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# Rectax transmission lines

Updated July 19, 2013

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 of "recticoax".

The words "rectax", "recticoax", and "squarax" are all examples of portmanteaux.

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.

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, D , G and R .

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 easily solvable.

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 exceed.

### Squarax versus rectax

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.

### Rectax equations

Coming soon?

Characteristic impedance

Cutoff frequency

Attenuation

Power handling

### DARPA's 3D-MERFS program (now known as PolyStrata)

DARPA's 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!

Update August 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 for it...

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.

### Rectax Rule of Thumb

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!

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