ECE 546 Lecture 08 Nonideal Conductors and Dielectrics

ECE 546 Lecture - 08 Nonideal Conductors and Dielectrics Spring 2018 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois. edu ECE 546 – Jose Schutt-Aine 1

Material Medium or s: conductivity of material medium (W-1 m-1) since then ECE 546 – Jose Schutt-Aine 2

Wave in Material Medium g is complex propagation constant a: associated with attenuation of wave b: associated with propagation of wave ECE 546 – Jose Schutt-Aine 3

Wave in Material Medium Solution: decaying exponential Complex intrinsic impedance Magnetic field ECE 546 – Jose Schutt-Aine 4

Wave in Material Medium is the loss tangent Two special cases can be distinguished: : poor conductor ECE 546 – Jose Schutt-Aine 5

Wave in Material Medium : good conductor ECE 546 – Jose Schutt-Aine 6

Skin Depth Wave decay The decay of electromagnetic wave propagating into a conductor is measured in terms of the skin depth Definition: skin depth d is distance over which amplitude of wave drops by 1/e. For good conductors: ECE 546 – Jose Schutt-Aine 7

Skin Depth e-1 Wave motion d For perfect conductor, d = 0 and current only flows on the surface ECE 546 – Jose Schutt-Aine 8

DC Resistance l: conductor length s: conductivity ECE 546 – Jose Schutt-Aine 9

AC Resistance l: conductor length s: conductivity f: frequency ECE 546 – Jose Schutt-Aine 10

Frequency-Dependent Resistance Approximation is to assume that all the current is flowing uniformly within a skin depth ECE 546 – Jose Schutt-Aine 11

Frequency-Dependent Resistance changes with Resistance is ~ constant when d >t ECE 546 – Jose Schutt-Aine 12

Reference Plane Current ECE 546 – Jose Schutt-Aine 13

Skin Effect in Microstrip er H. A. Wheeler, "Formulas for the skin effect, " Proc. IRE, vol. 30, pp. 412 -424, 1942 ECE 546 – Jose Schutt-Aine 14

Skin Effect in Microstrip Current density varies as Note that the phase of the current density varies as a function of y The voltage measured over a section of conductor of length D is: ECE 546 – Jose Schutt-Aine 15

Skin Effect in Microstrip The skin effect impedance is where is the bulk resistivity of the conductor with Skin effect has reactive (inductive) component ECE 546 – Jose Schutt-Aine 16

Internal Inductance The internal inductance can be calculated directly from the ac resistance Skin effect resistance goes up with frequency Skin effect inductance goes down with frequency ECE 546 – Jose Schutt-Aine 17

Surface Roughness Copper surfaces are rough to facilitate adhesion to dielectric during PCB manufacturing When the tooth height is comparable to the skin depth, roughness effects cannot be ignored Surface roughness will increase ohmic losses ECE 546 – Jose Schutt-Aine 18

Hammerstad Model ECE 546 – Jose Schutt-Aine 19

Hammerstad Model h. RMS: root mean square value of surface roughness height d: skin depth fd=t: frequency where the skin depth is equal to the thickness of the conductor ECE 546 – Jose Schutt-Aine 20

Hemispherical Model ECE 546 – Jose Schutt-Aine 21

Hemispherical Model ECE 546 – Jose Schutt-Aine 22

Huray Model ECE 546 – Jose Schutt-Aine 23

Huray Model Ho: magnitude of applied H field. ECE 546 – Jose Schutt-Aine 24

Dielectrics and Polarization No field Applied field Field causes the formation of dipoles polarization Bound surface charge density –qsp on upper surface and +qsp on lower surface of the slab. ECE 546 – Jose Schutt-Aine 25

Dielectrics and Polarization : polarization vector : electric flux density : applied electric field : electric susceptibility : free-space permittivity : static permittivity ECE 546 – Jose Schutt-Aine 26

Dielectric Constant Material Air Styrofoam Paraffin Teflon Plywood RT/duroid 5880 Polyethylene RT/duroid 5870 Glass-reinforced teflon (microfiber) Teflon quartz (woven) Glass-reinforced teflon (woven) Cross-linked polystyrene (unreinforced) Polyphenelene oxide (PPO) Glass-reinforced polystyrene Amber Rubber Plexiglas ECE 546 – Jose Schutt-Aine e r 1. 0006 1. 03 2. 1 2. 20 2. 26 2. 35 2. 32 -2. 40 2. 47 2. 4 -2. 62 2. 56 2. 55 2. 62 3 3 3. 4 27

Dielectric Constants Material e r Lucite Fused silica Nylon (solid) Quartz Bakelite Formica Lead glass Mica Beryllium oxide (Be. O) Marble Flint glass Ferrite (Fq. O, ) Silicon (Si) Gallium arsenide (Ga. As) Ammonia (liquid) Glycerin Water 3. 6 3. 78 3. 8 4. 8 5 6 6 6. 8 -7. 0 8 10 12 -16 12 13 22 50 81 ECE 546 – Jose Schutt-Aine 28

AC Variations When a material is subjected to an applied electric field, the centroids of the positive and negative charges are displaced relative to each other forming a linear dipole. When the applied fields begin to alternate in polarity, the permittivities are affected and become functions of the frequency of the alternating fields. ECE 546 – Jose Schutt-Aine 29

AC Variations Reverses in polarity cause incremental changes in the static conductivity ss heating of materials using microwaves (e. g. food cooking) When an electric field is applied, it is assumed that the positive charge remains stationary and the negative charge moves relative to the positive along a platform that exhibits a friction (damping) coefficient d. ECE 546 – Jose Schutt-Aine 30

Complex Permittivity : dipole density : dipole charge : free space permittivity : mass : damping coefficient : natural frequency : spring (tension) factor : applied frequency ECE 546 – Jose Schutt-Aine 31

Complex Permittivity se: total conductivity composed of the static portion ss and the alternative part sa caused by the rotation of the dipoles ECE 546 – Jose Schutt-Aine 32

Complex Permittivity : total electric current density : impressed (source) electric current density : effective electric conduction current density : effective displacement electric current density ECE 546 – Jose Schutt-Aine 33

Complex Permittivity ECE 546 – Jose Schutt-Aine 34

Dielectric Properties Good Dielectrics: Good Conductors: ECE 546 – Jose Schutt-Aine 35

Dielectric Properties Good Dielectrics: Good Conductors: ECE 546 – Jose Schutt-Aine 36

Kramers-Kronig Relations There is a relation between the real and imaginary parts of the complex permittivity: Debye Equation ECE 546 – Jose Schutt-Aine 37

Kramers-Kronig Relations te is a relaxation time constant: ECE 546 – Jose Schutt-Aine 38

Dielectric Materials Material Air Alcohol (ethyl) Aluminum oxide Bakelite Carbon dioxide Germanium Glass Ice Mica Nylon Paper Plexiglas Polystyrene Porcelain e r’ 1. 0006 25 8. 8 4. 74 1. 001 16 4*7 4. 2 5. 4 3. 5 3 3. 45 2. 56 6 tand 0. 1 6 x 10 -4 22 x 10 -3 1 x 10 -3 0. 1 6 x 10 -4 2 x 10 -2 8 x 10 -3 4 x 10 -2 5 x 10 -5 14 x 10 -3 ECE 546 – Jose Schutt-Aine 39

Dielectric Materials Material Pyrex glass Quartz (fused) Rubber Silica (fused) Silicon Snow Sodium chloride Soil (dry) Styrofoam Teflon Titanium dioxide Water (distilled) Water (sea) Water (dehydrated) Wood (dry) e r’ 4 3. 8 2. 5 -3 3. 8 11. 8 3. 3 5. 9 2. 8 1. 03 2. 1 100 80 81 1 1. 5 -4 tand 6 x 10 -4 7. 5 x 10 -4 2 x 10 -3 7. 5 x 10 -4 0. 5 1 x 10 -4 7 x 10 -2 1 x 10 -4 3 x 10 -4 15 x 10 -4 4 x 10 -2 4. 64 0 1 x 10 -2 ECE 546 – Jose Schutt-Aine 40

PCB Stackup Source: H. Barnes et al, "ATE Interconnect Performance to 43 Gps Using Advanced PCB Materials", Design. Con 2008 ECE 546 – Jose Schutt-Aine 41

Differential Signaling Differential signaling is widely used in the industry today. High-speed serial interfaces such as PCI-E, XAUI, OC 768, and CEI use differential signaling for transmitting and receiving data in point-to-point topology between a driver (TX) and receiver (RX) connected by a differential pair. The skew (time delay) between the two traces of the differential pair should be zero. Any skew between the two traces causes the differential signal to convert into a common signal. ECE 546 – Jose Schutt-Aine 42

Fiber Weave Effect Fiberglass weave pattern causes signals to propagate at different speeds in differential pairs Source: S. Mc. Morrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", Design. Con 2005. ECE 546 – Jose Schutt-Aine 43

Fiber Weave Effect Source: Lambert Simonovich, "Practical Fiber Weave Effect Modeling", White Paper-Issue 3, March 2, 2012. ECE 546 – Jose Schutt-Aine 44

Fiber Weave Effect Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009. ECE 546 – Jose Schutt-Aine 45

Fiber Weave Effect Group delay variation Source: S. Mc. Morrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", Design. Con 2005. ECE 546 – Jose Schutt-Aine 46

Fiber Weave Effect Group delay variation: effect of angle Source: S. Mc. Morrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", Design. Con 2005. ECE 546 – Jose Schutt-Aine 47

Fiber Weave Effect Straight traces Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009. ECE 546 – Jose Schutt-Aine 48

Fiber Weave Effect 45 o traces Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009. ECE 546 – Jose Schutt-Aine 49

Fiber Weave Effect straight traces zig-zag traces Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528 -1. 1, January 2011. ECE 546 – Jose Schutt-Aine 50

Fiber Weave Effect Skew on straight traces Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528 -1. 1, January 2011. ECE 546 – Jose Schutt-Aine 51

Fiber Weave Effect Skew on zig-zag traces Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528 -1. 1, January 2011. ECE 546 – Jose Schutt-Aine 52

Fiber Weave Effect • Mitigation Techniques Ø Use wider widths to achieve impedance targets. Ø Specify a denser weave (2116, 2113, 7268, 1652) compared to a sparse weave (106, 1080). Ø Move to a better substrate such as Nelco 4000 -13 Ø Perform floor planning such that routing is at an angle rather than orthogonal. Ø Make use of zig-zag routing ECE 546 – Jose Schutt-Aine 53