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July 2, 1998
How fast is fast?
Howard Johnson, PhD
Signal Integrity
Out at the swing set this morning, my daughter Sandy asked me what I do for a living.
It's not easy to explain to a five-year-old child the meaning of "high-speed digital
design," but I tried. After a while, she asked, "How fast is high speed,
Daddy?"
I took a rock and set it on the swing. We pushed the swing back and forth, and
everything seemed fine. Then I jerked the swing back and forth really quickly, and the
rock flew off the seat. Every physical system has its design limits. You aren't supposed
to work the swing at such a high speed, or else whatever object you place on the seat will
fly off. For a swing, I explained, 10 Hz is a very high speed.
Sandy has little understanding of frequencies above 10 Hz. Fortunately, she doesn't
need to know much about them at this point in her life. Speed is a relative concept--you
need to know about things only within the range of frequencies that matters to you
personally. To get around the playground, Sandy probably needs to understand only the
physical properties of rubber balls and swing sets at frequencies of 10 Hz or less.
In other areas of life, a working knowledge of high-frequency effects may be advisable.
For example, an audio-circuit-design engineer needs a good understanding of nonlinear and
parasitic effects at frequencies as high as 100 kHz but does not necessarily need to
understand much about higher realms.
In the same way, designers of FM-radio receivers need to know about frequencies as high
as 200 MHz. Microwave engineers need to understand frequencies as high as 100 GHz. For
each application, there is a clearly defined band of frequencies in which the circuitry
must function. Outside that band, additional knowledge of parasitic effects doesn't matter
much. That's a good thing, because it helps these designers focus their attention on
developing good, solid intuition about which design techniques in their target range of
frequencies work and which don't.
In the digital world, things work differently. In digital systems, the frequencies of
interest depend on the edge transition time of the logic involved. Every time you double
switching speed, the frequencies involved rise by a factor of two. I call this the
"speed-inflation" factor. In case you haven't noticed, digital designers have
been swept along at a 40% speed-inflation rate for the last 30 years. Each new project
operates at a higher speed than the last one. As a consequence, there is no well-defined
range of frequencies over which a digital-circuit designer can begin to build his or her
intuition.
Digital designers must develop rules of scaling that they can use to help apply old
knowledge to new projects.
For example, suppose you have a net that is working perfectly well at speed X. Now,
suppose you wish to scale up the net's speed by a factor of K, creating a new net in a new
product that operates at speed of K*X. One way to design the new net is to scale all of
the critical parameters of the net, like this:
- Keep the same net topology, but shrink the length of each trace segment by a factor of
K.
- Shrink the rise time of the driver by a factor of K.
- Shrink all the capacitive loads by a factor of K.
- Shrink the lead inductance of the chip packages by a factor of K (that is, use better
packages).
- Shrink all trace stubs, pads, vias, and passive-component package sizes by a factor of
K.
- Shrink the overall board thickness by a factor of K.
- Keep the trace impedance the same.
- Keep the driver source impedance the same.
If you follow these guidelines, the new trace will exhibit the same percentage of
overshoot and ringing as the old trace. The new settling time will be 1/K of the old
settling time.
In practice, when you attempt to scale a net, you will find that you cannot scale some
factors. To make up the difference, you must then make additional modifications to the
remaining factors or change the net topology. As a consequence, each time you scale up the
operating speed, you must adjust your mental definition of a "typical" net.
How long will frequency inflation continue? Nobody knows for sure, but the way computer
technology is going, one thing is certain: When Sandy grows up, what seems fast to you and
me won't seem fast to her at all.
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