RoT: Signal Propogation in a PCB

RoT: Signal propagation in FR4 is about 6”/ns. The wavelength of a 1GHz signal in a PCB is approximately 6”. 

Everyone knows that the speed of light (in a frictionless vacuum, you physics nerds) is 300Mm/s (that’s Mega-meters per second). I didn’t have to look up that constant when writing this, at all. In different medium, the speed can be expressed as: 

Where Vs is the signal velocity, c is the speed of light in a vacuum, εr is the relative permittivity of the medium, and μr is the relative permeability of the medium. The approximation shown is used in many practical applications as for most common materials, μr is approximately 1. 

Since this is a rule of thumb, we don't need to be precise. Let's take εr of our material to be 4, even though there's some variation, and we'll convert to freedom units while we're at it. 

This approximation works great even for high-performance laminates with a Dk (εr) of 3.5 (6.3”/ns), and serves an okayish approximation for coaxial cables with low Dk (e.g., RG 8 with foam polyethylene dielectric material, Dk ≈ 1.7, Vs ≈ 9”/ns). Remember, the goal is to build intuition, not to be exact!

(And no, the 4 in FR4 does not stand for permeability. FR4 is a NEMA grade designation for glass-reinforced epoxy laminate material and stands for “Flame Retardant Type 4,” and indicates a woven glass-reinforced epoxy resin. There are multiple types of FR4 laminate, but that’s for another article.)

Now, if the propagation velocity is about 6”/ns, we can flip that on its head and say in one nanosecond, a signal will propagate about 6”. A 1GHz signal has a period of 1ns, and we can therefore conclude that the wavelength of a 1GHz signal is about 6” in a PCB, or a 10GHz signal would have a wavelength of about 0.6” in PCB, or a 100MHz signal has a wavelength of about 60” in a PCB. These are handy to remember when considering how long one can make a trace before worrying too much about reflections interfering with digital signals or laying out for emissions. 

A rule of thumb is fantastic to build intuition, but may not be accurate. Plugging in some numbers to a microstrip impedance calculator shows for a 50Ω line, the propagation is closer to 814ps/6". The number are: 1/2 oz copper, 5mil trace, 3mil dielectric, εr of 4 is a 50.1Ω line with a propagation delay of 135.72ps/in. 

For even more fun, one could look at this on a full-wave simulator. The model is a 6" stripline placed 3mil above a plane with a dielectric layer with εr of 4. The trace is 5mil wide and 0.7mil tall (1/2 oz copper). The ground plane has dimensions of 6.06" x 3" x 0.7" (also 1/2 oz copper). The simulation results show group delay vs. frequency.  The simulation results show a group delay of about 900ps for the 6" line, which is somewhere between what the calculator provides, and our rule of thumb. 

From these results, thinking of signal propagation as 6"/ns in an FR4 material is a good approximation!

Always remember Rule 0, and remember when you can get away with using the rules of thumb and when you’ll need to do further analysis. It’s a tradeoff between speed and accuracy!