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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:

enter image description here

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?

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  • \$\begingroup\$ The surface roughness of the copper foil, and the skin--depth, introduce larger and larger losses; from what I've heard, about 3GHz. Thus the moding gets attenuated before has a chance to upset the waveforms. \$\endgroup\$ – analogsystemsrf Jun 6 at 1:57
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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.

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  • \$\begingroup\$ You are absolutely correct! This was very sloppy of me, I am sorry. Thank you! This results explains why you should not worry about moding issues :) \$\endgroup\$ – Ivan Vlaykov Jun 5 at 20:20
  • \$\begingroup\$ Yes, well, I had my middle term off by a factor of \$10^9\$ and neither of us noticed until I read your comment! \$\endgroup\$ – TimWescott Jun 5 at 20:23
  • \$\begingroup\$ @ThePhoton I keep telling myself not to do math in my head, even if it's simple. Then I go and do it because -- hey, it's simple, what could go wrong? \$\endgroup\$ – TimWescott Jun 5 at 21:13
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You're right to be concerned.

One source I found gives a formula for the cut-off frequency of the 1st higher-order mode in microstrip:

$$f_c = \frac{c}{n\left(2W+0.8h\right)}$$

However, the microstrip line will become dispersive (the propagation velocity will start to vary with frequency) well below the higher-order-mode cut-off frequency. Microwaves101 recommends keeping

$$h<\frac{\lambda}{10},$$

where \$h\$ is the substrate thickness and \$\lambda\$ is the signal wavelength in the substrate material, in order to avoid dispersion effects.

If you need to design for higher frequencies, you might consider switching to coplanar waveguide, which can be designed to be less dispersive up to higher frequencies.

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  • \$\begingroup\$ Thank you for the response! If I understand correctly you are talking about dispersion due to the frequency variations of the permittivity of FR4. The coplanar waveguide seems like an interesting solution to this. This is the first time I see it, so I will try to find more information about it. \$\endgroup\$ – Ivan Vlaykov Jun 5 at 21:26
  • \$\begingroup\$ No, it's not about the properties of the dielectric. It's because the mode pattern starts to change when the wavelength is not much larger than the dielectric height. (or another way to say it, your quasi-TEM mode becomes less TEM-like) \$\endgroup\$ – The Photon Jun 5 at 21:45
  • \$\begingroup\$ Oooh OK, now I see. So it is again a type of moding issue. Thank you! \$\endgroup\$ – Ivan Vlaykov Jun 6 at 16:04

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