ECE 546 Lecture - 07 Nonideal Conductors and Dielectrics

1. ECE 546 Lecture - 07 Nonideal Conductors and Dielectrics Spring 2014 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu

2. Material Medium or s: conductivity of material medium (W-1m-1) since then

3. Wave in Material Medium g is complex propagation constant a: associated with attenuation of wave b: associated with propagation of wave

4. Wave in Material Medium Solution: decaying exponential Complex intrinsic impedance Magnetic field

5. 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:

6. Skin Depth e-1 Wave motion d For perfect conductor, d= 0 and current only flows on the surface

7. DC Resistance l: conductor length s: conductivity

8. AC Resistance l: conductor length s: conductivity f: frequency

9. Frequency-Dependent Resistance Approximation is to assume that all the current is flowing uniformly within a skin depth

10. Frequency-Dependent Resistance Resistance changes with Resistance is ~ constant when d >t

11. Reference Plane Current

12. Skin Effect in Microstrip er H. A. Wheeler, "Formulas for the skin effect," Proc. IRE, vol. 30, pp. 412-424,1942

13. 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:

14. Skin Effect in Microstrip The skin effect impedance is is the bulk resistivity of the conductor where with  Skin effect has reactive (inductive) component

15. 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

16. 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

17. Hammerstad Model

18. Hammerstad Model hRMS: 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

19. Hemispherical Model

20. Hemispherical Model

21. Huray Model

22. Huray Model Ho: magnitude of applied H field.

23. Dielectrics and Polarization No field Applied field Field causes the formation of dipoles  polarization Bound surface charge density –qspon 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

26. Dielectric Constants

27. 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.

28. 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.

29. Complex Permittivity : dipole density : mass : damping coefficient : dipole charge : free space permittivity : natural frequency : applied frequency : spring (tension) factor

30. Complex Permittivity se: 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

32. Complex Permittivity

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

38. Dielectric Materials

39. PCB Stackup Source: 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 Effect Fiberglass weave pattern causes signals to propagate at different speeds in differential pairs 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.

42. Fiber Weave Effect Source: Lambert Simonovich, "Practical Fiber Weave Effect Modeling", White Paper-Issue 3, March 2, 2012.

43. Fiber Weave Effect Source: 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-528-1.1, 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-528-1.1, 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-528-1.1, January 2011.