## How Fast is Fast?

Out at the swing set this morning, my daughter Alexandra 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 with fast signals," but I tried. After a while, she asked, "How fast is fast, 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, a quick jerk represents is a very high speed.

Sandy has little understanding of the frequency specturm. Fortunately, she doesn't need to know much about it 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 in the "quick jerk" range.

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 Y. 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×Y. 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 behavior will be an exact copy of the old setting behavior, scaled in time by 1/K.

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 Alexandra grows up, what seems fast to you and me won't seem fast to her at all.

### Postlog:

Alexandra graduated in 2014 from Carnegie-Mellon University, near the top of her class, studying computer science.