# Low Frequency Dispersion in TEM Lines

Click here to go to our main page on dispersion

Click here to go to our page on TEM mode

TEM transmission lines are widely touted as being dispersion-free, up to the point where they support a spurious mode. This means that their impedance and propagation constant are constant with frequency.

There are approximations that are used at high frequency, when solving for Z0 and propagation constant. The one that gets us into trouble at low frequency is the approximation that R' is small compared to jwL'. If you need to leave that term in the equation, Z0 is revealed to be a complex number!

Here is a good reference on dispersion in coax (updated May 2023 thanks to Marcus)

Referring to our page on transmission line model, the equation for propagation constant is:

Usually we ignore the R' and G' terms, and the equation collapses neatly:

A similar approximation in Z0 takes place. The general form is:

After the approximation you get:

But if R' is large compared to jwL' (as it will be at low frequency), again, you can't make this approximation. the net effect is that delay will be anywhere from 5% to 40% *longer* at low frequency than at microwave frequency. We'll add a graph on this later.

When should you care about this? If you were arraying large antennas (space telescopes) and the baseband signal you are manipulating covers 1 to 500 MHz, then you have a problem on your hands. Trying to put a square pulse down a long coax, you might notice it gets distorted at the receiving end. In electronic warfare, time delay units will have significant delay errors below about 500 MHz.

How do you minimize the effect? short of using superconductors, probably the best you can do is use the biggest conductors possible (largest diameter coax for example).

We believe that expensive simulators such as Agilent's ADS model take this phenomenon into account only in the coax model, which is the easiest transmission line to solve into closed form equations. But what about microstrip and stripline and...?

Out coax calculator spreadsheet, a free download, does NOT take this into account, but it is on our list of things to do.

Anyone would like to contribute to this topic, be our guest(s)!

**Author : **Unknown Editor