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Effective Power/Ground Plane Decoupling for PCB Dr. Bruce - PowerPoint PPT Presentation

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Effective Power/Ground Plane Decoupling for PCB Dr. Bruce Archambeault IBM Distinguished Engineer IEEE Fellow IBM Research Triangle Park, NC Barch@us.ibm.com October 2007 IEEE IEEE Power Plane Noise Control Ground Bounce October

  1. Current in IC During Logic Transitions (CMOS) V CC switch IC IC load driver V DC C L Z 0 , v p GND V CC V CC IC IC IC load IC load discharge charge driver driver V CC 0 V Z 0 , v p Z 0 , v p shoot-thru shoot- current GND thru GND logic 0-1 logic 1-0 current October 2007 Dr. Bruce Archambeault 34

  2. Typical PCB Power Delivery DC/DC converter (Power source) electrolytic SMT capacitors capacitor GND V CC GND GND V CC V CC IC load GND GND IC driver V CC V CC GND V CC October 2007 Dr. Bruce Archambeault 35

  3. Equivalent Circuit for Power Current Delivery to IC PCB connector wiring and wiring via interconnect capacitor L trace L ps leads L bulk L via IC load C planes V DC switch C bulk C SMT SMT DC/DC electrolytic capacitors V CC /GND converter capacitors plane October 2007 Dr. Bruce Archambeault 36

  4. Traditional Analysis #1 • Use impedance of capacitors in parallel ESR 1 ESR 2 ESR 3 ESR 4 ESL 1 ESL 2 ESL 3 ESL 4 1uF 0. 1uF 0.01uF .001uF Impedance to IC No Effect of Distance Between Capacitors power/gnd pins and IC Included! October 2007 Dr. Bruce Archambeault 37

  5. Traditional Impedance Calculation for Four Decoupling Capacitor Values 1000 100 .1uF .01uF .001uF .0001uF Impedance (ohms) 10 All in Parallel 1 0.1 0.01 1.00E+07 1.00E+08 1.00E+09 Frequency (Hz) October 2007 Dr. Bruce Archambeault 38

  6. Traditional Analysis #2 • Calculate loop area – Traditional loop Inductance formulas – Which loop area? Which size conductor ESR 1 ESR 2 ESR 3 ESR 4 ESL 1 +L d1 ESL 2 +L d2 ESL 3 +L d3 ESL 4 +L d4 1uF 0. 1uF 0.01uF .001uF Impedance to IC power/gnd pins Over Estimates L and Ignores Distributed Capacitance October 2007 Dr. Bruce Archambeault 39

  7. More Accurate Model Includes Distributed Capacitance Intentional Decoupling Capacitors Intentional Decoupling Capacitors IC Power Pin Distributed Distributed capacitors capacitors October 2007 Dr. Bruce Archambeault 40

  8. Distributed Capacitance Schematic Intentional Intentional Distributed Capacitance Distributed Capacitance Capacitor Capacitor ESR ESR Loop L Loop L Note: L increases Note: L increases C apacitance C apacitance as distance from as distance from source increases source increases Source Source Source October 2007 Dr. Bruce Archambeault 41

  9. Effect of Distributed Capacitance • Can NOT be calculated/estimated using traditional capacitance equation • Displacement current amplitude changes with position and distance from the source October 2007 Dr. Bruce Archambeault 42

  10. Displacement Current 500 MHz via @450 mils from Source October 2007 Dr. Bruce Archambeault 43

  11. Need to Find the Real Effect of Decoupling Capacitor Distance • Perfect decoupling capacitor is a via between planes • FDTD simulation to find the effect of shorting via distance from source • Vary spacing between planes, distance to via, frequency, etc October 2007 Dr. Bruce Archambeault 44

  12. Impedance of Shorting Via vs. Frequency Four Via Case (20 mil Seperation Between Plates) 100 10 Impedance (ohms) 20mils 40mils 50mils 60mils 70mils 80mils 90mils 100mils 1 120mils 130mils 140mils 150mils 160mils 180mils 200mils 220mils 240mils 250mils 350mils 450mils 0.1 1.E+08 1.E+09 1.E+10 Frequency (Hz) October 2007 Dr. Bruce Archambeault 45

  13. Impedance Result • Linear with frequency (on log scale) • Looks like an inductance only! • Consider this inductance an Apparent Inductance • Apparent inductance is constant with frequency October 2007 Dr. Bruce Archambeault 46

  14. Apparent Inductance for One Shorting Via Case 20 mil Plate Separation 1.2 1 0.8 Inductance (nH) 0.6 50mils 0.4 110mils 120mils 200mils 250mils 0.2 350mils 450mils 0 1.E+08 1.E+09 1.E+1 Frequency (Hz) October 2007 Dr. Bruce Archambeault 47

  15. Formulas to Predict Apparent Inductance = − + − + L ( 0 . 1336 s 0 . 0654 ) Ln ( dist ) ( 0 . 2609 s 0 . 2675 ) − one via = − + − + L ( 0 . 1307 s 0 . 0492 ) Ln ( dist ) ( 0 . 2948 s 0 . 1943 ) − two via = − + − + L ( 0 . 1242 s 0 . 0447 ) Ln ( dist ) ( 0 . 2848 s 0 . 1763 ) − three via = − + − + L ( 0 . 1192 s 0 . 0403 ) Ln ( dist ) ( 0 . 2774 s 0 . 1592 ) − four via s = separation between plates (mils/10) dist = distance to via October 2007 Dr. Bruce Archambeault 48

  16. True Impedance for Decoupling Capacitor IC Capacitor Power Gnd L IC L cap L apparent L apparent ESR L cap + L IC Source Nominal Capacitance October 2007 Dr. Bruce Archambeault 49

  17. Impedance Calculation with Apparent Inductance for Four Decoupling Capacitor Values 10 Case1 Cap Value Distance to Cap from IC Case 1 Case 2 Case 3 Case2 0.1 uF 800mils 1200mils 1500mils Case3 0.01 uF 600mils 900mils 1100mils Traditional Calculation 0.001uF 400mils 700mils 800mils 0.0001uF 200mils 400mils 400mils 1 Impedance (ohms) 0.1 0.01 1.E+07 1.E+08 1.E+09 Frequency (Hz) October 2007 Dr. Bruce Archambeault 50

  18. Effect of Distributed Capacitance • Can NOT be calculated/estimated using traditional capacitance equation • Displacement current amplitude changes with position and distance from the source • Following examples use cavity resonance technique (EZ-PowerPlane) – Frequency Domain to compare to measurements – Time Domain using SPICE circuit from cavity resonance analysis October 2007 Dr. Bruce Archambeault 51

  19. Parameters for Comparison to Measurements • Dielectric thickness = 35 mils • Dielectric constant = 4.5, Loss tan = 0.02 • Copper conductivity = 5.8 e7 S/m October 2007 Dr. Bruce Archambeault 52

  20. Measured vs Model (MoM) S21 for 12" x 10" PC Power/gnd with 25 .01uF caps Position 8-to-1 0 No Caps - Measured -10 EZ-PP No Caps -20 S21 (dB) -30 -40 -50 1.0E+07 1.0E+08 1.0E+09 1.0E+10 Frequency (Hz) October 2007 Dr. Bruce Archambeault 53

  21. Measured vs Model (EZ-PP) S21 for 12" x 10" PC Power/gnd with 25 .01uF caps Position 8-to-1 0.0 -10.0 -20.0 -30.0 -40.0 S21 (dB) -50.0 -60.0 Measured -70.0 EZ-PP 25 caps -80.0 -90.0 -100.0 1.0E+07 1.0E+08 1.0E+09 1.0E+10 Frequency (Hz) October 2007 Dr. Bruce Archambeault 54

  22. Measured vs Model (EZ-PP) S21 for 12" x 10" PC Power/gnd with 95 .01uF caps Position 8-to-1 0.0 -10.0 -20.0 -30.0 -40.0 S21 (dB) -50.0 -60.0 95 Caps - Measured -70.0 95 Caps - EZ-PP -80.0 -90.0 -100.0 1.0E+07 1.0E+08 1.0E+09 1.0E+10 Frequency (Hz) October 2007 Dr. Bruce Archambeault 55

  23. Impedance at Port #1 Single 0.01 uF Capacitor at Various Distances (35mil Dielectric) 30 20 10 Impedance (dBohms) 0 -10 -20 no caps 300 mils 500 mils 700 mils -30 1000 mils -40 1.0E+07 1.0E+08 1.0E+09 1.0E+10 October 2007 Dr. Bruce Archambeault 56 Frequency (Hz)

  24. Z11 Phase Comparison as Capacitor distance Varies for 35 mils FR4 ESL = 0.5nH 2 1.5 1 0.5 Phase (rad) 0 -0.5 100 mils 200 mils -1 300 mils 400 mils 1000 mils -1.5 2000 mils -2 1.0E+06 1.0E+07 1.0E+08 1.0E+09 Frequency (Hz) October 2007 Dr. Bruce Archambeault 57

  25. Impedance at Port #1 Single 0.01 uF Capacitor at Various Distances (10mil Dielectric) 20 10 0 no caps Impedance (dBohms) 300 mils -10 500 mils 700 mils 1000 mils -20 -30 -40 -50 1.0E+07 1.0E+08 1.0E+09 1.0E+10 October 2007 Dr. Bruce Archambeault 58 Frequency (Hz)

  26. Cavity Resonance (EZ-PowerPlane) Equivalent Circuit for HSPICE L ij Port i Port j L ii L jj Port n N mni L mn G mn C 0 N mnj C 0 N 01i L 01 G 01 N 01j N 00i N 00j C 0 G 00 October 2007 Dr. Bruce Archambeault 59

  27. Impedance Comparison (EZ-PP vs HSPICE) at Port #1 Single 0.01 uF Capacitor at Various Distances (10mil Dielectric) 20 10 0 Impedance (dBohms) -10 -20 300 mils -30 300 mils (HSPICE) 1000 mils 1000 mils (HSPICE) -40 -50 1.0E+07 1.0E+08 1.0E+09 1.0E+10 October 2007 Dr. Bruce Archambeault 60 Frequency (Hz)

  28. Current Source Pulse for Simulated IC Power/GND 750 ps Rise/Fall 1.2 1 0.8 Current (amps) 0.6 0.4 0.2 0 -0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 61

  29. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor (with 2 nH) at Various Distances (Fullwave Simulation) 2 1.5 750ps Rise, 35 mil planes,1uF @ 10mils 750ps Rise, 35 mil planes, 1uF @ 400mils 1 750ps Rise, 35 mil planes,1uF @ 800mils 750ps Rise, 35 mil planes,1uF @ 1200mils 750ps Rise, 35 mil planes,1uF @ 1600mils Level (volts) 0.5 0 -0.5 -1 -1.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 62

  30. Time Domain Current through Capacitor From Simulated IC Power/GND (1 amp) Single Capacitor (with 2nH) at Various Distances 50 0 -50 -100 Current (milliamps) -150 -200 -250 750ps Rise, 35 mil planes,1uF @ 10mils 750ps Rise, 35 mil planes,1uF @ 400mils -300 750ps Rise, 35 mil planes,1uF @ 800mils 750ps Rise, 35 mil planes,1uF @ 1200mils 750ps Rise, 35 mil planes,1uF @ 1600mils -350 -400 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 63

  31. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor (with No L) at Various Distances 2 750ps Rise, 35 mil planes,1uF @ 10mils 750ps Rise, 35 mil planes,1uF @ 400mils 1.5 750ps Rise, 35 mil planes,1uF @ 800mils 750ps Rise, 35 mil planes,1uF @ 1200mils 750ps Rise, 35 mil planes,1uF @ 1600mils 1 0.5 Level (volts) 0 -0.5 -1 -1.5 -2 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 64

  32. Time Domain Current through Capacitor From Simulated IC Power/GND (1 amp) Single Capacitor (with no L) at Various Distances 400 200 0 Current (milliamps) -200 -400 -600 750ps Rise, 35 mil planes,1uF @ 10mils 750ps Rise, 35 mil planes,1uF @ 10mils 750ps Rise, 35 mil planes,1uF @ 800mils -800 750ps Rise, 35 mil planes,1uF @ 1200mils 750ps Rise, 35 mil planes,1uF @ 1600mils -1000 -1200 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 65

  33. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor with Various Capacitor Connection Inductance 0.6 0.5 0.4 0.3 750ps Rise, 10 mil planes, 1uF @ 400mils 750ps Rise, 10 mil planes, (2nH) 1uF @ 400mils 0.2 750ps Rise, 10 mil planes, (1nH) 1uF @ 400mils Level (volts) 0.1 0 -0.1 -0.2 -0.3 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time (ns) October 2007 Dr. Bruce Archambeault 66

  34. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor with Various Capacitor Connection Inductance 2 750ps Rise, 10 mil planes, 1uF @ 400mils 1.5 750ps Rise, 10 mil planes, (2nH) 1uF @ 400mils 750ps Rise, 35 mil planes,1uF @ 400mils 750ps Rise, 35 mil planes,(2nH) 1uF @ 400mils 1 Level (volts) 0.5 0 -0.5 -1 -1.5 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 67

  35. Maximum Time Domain Noise Voltage Across Simulated IC Power/GND Pin Single Capacitor at Various Distances (Fullwave Simulation) 0.8 0.7 0.6 0.5 Voltage (volts) 0.4 750 ps Rise, 10 mil planes,1uF, 2 nH 0.3 750 ps Rise, 10 mil planes,1uF, 1 nH 750 ps Rise, 10 mil planes,1uF, 0.5 nH 750 ps Rise, 10 mil planes,1uF, No L 0.2 0.1 0 0 200 400 600 800 1000 1200 1400 1600 1800 Distance (mils) October 2007 Dr. Bruce Archambeault 68

  36. Maximum Time Domain Noise Voltage Across Simulated IC Power/GND Pin Single Capacitor at Various Distances (Fullwave Simulation) 0.8 0.7 0.6 0.5 Voltage (volts) 0.4 1 ns Rise, 10 mil planes,1uF, 2 nH 0.3 1 ns Rise, 10 mil planes,1uF, 1 nH 1 ns Rise, 10 mil planes,1uF, 0.5 nH 1 ns Rise, 10 mil planes,1uF, No L 0.2 0.1 0 0 200 400 600 800 1000 1200 1400 1600 1800 Distance (mils) October 2007 Dr. Bruce Archambeault 69

  37. Maximum Time Domain Noise Voltage Across Simulated IC Power/GND Pin Single Capacitor at Various Distances (Fullwave Simulation) 1.8 1.6 1.4 1.2 Voltage (volts) 1 750 ps Rise, 35 mil planes,1uF, 2 nH 750 ps Rise, 35 mil planes,1uF, 1 nH 0.8 750 ps Rise, 35 mil planes,1uF, 0.5 nH 750 ps Rise, 35 mil planes,1uF, No L 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 1600 1800 Distance (mils) October 2007 Dr. Bruce Archambeault 70

  38. Maximum Time Domain Noise Voltage Across Simulated IC Power/GND Pin Single Capacitor at Various Distances (Fullwave Simulation) 1.6 1.4 1.2 1 Voltage (volts) 1 ns Rise, 35 mil planes,1uF, 2 nH 0.8 1 ns Rise, 35 mil planes,1uF, No L 1 ns Rise, 35 mil planes,1uF, 0.5 nH 1 ns Rise, 35 mil planes,1uF, 1 nH 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 1600 1800 Distance (mils) October 2007 Dr. Bruce Archambeault 71

  39. Maximum Voltage vs Distance to Capacitor for 1 ns Rise/fall time 0.01 uF Capacitor with 0.5 nH ESL and 30 mOhm ESR 1.4 1.2 Maximum Voltage at source (volts) 35 mil FR4 1 10 mil FR4 2 mil FR4 0.8 1 mil FR4 0.5 mil FR4 0.6 0.4 0.2 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Distance From Capacitor (mils) October 2007 Dr. Bruce Archambeault 72

  40. So Far…… • Frequency domain simulations not optimum for charge delivery decoupling calculations (phase not considered) • Time domain simulations using single pulse of current indicate limited capacitor location effect – Connection inductance of capacitor much higher than inductance between planes – Charge delivered only from the planes October 2007 Dr. Bruce Archambeault 73

  41. Charge Depletion • IC draws charge from planes • Capacitors will re-charge planes – Location does matter! October 2007 Dr. Bruce Archambeault 74

  42. Model for Plane Recharge Investigations ε ε = = 4 4 . . 5 5 r r b = 10 b = 10 b = 10 b = 10 Port2 Port2 Port2 Port2 Port1 Port1 Port1 Port1 (4,5) (4,5) (8,7) (8,7) (4,5) (4,5) (8,7) (8,7) d = 35 mil d = 35 mil d = 35 mil d = 35 mil Cdec Cdec Cdec Cdec Port3 Port3 Port3 Port3 (4.05,5) (4.05,5) (4.05,5) (4.05,5) (4,4.95) (4,4.95) (4,4.95) (4,4.95) Vdc Vdc Vdc Vdc a = 12 a = 12 a = 12 a = 12 Decoupling Capacitor : Decoupling Capacitor : I input I input I input I input C = 1uF C = 1uF ESR = 30mOhm ESR = 30mOhm ESL = 0.5nH ESL = 0.5nH DC voltage used to DC voltage used to DC voltage used to DC voltage used to charge the power charge the power charge the power charge the power plane plane plane plane Port 2 represents IC current draw October 2007 Dr. Bruce Archambeault 75

  43. Charge Between Planes vs.. Charge Drawn by IC Board total charge : C*V = 3.5nF*3.3V = 11nC Pulse charge 5A peak : I*dt/2 = (1ns*5A)/2=2.5nC October 2007 Dr. Bruce Archambeault 76

  44. Triangular pulses (5 Amps Peak) October 2007 Dr. Bruce Archambeault 77

  45. Noise Voltage from Inductive Effect of Current Draw (a) (b) Current pulses too small to see charge depletion effects in this time scale October 2007 Dr. Bruce Archambeault 78

  46. Charge Depletion � Voltage Drop 4 3.5 3 V plane [V] 2.5 L s = 1nH 2 L s = 10 nH L s = 50 nH 1.5 1 0 2 4 6 8 10 Time [ns] October 2007 Dr. Bruce Archambeault 79

  47. Charge Depletion vs. Capacitor Distance October 2007 Dr. Bruce Archambeault 80

  48. Charge Depletion for Capacitor @ 400 mils for Various Connection Inductance October 2007 Dr. Bruce Archambeault 81

  49. Effect of Multiple Capacitors While Keeping Total Capacitance Constant The decap locations are 800mils, 1200mils, 2700mils from the power pin (power-ground pins at IC center) Port1 (8,7) (Ls 50nH) • C=1uF • ESL=0.5nH Decap • ESR=1 Ω 10” 1 inch Ground pin Port2 (4,5) (power pin) ε r =4.5 12” October 2007 Dr. Bruce Archambeault 82

  50. Effect of Multiple Capacitors While Keeping Total Capacitance Constant The decap locations are 800mils, 1200mils, 2700mils from the power pin (power-ground pins at IC center) Port1 (8,7) (Ls 50nH) • C=0.5uF • ESL=0.5nH Decap • ESR=1 Ω 10” 1 inch Ground pin Port2 (4,5) (power pin) ε r =4.5 12” October 2007 Dr. Bruce Archambeault 83

  51. Effect of Multiple Capacitors While Keeping Total Capacitance Constant The decap locations are 800mils, 1200mils, 2700mils from the power pin (power-ground pins at IC center) Port1 (8,7) (Ls 50nH) • C=0.25uF • ESL=0.5nH Decap • ESR=1 Ω 10” 1 inch Ground pin Port2 (4,5) ε r =4.5 (power pin) 12” October 2007 Dr. Bruce Archambeault 84

  52. Constant Capacitance 800 mil Distance October 2007 Dr. Bruce Archambeault 85

  53. Constant Capacitance 800 mil Distance October 2007 Dr. Bruce Archambeault 86

  54. Constant Capacitance 1200 mil Distance October 2007 Dr. Bruce Archambeault 87

  55. Constant Capacitance 1200 mil Distance October 2007 Dr. Bruce Archambeault 88

  56. Constant Capacitance 2700 mil Distance October 2007 Dr. Bruce Archambeault 89

  57. Constant Capacitance 2700 mil Distance October 2007 Dr. Bruce Archambeault 90

  58. Example #1 Low Cap Connection Inductance Cap IC PWR GND PCB October 2007 Dr. Bruce Archambeault 91

  59. Example #2 High Cap Connection Inductance Cap IC PWR GND PCB October 2007 Dr. Bruce Archambeault 92

  60. Example #1 Hi Cap Connection Inductance Cap IC PCB PWR GND October 2007 Dr. Bruce Archambeault 93

  61. Example #1 Lower Cap Connection Inductance IC PCB PWR GND Cap October 2007 Dr. Bruce Archambeault 94

  62. Mutual Inductance Helps Reduce Path Inductance Do’s Don’ts J. L Knighten, B. Archambeault, J. Fan, et. al., “PDN Design Strategies: II. Ceramic SMT Decoupling Capacitors – Does Location Matter?,” IEEE EMC Society Newsletter , Issue No. 207, Winter 2006, pp. 56-67. October 2007 Dr. Bruce Archambeault 95

  63. Effect of Capacitor Value?? • Need enough charge to supply need • Depends on connection inductance Charge = C*V October 2007 Dr. Bruce Archambeault 96

  64. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor (with No L) with Various Capacitor Values 0.6 0.5 750ps Rise, 10 mil planes, (0.0 nH) 1uF @ 400mils 750ps Rise, 10 mil planes,0.01uF @ 400mils 0.4 750ps Rise, 10 mil planes, 100pF @ 400mils 0.3 0.2 Level (volts) 0.1 0 -0.1 -0.2 -0.3 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 97

  65. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor (with 0.5 nH Connection L) with Various Capacitor Values 0.6 0.5 750ps Rise, 10 mil planes, (0.5nH) 1uF @ 400mils 0.4 750ps Rise, 10 mil planes, (0.5nH) 0.01 uF @ 400mils 750ps Rise, 10 mil planes, (0.5nH) 100 pF @ 400mils 0.3 0.2 Level (volts) 0.1 0 -0.1 -0.2 -0.3 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 98

  66. Time Domain Noise Voltage Across Simulated IC Power/GND Pin (1 amp) Single Capacitor (with 1 nH Connection L) with Various Capacitor Values 0.6 0.5 750ps Rise, 10 mil planes, (1nH) 1uF @ 400mils 750ps Rise, 10 mil planes, (1nH) 0.01uF @ 400mils 0.4 750ps Rise, 10 mil planes, (1nH) 1000pF @ 400mils 750ps Rise, 10 mil planes, (1nH) 100pF @ 400mils 0.3 0.2 Level (volts) 0.1 0 -0.1 -0.2 -0.3 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (ns) October 2007 Dr. Bruce Archambeault 99

  67. Noise Voltage is INDEPENDENT of Amount of Capacitance! As long as there is ‘enough’ charge Dist=400 mils ESR=30mOhms ESL=0.5nH October 2007 Dr. Bruce Archambeault 100

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