Presentation on theme: "Nonideal Conductors and Dielectrics"— Presentation transcript:
1 Nonideal Conductors and Dielectrics ECE 546Lecture - 07Nonideal Conductors and DielectricsSpring 2014Jose E. Schutt-AineElectrical & Computer EngineeringUniversity of Illinois
2 s: conductivity of material medium (W-1m-1) ors: conductivity of material medium (W-1m-1)sincethen
3 Wave in Material Medium g is complex propagation constanta: associated with attenuation of waveb: associated with propagation of wave
4 Wave in Material Medium Solution:decaying exponentialComplex intrinsicimpedanceMagnetic field
5 Skin Depth Wave decayThe decay of electromagnetic wave propagating into a conductor is measured in terms of the skin depthDefinition: skin depth d is distance over which amplitude of wave drops by 1/e.For good conductors:
6 Skin Depthde-1Wave motionFor perfect conductor, d = 0 and current only flows on the surface
12 Skin Effect in Microstrip erH. A. Wheeler, "Formulas for the skin effect," Proc. IRE, vol. 30, pp ,1942
13 Skin Effect in Microstrip Current density varies asNote that the phase of the current density varies as a function of yThe voltage measured over a section of conductor of length D is:
14 Skin Effect in Microstrip The skin effect impedance iswhereis the bulk resistivity of the conductorwith Skin effect has reactive (inductive) component
15 Internal InductanceThe internal inductance can be calculated directly from the ac resistance Skin effect resistance goes up with frequency Skin effect inductance goes down with frequency
16 Surface RoughnessCopper surfaces are rough to facilitate adhesion to dielectric during PCB manufacturingWhen the tooth height is comparable to the skin depth, roughness effects cannot be ignoredSurface roughness will increase ohmic losses
23 Dielectrics and Polarization No fieldApplied fieldField causes the formation of dipoles polarizationBound surface charge density –qsp on upper surface and +qsp on lower surface of the slab.
24 Dielectrics and Polarization : polarization vector: electric flux density: applied electric field: electric susceptibility: free-space permittivity: static permittivity
25 Dielectric Constant Material e r Air Styrofoam Paraffin Teflon Plywood RT/duroid 5880PolyethyleneRT/duroid 5870Glass-reinforced teflon (microfiber)Teflon quartz (woven)Glass-reinforced teflon (woven)Cross-linked polystyrene (unreinforced)Polyphenelene oxide (PPO)Glass-reinf orced polystyreneAmberRubberPlexiglas1.00061.032.12.202.262.352.472.562.552.6233.4
26 Dielectric Constants Material e r Lucite Fused silica Nylon (solid) QuartzBakeliteFormicaLead glassMicaBeryllium oxide (BeO)MarbleFlint glassFerrite (FqO,)Silicon (Si)Gallium arsenide (GaAs)Ammonia (liquid)GlycerinWater3.63.783.84.85681012-161213225081
27 AC VariationsWhen 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.
28 AC VariationsReverses in polarity cause incremental changes in the static conductivity ssheating 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.
29 Complex Permittivity : dipole density : mass : dipole charge : damping coefficient: free space permittivity: natural frequency: spring (tension) factor: applied frequency
30 Complex Permittivityse: total conductivity composed of the static portion ss and the alternative part sa caused by the rotation of the dipoles
31 Complex Permittivity : total electric current density : impressed (source) electric current density: effective electric conduction current density: effective displacement electric current density
33 Dielectric Properties Good Dielectrics:Good Conductors:
34 Dielectric Properties Good Dielectrics:Good Conductors:
35 Kramers-Kronig Relations There is a relation between the real and imaginary parts of the complex permittivity:Debye Equation
36 Kramers-Kronig Relations te is a relaxation time constant:
37 Dielectric Materials Material er’ tand Air Alcohol (ethyl) Aluminum oxideBakeliteCarbon dioxideGermaniumGlassIceMicaNylonPaperPlexiglasPolystyrenePorcelain1.0006258.84.741.001164*220.127.116.113.452.5660.16 x 10-422x10-31 x 10-36x10-42x10-28 x 10-34 x 10-25x10-514x10-3
38 Dielectric Materials Material er’ tand Pyrex glass Quartz (fused) RubberSilica (fused)SiliconSnowSodium chlorideSoil (dry)StyrofoamTeflonTitanium dioxideWater (distilled)Water (sea)Water (dehydrated)Wood (dry)43.82.5-318.104.22.168.81.032.1100808111.5-46x10-47.5x10-42 x 10-37.5 x 10-40.51x10-47 x 10-23x10-415 x 10-44x10-24.641x10-2
39 PCB StackupSource: H. Barnes et al, "ATE Interconnect Performance to 43 Gps Using Advanced PCB Materials", DesignCon 2008
40 Differential Signaling Differential signaling is widely used in the industry today. High-speed serial interfaces such as PCI-E, XAUI, OC768, 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.
41 Fiber Weave EffectFiberglass weave pattern causes signals to propagate at different speeds in differential pairsSource: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
43 Fiber Weave EffectSource: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
44 Fiber Weave Effect Group delay variation Source: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
45 Fiber Weave Effect Group delay variation: effect of angle Source: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
46 Fiber Weave Effect Straight traces Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
47 Fiber Weave Effect 45o traces Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
48 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 , January 2011.
49 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 , January 2011.
50 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 , January 2011.
51 Fiber Weave Effect Mitigation Techniques Use wider widths to achieve impedance targets.Specify a denser weave (2116, 2113, 7268, 1652) compared to a sparse weave (106, 1080).Move to a better substrate such as NelcoPerform floor planning such that routing is at an angle rather than orthogonal.Make use of zig-zag routing