Appendix B. 100 Collected Rules of Thumb to Help Estimate Signal-Integrity Effects

A rule of thumb should be used only when an okay answer right now is more important than a good answer later.

A rule of thumb is only meant to provide a very rough approximation. It is designed to help feed our intuition and to help find a quick answer with very little effort. It should always be the starting place for any estimate. It can help us distinguish between a 5 or a 50. It can help us see the big picture early in the design phase. In the balance between quick and accurate, a rule of thumb is quick; it is not meant to be accurate.

Of course, you can’t use a rule of thumb blindly. It must be coupled with an understanding of the principles and good engineering judgment.

When accuracy is important, such as in a design sign-off, where being off by a few percent may have a $1 million impact, why use anything other than a verified numerical simulation tool?

This appendix provides a collection of the most useful rules of thumb, separated by the chapters in which they are introduced.

2. The amplitude of the nth harmonic of an ideal square wave is ~2/(πn) times the magnitude of the clock voltage. For example, the first harmonic amplitude of a 1-v clock signal is about 0.6. The third harmonic is about 0.2.

3. The bandwidth, BW, and rise time, RT, of a signal are related by BW = 0.35/RT. For example, if the rise time is 1 nsec, the bandwidth is 350 MHz. If the bandwidth of an interconnect is 3 GHz, the shortest rise time it can transmit is about 0.1 nsec.

4. If you don’t know the rise time, you can estimate the bandwidth of a signal as roughly five times the clock frequency. For example, if the clock frequency is 1 GHz, the bandwidth of the signal is about 5 GHz.

7. The ESL of an axial lead resistor is about 8 nH. The ESL of an SMT resistor is about 2 nH.

8. The resistance per length of a 1-mil-diameter gold wire bond is about 1 Ohm/inch. For example, a 50-mil-long wire bond has a resistance of about 50 milliOhms.

9. A length of 24 AWG wire has a diameter of about 20 mils and a resistance per length of about 25 milliOhms/foot.

10. The sheet resistance of 1-ounce copper is about 0.5 milliOhm/square. For example, a trace 5 mils wide and 1 inch long has 200 squares and would have a series resistance of 200 × 0.5 = 100 milliOhms = 0.1 Ohm.

11. The skin-depth effects for 1-ounce copper begin at about 10 MHz.

13. The capacitance of a pair of plates the size of a penny, with air between the faces, is about 1 pF.

14. When the plates of a capacitor are as far apart as the plates are wide, the fringe fields contribute just as much capacitance as the parallel-plate fields. For example, if we estimate the parallel-plate capacitance for a microstrip with line width of 10 mils and dielectric thickness of 10 mils to be 1 pF/inch, the actual capacitance will be about twice this value, or 2 pF/inch.

15. If we don’t know anything else about a material except that it is an organic laminate, a good estimate for its dielectric constant is 4.

16. For a 1-watt chip, the amount of time, in sec, a decoupling capacitance, in F, will provide the charge with less than 5% voltage droop is C/2. For example, if there is a decoupling capacitance of 10 nF, it will provide decoupling for only 5 nsec. If we require 10 microseconds of decoupling, we need 20 μF of capacitance.

17. The capacitance available in the power and ground planes of a typical circuit board when the separation is 1 mils is 1 nF/square inch, and it scales inversely with the dielectric thickness. For example, in a 10-mil separation board, the total board area available for decoupling an ASIC may be only 4 square inches. The capacitance would be 4 in² × 1 nF/in² /10 = 0.4 nF, and it would provide decoupling for about 0.2 nsec.

18. The effective dielectric constant in a 50-Ohm microstrip is 3 when the bulk dielectric constant is 4.

20. The loop self-inductance of a 1-inch-diameter round loop, made from 10-mil-thick wire about the size of your finger and thumb held together in a circle, is 85 nH.

21. The total inductance per length for a section taken out of a 1-inch-diameter loop is about 25 nH/inch, or 1 nH/mm. For example, if a package lead is part of a loop and is 0.5 inch long, it has a total inductance of about 12 nH.

22. When the center-to-center separation of a pair of round rods is 10% of their length, the partial mutual inductance will be about 50% of the partial self-inductance of either one. For example, if we have two wire bonds, 1 mm long on 0.1 mm centers, the partial self-inductance of either one is about 1 nH, while their partial mutual inductance will be about 0.5 nH.

23. When the center-to-center separation between two round rods is about equal to their length, the partial mutual inductance between them is less than 10% of the partial self-inductance of either one. For example, if we space 25-mil-long vias more than 25 mils center-to-center, there is virtually no inductive coupling between them.

24. The loop inductance of an SMT capacitor is roughly 2 nH, including the surface traces, vias, and capacitor body. Good engineering efforts are required to reduce this below 1 nH.

25. The loop inductance per square of a pair of planes is 33 pH per square per mil of spacing. For example, if the dielectric spacing is 2 mils, there is 66 pH/square of loop inductance between the planes.

26. The loop inductance of a pair of planes having a field of clearance holes with 50% open area will increase by about 50%.

27. The skin depth in copper is 2 microns at 1 GHz and increases with the square root of frequency. For example, at 10 MHz, the skin depth is 20 microns.

28. In a 50-Ohm transmission line of 1-ounce copper, the loop inductance per length is constant at frequencies above about 50 MHz. This means characteristic impedance is constant above 50 MHz.

30. The speed of a signal in air is about 12 inches/nsec. The speed of a signal in most polymer materials is about 6 inches/nsec.

31. The wiring delay, 1/v, in most laminates is about 170 psec/inch.

32. The spatial extent of the signal is the rise time multiplied by the speed, or RT × 6 inches/nsec. For example, if the rise time is 0.5 nsec, the spatial extent of the edge as the signal propagates down a board is 3 inches.

33. The characteristic impedance of a transmission line varies inversely with the capacitance per length. The characteristic impedance is about 160 Ohms/C_len, with C_len in pF/inch.

34. All 50-Ohm lines in FR4 have a capacitance per length of about 3.3 pF/inch. For example, if a BGA lead is designed as 50 Ohms and is 0.5 inch long, it has a capacitance of about 1.7 pF.

35. All 50-Ohm lines in FR4 have an inductance per length of about 8.3 nH/inch. For example, if a connector is designed for 50 Ohms and is 0.5 inch long, the loop inductance of the signal and return path-loop is about 4 nH.

36. A 50-Ohm microstrip in FR4 has a dielectric thickness about half the line width of the trace. For example, if the line width is 10 mils, the dielectric thickness will be 5 mils.

37. A 50-Ohm stripline in FR4 has a plane-to-plane spacing about twice the line width of the signal trace. For example, if the line width is 10 mils, the spacing between the two planes will be 20 mils.

38. The impedance looking into a transmission line will be the characteristic impedance for a time shorter than the round-trip time of flight. For example, if a 50-Ohm line is 3 inches long, all drivers with a rise time shorter than 1 nsec will see a constant 50-Ohm load during the transition time when driving the line.

39. The total capacitance in a section of transmission line with a time delay of TD is C = TD/Z₀. For example, if the TD of a line is 1 nsec and the characteristic impedance is 50 Ohms, there is 20 pF of capacitance between the signal and return paths.

40. The total loop inductance in a section of a transmission line with a time delay of TD is L = TD × Z₀. For example, if the TD of a line is 1 nsec and the characteristic impedance is 50 Ohms, there is 50 nH of loop inductance between the signal and return paths.

41. If the width of the return path in a 50-Ohm microstrip is equal to the signal line width, the characteristic impedance is 20% higher than the characteristic impedance when the return path is infinitely wide.

42. If the width of the return path in a 50-Ohm microstrip is at least three times the signal line width, the characteristic impedance is within 1% of the characteristic impedance when the return path is infinitely wide.

43. Trace thickness will decrease the characteristic impedance of a line by about 2 Ohms per mil of thickness. For example, from 1/2-ounce copper to 1-ounce copper, the thickness increases by 0.7 mil. The impedance of the line would decrease by about 1 Ohm.

44. Solder mask on top of a microstrip will decrease its characteristic impedance by about 2 Ohms per mil of thickness. For example, a 0.5-mil-thick solder mask will decrease the characteristic impedance by about 1 Ohm.

45. For an accurate lumped-circuit approximation, you need at least 3.5 LC sections per spatial extent of the rise time. For example, if the rise time is 1 nsec, in FR4, the spatial extent is 6 inches. You would need at least 3.5 LC sections per 6 inches—or about one section every 2 inches of trace—for an accurate approximation.

46. The bandwidth of a single-section LC model is 0.1/TD. For example, if the time delay of a transmission line is 1 nsec, using a single LC section to model it would be accurate up to a bandwidth of about 100 MHz.

48. In a 50-Ohm system, an impedance change of 5 Ohms will give a reflection coefficient of 5%.

49. Keep all discontinuities shorter, in inches, than the rise time, in nsec. For example, if the rise time is 0.5 nsec, keep all impedance discontinuities, such as a neck-down to pass through a via field, less than 0.5 inch long, and it may be acceptable.

50. A capacitive load at the far end will increase the rise time of the signal. The 10–90 rise time is about 100 × C psec, for C in pF. For example, if the capacitance is 2 pF, typical of the input-gate capacitance of a receiver, the RC limited rise time would be about 200 psec.

51. If the capacitance of a discontinuity is less than 0.004 × RT, it may not cause a problem. For example, if the rise time is 1 nsec, capacitive discontinuities should be less than 0.004 nF, or less than 4 pF.

52. The capacitance, in fF, of a corner in a 50-Ohm line is twice the line width, in mils. For example, if the line width of a 50-Ohm trace is 10 mils, a 90-degree bend would have a capacitance of about 20 fF. It might cause reflection problems for rise times of 0.02 pF/4 = 5 psec.

53. A capacitive discontinuity will add a delay time to the 50% threshold point of about 0.5 × Z₀ × C. For example, if the capacitance is 1 pF in a 50-Ohm line, the delay adder will be about 25 psec.

54. If the inductance, in nH, of a discontinuity is less than 10 times the rise time, in nsec, it may not cause a problem. For example, if the rise time is 1 nsec, the maximum inductive discontinuity that may be acceptable is about 10 nH.

55. An axial lead resistor with a loop inductance of about 10 nH may contribute too much reflection noise for rise times less than 1 nsec. Switch to surface-mount resistors.

56. To compensate for a 10-nH inductance, a 4-pF capacitance in a 50-Ohm system is required.

58. At 1 GHz, the attenuation from the resistance of an 8-mil-wide trace is comparable to the attenuation from the dielectric, and the attenuation from the dielectric will get larger faster with frequency.

59. The low-loss regime, for lines 3 mils or wider, is all frequencies above about 10 MHz. In the low-loss regime, the characteristic impedance and signal speed are independent of the loss and of frequency. There is no dispersion due to loss in typical board-level interconnects.

60. A −3-dB attenuation is a drop to 50% of the initial power level and a drop to 70% of the initial amplitude.

61. A −20-dB attenuation is a drop to 1% of the initial power level and a drop to 10% of the initial amplitude.

62. When in the skin-depth regime, the series resistance per inch of a signal- and return-path line, of width w in mils, is about 8/w × sqrt(f), with f in GHz. For example, a line 10 mils wide has a series resistance of about 0.8 Ohm/inch, and it increases with the square root of frequency.

63. In a 50-Ohm line, the attenuation from the conductor is about 36/wZ₀ in dB per inch. For example, if the line width is 10 mils in a 50-Ohm line, the attenuation is 36/(10 × 50) = 0.07 dB/inch.

64. The dissipation factor of FR4 is about 0.02.

65. In FR4, the attenuation from the dielectric is about 0.1 dB/inch at 1 GHz and increases linearly with frequency.

66. At 1 GHz, a 50-Ohm line in FR4 with a line width of 8 mils has the same conductor loss as the dielectric loss at 1 GHz.

67. The bandwidth of an FR4 interconnect Len inches long, when limited by dissipation factor, is 30 GHz/Len. For example, a 50-Ohm line 10 inches long has a bandwidth of 3 GHz.

68. The shortest rise time that can be propagated by an FR4 interconnect is 10 psec/inch × Len. For example, a signal propagating down a 10-inch length of 50-Ohm line in FR4 will have a rise time of at least 100 psec.

69. The rise-time degradation from losses will be important in FR4 laminates if the interconnect length, in inches, is greater than 50 times the rise time, in nsec. For example, if the rise time is 200 psec, worry about losses when line lengths are greater than 10 inches.

71. In a pair of 50-Ohm microstrip transmission lines, with spacing equal to the line width, the coupling inductance between the signal lines is about 15%.

72. The saturation length for near-end noise in FR4 is 3 inches for a 1-nsec rise time, and it scales with the rise time. For example, if the rise time is 0.5 nsec, the saturation length is 1.5 inches.

73. The loaded capacitance of a trace is constant and independent of the proximity of other traces nearby.

74. The near-end cross talk for 50-Ohm microstrip traces with spacing equal to the line width is 5%.

75. The near-end cross talk for 50-Ohm microstrip traces with spacing equal to twice the line width is 2%.

76. The near-end cross talk for 50-Ohm microstrip traces with spacing equal to three times the line width is 1%.

77. The near-end cross talk for 50-Ohm stripline traces with spacing equal to the line width is 6%.

78. The near-end cross talk for 50-Ohm stripline traces with spacing equal to twice the line width is 2%.

79. The near-end cross talk for 50-Ohm stripline traces with spacing equal to three times the line width is 0.5%.

80. In a pair of 50-Ohm microstrip traces with spacing equal to the line width, the far-end noise is 4% × TD/RT. If the time delay of the line is 1 nsec and the rise time is 0.5 nsec, the far-end noise is 8%.

81. In a pair of 50-Ohm microstrip traces with spacing equal to twice the line width, the far-end noise is 2% × TD/RT. If the time delay of the line is 1 nsec and the rise time is 0.5 nsec, the far-end noise is 4%.

82. In a pair of 50-Ohm microstrip traces, with spacing equal to three times the line width, the far-end noise is 1.5% × TD/RT. If the time delay of the line is 1 nsec and the rise time is 0.5 nsec, the far-end noise is 3%.

83. There is no far-end noise in stripline or fully embedded microstrip.

84. In a 50-Ohm bus, stripline or microstrip, to keep the worst-case near-end noise below 5%, keep the spacing between the lines more than twice the line width.

85. In a 50-Ohm bus with a spacing equal to the line width, 75% of all the cross talk on any victim line is from the trace on either side of the victim line.

86. In a 50-Ohm bus with a spacing equal to the line width, 95% of all the cross talk on any victim line is from the nearest two traces on either side of the victim line.

87. In a 50-Ohm bus with a spacing equal to twice the line width, 100% of all the cross talk on any victim line is from the trace on either side of the victim line. You can ignore the coupling from all other traces in the bus.

88. For surface traces, separating the adjacent signal traces sufficiently to add a guard trace will often reduce the cross talk to an acceptable level, eliminating the need for a guard trace. Adding a guard trace with the ends shorted can reduce the cross talk by about 50%.

89. For stripline traces, using a guard trace can reduce the cross talk to less than 10% of the level without the guard trace.

90. To keep the switching noise below an acceptable level, keep the mutual inductance less than 2.5 nH times the rise time, in nsec. For example, if the rise time is 0.5 nsec, the mutual inductance should be less than 1.3 nH for acceptable switching-noise cross talk due to coupling between only two signal/return-path pairs.

91. For a connector or package that is limited by switching noise, the maximum usable clock frequency is 250 MHz/(n × L_m) for a mutual inductance between pairs of signal and return paths, in nH, and a number of simultaneous switching lines, n. For example, if there are four pins that share the same return path and their mutual inductance is about 1 nH between pairs, the maximum usable clock frequency for the connector will be 250 MHz/4 ~ 60 MHz.

93. With no coupling, the differential impedance in a differential pair is twice the single-ended impedance of either line.

94. In a pair of 50-Ohm microstrip lines, the single-ended characteristic impedance of one line is completely independent of the proximity of the adjacent line, as long as the other line is tied low or tied high.

95. In the tightest coupled differential microstrip, a line width equal to the spacing, the differential impedance drops only about 10% from the differential impedance when the traces are far apart with no coupling.

96. In a broad-side coupled differential pair, the trace-to-trace separation must be at least larger than the line width in order to have the possibility of getting as high as a 100-Ohm differential impedance.

97. The FCC Class B requirement is a far-field strength less than about 150 microV/m at 100 MHz and 3 meters distance.

98. It takes only about 3 uA of common current on unshielded twisted-pair cables to fail an FCC Class B EMC certification test.

99. A highly coupled differential pair will have 30% less differential-signal cross talk than a weakly coupled pair, from a closely spaced single-ended aggressor, provided that the line widths and dielectric thicknesses are kept the same. This means the differential impedance decreases when the traces are more tightly coupled.

100. A highly coupled differential pair will have about 30% more common-signal cross talk than a weakly coupled pair, from a closely spaced single-ended aggressor.