frequency dispersion in TEM lines
Updated February 18,
here to go to our main page on dispersion
Click here to go to our page on TEM mode
New for June 2011! 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
Here is a good reference on dispersion
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)!