here to go to our main page on transmission lines
here to go to our main page on coax
This page has two rules
of thumb: the air coax rule, and converting to round coax conversion rule.
What do you call
a coaxial transmission line that is square or rectangular in cross-section,
instead of the usual round variety? The general case of rectangular
transmission lines we'll call rectax, although we've heard the term
"recticoax" used. Reminds us of an old joke about an unfortunate
cow, but we'd better not go into that here...
The word "coaxial"
implies that the conductors nominally share the same centerline.
However, we don't want to make such restrictions on the technology,
that's another reason why we'll use "rectax" in favor
The words "rectax",
"recticoax", and "squarax" are all examples
When would you use
a rectax a transmission line? Whenever it is economical! You might
consider using the technology that DARPA is developed under the
3D-MERFS program described below, which provides
a very low-loss transmission line structure that is capable of carrying
millimeterwave frequencies at unheard of low loss and is manufactured
in a batch process.
Advantages of rectax
What are the advantages
of rectax, versus waveguide, stripline, or microstrip? The tradeoffs
of any transmission line start with its attenuation characteristics.
Read our page on transmission line
loss, to become familiar with the four loss mechanisms C,
Compared to stripline,
you can get about half the RF loss due to metal (C)
in the same height. This is because all four sides of the center
conductor are are exposed to the RF current. Recall that the loss
of a transmission line is related to skin
depth, which limits how far into the conductor the EM wave penetrates.
The metal loss comparison to microstrip is even more favorable.
Like coax, rectax
provides a pure TEM mode, which means no dispersion,
which you would encounter in waveguide and to a lesser extent in
microstrip. Well, in truth there is always low-frequency
dispersion for any TEM mode with non-infinite conductivity.
The shielded structure
rectax offers excellent isolation for adjacent signals, as good
as coax or waveguide. In microstrip or stripline, bringing traces
anywhere near each other spells isolation problems that are not
Rectax has similar
properties to coax, in that its characteristic impedance doe not
change when the cross-section of the squarax is scaled up or down.
There is a limitation on upper frequency that the squarax line can
pass before funny modes that you want to avoid start to occur. Just
like coax, rectax has a cutoff frequency that you don't want to
The square case
(height = width) we will call squarax (square-coax, get it?)
Now it's time for
a Microwaves101 rule of thumb!
For air-filled squarax, a characteristic impedance
is achieved when the center conductor's height and width are 40%
of the width and height of the cavity.
3D-MERFS program (now known as PolyStrata)
3-D Micro Electromagnetic Radio Frequency Systems (3D-MERFS) program
represents one of the few new transmission lines to come along in
a lifetime, ranking up there with stripline, microstrip and coplanar
waveguide. It's also a rare example of a DARPA program that spun
off a private company to commercialize a technology that we taxpayers
paid for: Nuvotronics, in Blacksburg VA. We won't add a link here
because they aren't a Microwaves101 sponsor, but you can probably
find their web site even without googling it... by the way, the
unfortunately-named 3D-MERFS platform is now called "PolyStrata".
If you call on Nuvotronics, tell them you heard about PolyStrata
on Microwaves101! Nuvotronics sponsors
our page on coax.
We found this image
on www.darpa.mil. 3D-MERFS creates miniature air-dielectric rectangular
coax by sequentially plating thick layers of copper, much like a
printed wiring board process. The openings are vertical transitions
that you can access using CPW probes. This picture doesn't do justice
to the types of circuits that you can build, one important feature
is that you can have fully shielded RF lines crossing over each
other. You can't do that in microstrip or CPW, and shielded crossovers
would make stripline way more complicated!
2009: Here's an article in Microwave
Journal that provides background information on 3D-MERFS (PolyStrata). Some of the data
on 3D-MERFS may be subject to ITAR. We copied
this info from DARPA's web site so you don't have to go looking
The 3-D Micro
Electromagnetic Radio Frequency Systems (3-D MERFS) program was
launched in mid-2004 to revolutionize the performance, cost, and
form factor for advanced RF and MMW radar and communications systems,
thereby fulfilling the unmet military & national security need
for widely deployable high-performance multifunction MMW systems.
Such systems include secure high-data rate communications, vehicle
protection radar, on-the-move satellite communication systems, and
compact solid-state missile seekers. Although prototype systems
with some level of performance can be realized for most of these
applications, these prototypes are typically heavy, bulky, fragile,
UN-mass producible, lack desired capabilities, and often cost 1000
times more than established cost targets.
Much of the difficulty associated
with MMW systems arises because there exists no MMW analog to the
Printed Circuit Board (PCB). Thus, instead of integrating MMW components
compactly on a single system-scale substrate as is done in digital
computers, MMW components are typically manually assembled, first
at the module level, then the rack level, and then at the system
level, thereby degrading performance and reliability, and making
the systems UN-mass producible.
Through developing a printed
circuit board analog for MMW systems, the 3-D MERFS program seeks
to extend the same system-level integration paradigm used in digital
systems to MMW systems. The program is developing a novel high performance
printed circuit board technology for MWW/RF, that instead of using
planar microstrip waveguide structures, uses 3-dimensional recta-coax
structures - recta-coax much like the wire that carries cable-TV
to your home, but 1000s and 1000s of them, miniaturized and integrated
into one monolithic substrate.
Though made only of low cost
metal and plastic, these structures outperform transmission lines
printed on the most expensive semiconductor materials - with 10x
less loss, carrying 10x-100x more power, with 100x component density,
and having >1,000x better isolation. They also have much better
dispersion, enabling Broadband operations.
If you want to simulate rectangular
coax with a linear simulator such as Microwave Office or ADS, you
can model it quite accurately as a round coax line, subject to one
condition described below. Just compute the perimeter of the center conductor cross-section (2T+2W) and divide it by pi to get the diameter
of an equivalent coax (thanks to Cheng for the correction!) Set the outer conductor to whatever you need
to get the impedance you want (generally 50 ohms). Example: a fifty-ohm
rectax with 200 x 300 um diameter, is equivalent to a round coax
with 318 um diameter center conductor (1000/pi).
What's the caveat? the E-fields
are distributed such that the capacitance/length of the four faces
are equal. So the gap is wider along the wider dimension.
If someone wants to follow up with an HFSS analysis of rectax that
we can correlate to a round model, we'd appreciate it!