An exploration of a cophased collinear array with coax phasing stubs explored various structures for encouraging co-phase operation of a 3/4λ vertical over perfectly conducting earth (PCE).
This article expands that set with NEC-4.2 models of some variations on the traditional Franklin form of the antenna.
Let’s start with review of the traditional Franklin form
Franklin form
The graphic above shows the topology of the Franklin form. It comprises a half wave vertical element over a quarter wave element, with a quarter wave horizontal s/c stub as the device to encourage co-phased operation of the elements. The current magnitude and phase distribution is shown in green.
The current in the upper and lower element are approximately co-phased.
The radiation pattern above is evidence of the co-phased elements, maximum gain is high and at 0° elevation, and the pattern is slightly skewed by the asymmetric structure.
It is commonly explained that the stub device works because it is a half wave delay line following the conductor path from lower element to upper element connections. This is an incomplete explanation, as is evidenced by the failure of the stub if contained coaxially inside one of the elements. There is more than simply the differential mode currents of the stub at play.
When the system is adjusted for the classic current distribution, the linear distance around the stub is very close to λ/2.
Circular Franklin stub
Others have shown that forming the Franklin stub into an arc concentric to the vertical elements works properly. This enables a more compact structure with more symmetric pattern that can be further improved by changes to the stub geometry.
Folding the Franklin stub into a loop
Another variation is to fold the stub back around the vertical elements, opening the transmission line into the form of a one turn loop.
The graphic above shows the topology of the modified Franklin form. It comprises a half wave vertical element over a quarter wave element, with a shorter stub and single turn loop concentric with the vertical elements to complete the phasing device. The current magnitude and phase distribution is shown in green.
When the system is adjusted for the classic current distribution, the linear distance around the stub and loop is 95% of λ/2.
Folding the Franklin stub into a two turn loop
A further variation on the one turn loop is a short TL section with two turn loop about the vertical elements.
The graphic above shows the topology of the modified Franklin form. It comprises a half wave vertical element over a quarter wave element, with a shorter stub and two turn loop concentric with the vertical elements to complete the phasing device. The current magnitude and phase distribution is shown in green.
When the system is adjusted for the classic current distribution, the linear distance around the stub and loop is 102% of λ/2.
Longer coil devices
The trend observed so far sets the pattern that as the radius is decreased, overall length of the coil and number of turns is increased, that the helix length for proper current distribution increases towards 200% of λ/2.
(Huggins 2012) showed a variation with a longer narrower coil and considerably greater vertical separation of the co-phased elements to achieve slightly higher gain.
The graphic above shows the topology of a structure similar to Huggins. The current magnitude and phase distribution is shown in green.
The increased vertical separation achieves higher gain, but creates more distinct higher lobes.
Closing notes
These are all models created in NEC-4.2. They use a PCE, and thin wire. Practical antennas might use a radial ground plane for feed line decoupling, and the structure would usually be located some height above real ground. All of these factors will result in different behavior to some extent, most notably that maximum gain will no longer be at 0° elevation. Needless to say that none of these designs has been proven by measurement of a prototype.
References
Duffy, O. Mar 2009. An exploration of a cophased collinear array with coax phasing stubs accessed 17/11/2018.
Huggins, J. Aug 2012. Improving the Super-J. https://www.hamradio.me/antennas/improving-the-super-j.html accessed 17/11/2018.