## Ground Bounce Calculations

It's been a wild summer (1997)! As you may know, I was recently elected chief technical editor of the new IEEE Gigabit Ethernet technical specification (thank you, Packet Engines, for sponsoring my work on that project). That standard, when complete, will advance the Ethernet operating speed to one gigabit-per-second (10E+09 bits per second).

This summer, the Gigabit Ethernet effort has moved into its final home stretch. We issued our first official IEEE working group ballot (all 450 pages) about two weeks ago. This move signals the achievement of a significant technical consensus among the 650 people monitoring and working with our standards task force. We are now ready to accept comments from the outside world. We anticipate receiving several thousand detailed comments on our draft between now and the close of balloting, Sept. 2, 1997.

Needless to say, I've been busy. Anyway...

My name is Alec Cohen - I completed the High-Speed Digital Design class you gave at VLSI Technology in San Jose CA on 10/25/96.

I am currently doing some SSO/Ground Bounce characterization work at the Semiconductor level and am using your text as reference- but have a quick question I hope you can clarify for me...

On page 62 of the High-Speed Digital Design Text (A Handbook of Black Magic) you introduce the idea that the maximum current slew rate to voltage rise time= (maximum rate of change of current through capacitor?)

di/dt = 1.52*Cl*V/ T^2

Where did the 1.52 come from?

What you need is to know the voltage waveform that I assumed. It cannot be inferred from the equations listed on the slides.

My assumption is that the voltage waveform right out of the driver looks like the integral of a Gaussian bell-shaped curve, adjusted to fit the 10-90% risetime of the driver. Such a shape would be the natural step response of a system comprised of many bandwidth-limiting effects, all at or near the same cutoff frequency (that's kind of how the output stage of an IC works). The integrated Gaussian curve has nice rounded corners at both leading and trailing edges, and looks a lot like what you see on a scope coming out of most drivers. That's why I use it.

By the way, the general equation for a Gaussian bell-shaped curve is exp(-(t/a)^^2). There is no analytic formula for the integral of this curve, although there are many software routines for approximating the values of this integral.

Best regards,
Dr. Howard Johnson