Next No Myths Allowed Webinar: Frequency Dependent Material Properties, so what?, Thurs, Feb 25, 2010, 1 pm EST. Free, but you must pre-register here.

Spring Institute of Signal Integrity Classes, April thru May 2010, San Jose, more info and online registration here.

 

I presented a paper at this year’s DesignCon on the topic of causal models for materials. Whenever you go from a frequency domain description of a function into the time domain, you have to worry about causality.

Causality means a response can’t happen before the stimulus. This is the essence of cause and effect. The problem is that sine waves, and arbitrary combinations of sine waves in the time domain, are not usually causal. They extend back to minus infinity in time.

To make combinations of sine waves appear causal and be useful to describe time domain responses of real systems, we need to conspire the real and imaginary parts of the frequency domain response so all the waves at t < 0 cancel out leaving just stuff that happens after t = 0.

Any dielectric properties, described by the real part of the dielectric constant, Dk, and the ratio of the imaginary to the real, Df, must be causal, and so must have this relationship between their real and imaginary parts. This is described by the Kramers-Kronig relationship.

This means that “to know the real part of the dielectric constant is to know the imaginary part.” If we make the assumption that the real part decreases with the log of the frequency, then we can build a simple analytical expression for the dissipation factor Df.

We find that if the Dk drops with the log of the frequency, the Df will be roughly proportional to the slope of Dk and log F. This means the higher the dissipation factor the more dispersion.

It’s the dispersion that causes increased rise time degradation, above and beyond what we expect from just the losses. If your simulator does not include this frequency dependent dielectric constant, you will under estimate the rise time and actual performance may be worse than you predict.

If you care about high speed serial links and use FR4 like materials, you should care about frequency dependent material properties. In which case, here are three places for more information:

The webinar I am doing on Feb 25, 2010, will review this topic in great detail, and in a way that anyone can understand.

You can download a copy of the paper I wrote with my partners which was presented at DesignCon.

You can download a copy of the slides from this DesignCon presentation.

I am turning the DesignCon presentation into a video lecture. This will be posted on the web site in the next few weeks. Stay tuned!