Dispersion

Updated April 3, 2005

New for April 2005! Frequency dispersion refers to the property of microwave transmission lines that have different group velocity versus frequency. This is true for non-TEM transmission lines such as waveguide and microstrip. For wideband signals, you may have to worry about the effects of dispersion distorting your signal, for example, when you are trying to put a one nanosecond pulse through a waveguide near the lower cutoff frequency, you could be in a heap of trouble.

In quasi-TEM media such as microstrip, dispersion is a well-known phenomenon. The dispersion of microstrip is just a few percent over a moderate frequency band, and can often be ignored.

TEM media

What's TEM mean? Transverse electromagnetic! Coax and stripline are TEM media. We're not sure of the exact conditions that are needed for TEM, but if you have a two-conductor system with a single dielectric constant everywhere, you probable are supporting TEM. This rules out waveguide and microstrip.

Below is a plot generated using Agilent ADS of the group delay of three fifty-ohm transmission lines, each one foot long, realized on Rogers 5880 Duroid (Er=2.3). The purple line (delay(6,5)) is coplanar-waveguide, the green line (delay (8,7)) is microstrip, and the red line (delay(4,3)) is stripline. Note that the stripline provides a constant group delay of 1.54 nanoseconds across frequency, which is very close to the one nanosecond per foot rule, multiplied by the square-root of the dielectric constant. See that the CPW transmission line is also quite constant group delay, but it's value is approximately 1.22 nanoseconds. This is because the effective dielectric constant of CPW is roughly equal to (1+ER)/2, or the average of free space and the substrate dielectric constant, or 1.65 in this case. Neither CPW or stripline is suffers from dispersion.

Now check out the slope on the microstrip group delay... this is what we are talking about when we say frequency dispersion. Why does this matter? Distributed elements formed on microstrip will have less bandwidth than comparable elements formed in stripline. Microstrip is an industry standard for microwave circuits, because it is easy to fabricate. But it is not as good a solution compared to stripline.

Now let's look at the dispersion of waveguide. Below is a plot of the group delay for a 12 inch piece of WR-90 waveguide. It is much more dispersive than even microstrip, especially near the lower cutoff frequency.

Two things to remember about dispersion: for small bandwidths, it is usually not a problem. And the longer your dispersive transmission lines (waveguide or microstrip), the worse the problem gets!