Coax
Updated August
29, 2008
Click
here to go to our main page on microwave transmission lines
Click
here to go to our main page on microwave connectors
New for August
2008! We finally stated adding content to our page on coax
power handling!
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 the 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!
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 pert 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
fc? The desirable TEM mode is allowed to propagate at
all frequencies, but at frequencies above fc 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 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 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:

Last, we offer simplifications for
cutoff frequency in both SI and English units, with the assumption
that R
is usually =1 for any dielectric we might be interested in. We've
also tweaked the equations so units for frequency are GHz (instead
of Hertz).

Some
industry-standard coax cables
Below is a table the characteristics
of many popular coaxial cables. If you are a cable vendor and would
like to help us by contributing some in-line technical content (and
advertise your wares) on this page, drop us an appropriate bribe
at Marketing@microwaves101.com
and get in on the ground floor of a truly great thing before your
competition eats your lunch!
RG cables refer to an ancient
MIL spec, where RG refers to "radio guide". These
are typically not used beyond a few GHz.
SR cables refer to semi-rigid.
D is the outer diameter of the
dielectric, and d is the diameter of the center conductor.
One of these days we'll compile
more cable data and offer it as an Excel download.
Feel free to contribute!
| Cable Type |
OD
(inches)
|
D
(inches)
|
d
(inches)
|
Z0
(ohms)
|
fc
(GHz)
|
| RG-8A |
0.405
|
0.285
|
0.089
|
50
|
14.0
|
| RG-9A |
0.420
|
0.280
|
0.085
|
51
|
14.2
|
| RG-58A |
0.195
|
0.116
|
0.031
|
50
|
35.3
|
| RG-59A |
0.242
|
0.146
|
0.083
|
75
|
30.5
|
| RG-62A |
0.242
|
0.146
|
0.025
|
93
|
32.2
|
| RG-174 |
0.100
|
0.060
|
0.019
|
50
|
65.6
|
| RG-196 |
0.080
|
0.034
|
0.012
|
50
|
112
|
| RG-214 |
0.360
|
0.285
|
0.087
|
50
|
13.9
|
| RG-223 |
0.216
|
0.113
|
0.037
|
50
|
34.6
|
| SR-085 |
0.085
|
0.066
|
.0201
|
50
|
60.2
|
| SR-141 |
0.141
|
0.1175
|
0.0359
|
50
|
33.8
|
| SR-250 |
0.250
|
0.210
|
0.0641
|
50
|
18.9
|
Coax cable
vendors
Sorry, we no longer recommend
coax cable vendors for free! Mr. Cable Vendor, you can put a banner
ad here, if you show us the money! Why would you want potential
cable customers to see your name on this page 1000 times per month?
The internet isn't just for porn, Einstein!
|