Are You Over-Engineering Your Boards?
When asked the loaded question “What is the frequency of your circuit?”, many engineers will reply with the clock frequency they found in a datasheet. But unfortunately, that is the wrong answer. The clock frequency doesn’t really matter. What matters are the frequencies hidden in the fast transitions of rise-time and fall-times. If you’ve made this mistake, but your boards still work, you’ve gotten lucky, and are likely overengineering your boards. By slowing down and doing some simple math, you can see if your rise times and trace lengths are in the right order-of-magnitude to start causing problems.
The rise time of a signal is measured between 20% and 80 % of the difference (or 10% and 90%) between logic low and logic high (ignoring overshoot).
The rise-time is measured as either the time to rise from 20% to 80% of the maximum potential difference or from 10% to 90% of the maximum potential difference.
We often look at signals in the time-domain. Hidden from view, inside the frequency domain of that sharp increase is a series of harmonics that have sufficient amplitude to disrupt your circuit.
On the left side of the graphic is a square wave composed of a series of low amplitude sine waves. On the right side of the image is a bar chart that indicates the relative amplitudes of each component wave.
To get an estimate of the frequencies you actually need to worry about, take the reciprocal of your 20%/80% rise time. That frequency component contains the greatest amplitude and can cause the most trouble in your circuit — but even the harmonics need your attention — usually out to the 5th harmonic or so.
To measure it, you need an oscilloscope with a bandwidth sufficient to sample along the rising edge without having to worry about aliasing. As a general rule of thumb, you can divide your rise time into 0.6 to determine a suitable bandwidth for an oscilloscope, and then round up to the nearest specification oscilloscope.
This equation gets you into the right neighborhood, but don’t let it guide your purchasing decision, as there are many other considerations when selecting an oscilloscope — you should get on the phone with manufacturers’ field application engineer to learn more.
The rise/time and fall/time for integrated circuits continue to inch towards picosecond ranges. Chip designers have outputs that appear to be square waves on lower-end oscilloscopes. But it’s not a step function, it is a transition, you just might not be able to see it with your test equipment.
Each of these diagrams represents sampling points on a square wave. The image on the left represents a 250 MHz bandwidth and the image on the right represents a 1 GHz bandwidth. The 1 GHz is borderline sufficient to capture the rise time.
Transitions don’t happen at points in time they occur over intervals of time and take time to propagate along a trace. If the beginning and end of the transition can simultaneously exist along the length of a trace, you have an electrically short interconnect that will behave like a transmission line, and you need to pay attention to what you are doing. In fact, if you pretended your trace was ten times as long (to account for harmonics), and the transition could complete in that length, you still need to pay attention to your interconnect and possibly treat it as a transmission line.
In the image on the left, the transition happens quickly, and in the image on the right, the transition is spread out over a greater length of time.
If the beginning of the transition will disappear from the trace long before the end of the transition, you don’t really have a high-speed circuit and don’t need to be as careful as you might think.
The question then becomes, when do you need to start paying attention to your dielectric material selection and trace routing? For that, let’s turn to Mr. Rick Hartley and Dr. Eric Bogatin. In their recent 2020 PCBWest presentation, they provided separate recommendations for when you should start paying attention, and it depends on the rise/fall time of your signal, not the clock frequency.
Dr. Bogatin provides a very simple rule of thumb — signals travel 6 inches per nanosecond. Multiply your rise time, in nanoseconds, by 6 inches/nanosecond and compare it to the length of your interconnect. If your calculated length is less than your actual interconnect length, you likely have a transmission line.
Mr. Hartley went to the trouble of using Polar Instrument’s 2-D field solver and calculated the inner and outer trace propagation speeds to come up with an order-of-magnitude improvement over Dr. Bogatin’s Rule of Thumb.
Who is right? Well, the answer is “Both of them” and “Neither one of them” because they have no idea how your board is constructed, only you do. And they have no idea how energetic the harmonics of your signal are. These are simply guidelines that tell you when you need to start worrying if you’ve unknowingly created a transmission line out of your interconnect.
If you have a 100 ns rise time, you don’t have a care in the world. Your signal lines don’t require special attention unless perhaps you are designing a board the size of a panel. But when your rise times shrink beyond 100 picoseconds, your interconnects are likely a problem.
We see boards every day that are over-engineered, and under-engineered. As a designer, it’s up to you to find where the critical design thresholds are and approach them with a suitable margin for safety. If you consistently over-engineer your boards, we will happily build them, but they will cost more than they might need to. And if you under-engineer your boards, they won’t work. So approach the line with caution.