Having skimmed a presentation published on the net, an interesting example is presented of an 80m half wave centre dipole with feed line and various plots from the nanoVNA used to illustrate the author’s take on things.

The author is obsessed with resonance and obsessed with phase, guiding the audience to phase as ‘the’ optimisation target. Phase of what you might ask… all the plots the author used to illustrate his point are phase of s11.

I have constructed an NEC-4.2 model of a somewhat similar antenna to illustrate sound concepts. Since NEC-4.2 does not model lossy transmission lines (TL elements), we will import the feed point data into Simsmith to include transmission line loss in the model.

Above is the Simsmith model.

The dipole is fed with around 20m (66′) of RG58A/U 50Ω line with vf=0.67.

Above is the Smith chart looking into the feed line (click for a larger image).

There are three markers, from right to left:

- 3.738MHz: phase of s11 is very low (0.006°, approximately zero), Z=129.9+j0.0153Ω, VSWR=2.60;
- 3.636MHz: phase of s11 is very low (0.17°, approximately zero), Z=74.18+j0.0902Ω, VSWR=1.48; and
- 3.600MHz: phase of s11 is nowhere near zero (30.8°), Z=63.22+j9.443Ω, VSWR=1.33

Lets look at the power delivered to the antenna.

Above, we see that the power is maximum at approximately the same frequency as where VSWR is minimum. That is no coincidence, standing waves result in higher line loss in this scenario.

Again the same three markers, and the two frequencies where phase of s11 is approximately zero have higher loss, less power reaching the antenna, than the one at minimum VSWR where phase of s11 is 30°.

It turns out that with practical feed lines and antenna conductors with this type of antenna, the loss in the antenna conductors is small compared to the feed line:

- dipole radiation efficiency is not very sensitive to frequency, small departure from resonance does not change the radiation efficiency of the dipole itself much; and
- feed line loss will be lowest where VSWR is minimum.

So, this antenna system will have best radiation efficiency at 3.6MHz because feed line losses are least.

Where the reference impedance for calculation of the complex reflection coefficient Γ or s11 is real, then when the angle of gamma is zero at some point, the ratio or V/I or impedance at that point is purely real (ie, zero reactance).

That says nothing for the value of the resistance, nor of the magnitude of Γ or s11 or of the VSWR.

Further, when the magnitude of s11 is very small (and VSWR is close to unity), the angle of Γ or s11 as measured is dominated by instrument noise and at the limit is essentially a random number and is meaningless.

So any optimisation based simply on angle of Γ or s11 is naive in the extreme.

Optimisation for phase of load impedance at the source equal to zero means reactance X is equal to zero, but says nothing about the resistance component, and therefore about VSWR.

In the example above, at the frequency of minimum VSWR (least line loss, maximum power delivered to the antenna) the impedance looking into the line has a phase angle of -8.5°.

So any optimisation based simply on angle of impedance seen by the source is naive in the extreme.

It was stated above that the angle (or phase) of s11 or Γ is not the same as the angle (or phase) of Z.

Given Zo and Γ, we can find θ, the angle of Z.

\(

Z=Z_0\frac{1+\Gamma}{1-\Gamma}\)

Zo and Γ are complex values, so we will separate them into the modulus and angle.

\(

\left | Z \right | \angle \theta =\left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \\

\theta =arg \left ( \left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \right )\)

We can see that the θ, the angle of Z, is not simply equal to φ, the angle of Γ, but is a function of four variables: \(\left | Z_0 \right |, \psi , \left| \Gamma \right |, \& \: \phi\) .

It is true that if ψ=0 and φ=0 that θ=0, but that does not imply a wider simple equality. This particular combination is sometimes convenient, particularly when ψ=0 as if often the case with a VNA.

So, pursuit of:

- feed point X equal to zero;
- feed point phase of Z equal to zero; and
- some notion of ‘resonance’ at the feed point

for this type of antenna system are all misguided.

Claims that phase alone is some magic quantity that drives optimisation is misguided.

This type of antenna system can be optimised with the nanoVNA, and the optimisation target is VSWR.

Read widely, don’t accept plausible looking explanations that appeal simply because they appeal, without understanding them, specious works are widespread and swallowed by the gullible.

]]>This article builds an NEC model for an EFHW antenna at 3.6MHz incorporating a realistic model of the above transformer.

NEC provides for a NT card characterising a two port network using Y parameters.

The Y parameter model is based on measured input impedance with port 2 open circuit, and short circuit, and the observed turns ratio.

Impedance was measured with the transformer at 3.6MHz using an AA-600.

Above, the calculated Y parameter model including a prototype NT card. This model captures the various loss components of the transformer, mainly magnetising loss, at 3.6MHz.

Note that the Y parameter model is frequency specific.

Above is a graphic showing the geometry of the NEC model. Essentially the feed point has about λ/10 ‘counterpoise’ at a height of 0.3m to the left of the feed point, and a wire sloping upwards at about 45° for the main antenna conductor.

Although the NT card is frequency specific to 3.6MHz, we get a fair idea of the VSWR response over a narrow frequency range. The minimum VSWR of 1.06 at 3.6MHz is correct.

Above is a summary of the NEC model. Network loss captures the loss in the transformer, and at 100W input the transformer loss is 9W. This is much better transformer efficiency than almost all of the published designs that I have reviewed.

Radiation efficiency is 39%, a combination of conductor loss, transformer loss and ground loss, mostly ground loss.

Above is the pattern, highest gain is at towards the zenith as can be expected of a low antenna. Maximum gain is about 1dBi.

Above, at lower elevation (30°) the pattern shows a little skew due to the sloping radiator.

If this looks like an improvised antenna that performs well, keep in mind that the top of the sloping wire is at 28m height.

The cause is often that the antenna system was changed significantly to connect the analyser.

Seeing recent discussion by the online experts of how the measure the impedance of an antenna system looking into a so-called balanced feed line gives advice that is likely to cause reconciliation failure.

I will make the point firstly that the line is not intrinsically balanced, it is the way the it is used that may or may not achieve balance of some type. I will refer to that type of line as open wire line.

Let’s explore the subject using some NEC models.

I have constructed an NEC-4.2 model of an approximately half wave dipole at 7MHz, it is 20m above the ground, and fed slightly off centre with open wire line constructed using GW elements. At the bottom, I have connected a 2 segment wire between the feed line ends, and two sources in series.

The impedance seen by the sources is 71.66-j217.8Ω. This is what you would expect if you connected your trusty nanoVNA or other stand alone analyser to the lower end of the open wire line.

Job’s done!

Wrong! The measured scenario does not represent what might be seen by a transmitter, it has ignored the existence of the ‘ground terminal’.

Lets model the case where the two sources used are from an ideal voltage balun with its centre ground immediately below. There is a 3m deep ground electrode used as a ground point (NEC-4.2 can do this).

Zooming in on the geometry above, we can see there is significant common mode current on the ground connection, so connecting the voltage balun source has changed the antenna, and now the impedance measures 85.56-j199.5Ω.

This example shows that:

- making isolated two terminal measurements might be quite inadequate; and
- if the measurement scenario does not provide for exactly the same transmission line and common mode current paths, then you are measuring ‘something else’.

Whilst it is often relatively easy to properly maintain the common mode current path when measuring a coax fed antenna, it can be more challenging in the case of open wire feed. If the antenna system includes a balun, it may be more practical to measure looking into the balun (whilst maintaining the common mode current path.

Application of isolated small stand alone antenna analysers to open wire fed antenna terminals is naively over simplified.

]]>The original transformer above comprised a 32t of 0.65mm enamelled copper winding on a FT240-43 ferrite core, tapped at 4t to be used as an autotransformer to step down a load impedance of around 3300Ω to around 50Ω.

The FT114 core has a quite low ΣA/l value (0.000505), essentially a poor magnetic geometry.

A better choice for his enclosure is the locally available LO1238 core from Jaycar (2 for $5) with ΣA/l=0.0009756/m which is comparable with the FT240 form (though smaller in size) and nearly double that of the FT114. The LO1238 is a toroid of size 35x21x13 mm, and medium µ (L15 material).

A more detailed analysis of a 3t primary winding of the effects of magnetising impedance on InsertionVSWR and system loss when it is in shunt with a 50Ω load was performed.

Above is the expected core loss.

Above is the expected InsertionVSWR.

These both look encouraging, and the next step would be to build and measure some prototypes.

Above, VK4MQ’s prototype in development. (I do not recommend the pink tape.)

]]>The original transformer above comprised a 32t of 0.65mm enamelled copper winding on a FT240-43 ferrite core, tapped at 4t to be used as an autotransformer to step down a load impedance of around 3300Ω to around 50Ω.

A very rough approximation would be that with two stacked cores, the number of turns would be around the inverse of square root of two, so 70% of the original.

A more detailed analysis of the effects of magnetising impedance on InsertionVSWR and system loss when it is in shunt with a 50Ω load was performed.

Above is the expected core loss.

Above is the expected InsertionVSWR.

These both look encouraging, and the next step would be to build and measure some prototypes.

To the original question, would half the turns be enough? No. Notwithstanding that, you are likely to find such being used, being sold.

]]>The EFHW can be deployed in a miriad of topologies, this article goes on to explore three popular practical means of feeding such a dipole.

The models are of the antenna system over average ground, and do not include conductive support structures (eg towers / masts), other conductors (power lines, antennas, conductors on or in buildings). Note that the model results apply to the exact scenarios, and extrapolation to other scenarios may introduce significant error.

A very old end fed antenna system is the End Fed Zepp. In this example, a half wave dipole at λ/4 height is driven with a λ/4 600Ω vertical feed line driven by a balanced current source (ie an effective current balun).

Above is a plot of the current magnitudes. The currents on the feed line conductor are almost exactly antiphase, and the plot of magnitude shows that they are equal at the bottom but not so at the top. The difference between the currents is the total common mode current, and it is maximum at the top and tapers down to zero at the bottom. Icm at the top is about one third of the current at the middle of the dipole.

End fed Zepp deals in more detail with the common mode current on the EFZ.

One manufacturer of a popular EFHW antenna system that uses a 2/3 terminal matching device recommends that where the fed end of the dipole is elevated, that the match device be installed there and that the coax be grounded where it reaches ground. In this model, a 2m driven ground electrode is used to ground the coax.

Above, the plot of current magnitudes shows substantial common mode current on the feed line, with a maximum at the lower end approximately the same as the current in the middle of the dipole.

The relatively high common mode current on the feed line, and particularly at lower height is a distinct disadvantage bring risk of higher rx noise and transmitter interference to nearby electronics. The magic of End Fed Half Waves (EFHW) gives further information on the common mode current in this configuration.

This antenna is advertised as “no counterpoise needed” by at least one seller, which questions the term “counterpoise”: https://owenduffy.net/files/Counterpoise.pdf.

One popular author recommends a “0.05λ counterpoise” as he calls it. Again a 2/3 terminal matching device is used the coax is grounded where it reaches ground. In this model, a 2m driven ground electrode is used to ground the coax. This is essentially the same as the previous model but with the dipole fed 0.05λ from end.

Above, the plot of current magnitudes shows substantial common mode current on the feed line, with a maximum at the lower end approximately the same as the current in the middle of the dipole.

The relatively high common mode current on the feed line, and particularly at lower height is a distinct disadvantage bring risk of higher rx noise and transmitter interference to nearby electronics.

This is almost the same as the previous model, the so-called “counterpoise” has done little for the relatively high common mode current.

The three scenarios modelled are quite similar configurations, but the detail of the feed arrangement results in the first being significantly different to the later two.

The third model shows that the so-called “counterpoise” variation to the second model has negligible effect, and questions the credibility of sources suggesting otherwise.

Relatively high feed line common mode current is a risk, again dependent on implementation.

The concept of a “no counterpoise” EFHW as commonly used is questionable.

Because of the sensitivity to implementation detail, the term End Fed Half Wave is not very descriptive.

You might like: more articles on EFHW.

- Duffy, O. Oct 2010. Counterpoise. https://owenduffy.net/files/Counterpoise.pdf.

This article presents some NEC-4.2 model results for a 7MHz λ/2 horizontal 2mm copper wire at height of λ/4 above average ground.

The model is impractical in a sense that it does not include unavoidable by-products of a practical way to supply RF power to the antenna, but it is useful in providing insight into the basic antenna.

The NEC model has 200 segments, and varying the feed segment gives insight to what happens to feed point impedance.

Above, it can be seen that as the wire is fed closer to the end (segment 1), feed point Z includes a rapidly increase capacitive reactance.

The very large series reactance close to the end makes feeding at those points impractical as any impedance transformation network needs to deliver power to a very reactive very high impedance load.

As the feed point approaches the end, the feed point reactance approaches -∞ and the feed point voltage approaches ∞.

Let’s analyse the antenna at a feed point that is close to the end, but a compromise for more practical feed point impedance. We will look at the case at segment 10 (1m from the end) which is 5% of the dipole length or 2.5% of wavelength.

Above is a 3D magnitude and phase current plot from 4NEC2. It can be seen that there is a significant change in phase near the feed point.

Above, the magnitude of current an phase are plotted.

Many authors insist that the behavior of a half wave dipole is independent of where it is fed, that the current distribution is exactly identical for all feed points, and often give the familiar sine current distribution to support their argument.

The chart above shows that the magnitude of current is close to a sinusoidal distribution, but there is a glitch near the feed point… but more importantly there is a significant variation in phase in the last quarter wavelength, culminating in a discontinuity at the feed point.

The current distribution is not the same as a centre fed half wave dipole, though it is somewhat similar.

The gain pattern at 10° elevation shows some asymmetry, not large, but evidence again that the thing is not exactly the same as a centre fed half wave dipole, but somewhat similar.

The radiation efficiency of the modelled system is 75%, it has no feed or impedance transformation losses factored in, just conductor loss (which is very small) and ground loss.

An NEC-4.2 model of a 7MHz λ/2 horizontal 2mm copper wire at height of λ/4 above average ground reveals:

- feed point impedance vs displacement for a somewhat idealised or ‘pure’ antenna, ‘pure’ in the sense of not including a feed line or other elements that would alter its operation; and
- current distribution (magnitude and phase) that are a little different to a centre fed dipole.

1 highlights the impractical nature of feeding such a ‘pure’ antenna very close to the end.

2 questions the assumption that underlies most discussions of an EFHW that it works identically to a centre fed dipole as even in this ‘pure’ form, the current distribution is not exactly the same.

Further articles will explore the effects of popular practical feed arrangements on the system.

]]>Above is a diagram of a Pawsey Balun used with a half wave dipole (ARRL).

Pawsey Balun on an asymmetric load reported model results in an asymetric dipole antenna, and showed very high common mode feed line current.

Pawsey Balun on an asymmetric load – bench load simulation showed that although the Pawsey balun is not of itself an effective voltage balun or current balun, it can be augmented to be one or the other.

So, you might ask what they do, what they are good for, and why they are used.

If you were to construct a quite symmetric half wave dipole and directly connected a coax transmission line to the centre, you would destroy the symmetry of the system as connection of the shield to one dipole leg only effectively connects the common mode conductor (the outer surface of the shield) to one leg of the dipole.

The Pawsey stub or balun is a narrowband device (ie tuned) that adapts the coaxial feed line to a pair of symmetric terminals for attachment to the antenna feed point.

In a perfectly symmetric system (source, feedline type and topology, antenna), current in the radiator will be symmetric and there will be negligible common mode current on the feed line.

Symmetry is easier to achieve with some types of VHF/UHF/SHF antennas than at HF.

Equivalent circuit of an antenna system gives measurements of a fairly symmetric G5RV Inverted V dipole + feed line and in that case, the Z1 and Z2 values are different on the two bands reported, more so on 80m.

On the other hand, a corner reflector with half wave dipole feed for 1296MHz can be constructed with very good symmetry, and fed from behind the reflector, a Pawsey balun should give the necessary feed symmetry to preserve system symmetry and have symmetric dipole currents and negligible common mode current on the feed assembly.

The question of why are they used is more difficult than the other questions. They do have application, but they are also used inappropriately and given that it is most unusual to seem validation of balun performance by measurement, such use highlights the bliss of ignorance.

]]>The article Baluns in antenna systems explores some different dipole and feed line configurations and the effectiveness of common mode chokes at various locations on the feed line.

Models 1, 2 and 3 particularly show the effect of a quarter wave vertical common mode conductor grounded and isolated, and a half wave vertical common mode conductor grounded.

These illustrate that those common mode conductors can be viewed to some extent as a ‘single wire’ transmission line, and the impedance presented at the dipole feed point is low or high in keeping with simple transmission line analysis of a shorted or open line of quarter or half wave length.

The question then arises with the Radcom “cable balun”, does it behave similarly, to what extent does the folding of the conductor affect its quarter wave resonance.

One way to explore this is to construct an NEC model of the structure and a reflection of itself.

Above is the serpentine structure of three quarter wavelength folded, and below it, a reflection of itself. The whole structure is fed in the middle and the impedance vs frequency charted.

Above, the impedance vs freq, both in cartesian and polar form are plotted and show a clear self resonance around 7.15MHz.

For comparison, a plain dipole of the same total wire length is modelled.

Above, the plain dipole of same total wire length.

Above, the impedance vs freq, both in cartesian and polar form are plotted and show a clear self resonance around 7.15MHz.

There is a little difference in the resistance plots as might be expected because it is mainly radiation resistance which is affected by the folding of the conductor. The reactance plots are very similar, and importantly, the resonant frequencies are almost equal.

To all intents and purposes, they are both radiating transmission lines of 3λ/4.

So there should be little surprise when the 3λ/4 “cable balun” is extended by a further λ/4 to make a total of λ and connected to ground, that a low impedance to common mode current is presented at the feed point.

Above is the current distribution diagram from the model, the dark green curve is the magnitude of current. Note the common mode current on the vertical feed line, its magnitude relative to that on the dipole elements is relevant.

It does exactly what is predicted from a very simple analysis. If you follow the thinking, you can see that it is quite naive to think the “cable balun” alone effectively reduces common mode current in general.

]]>Above is the current distribution on the half square voltage fed. It is essentially two in-phase vertical quarter waves separated a half wavelength, a broadside array.

Feed point impedance at resonance is very high 5700Ω, and being a high Q antenna, they are very sensitive to dimensions, nearby clutter etc. Note that this is calculated for an antenna in the clear, it will be different where trees or conductive mast exist nearby.

Above is a diagram of one of several feed arrangements from the ARRL.

The classic ham design would be to transform 50 to 5700 we need a turns ratio of (50/5700)^0.5=0.093, so you would design an inductor to resonate with an available capacitor and tap it at 9.3%. Of course this method cannot deal with a reactive load and pretends the transformer does not contribute significant reactance.

Well, that back of the envelope design will not work exactly for an air cored solenoid at RF because of the practical flux leakag (though sometimes it might be close), designing coupled coils (for that is what we have) is more complicated than that.

Solution 1 uses a tapped inductor and variable capacitor as in the schematic. The inductor is an air solenoid of 28t of diameter 52mm and pitch 5mm, tapped at 3.5t. These calcs assume a low loss capacitor because of the very high load impedance. The capacitor needs to be at least 200pF, and more importantly, at 1500W it needs to withstand 5kVpk… a vacuum variable is the obvious choice and has advantages for outdoor deployment.

But vacuum variables are quite expensive!

Solution 2 uses a mid Q (200) tapped inductor and fixed capacitor, and is tuned / matched by adjusting a tap on the top of the coil and one nearer the bottom of the coil. The inductor is an air solenoid of 30t of diameter 52mm and pitch 5mm, antenna tapped at about 22.3t and feed tapped at 2.8t. These calcs assume a low loss capacitor because of the very high load impedance. The capacitor used is 200pF, and more importantly, at 1500W it needs to withstand 5kVpk.. a vacuum fixed capacitor is the obvious choice and has advantages for outdoor deployment.

These can still be bought on eBay out of Russia for less than $40 inc shipping.

Above is a Smith chart model of match (from SimSmith). The three L elements are inextricably linked and cannot be individually varied as they form an equivalent circuit for the autotransformer / inductor. The inductor Q values come from distribution of the total coil resistance over the parts, and the mutual inductance components are lossless. The -1GQ is to force a near lossless inductance, and a quirk of SimSmith’s unconventional meaning of Q is that it needs to be negative in this case.

Above is the Smith chart plot of the match.

Lots of ham articles show matches of this type without the shunt capacitance (the red element on the Smith chart) but the capacitance is essential to its operation. In the case of antennas (particularly VHF) that seem to work without it, it is inherent in the mount for the radiator.

Increasing Q of the tapped inductor reduces losses. Winding the inductor with 2mm copper should raise Q for the whole inductor to around 500.

The inductor is an air solenoid of 30t of diameter 52mm and pitch 5mm, antenna tapped at about 22.3t and feed tapped at 2.8t. These calcs assume a low loss capacitor because of the very high load impedance. The capacitor used is 200pF, and more importantly, at 1500W it needs to withstand 5kVpk.. a vacuum fixed capacitor is the obvious choice and has advantages for outdoor deployment.

The model above uses the higher Q inductor and the losses are reduced by about 0.3dB, about 7% improvement in radiation efficiency. Note that the turns are space to reduce proximity effect driving higher coil loss.

For a practical deployment, I will tune this initially with an analyser using a silvered mica capacitor to confirm the design, and then based on that experience, buy a vacuum capacitor that will be compatible.

Fixed capacitance choices range from transmission line sections to doorknob capacitors. both are much lower Q than a vacuum capacitor, you need to do calcs and assess whether the loss is acceptable.

Variable capacitors can be mid range Q, but long term weather resistance may be an issue.

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