## Strange Microstrip Mailbag

I would like to thank you for your April 26, 2001 column in EDN, "Strange Microstrip Modes." I almost followed it but I have a few problems. Starting near the bottom with the first column, you address a ray-tracing analogy and talk about a portion of the high-frequency signal power bouncing up and down between the trace and the underlying reference plane. I'm o.k. with this and I understand the different arrival times. However, near the top of the second column you speak of... "Another part bounces up and down along the way, spending much of its time in the air, and arriving at a different time." I thought we were between trace and reference plane, which is FR-4, not air. If we bounced off the top of the trace, what would bring us back? Wouldn't we just radiate?

So ... If we stay between the reference plane and the trace, I understand this high-frequency dispersion (I'm assuming the really high frequencies propagate slower due to their longer path length). But then I don't understand why stripline would not have the same difficulty. It would seem that the bottom of the trace would bounce signals off the bottom reference plane while the top of the trace would bounce signals off the top reference.

Would appreciate any light you could shed on my confusion. Thank you.

Thanks for your interest in High-Speed Digital Design.

In a ray-tracing sense, the waves (for a microstrip) are bouncing between the reference plane and the dielectric-to-air interface (not off the trace itself). As they bounce (and I don't have a good way to describe this) they seem to spend some portion of the time in the air above the dielectric-to-air interface, and so go faster than you would think - enough faster to overcome the natural disadvantage they have due to the longer path length over which they must travel. If this doesn't make total sense (and I admit it doesn't) we have to chalk it up to the inadequacy of the ray- tracing analogy. To fix this problem, ray-tracing enthusiasts insert a phase constant at the point of reflection that changes the phase of the reflected wave just enough to account for the faster propagation that actually occurs. The best descriptions of microstrip dispersion I have seen are in these two books:

K.C. Gupta, "Microstrip Lines and Slotlines", 2nd ed., 1996, Artech House, ISBN 0-89006-766-X.

Constantine A. Balanis, "Advanced Engineering Electromagnetics", 1989, John Wiley & Sons ISBN 0- 471-62194-3.

Both books describe how the effective dielectric constant associated with a microstrip SHRINKS when you approach frequencies for which the signal wavelengths become comparable to (or even within a factor of ten of) the thickness of the dielectric layer.

The authors of both books describe how the operative mode of propagation for a microstrip is not a pure TEM mode, it is instead called a "quasi- TEM" mode for which the field patterns are mostly TEM, but include a little longitudinal component (of either E or M depending on how you interpret their statements). At higher frequencies, the quasi- TEM mode just happens to propagate a little faster than it does at lower frequencies. It's difficult for me to come up with a better explanation for "why" than the ray-tracing analogy I've supplied.

Another, related issue is how the existence of strange non-TEM modes of propagation in a microstrip will cause a peculiar current concentration along the sides of the trace, above and beyond the skin-effect and proximity-effect distributions you may be used to seeing. This tends to increase the (already horrible) skin-effect losses in microstrip traces.

Striplines don't seem to be quite as susceptible to funny quasi-TEM effects, because waves on a stripline can and do propagate in a perfect TEM configuration. The power contained within the TEM mode propagates at a uniform speed without dispersion at all frequencies (assuming a perfect dielectric with no losses and no intrinsic change in Er over frequency and zero trace resistance).

Of course, every stripline can and does support non- TEM modes. The lowest-order non-TEM modes in a stripline (either TE or TM modes) bounce up and down within the cavity, from reference plane to reference plane. [NOTE: I haven't heard of any analysis of waves bouncing between the reference plane and the trace, only vertically between the two big, solid reference planes that bound the stripline cavity]. The microwave literature suggests that the lowest-order non-TEM mode for a stripline occurs at a cutoff frequency of:

_{c}= (C/sqrt(Er))/(2*B)

**Where:**

- C is the speed of light in a vacuum,
- Er is the relative permittivity of the dielectric medium,
- B is the spacing between planes, and
- f is the frequency in Hz.

Example:For a 0.020-inch cavity filled with FR-4 (Er=4.3) the first-order non-TEM mode happens at:

_{c}= (C/sqrt(4.3))/(2*.020 in.) = 141 GHz

Where:

- C = 11.76E+09 in/sec.

In the stripline configuration you get different
combinations of modes depending upon the frequency
of operation. Below f_{c} you get pure TEM modes.
Above f_{c} you get the same pure TEM modes, plus the
funny bouncing non-TEM wave guide modes. As long as
you stay below fc, the non-TEM stripline modes
simply cannot propagate, so they aren't usually a
problem. It's going to be a while before we have to
worry about 141 GHz.

In the stripline configuration below f_{c} your
signals propagate in a pure TEM mode whose
propagation velocity remains constant at
frequencies from DC all the way up to very near f_{c} (except for consideration of changes in the
dielectric constant of the material and trace
resistance).

The problem with microstrips is the lack of a clean cutoff frequency for non-TEM operation. In a microstrip configuration, as you approach within even 1/10th of fc the apparent propagation velocity of the quasi-TEM mode begins to change, creating microstrip dispersion.

Best Regards,

Dr. Howard Johnson