Inductance and Partial Inductance What's it all mean? Bruce - PowerPoint PPT Presentation

Inductance and Partial Inductance What's it all mean? Bruce Archambeault, PhD IEEE Fellow, IBM Distinguished Engineer Bruce.arch@ieee.org

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

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 = π X L 2 fL Bruce Archambeault, PhD 3

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

Inductance Definition ∂ • Faraday’s Law B ∫ ∫∫ ⋅ = − ⋅ E dl d S ∂ t • For a simple rectangular loop Area = A ∂ B = − V A ∂ V t B Bruce Archambeault, PhD 5

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

Self Inductance ⎛ ⎞ 8 a • Isolated circular loop ⎜ ⎟ ≈ μ − L a ln 2 ⎜ ⎟ 0 ⎝ ⎠ r 0 • Isolated rectangular loop ⎛ ⎞ + + μ 2 p 1 p 2 a ⎜ 1 1 ⎟ = + − + − + 2 0 L ln 1 2 1 p ⎜ ⎟ π + p p 1 2 ⎝ ⎠ length of side Note that inductance is directly influenced p = by loop AREA and less influenced by wire radius conductor size ! Bruce Archambeault, PhD 7

Mutual Inductance Φ = M I How much magnetic flux is 2 21 1 induced in loop #2 from a Φ = current in loop #1? 2 M 21 I 1 r Loop #2 ( ) ∫ Loop #1 Φ = ⋅ ˆ B r n dS 2 1 2 S 2 Bruce Archambeault, PhD 8

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

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

Change in mutual inductance with spacing 2 X: 24 Y: 1.835 1.5 Mutual Inductance (nH) The magnetic field drops off rapidly, so then does the mutual inductance 1 X: 100 Y: 0.7312 0.5 X: 500 X: 1000 Y: 0.02507 Y: 0.01955 0 0 200 400 600 800 1000 Spacing between the coils(mils) Bruce Archambeault, PhD 11

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

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

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

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 p2-4 M p1-3 L p3 L p1 L p4 Courtesy of Dr. Clayton Paul Bruce Archambeault, PhD 15

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

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

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

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

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

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

Comparison of Decoupling Capacitor Impedance 100 mil Between Vias & 10 mil to Planes 1000 1000pF 100 0.01uF 0.1uF 1.0uF Impedance (ohms) 10 1 0.1 0.01 1.0E+06 1.0E+07 1.0E+08 1.0E+09 1.0E+10 Frequency (Hz) Bruce Archambeault, PhD 22

0603 Size Cap Typical Mounting 9 mils 9 mils 20 mils 10 mils* Via Barrel 10 mils 10 mils* 60 mils 108 mils minimum 128 mils typical *Note: Minimum distance is 10 mils but more typical distance is 20 mils Bruce Archambeault, PhD 23

0402 Size Cap Typical Mounting 8 mils 8 mils 20 mils 10 mils* Via Barrel 10 mils 10 mils* 40 mils 86 mils minimum 106 mils typical *Note: Minimum distance is 10 mils but more typical distance is 20 mils Bruce Archambeault, PhD 24

Connection Inductance for Typical Capacitor Configurations Distance into 0805 0603 0402 board typical/minimum typical/minimu typical/minimum to planes (mils) (148 mils m (106 mils between via (128 mils between via barrels) between via barrels) barrels) 10 1.2 nH 1.1 nH 0.9 nH 20 1.8 nH 1.6 nH 1.3 nH 30 2.2 nH 1.9 nH 1.6 nH 40 2.5 nH 2.2 nH 1.9 nH 50 2.8 nH 2.5 nH 2.1 nH 60 3.1 nH 2.7 nH 2.3 nH 70 3.4 nH 3.0 nH 2.6 nH 80 3.6 nH 3.2 nH 2.8 nH 90 3.9 nH 3.5 nH 3.0 nH 100 4.2 nH 3.7 nH 3.2 nH Bruce Archambeault, PhD 25

Connection Inductance for Typical Capacitor Configurations with 50 mils from Capacitor Pad to Via Pad 0805 0603 0402 Distance into (208 mils (188 mils (166 mils board between via between via between via to planes (mils) barrels) barrels) barrels) 10 1.7 nH 1.6 nH 1.4 nH 20 2.5 nH 2.3 nH 2.0 nH 30 3.0 nH 2.8 nH 2.5 nH 40 3.5 nH 3.2 nH 2.8 nH 50 3.9 nH 3.5 nH 3.1 nH 60 4.2 nH 3.9 nH 3.5 nH 70 4.5 nH 4.2 nH 3.7 nH 80 4.9 nH 4.5 nH 4.0 nH 90 5.2 nH 4.7 nH 4.3 nH 100 5.5 nH 5.0 nH 4.6 nH Bruce Archambeault, PhD 26

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

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

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

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

U-shaped Trace Inductance PowerPEEC Results 0.6 0.55 0.5 0.45 inductance (uH) 0.4 0.35 0.3 0.25 0.2 0.15 0.1 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 Frequency (Hz) Bruce Archambeault, PhD 31

Two Wires in Parallel • Reduce inductance by factor of two? NO! − 2 L L M = p 1 p 2 p L + − Parallel L L 2 M p 1 p 2 p = = L L L p 1 p 2 p + L M = p p L Parallel 2 Only if parallel wires are FAR APART! Courtesy of Dr. Clayton Paul Bruce Archambeault, PhD 32

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

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

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