Inductance and Partial Inductance What's it all mean?

Transcription

1 Inductance and Partial Inductance What's it all mean? Bruce Archambeault, PhD IEEE Fellow, IBM Distinguished Engineer

2 Inductance Probably the most misunderstood concept in electrical engineering Do not confuse inductance with inductors Common Usage Self inductance Loop inductance Mutual inductance Equivalent inductance Partial inductance Partial self inductance Partial mutual inductance Apparent inductance Bruce Archambeault, PhD 2

3 Inductance Current flow through metal = inductance! Fundamental element in EVERYTHING Loop area first order concern Inductive impedance increases with frequency and is MAJOR concern at high frequencies X = 2πfL L Bruce Archambeault, PhD 3

4 Current Loop = Inductance Courtesy of Elya Joffe Bruce Archambeault, PhD 4

5 Inductance Definition Faraday s Law E dl = B t ds For a simple rectangular loop V B Area = A V = A B t Bruce Archambeault, PhD 5

6 Given the Definition of Inductance Do these have inductance? Ground Strap SMT Capacitor PCB Via Not until return path for current is identified! Bruce Archambeault, PhD 6

7 Self Inductance Isolated circular loop Isolated rectangular loop L a μ ln 2 0a r0 L = 2μ a π ln p + 1+ p p 1+ Note that inductance is directly influenced by loop AREA and less influenced by conductor size! Bruce Archambeault, PhD 7 1 p + p 2 length of side p = wire radius

8 Mutual Inductance Φ M 2 21 = M = 21 Φ I 1 2 I 1 How much magnetic flux is induced in loop #2 from a current in loop #1? Loop #1 Loop #2 r Φ = 2 B1( r) nˆ ds S 2 2 Bruce Archambeault, PhD

9 Flux from Current in Loop #1 Bruce Archambeault, PhD 9

10 Flux from Current in Loop #1 Bruce Archambeault, PhD 10

11 2 Change in mutual inductance with spacing X: 24 Y: 1.35 Mutual Inductance (nh) X: 100 Y: The magnetic field drops off rapidly, so then does the mutual inductance X: 500 Y: X: 1000 Y: Spacing between the coils(mils) Bruce Archambeault, PhD 11

12 Mutual Inductance Loop #1 Loop #2 Less loop area in loop #2 means less magnetic flux in loop #2 and less mutual inductance Loop #1 Loop #2 Less loop area perpendicular to the magnetic field in loop #2 means less magnetic flux in loop #2 and less mutual inductance Bruce Archambeault, PhD 12

13 Partial Inductance We now know that a loop of current has inductance We now know that there must be a complete loop to have inductance But where do we place this inductance in a circuit? Bruce Archambeault, PhD 13

14 Zero-to-One Transition Where s the Inductance Go?? Power Supply And how could you possibly calculate it? Courtesy of Dr. Clayton Paul Bruce Archambeault, PhD 14

15 Total Loop Inductance from Partial Inductance L total =L p1 + L p2 + L p3 + L p4 2M p1-3 2M p2-4 L p2 M p1-3 M p2-4 L p1 L p3 L p4 Courtesy of Dr. Clayton Paul Bruce Archambeault, PhD 15

16 Partial Inductance Simply a way to break the overall loop into pieces in order to find total inductance L2 L1 L3 L4 L total =L p11 + L p22 + L p33 + L p44-2l p13-2l p24 Bruce Archambeault, PhD 16

17 Important Points About Inductance Inductance is everywhere Loop area most important Inductance is everywhere Bruce Archambeault, PhD 17

18 Example Decoupling Capacitor Mounting Keep vias as close to capacitor pads as possible! Inductance Depends on Loop AREA Via Separation Height above Planes Bruce Archambeault, PhD 1

19 Via Configuration Can Change Inductance SMT Capacitor The Good The Bad The Ugly Via Capacitor Pads Best Better Really Ugly Bruce Archambeault, PhD 19

20 High Frequency Capacitors Myth or Fact? Bruce Archambeault, PhD 20

21 What is Capacitance? C = Q V Capacitance is the ability of a structure to hold charge (electrons) for a given voltage Q = CV Amount of charge stored is dependant on the size of the capacitance (and voltage) Consider a capacitor as a bucket holding lot s of electrons! Bruce Archambeault, PhD 21

22 Comparison of Decoupling Capacitor Impedance 100 mil Between Vias & 10 mil to Planes pF 0.01uF Impedance (ohms) uF 1.0uF E E E+0 1.0E E+10 Frequency (Hz) Bruce Archambeault, PhD 22

23 0603 Size Cap Typical Mounting 9 mils 9 mils 20 mils 10 mils* 10 mils* Via Barrel 10 mils 60 mils 10 mils minimum 12 mils typical *Note: Minimum distance is 10 mils but more typical distance is 20 mils Bruce Archambeault, PhD 23

24 0402 Size Cap Typical Mounting mils mils 20 mils 10 mils* 10 mils* Via Barrel 10 mils 40 mils 6 mils minimum 106 mils typical *Note: Minimum distance is 10 mils but more typical distance is 20 mils Bruce Archambeault, PhD 24

25 Connection Inductance for Typical Capacitor Configurations Distance into board to planes (mils) typical/minimum (14 mils between via barrels) 1.2 nh 1. nh 2.2 nh 2.5 nh 2. nh 3.1 nh 3.4 nh 3.6 nh 3.9 nh 4.2 nh 0603 typical/minimu m (12 mils between via barrels) 1.1 nh 1.6 nh 1.9 nh 2.2 nh 2.5 nh 2.7 nh 3.0 nh 3.2 nh 3.5 nh 3.7 nh 0402 typical/minimum (106 mils between via barrels) 0.9 nh 1.3 nh 1.6 nh 1.9 nh 2.1 nh 2.3 nh 2.6 nh 2. nh 3.0 nh 3.2 nh Bruce Archambeault, PhD 25

26 Connection Inductance for Typical Capacitor Configurations with 50 mils from Capacitor Pad to Via Pad Distance into board to planes (mils) 005 (20 mils between via barrels) 0603 (1 mils between via barrels) 0402 (166 mils between via barrels) nh 1.6 nh 1.4 nh nh 2.3 nh 2.0 nh nh 2. nh 2.5 nh nh 3.2 nh 2. nh nh 3.5 nh 3.1 nh nh 3.9 nh 3.5 nh nh 4.2 nh 3.7 nh nh 4.5 nh 4.0 nh nh 4.7 nh 4.3 nh nh 5.0 nh 4.6 nh Bruce Archambeault, PhD 26

27 PCB Example for Return Current Impedance Trace GND Plane 22 trace 10 mils wide, 1 mil thick, 10 mils above GND plane Bruce Archambeault, PhD 27

28 PCB Example for Return Current Impedance Trace GND Plane Shortest DC path For longest DC path, current returns under trace Bruce Archambeault, PhD 2

29 MoM Results for Current Density Frequency = 1 KHz Bruce Archambeault, PhD 29

30 MoM Results for Current Density Frequency = 1 MHz Bruce Archambeault, PhD 30

31 U-shaped Trace Inductance PowerPEEC Results inductance (uh) E E E E E E+0 Frequency (Hz) Bruce Archambeault, PhD 31

32 Bruce Archambeault, PhD 32 Two Wires in Parallel Reduce inductance by factor of two? NO! p p p p p p Parallel M L L M L L L = p p Parallel p p p M L L L L L + = = = Only if parallel wires are FAR APART! Courtesy of Dr. Clayton Paul

33 Let s Apply this to Decoupling Capacitors Equivalent inductance Two capacitors vs one capacitor Relative location of two capacitors Use via between planes as ideal capacitor Bruce Archambeault, PhD 33

34 What Happens if a 2 nd Decoupling Capacitor is placed near the First Capacitor? Via #1 Observation Point distance 500 mils Via #2 Moved in arc around Observation point while maintaining 500 mil distance to observation point Bruce Archambeault, PhD 34

35 Second Via Around a circle L equiv d d Port = R ( x, y ) θ = 2 R sin 2 d 2 d 1 θ Port 2 Port 1 R 2 d1 + r 2 2 ln μ d ( R + r) ( d ) 1 + r μd R + r ln 3 4π ( ) r d + r d + r 2 4π 2 ln r 4 ( R + r ) ( ) 2R sin( θ / 2) + r μ d ln 4 π r = 3 R: distance between Port 1 and Port 2 in mil r: radius for all ports in mil d: thickness of dielectric layer in mil d1: distance between Port 3 and Port 1 in mil d2: distance between Port 2 and Port 3 in mil theta: angle as shown in the figure in degree Courtesy of Jingook Kim, Jun Fan, Jim Drewniak Missouri University of Science and Technology Bruce Archambeault, PhD 35

36 Effective Inductance for Various Distances to Decoupling Capacitor With Second Capacitor (Via) Equal Distance Around Circle Plane Seperation = 35 mil -- Via Diameter = 20 mil Inductnace (ph) mil 500mil 750 mil 1000 mil Angle (degrees) Bruce Archambeault, PhD 36

37 500 Effective Inductance for Various Distances to Decoupling Capacitor With Second Capacitor (Via) Equal Distance Around Circle Plane Seperation = 10 mil -- Via Diameter = 20 mil Inductnace (ph) mil 250 mil 750 mil 1000 mil Angle (degrees) Bruce Archambeault, PhD 37

38 400 Effective Inductance for Various Distances to Decoupling Capacitor With Second Capacitor (Via) Equal Distance Around Circle Plane Seperation = 5 mil -- Via Diameter = 20 mil 350 Inductnace (ph) mil 250 mil 750 mil 1000 mil Angle (degrees) Bruce Archambeault, PhD 3

39 Understanding Inductance Effects and Proximity 1 via 2 via with degree 30 10cm 10mm 20cm 10cm 2 via with degree 90 2 via with degree 10 20cm Bruce Archambeault, PhD 39

40 Current Density [m] [m] A/m 2 A/m 2 [m] [m] A/m 2 [m] [m] A/m 2 [m] [m] Bruce Archambeault, PhD 40

41 64 56 Current Density in Planes Bruce Archambeault, PhD 41

42 Effect of Plane width on Inductance Case1 : 10 inches Case2 : 5 inches Case3 : 2 inches 1 inch Port1 Port2 Bruce Archambeault, PhD 42

43 Loop Inductance is Affected by Plane Width Case1 : 10 inches Case2 : 5 inches ~ 330pH Case2 : 2 inches ~ 250pH ~ 560pH Bruce Archambeault, PhD 43

44 Current Spreads in a Plane Narrower planes means the multiple current paths are limited therefore effect of mutual inductance between parallel paths increases! Bruce Archambeault, PhD 44

45 Observations Added via (capacitor) does not lower effective inductance to 70-75% of original single via case Thicker dielectric results in higher inductance Normalizing inductance to single via case gives same curve for all dielectric thicknesses Bruce Archambeault, PhD 45

46 Summary Inductance has meaning only for current loops Size of the loop has the most impact on amount of inductance Current density also impact inductance Partial inductance is a very useful concept to understand which portions of the loop have the largest impact on loop inductance Bruce Archambeault, PhD 46