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

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.

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.

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.

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.

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.

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.

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.

]]>(Tester 2013) described a coaxial collinear array for VHF/UHF. Tester describes the antenna a collinear is a vertical antenna whose resonant elements are connected along a common line (ie co-linear) so that each element is opposite in phase to its neighbour

.

He is a little confused, in fact, the elements are in-phase with each other so that in the horizontal direction, the contribution of the current in each element to the far field is an additive or reinforcing one.

He goes on to say [i]f you are not into antennas, that mouthful is, fortunately, very easy to achieve

… but is it?

Fig 1 is from (Tester 2013) showing the construction.

He gives a formula for each of elements 1 to n as 0.5λ*vf.

Fig 2 shows the detail of the bottom connection. Note that the coax shield is connected to the outer conductor of the coax socket. The coax shield is therefore electrically continuous from the top of element 1 in Fig 1 over some arbitrary length to the equipment, then possibly on the building protective earth system, other radio ground system etc.

No attempt is made at impedance matching, but Tester states [a] properly designed antenna should be suitable for transmitting and receiving, so if you want to use the information later in this article to change dimensions and make (say) an antenna suitable for UHF CB radio (476-477MHz) you can easily do so

.

Though an explanation of operation is given and many claims are made, no measurement data is given in the article to validate operation in accordance with the explanation or confirm the claims.

In fact, as noted previously, the objective is to feed each element so that they are in-phase. So, in this implementation, the connections at each feed point are transposed to offset the 180° phase delay of the feed line within that section.

Failure to obtain in-phase feed spreads the directivity pattern and reduces gain, so phasing is a very important objective, and a concept to have clearly in the mind.

An NEC model was constructed of an antenna system using the design. The nominal radiator is three half waves dimensioned as per the article at 147MHz. To be realistic, the shield conductor is extended 10 quarter waves down to and connected to the ground. For simplicity, the model assumes a non-conducting supporting mast.

Note that the model makes some assumptions as stated in this article, and whilst those assumptions are reasonable for the purpose of showing significant issues with the antenna system design, different variations of feed line, height above ground, number of elements, treatment of any conductive supporting structures could all lead to different outcomes.

Fig 3 shows the current distribution (phase and magnitude) on the 10 quarter wave feed line exterior (common mode current) and the nominal radiator. It can be seen that:

- there is substantial common mode current flowing in the feed line; and
- the current in a small region near the top of the antenna of the antenna is co-phased, but the phase reverses at 2m from the top, and reverses again every half wavelength (~1m) below that, and reverses above a point 1m from the top, it is not in-phase, not nearly.

Fig 4 shows in blue the collinear far field pattern from the model. Lossless radiator gain is less than might be expected from three co-phased half waves with some separation. It has as much gain at high angles as at low angles, a sure sign of failure to achieve the intended directivity and gain. The gain figure does not include feed system loss (including 6.5dB of Mismatch Loss to be explained later).

The red line is a quarter wave ground plane 5m above real ground. It can be seen that the collinear does not have a significantly different pattern at low angles (where gain is a priority). The gain figure does not include feed system loss.

Fig 5 shows the modeled impedance at the coax connector.

If we make the assumption that a 50Ω receiver is connected by 50Ω line to this point, the antenna with source impedance around 680+j266Ω at 147MHz (the design frequency) with 50Ω load has a Mismatch Loss of 6.5dB.

When the Mismatch Loss is factored in, maximum antenna system gain is -2.8dBi (ignoring feed line losses), whereas the quarter wave ground plane would have much lower mismatch loss and maximum antenna system gain of 5.0 dB should be achievable.

If the modeled antenna system was used for transmitting, the VSWR(50) at the coax connector would be 16 @ 147MHz, minimum VSWR(50) is 10.

Whilst there are many issues with the design and the implementation, the single problem that drives the feed line common mode current path in alternating phase is the direct connection of it to the lower antenna element. This design problem hints a failure to understand the principles of operation of a collinear of this type and the role of the feed line.

Fig 6 is of the internals of a 3GHz commercial antenna that probably works (photograph by Martin Ehrenfried G8JNJ).

Note:

- it permits and excites in phase current distribution, at no point where there needs to be a high charge gradient is there a conductor to spoil it (all elements are end fed half waves);
- it has 20 almost half waves, so there are 20 high impedance feed points effectively in parallel which helps get closer to 50 ohms (it appears to have no additional impedance matching);
- the fat sleeve at the bottom is more effective in reducing common mode feed line current than a small diameter one; and
- most of it is silver plated.

An NEC model was constructed of an antenna system based on the design principles laid down in Tester’s article. The model serves as a tool for showing the behaviour of an antenna system based on the design.

The antenna system model casts serious doubt on:

- claims that it is an in-phase collinear array;
- that it has substantial gain; and
- that it has VSWR(50) suitable for transmitting.

- Tester, R. September 2013. Collinear antennas for ADS-B (or anywhere else) In Silicon Chip Sep 2013: 42-48.

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At Yet another dodgy coax collinear I wrote about a design published recently in QST.

More recently, a ‘design’ has emerged in eHam forums that appears to be identical.

These antennas are intended to be some number of close spaced co-phased half waves with a system of coax sections with transpositions at each feed point to provide the co-phase drive.

Given that the elements are fed at near to voltage maxima and they are effectively feed in shunt, it takes many such elements to obtain an impedance anywhere near 50Ω, so short arrays will require some form of impedance transformation if a 50Ω or similar feed point is needed.

There are three common failings with implementation of this type of antenna:

- There is a fundamental problem that the coaxial interior sections and exterior radiating surface cannot both be an electrical half wave unless the velocity factor of the coax is close to unity. The usual compromise is that high vf coax is used and the coax section is cut for an interior length of a half wave, and the less than half wave exterior is suffered with some degradation. The length of the coax section should then be 299792458*vf/f/2 (f in Hz).
- The top section is often wrong. Variously it is effectively around a quarter wave in length or the same length as the coax sections (~65-85% of a free space half wave) when what is needed is about 95% of a free space half wave depending on the diameter of the conductor.
- The bottom section (ie below the bottom feed point) should also be about 95% of a free space half wave depending on the diameter of the conductor, to some form of device to decouple the feed line (quarter wave radials or some form of effective common mode choke). This is omitted from most published designs.

So with that in mind, lets review the latest eHam forum design.

Above, an extract from the thread… and some more detail on lengths.

- The design uses coax with vf=0.83, an acceptable compromise and the sections should be an electrical half wave at 1090MHz which is 114.1mm, ok so far.
- Note that the top element is the same as the next element, failure #2 listed above. It should be longer.
- The bottom section is not delineated by some form of effective common mode current decoupling, failure #3 above.

The design includes a form of impedance matching, but it is matching a flawed antenna. Fixing the issues mentioned will change the input impedance and that will probably require a changed impedance match.

The impedance match was not shown conclusively to transform the load to 75Ω, but if it did, it suggests that the load offered by the dodgy collinear is around 260+j0 (VSWR(75)=3.5) at the lower coax transposition (not surprising). The Smith chart above (normalised to 75Ω) shows the transformation with 152° of 75Ω line and a series 1.5pF cap.

]]>More recently, a ‘design’ has emerged in eHam forums that appears to be identical.

These antennas are intended to be some number of close spaced co-phased half waves with a system of coax sections with transpositions at each feed point to provide the co-phase drive.

Given that the elements are fed at near to voltage maxima and they are effectively feed in shunt, it takes many such elements to obtain an impedance anywhere near 50Ω, so short arrays will require some form of impedance transformation if a 50Ω or similar feed point is needed.

There are three common failings with implementation of this type of antenna:

- There is a fundamental problem that the coaxial interior sections and exterior radiating surface cannot both be an electrical half wave unless the velocity factor of the coax is close to unity. The usual compromise is that high vf coax is used and the coax section is cut for an interior length of a half wave, and the less than half wave exterior is suffered with some degradation. The length of the coax section should then be 299792458*vf/f/2 (f in Hz).
- The top section is often wrong. Variously it is effectively around a quarter wave in length or the same length as the coax sections (~65-85% of a free space half wave) when what is needed is about 95% of a free space half wave depending on the diameter of the conductor.
- The bottom section (ie below the bottom feed point) should also be about 95% of a free space half wave depending on the diameter of the conductor, to some form of device to decouple the feed line (quarter wave radials or some form of effective common mode choke). This is omitted from most published designs.

So with that in mind, lets review the latest eHam forum design.

Above, an extract from the thread… and some more detail on lengths.

- The design uses coax with vf=0.83, an acceptable compromise and the sections should be an electrical half wave at 1090MHz which is 114.1mm, ok so far.
- Note that the top element is the same as the next element, failure #2 listed above. It should be longer.
- The bottom section is not delineated by some form of effective common mode current decoupling, failure #3 above.

The design includes a form of impedance matching, but it is matching a flawed antenna. Fixing the issues mentioned will change the input impedance and that will probably require a changed impedance match.

The impedance match was not shown conclusively to transform the load to 75Ω, but if it did, it suggests that the load offered by the dodgy collinear is around 260+j0 (VSWR(75)=3.5) at the lower coax transposition (not surprising). The Smith chart above (normalised to 75Ω) shows the transformation with 152° of 75Ω line and a series 1.5pF cap.

]]>Looking at the middle sections first, they are 4.5″ or 114.3mm or 182.45° if made from Belden 1694A RG6 coax. Lets call them a half wave interior electrical length.

For this type of antenna to be co-phased (or in-phase), the crossover points need to be at current minima on the exterior surface and an electrical half wave apart on the interior. Obviously that is not possible unless the coax has vf=1, and the designer has chosen a compromise where the drive phasing is approximately correct and the exterior sections are 82% of a half wave. This is a common compromise, and not too severe in the resultant degradation.

Next, the tip section is also 114.3mm which is 82% of a half wave, and there is no reason for it to be less than a half wave and better approach the objective of a current minimum at each of the 8 feed points that appear in parallel due to the interior electrical length of the sections and the transpositions.

As mentioned, ignoring the effects of coax loss, we effectively have 8 current minimum or high impedance feed points in parallel, and this would be the impedance seen by the feed line entering the bottom transposition.

Or is it???

Well, no, it isn’t. The bottom feed point is not like the others, rather than feeding one side of an almost half wave radiator on each side it has an indeterminate length of radiating feed line outer connected to the lower side. This severely compromises the design.

These types of antennas commonly suffer from problems in the compatibility of the top section and the bottom section with the phasing and current distribution of the middle sections, resulting in compromised gain and poor VSWR.

The author does not give input impedance, or even VSWR measurements, nor does he qualify the design as not suited to a transmitting application. Nevertheless, online discussion reveals that some hams are scaling the design for transmitting application even though it is severely flawed.

Some would argue that the feed point impedance is not important in a receiving application, but it is as the mismatch losses caused by the receiver load might well degrade the system gain to less than that of a simple quarter wave ground plane. The author provides no measurements comparing the design with a reference antenna.

One questions the method of joining the sections electrically. This type of antenna is renowned for noise problems when soldered joints between sections fatigue with flexure of the assembly in the wind and fail, and it seems likely that the construction used in the article will suffer these problems from the outset.

I wrote about these same issues in 9/13 on VK1OD.net (now offline) with an article in Silicon Chip magazine. Both articles may have been sourced from a single flawed Internet posting.

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