here to go to our main page on microwave transmission lines
here to go to our main page on microwave connectors
here to go to our page on RF cables
Click here to go to our page on waveguide-to-coax transitions (new for January 2013!)
Click here to learn about the undesirable TE11 mode in coax (new for October 2013!)
Watch this video
on the "Antelope" solid state power amp to learn about
the future of coax!
Our coax page is sponsored by Nuvotronics since 2010. Their PolyStrata copper conductor/air-dielectric technology is coax
for the twenty-first century, born from a Darpa
program. Be sure to check out our page on rectangular
symbol image for coax shown here is provided in our free schematic
symbols download which you can find
now has the most information on coax of any web site or text book
on the third planet. And we plan to add a lot more. Coax is unique
in that it is the easiest transmission line to analyze, most coax
properties can be described with exact closed-form equations. Not
like stripline, microstrip
or coplanar waveguide...
Go to our download
area and get the new Coax.xls spreadsheet! It calculates and
plots (over frequency) three types of loss (metal, loss tangent,
and dielectric conductivity), and uses a "more exact"
metal loss calculation, so it is more accurate (and way more convenient
and infinitely cheaper) than EDA software
such as Agilent ADS. It just might be our coolest spreadsheet yet!
There is also a new multi-dielectric coax spreadsheet in the download
area for your enjoyment, thanks to Alex!!
Here are the coax topics covered
on this page and other related pages:
and inductance per unit length
impedance of coax
coax impedance (separate page)
(and square) coax (separate page)
power handling (separate page)
loss calculations (separate page)
more exact calculation of coax loss due to metal (separate
derivation of coax loss due to dielectric loss tangent (separate
due to dielectric conduction (separate page)
fifty ohms? (separate page)
coax (separate page)
Coaxial cable is the solution
to many problems, from wide bandwidth, to low loss and high isolation.
Ask your cable company how many miles of it they string just so
you can enjoy the next “Tyson-Jameson Encounter” for 15 seconds.
Thanks for the Tyson update, James!
Coax provides the very desirable
mode of transmission. The filling
factor for coax is unity, and "Keff"
is equal to ER. Coax has no lower cutoff frequency (like waveguide
A coax transmission line (we
prefer the nickname here at Microwaves101 instead of the more academic
term "coaxial") consists of two round conductors in which one
completely surrounds the other, with the two separated by a continuous
solid dielectric (or sometimes by periodic dielectric spacers),
as shown below:
and inductance per unit length
These formulas are the exact
calculations for capacitance and inductance per length for coax
cable. We'll try to stick with the "prime" nomenclature
whenever we are talking about quantities that are normalized per
Note that the units of D and
d don't matter, both calculations only use the ratio D/d. We can
simplify them, noting that R
is usually =1 for any dielectric we might be interested in. Then
the equations can be expressed in SI units (per meter):
or in English units (per foot)
Characteristic impedance is always
the square-root of the ratio of inductance per length to capacitance
This can be simplified to the
familiar equation that is shown in almost all coax cable and feedthrough
wavelength and frequency
What is meant by the cutoff frequency
fc? The desirable TEM mode is allowed to propagate at
all frequencies, but at frequencies above fc the first higher-order mode called TE11 is also allowed to propagate. Higher-order mode that will screw up
your loss and VSWR and as they have different propagation velocity than
the TEM mode and will interfere with it. Higher modes will be
excited at small imperfections, bends, etc., but below cutoff they rapidly dissappear along straight sections of coax.
To be sure that only one mode propagates, thus keeping the signal
clean, you will need to stay below fc. To obtain good
performance at higher frequencies, smaller diameter cables are required
to stay below the cutoff frequency (thanks for the correction,
Gary!) This is the reason that precision air-dielectric connector families have progressed
from 3.5mm, to 2.9mm, to 2.4mm, to 1.85mm and now to 1mm as microwave
applications have moved from X-band to W-band frequencies. For more
info on connector species, check out our section on microwave
In order to minimize losses due
to skin depth, you want to use the BIGGEST coax cable you can that
won't support TE11 mode . The criteria for cutoff is that the circumference
at the midpoint inside the dielectric must be less than a wavelength.
Note: this is an APPROXIMATION of a transcendental equation which
must be solved numerically. If you are interested in reading about
the true solution, we suggest you pick up a copy of
If you have half a brain, like
us, you can easily prove to yourself that the average circumference
times the average of the inner and outer diameters. Therefore the
cutoff wavelength for the TE11 mode is:
Here the units must be consistent,
so use meters for d and D to get cutoff wavelength in meters. In
the above equation, we didn't take into account the reduction in
wavelength when a dielectric (or magnetic) material is used as the
coax insulator. So the cutoff wavelength for arbitrary dielectric
Now let's convert that to cutoff
frequency instead of cutoff wavelength:
Last, we offer simplifications for
cutoff frequency in both SI and English units, with the assumption
is usually =1 for any dielectric we might be interested in. We've
also tweaked the equations so units for frequency are GHz (instead
Microwaves101 Rule of thumb #117. New for October 2013.
The 90% rule: coax is never specified to operate beyond 90% of its TE11 cutoff frequency. Below is a list of commercial connector species' cutoff frequencies we calculated using our downloadable coax speadsheet, and the ratio of recommended to actual cutoff frequencies.
Calculated TE11 cutoff frequency
|Recommended maximum frequency
% cutoff frequency at
New for October 2013: we tried to compare the TE11 mode to TEM in Powerpoint. Not a very successful effort, there are better sketches dating back to WWII RadLab. What did that third grade teacher tell us on the playground 50 years ago? The important thing is we tried. Nah, that's BS, we failed. Someone send us some good plots generated in 3D EM tool and we'll send you a free gift!
TEM mode, cable sliced at maximum E-field strength
TE11 mode, cable also sliced at maximum E-field strength.
What we failed to capture is that there are field lines on the east and west side that start and stop on the outer jacket and by looping out and back. Note that in TE11 mode, the magnetic fields are no longer purely transverse, they point in radial and longitudinal directions, and as always, forming closed loops.
industry-standard coax cables
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