## Strange Microstrip Modes

By now, many of you are probably used to looking at the electromagnetic-field-pattern pictures that most signal-integrity simulators produce. These simulators show the pattern of electric and magnetic fields surrounding a microstrip trace (Figure 1). From these field patterns, a simulator can determine the quasistatic values of capacitance and inductance per unit length and, from those values, the characteristic impedance and line delay.

Figure 1—Contours of constant voltage (solid lines) encircle the signal conductor; electric lines of force (dotted lines) connect the signal conductor to the reference plane.

Wait a minute. The quasi-what?

The quasistatic values of capacitance and inductance. "Quasistatic" are the values of capacitance and inductance that you get at low frequencies, near dc.

Do quasistatic values differ from real-world values?

At low frequencies, where the signal wavelength looms far larger than the trace height, the quasistatic values are the correct values.

What about higher frequencies? Is there a place where quasistatic calculations don't work?

Yes there is, and our industry is rushing madly toward it. For example, a 10-Gbps serial data stream with a rise and fall time of 35 psec has a maximum bandwidth (–6dB) of approximately 15 GHz. The wavelength in FR-4 corresponding to 15 GHz is approximately 0.37 in. If you place this signal on a tiny trace, 10 mils wide and 5 mils above the nearest reference plane, the ratio of signal wavelength (0.37) to trace height (0.005) is a comfortable value of 74-to-1. No problem. If, on the other hand, in an attempt to mitigate skin-effect loss, you place the same signal on a huge, fat trace, 120 mils wide and 60 mils high, the ratio of signal wavelength (0.37) to trace height (0.060) is only 6-to-1. Such a small ratio causes big trouble.

What goes wrong?

Whenever the wavelengths of the signals conveyed approach the dimensions of your traces, strange modes of propagation begin to appear. Reference 1 provides a simple proof of the inevitability of these modes. You can't escape them. The idea that electromagnetic fields propagate straight down a microstrip structure in a simple and uniform manner is incorrect. To use a ray-tracing analogy, if the trace floats sufficiently high above the reference plane, a portion of the high-frequency signal power can actually bounce up and down between the trace and the underlying reference plane.

So it bounces. Doesn't all the signal power end up at the far end of the line anyway?

Yes it does, but with different timing from what you may have anticipated. Part of the signal propagates in the normal TEM (transverse electric-and-magnetic) mode straight down the trace, arriving all together at one time. Another part bounces up and down along the way, spending much of its time in the air, and arriving at a different time. This difference in delay for various parts of the signal is called microstrip dispersion.

If different parts of a signal arrive at different times, doesn't the received waveform look distorted?

Yes. That's the whole problem with the microstrip configuration. At frequencies high enough that the signal wavelength becomes comparable with the trace height, the microstrip introduces unavoidable distortion. Full-wave analysis of the microstrip predicts received waveforms that have what looks like severe overshoot and ringing, even if the line is perfectly terminated.

Is this effect similar to multimode dispersion in fiber optics?

Yes. As an optical signal bounces around within a multimode fiber, various modes of propagation spend different proportions of the time in the core of the fiber versus in the cladding. Because the core and cladding have different dielectric constants, the different modes arrive at slightly different times. Manufacturers of low-dispersion multimode fibers gracefully taper the dielectric constant of the glass near the core-cladding boundary to mitigate this effect.

Can I ever use microstrips again?

Of course. For normal digital signaling on FR-4 pc boards at 10 Gbps, you may use any trace height up to 20 mils without encountering significant microstrip dispersion. At lower frequencies, you can use correspondingly bigger traces. At frequencies higher than 10 Gbps, you must use correspondingly smaller ones.

Is there an optimum trace height?

Probably, but how to calculate it remains unclear. Skin-effect resistance varies inversely with the trace width. A fat trace, high above the planes, has little skin-effect dispersion, encouraging designers of high-speed systems to use huge, fat traces. Microstrip dispersion, on the other hand, compounds quadratically with trace height, discouraging the use of big, fat traces.

There's a happy medium somewhere (I think) around a trace height of 20 mils for minimum-dispersion 10-Gbps signaling on copper microstrips.

Does anything else go wrong with microstrips at very high speeds?

Even if the differential delay isn't bad enough to cause significant dispersion, the patterns of current flow associated with the non-TEM modes tend to concentrate the current near the edges of the trace, exacerbating the (already-horrible) skin-effect losses. A full-wave 3-D electromagnetic-field simulator can show you this effect.

Whatever trace size you use, the dielectric losses will always severely limit the attainable distance. Dielectric losses can be improved only by using a better dielectric material.

Do the same things happen on a stripline trace?

Microstrips suffer from the discontinuous boundary between the dielectric and the air. Electromagnetic fields can bounce off this boundary. A stripline is embedded between two solid reference layers, completely embedded in a uniform dielectric medium. There's no bounce. Striplines don't develop the multimodal dispersion problems that microstrips do. The field patterns in a stripline are exclusively TEM.

How do I fix microstrip dispersion?

First, don't let it sneak up on you. If you are planning a 10-Gbps system, get (or borrow) a full-wave 3-D electromagnetic-field simulator. Don't use megasized traces, and watch out for the extra resistive loss due to current concentration. You might try a lower-dielectric-constant substrate; it exhibits less of the effect. Alternatively, try a stripline. As a last resort, you can glue an extra piece of dielectric on top of the offending microstrip. It can somewhat reduce, but not completely cure, the microstrip dispersion.

### Reference

[1] Gupta, KC, et al, Microstrip Lines and Slotlines, Artech House, 1996.