Electronic – Considering Moding Issues in High Speed PCB Design

pcbpcb-designsignal integritytransmission linewaveguide

My question is a more generic one. I recently learnt about TE and TM propagation modes in waveguides. This made me think that when designing high-speed PCBs people always talk about matching the characteristic or differential impedance of the line; however, I have never heard somebody considering the case of moding issues in PCB design.

So the cutoff frequency for a mode m in a parallel plate waveguide is given by:

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where m is the number of the mode, c is the speed of light, n is the refractive index (for FR4 this is approximately 2.1) and d is the distance between the copper traces.

I calculated that if the thickness of the FR4 between the copper traces is 0.2mm then there will be TE and TM modes propagating down the transmission line at frequencies higher than 360MHz.

I know that moding causes dispersion which creates issues with signal integrity. This made me wander why I've never heard people considering this type of issues when designing PCBs. Are there any cases in which it must be considered?

Best Answer

You have slipped a digit. Or three. You have done your computation by plugging "0.2" into the formula while using m/s for \$c\$. If you use consistent units then for the first mode you get

\$\omega_{cm}=\frac{1 \cdot \pi \cdot c}{(2.1)(0.2\cdot 10^{-3}\mathrm{m})} \simeq 2.2 \cdot 10^{12} \mathrm{\frac{rad}{s}} \simeq 360\,\mathrm{GHz}\$

This passes my personal sniff test, in that the cutoff happens at around 1/2 of a wavelength at the cutoff frequency.