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Rule of thumb: Loss in a channel

23 Apr 2014  | Eric Bogatin

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In this rule of thumb, we try to estimate the attenuation at the Nyquist for a lossy, uniform channel.

Attenuation figure of merit: 0.2 dB/inch/GHz, for a lossy channel, 0.1 dB/inch/GHz for a low loss channel.

There are four important effects which contribute to inter-symbol interference (ISI) in high speed serial link channels: attenuation, reflection noise, crosstalk, and mode conversion.

If everything is done right in the interconnect design, the attenuation will still be left as a fundamental limit imposed by the choice of materials in the interconnect. It is the frequency dependent attenuation that causes the rise time to increase. When the rise time is long compared to the unit interval, ISI is the result.

Many channel specifications have a budget for how much attenuation is acceptable for the channel. With PCIe gen II, for example, the attenuation at the Nyquist for PC applications must be less than 13.5 dB. If we can estimate the expected attenuation at the Nyquist for the channel, we can estimate whether the channel may be acceptable.

The frequency dependent attenuation arises from two root causes, the conductor loss and the dielectric loss. When all the other problems are reduced, these two loss mechanism will always be left.

To a pretty good approximation, the attenuation, at a frequency, f, is:



where:

w = the line width in mils

f = the sine wave frequency in GHz, equivalent to the Nyquist

Df = the dissipation factor

Dk = the dielectric constant

This model assumes skin depth limited current in microstrip or stripline, the series resistance in the return path, and a factor of 2 increase in resistance from surface roughness and a 100 Ohm impedance line.

Let's put in the numbers for a PCIe III channel, at 8 Gbps or 4 GHz Nyquist, for the case of a 5 mil wide trace in FR4. This is a relatively lossy channel.



We see that the attenuation is comparable between the conductor and the dielectric loss. It is not strictly linear with frequency, but as a rough approximation, around 4 GHz, the attenuation is about 0.78 dB/in/4 GHz = 0.2 dB/in/GHz.

In a Megtron6 channel, we'd expect to see:



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