~.1-.2v?) • Serious layout worries 86
  87. 87. 2nd-order approximation in the small-signal averaged model 87
  88. 88. (Tan) 88
  89. 89. ][ˆ)1(]1[ˆ][ˆ ninini cLL   Discrete-time dynamics: )(ˆ)(ˆ zizi Lc  Z-transform: )(ˆ)1()(ˆ)(ˆ 1 zizzizi cLL    1 1 1 )(ˆ )(ˆ     zzi zi c L  Discrete-time (z-domain) control-to- inductor current transfer function: ss TjsT ee            1 1 1 1 Difference equation: • Pole at z =  • Stability condition: pole inside the unit circle, || < 1 • Frequency response (note that z1 corresponds to a delay of Ts in time domain): 89
  90. 90. Equivalent hold: )(ˆ)(ˆ),(ˆ][ˆ sizitini LLLL  ic[n] m1 m2 ic + ic iL[n] d[n]Ts iL[n-1] ma(t) iL(t) iL[n] Ts 90
  91. 91. Equivalent hold • The response from the samples iL[n] of the inductor current to the inductor current perturbation iL(t) is a pulse of amplitude iL[n] and length Ts • Hence, in frequency domain, the equivalent hold has the transfer function previously derived for the zero-order hold: s e ssT 1 £[u(t)-u(t)𝛿(t+Ts)]= 91
  92. 92. Complete sampled-data “transfer function” s sT sT c L sT e esi si s s       1 1 1 )(ˆ )(ˆ   2 2 1 2 ' 1 m m D D m m mm mm a a a a       Control-to-inductor current small-signal response: Ridley, Tan, Middlebrook- whoever. The central issue is this equation. How do we approximate it? 92
  93. 93. Example • CPM buck converter: Vg = 10V, L = 5 mH, C = 75 mF, D = 0.5, V = 5 V, I = 20 A, R = V/I = 0.25 W, fs = 100 kHz • Inductor current slopes: m1 = (Vg – V)/L = 1 A/ms m2 = V/L = 1 A/ms 2 2 2 2 1 2 1 1 ' 1 m m m m m m D D m m mm mm a a a a a a          s sT sT c L sT e esi si s s       1 1 1 )(ˆ )(ˆ   D = 0.5: CPM controller is stable for any compensation ramp, ma/m2 > 0 93
  94. 94. Control-to-inductor current responses for several compensation ramps (ma/m2 is a parameter) 10 2 10 3 10 4 10 5 -40 -30 -20 -10 0 10 20 magnitude[db] iL/ic magnitude and phase responses 10 2 10 3 10 4 10 5 -150 -100 -50 0 frequency [Hz] phase[deg] ma/m2=0.1 ma/m2=0.5 ma/m2=1 ma/m2=5 5 1 0.5 0.1 MATLAB file: CPMfr.m Look how the comp ramp kills the Ti loop gain and BW Large Fm approx 94
  95. 95. First-order approximation hfs s sT sT c L sssT e esi si s s                1 1 )/(1 1 1 11 1 1 )(ˆ )(ˆ )/( 1 )/( 1   s ssT s s e s    Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at Same prediction as HF pole in basic model (4) (Tan)   s a s hf f m m DD f f 2 221 1 1 1      PADE 1st order Delay of the control signal 95
  96. 96. Control-to-inductor current responses for several compensation ramps (ma/m2 = 0.1, 0.5, 1, 5) 10 2 10 3 10 4 10 5 -40 -30 -20 -10 0 10 20 magnitude[db] iL/ic magnitude and phase responses 10 2 10 3 10 4 10 5 -150 -100 -50 0 frequency [Hz] phase[deg] 1st-order transfer-function approximation 96
  97. 97. Second-order approximation 2 2/)2/(1 1 2 1 11 1 1 )(ˆ )(ˆ                       ss s sT sT c L sssT e esi si s s    2 2 2/)2/(2 1 2/)2/(2 1                ss sssT ss ss e s     2 221 12 1 12 m m DD Q a         Control-to-inductor current response behaves approximately as a second- order transfer function with corner frequency fs/2 and Q-factor given by Pade 2nd order approximate 2nd order polynomial 97
  98. 98. 10 2 10 3 10 4 10 5 -40 -30 -20 -10 0 10 20 magnitude[db] iL/ic magnitude and phase responses 10 2 10 3 10 4 10 5 -150 -100 -50 0 frequency [Hz] phase[deg] Control-to-inductor current responses for several compensation ramps (ma/m2 = 0.1, 0.5, 1, 5) 2nd-order transfer-function approximation Vs Ideal transfer function 98
  99. 99. 99
  100. 100. 100
  101. 101. Example • CPM buck converter: Vg = 10V, L = 5 mH, C = 75 mF, D = 0.5, V = 5 V, I = 20 A, R = V/I = 0.25 W, fs = 100 kHz • Inductor current slopes: m1 = (Vg – V)/L = 1 A/ms m2 = V/L = 1 A/ms A/V25.0 2 '  L TDD F s g D = 0.5: CPM controller is stable for any compensation ramp, ma/m2 > 0 Select: ma/m2 = Ma/M2 = 1, Ma = 1 A/ms 1/A1.0 1 2 1 21     s a m TMM M F 101
  102. 102. Example (cont.) kHz2.8 1 2 1  LC fo  1 L C RQ 47.047.0 1 1     Q L VRCF R VF QQ gm gm ckHz3.1851  o gm oc f R VF ff kHz4.81  ccp fQf kHz39/2  cchfp Qfff Duty-cycle control Peak current-mode control (CPM) 102
  103. 103. 103
  104. 104. Fig. 9 These is the key point 104
  105. 105. Here’s the another key point, look at the phase at fs/10 105
  106. 106. Placeholder until I do my sense section 106
  107. 107. 107
  108. 108. 108
  109. 109. Fig. 6 109
  110. 110. Fig. 6 110
  111. 111. 111
  112. 112. How Do I Model Current Mode Converters? I follow a dual Pantheon of “Gods” Middlebrook Erickson Ridley Tymerski/Vorperian Basso Dixon Lehman Brooks Versus • My goal to get a solid physical insight into the operation and modeli