Amateur Radio (G3TXQ) - Coaxial Antennas

From time to time I see suggestions that wire antennas can be constructed using coaxial cable for their elements as a way of reducing their size by exploiting the Velocity Factor of the cable. At first sight this is an attractive option: using typical 50 Ohm coax cable it might shrink an antenna to 67% its full size value. But I have often puzzled why, if it is that simple and effective, the technique is not more widely used. I decided to carry out some experiments, backed up by computer modelling, to explore the technique in more detail.

A. Does the use of coaxial elements reduce antenna size?

I constructed a simple horizontal dipole with each half comprising RG58 coaxial cable about 35 inches (900mm) long. I measured its lowest SWR, and the frequency at which the minimum SWR occured, for 5 different ways of connecting the inner and braid of the coax at the feedpoint. The 5 configurations were:

1. Inners disconnected - fed between the braids
2. Inners joined to one another - fed between the braids
3. Braids disconnected - fed between the inners
4. Braids joined to one another - fed between the inners
5. Inners connected to their corresponding braids - fed between the braids

For each of these 5 configurations I made measurements with the tips of the elements firstly shorted, and then open circuit - making 10 combinations in total.

Configuration 4 failed to produce any noticeable resonant dip in SWR, with or without the tips short circuited. Of the remaining 8 combinations, all but one resonated in the range 72-76 MHz, typical for a conventional dipole of this size.

In passing, note that these findings confirm that replacing the Reflector element of a parasitic wire beam with a single piece of coaxial cable whose inner conductor and braid are shorted at the tips cannot exhibit any Velocity Factor shortening effect, even though I have seen this advocated in some designs published on the Web.

Just one combination exhibited a significantly lower resonance - at 49.5 MHz. It was configuration 3 with the tips short circuited, and is illustrated in the diagram to the right. Not only was the resonant frequency lower, it exhibited a surprisingly good match to 50 Ohm (VSWR = 1.1).

The drop in resonant frequency from 72 MHz to 49.5 MHz (68%) appears to indicate that the Velocity Factor of the coaxial cable does indeed shorten the dipole by an equivalent factor.

B. What is causing the reduction in size?

It is too simplistic to assume that using coaxial cable in place of a normal single wire element must produce a reduction in resonant length by virtue of its lower velocity factor. There is more going on here than at first meets the eye!

It is important to understand that the Velocity Factor of coaxial cable is a measure of the speed at which RF energy travels along the transmission line; and this in turn is dependent on RF energy being stored in the dielectric material which insulates the braid from the centre conductor. For energy to be stored in this dielectric, there must be a voltage differential across it, and this in turn means there must be opposing currents flowing in the braid and the centre conductor. If we examine all of the 10 combinations used in my experiment we will see that only in the configuration illustrated above is there a mechanism for producing these opposing currents; so it's not surprising that this is the only configuration that produces any significant shortening effect.

The diagram to the right illustrates, for one half of the dipole, the various current paths involved. The Red arrow shows the current flowing down the centre conductor of the coax from the feedpoint. There is an equal and opposing current shown by the Green arrow which is constrained to the inner surface of the braid. Finally, shown by the Blue arrow, there is a current flowing down the outside surface of the braid. If you doubt the ability of the braid to carry separate currents on its inner and outer surfaces, just think for a moment how a coaxial feedline often carries the differential-mode currents which drive an antenna whilst at the same time carrying (often troublesome) common-mode currents on its outer surface.

The next step in our understanding is to realise that only the Blue current can contribute to radiation from the antenna; the Red and Green currents are in opposition and cannot contribute because their fields cancel. It is therefore legitimate to think of each half of the dipole as a radiating element carrying the Blue current and a separate coaxial transmission line element carrying the Red and Green currents; moreover, because the transmission line element does not radiate we can draw it as a separate entity in any orientation we like, as shown on the right. In fact this is the recommended method of modelling coaxial radiating elements. To quote from the EZNEC computer modelling "Help" documentation:

"A radiating coaxial cable can be modeled quite well with a combination of transmission line model and a wire. The transmission line model represents the inside of the coax, and the wire represents the outside of the shield. The wire is the diameter of the shield, and connected where the shield of the actual cable is."

Broken down into its component elements this dipole is now a lot easier to understand. The radiating element forms a conventional large diameter conductor, whilst the coaxial element forms a short-circuit stub in series with the feedpoint.

Now consider the behaviour of the antenna at a frequency where the length of the coax cable is just short of an electrical quarter wavelength. Because the radiating element is not subject to any Velocity Factor effect, it is well short of a quarter wavelength and so its complex feedpoint impedance will exhibit a large capacitive reactance. The short-circuit coaxial stub, being close to an electrical quarter wavelength, will represent a large inductive reactance in series with the feedpoint; this will cancel the capacitive reactance of the radiating element and bring the system to resonance. In fact the stub needs to be just short of an electrical quarter wavelength long; if it were exactly a quarter wavelength long it would theoretically represent an infinite reactance.

So we can see that the shortening effect is not caused by a radiating element that is somehow scaled in size by the Velocity Factor. Rather, it is an electrically-short radiating element that is brought to resonance by the inductive loading produced by a short-circuit coaxial stub. The distinguishing feature of the technique is that the inductive loading stub is conveniently made part of an "existing" antenna element.

C. What's the catch?

i) Losses

I modelled my experimental dipole using EZNEC, employing the modelling device discussed above whereby the transmission line component is separated from the radiating element. The model predicted resonant frquencies, SWRs and impedances in close agreement to my measured results, giving me confidence that the model is valid. It will be instructive to use the model to explore some of the finer detail of this technique

Firstly, we will model the experimental dipole without the inductive loading effect of the coaxial stubs. At 49.5 MHz we would expect the feedpoint impedance of the unloaded dipole to be highly capacitive and for the radiation resistance to have dropped significantly from its "full-size" value of 72 Ohms; reassuringly, the model predicts an impedance of 20-j400 Ohms.

Let's now separately model the short-circuit coaxial stub. We find that at 49.5 MHz the stub exhibits an impedance close to 0+j200 Ohms. This fits our model nicely: the inductive reactance of the two stubs (2 x +j200) cancels the capacitive reactance (-j400) of the radiating elements, leaving a purely resistive component of 20 Ohms. But wait ..... this ought to result in an SWR figure of 2.5:1, whereas I measured a much lower value.

What we have not yet factored into the model are the losses in the coaxial stubs. At first sight we may think these losses are not significant - after all, a 900mm length of RG58 has a matched loss of only 0.1dB at 50 MHz. However if we look more carefully at the effect of this loss on the stub's performance as an inductor we shall find that is very significant indeed:

The Smith Chart plot shown above in green represents the impedance of a short-circuit stub as it's length is increased. The left-most point represents the short-circuit, and as the stub's length is increased the impedance "moves" clockwise around the "zero resistance" perimeter of the chart, exhibiting increasing inductive reactance, until at 900mm it's impedance is essentially 0+j209 Ohms. But if we now factor in the cable loss, we get the plot shown on the right in red. As expected, the loss has caused the impedance plot to spiral slightly inwards towards the centre of the chart and away from the "zero resistance" perimeter. Although the movement inwards is only slight, in this high impedance area of the Smith Chart it has added a resistive component of 13 Ohms. This represents a Q Factor of only 16.

In total the two stubs will introduce an extra 26 Ohms resistance which, added to the 20 Ohms of the radiating elements, produces a total of 46 Ohms and an excellent SWR of 1.08 - very close to the 1.1 figure I measured. The bad news, of course, is that this stub resistance of 26 Ohms absorbs power and reduces our radiated signal by over 3dB. We would have done better to replace the stubs with 0.65uH lumped inductors - with an inductor Q of around 200 the loss would be reduced to less than 0.5dB.

If our dipole had a radiation resistance significantly lower than 20 Ohms, the effect would be even more marked. For example, I modelled a shortened 9MHz Hexbeam driver constructed from RG58; it had an "unloaded" feedpoint impedance of 5-j500 Ohms. The loading stubs each exhibit an impedance of 45+j250 Ohms (Q=5.5), resulting in an aggregate feedpoint resistance of 95 Ohms, of which only 5 Ohms is contributing to radiation; the result is a massive 13dB reduction in transmitted signal.

ii) Bandwidth

The 2:1 SWR bandwidth of a full-size dipole is typically around 8% of its centre frequency, whereas for a coaxial dipole with lossless stubs it is just 1%. The explanation is that the inductive reactance of a quarter-wave stub varies abruptly with small changes of frequency; worse still, its reactance changes in a direction which exacerbates the situation: as the frequency drops, the capacitive reactance of the dipole increases, whereas the stub's inductive reactance decreases. The result is that there is only a narrow band of frequencies over which the stub can cancel the capacitive reactance of the radiating elements.

When stub losses are factored into the model the SWR bandwidth improves somewhat (because the Q is lowered) but only to 1.8%. Again, lumped inductor loading would have been a better option. An inductor's reactance does not change so abruptly with changes of frequency and this option delivers an SWR bandwidth of 2.5% without the punitive losses of the stub; it also offers the flexibility to place the loading somewhere other than at the centre of the dipole with further improvements in bandwidth.

iii) Antenna size reduction

Although the use of coaxial elements can reduce the size of some antenna dimensions, other dimensions may remain unaffected. For example in a 2 element Yagi the Driver / Reflector spacing would stay substantially the same even if the elements were able to be shortened. It is naive to expect that the antenna will "shrink" uniformly in all dimensions. LB Cebik modelled a version of the VK2ABQ 2-element array built with RG58 cable and found that the perimeter of the antenna was only reduced to 80% of the full-size version - not the 67% which might have been anticipated - simply because the end spacing had to be increased in order to preserve the antenna's performance.

If this is not appreciated, performance is likely to be very disappointing. By way of example, I took the dimensions of a 20m Hexbeam and simply replaced the wire elements with RG58 coax. Encouragingly, the resonant frequency dropped to under 9MHz, but there were massive losses of 15dB and the F/B never bettered 3dB. The feedpoint impedance was above 100 Ohms - something that should really set alarm bells ringing on a small antenna.

D. Conclusions

We conclude that the use of coaxial cable can reduce an element's length by something approaching the Velocity Factor of the cable. However, the penalties are significant power losses and a much reduced performance bandwidth. Finally, in anything other than a simple dipole, the size reduction is likely to be significantly less than that predicted by a simple scaling based on the Velocity Factor.