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Digital Circuit Boards: Mach 1 GHz by Ralph Morrison

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4.12 Dielectric Losses

Dielectric losses are the result of molecular activity in the board. This dissipation is limited to the areas where a wave is in transition. This dissipation increases the rise time of a wave, as it progresses along a transmission line. The attenuation factor α in decibels per inch for sine waves is

4.6 4.6

where f is frequency in gigahertz and δ is the shift in phase resulting from transmission losses at the frequency f. The term loss tangent is applied to the factor tan(δ). This factor is given in the literature for different materials. The value of tan(δ) for FR-4 board material at 1 GHz is 0.02. For higher grades of dielectric, the loss tangent can be as low as 0.002.

Skin effect has a moderate impact on rise time. Note that skin effect causes the resistance of the line to increase proportional to the square root of frequency. Dielectric losses increase exponentially with frequency. This means that above some frequency, the dielectric losses will dominate. To see the effect on square waves, the amplitude of the fundamental might be attenuated by 0.1 dB/in. At the seventh harmonic, dielectric losses would dominate and the attenuation would be 0.7 dB/in. A 1-dB attenuation is a loss of about 10%. If the loss tangent is 0.02, the effect is to increase the rise time 8 ps/in of line. For a material with a loss tangent of 0.002, the impact is only 0.8 ps/in. Clock ...

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