Coax

Updated December 30, 2012

Click here to go to our main page on microwave transmission lines

Click here to go to our main page on microwave connectors

Click 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!)

Watch this video on the "Antelope" solid state power amp to learn about the future of coax!

New for August 2010! Our coax page is sponsored by Nuvotronics! 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 coax, we'll be adding more material there shortly. Welcome aboard, Nuvotronics!

Microwaves101 by 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:

Coax overview

Capacitance and inductance per unit length

Characteristic impedance of coax

Cutoff wavelength and frequency

Some industry-standard coax cables

Coax cable vendors

Off-center coax impedance (separate page)

Rectangular (and square) coax (separate page)

Coax power handling (separate page)

Coax loss calculations (separate page)

A more exact calculation of coax loss due to metal (separate page)

The derivation of coax loss due to dielectric loss tangent (separate page)

Loss due to dielectric conduction (separate page)

Why fifty ohms? (separate page)

Multi-dielectric coax (separate page)

Coax overview

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 transverse-electromagnetic (TEM) mode of transmission. The filling factor for coax is unity, and "Keff" is equal to ER. Coax has no lower cutoff frequency (like waveguide does).

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:

Capacitance 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 unit length.

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

Characteristic impedance is always the square-root of the ratio of inductance per length to capacitance per length:

This can be simplified to the familiar equation that is shown in almost all coax cable and feedthrough catalogs:

Cutoff wavelength and frequency

What is meant by the cutoff frequency f_c? The desirable TEM mode is allowed to propagate at all frequencies, but at frequencies above f_c an ugly higher-order mode is also allowed to propagate. This mode will be excited at small imperfections, bends, etc., and it will propagate with a different phase velocity and interfere with the TEM mode. To be sure that only one mode propagates, thus keeping the signal clean, you will need to stay below f_c. 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 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 connectors!

In order to minimize losses due to skin depth, you want to use the BIGGEST coax cable you can that won't support a TE11 mode (a higher-order mode that will screw up your loss and VSWR and has a different propagation velocity than the TEM 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 Pozar's book.

If you have half a brain, like us, you can easily prove to yourself that the average circumference is just 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 is:

Now let's convert that to cutoff frequency instead of cutoff wavelength:

Some industry-standard coax cables

This material was moved here.