What is the spatial extent of an edge?: Rule of Thumb #29
If you really want to build your engineering intuition about signal integrity, the most important principle you can apply is the Zen approach, “be the signal”. As you propagate down an interconnect, you have a spatial extent along the interconnect. How large you are compared to interconnect features strongly influences what you see and how you react.
This is the origin of the name of my web site, and my twitter handle, beTheSignal. It is a powerful way of thinking about signals and how they interact with interconnects.
Spoiler summary: The length of the rising (or falling) edge of a signal, as it propagates down a transmission line, in inches (cm), is about 6 inches/ns (15 cm/ns) × rise time [ns] (in FR4 type interconnects).
Remember: before you start using rules of thumb, be sure to read the Rule of Thumb #0: Using rules of thumb wisely.
The starting place is to imagine you are the edge of the signal as it propagates down an interconnect. In Rule of Thumb #3, we introduced a rough estimate for the speed of a signal as it propagates down a transmission line. In FR4 type materials, the Dk is about 4, and the speed of a signal is about 6 inches/ns (15 cm/ns).
As this rising edge runs down the interconnect, its leading edge, with a finite rise time, RT[ns], spreads over the interconnect and has a spatial extent, ∆x. This is the region in which the voltage between the signal and return is changing. We usually use the 10% & 90% points to define the limits to the edge. This is illustrated in Figure 1.
Figure 1 The rising edge of a signal spreads out over the interconnect as it propagates.
As the edge leaves the transmitter, it propagates at 6 inches/ns (15 cm/ns). During the time the edge comes out of the transmitter, the leading edge has propagated a distance:
For example, in a typical low end CMOS logic device with a rise time of 1 ns, the spatial extent of the edge is 6 inches (15 cm).
In a DDR3 signal with a rise time of 0.3 ns, the spatial extent of the leading edge is 1.8 inches (4.5 cm).
And, in a 28 Gbps signal, with a rise time of 20 ps, the spatial extent is about 0.12 inches (3 mm).
Now that you have the image in your head of this edge moving down the interconnect, think about the structures it sees. If the interconnect is uniform, the edge just propagates down the line, of course, with losses.
If the signal sees a change in geometry which is shorter than about 1/3 the spatial extent of the leading edge, the discontinuity will be just a tiny pebble in the road, hardly affecting the signal.
If the discontinuity is longer than about 1/3 of the spatial extent of the edge time, there is the possibility it will be more of a speed bump, and distort the signal.
If you want to make a discontinuity transparent, keep its length shorter than 1/3 the spatial extent of the rise time. With a little algebra, we can show this condition is the same as keeping the length of the transparent discontinuity shorter than 1/10th the wavelength of the highest frequency component of the signal.
For the 28 Gbps signal, this means shorter than about 1/3 × 120 mils (3 mm) = 40 mils (1 mm). Now we suddenly see one reason why 28 Gbps systems are a lot harder to design and fab than 8 Gbps systems.
- Bogatin's Rules of Thumb
- Rule of Thumb #1: Bandwidth of a signal from its rise time
- Rule of Thumb #3: Signal speed on an interconnect
Additional information on this and other signal integrity topics can be found at the Signal Integrity Academy, www.beTheSignal.com.