Helical vs. Linear Monopole Antennas

[rfry]

There is a rather common belief that if a 1/4-wavelength of wire is wound in a helix so that the helix is only 3 meters in overall height, that helical radiator would have the same pattern and gain characteristics as a 1/4-wave monopole -- which would be useful for Part 15 AM operators.

The link below leads to an investigation of this.

http://i62.photobucket.com/albums/h85/rfry-100/Helix_vs_Linear_Monopole.gif

 

[druidhillsradio]

I am confused. How can one wind only 30 turns 3 meters in length and equal roughly 138 feet?

 

[rfry]

How can one wind only 30 turns 3 meters in length and equal roughly 138 feet?

It doesn't, but that doesn't change the conclusion. I used a larger pitch for the turns in this comparison so that the form of the helix could be seen easily in the graphic.

The important thing to note is that the radiation resistance (the first term in the feedpoint impedance) stayed the same for the two radiators. The helical form has less reactance (the second term), and if more turns were used the reactance could be reduced to zero. But the radiation resistance would remain the same -- which means that pattern shapes and gains are the same for the two radiator forms -- as shown in my comparison.

The only advantage to the helical over the monopole is that the a-c resistance in the inductance needed to resonate the system may be smaller for the helix.

Here is a link to a page from Antennas for All Applications by John Kraus, with further on this.

http://i62.photobucket.com/albums/h85/rfry-100/Helically-woundVertical.gif

 

[Ermi Roos]

At one time, I also bought the popular notion that the length of the wire on a self-resonant continuously-loaded (i.e. helical) monopole is roughly 1/4 wavelength. In reality, depending on the geometry of the monopole, the wire length can vary considerably from 1/4 wavelength.

The self-resonant frequency is determined by the inductance of the coil and the self-capacitance of the coil. The self-capacitance is higher for fatter monopoles than thinner ones, which means that less inductance is needed for resonance for a continuously-loaded fat monopole of a given height than a thin one.

For best Q (and therefore, efficiency) of a continuously-loaded monopole, make the antenna as fat as possible (2/1 height-width ratio is about optimum, but is maybe much too fat to use for Part 15 because the antenna would look odd to an FCC inspector). Also, use as large diameter wire as possible as will allow at least one wire diameter spacing between turns. For really large wire diameter, use copper tubing.

 

[Ermi Roos]

Here is the only formula I know of for the self-capacitance of a grounded solenoid:

C = 0.29L 0.41R + 1.94{SQRT[(R^3)/L]}, where

C = self-capacitance in picofarads
R = radius of coil in inches
L = length of coil in inches

This formula is derived from empirical data by Medhurst. It applies to coils with a uniforn current along the length. Unfortunately, a self-resonant helical monopole does not have a uniform current distibution, but rather a cosinusoidal distribution. Because of this, the self-resonant coil will have somewhat lower self-capacitance than the coil with uniform current distribution. Nevertheless, the Medhurst self-capacitance can be used as a rough guess.

Once the approximate self-capacitance of the coil is calculated using the Medhurst formula, the inductance for self-resonance of the helical monopole can be calculated. Then the Wheeler formula can be used to calculate the number of turns required for the inductance at resonance. The Wheeler formula is very well-known:

inducance in microhenries = [(n^2)(R^2)]/(9R+10L), where n = number of turns

Since the Medhurst self-capacitance formula is a rough approximation, the actual number of turns for resonance has to be found by testing. Taps can be added to one end of the coil to set it to resonance.

 

[rfry]

At one time, I also bought the popular notion that the length of the wire on a self-resonant continuously-loaded (i.e. helical) monopole is roughly 1/4 wavelength. In reality, depending on the geometry of the monopole, the wire length can vary considerably from 1/4 wavelength. (etc)

Just to note that it is the end-end length (height) of a vertical, linear monopole and/or normal-mode helix that determines its radiation resistance at a specified operating frequency.

Other things equal, radiation resistance sets the relative percentage of the matched power applied to the feedpoint of the antenna system that will be radiated.

It doesn't really matter to radiation resistance whether such a radiator has a helical or linear form.

 

[Ermi Roos]

The short self-resonant helical monopole has higher radiation resistance than a bottom-loaded vertical monopole of the same height. This is because the current distribution along the length of the base-loaded monopole is triangular, while the current distribution along the axis of the self-resonant helical monopole is cosinusoidal. This difference in current distibutions gives the helical monopole about a 2dB advantage in gain.

 

[rfry]

The short self-resonant helical monopole has higher radiation resistance than a bottom-loaded vertical monopole of the same height. etc

NEC-2 shows virtually the same radiation resistance for both of the models (about 0.12 Ω), and virtually identical pattern shape and peak gain (-19.38 dBi) for both models. A peak gain difference of 2 dB between them would be seen in the NEC comparison I posted.

This conclusion also is supported in the page by John Kraus linked earlier, where he states about the helix, "The radiation resistance is nearly the same as for a short monopole..."

Radiation resistance would have to be quite a bit higher for the helix to account for a 2 dB improvement in peak gain from the system.

 

[Ermi Roos]

It is well-established that the current distibution along the axis of a self-resonant short vertical helical monopole is cosinusoidal, and not triangular, as in a vertical rod. It is the difference in the current distributions of these two vertical antennas of equal height that cause the differnce in radiation resiatances. Consequently, the gain of a helical monopole compared to a rod the same height is (4/pi)^2 = 1.621, which is about 2dB.

NEC-2: When automatically creating a long, narrow, helix for NEC analysis, care must be taken to avoid overly short segments for modeling the turns, because this can cause numerical instability in the simulation. This is just a suggestion. I don't actually know why the wrong results were obtained. Repeating the analysis with a fatter coil with fewer turns might give more realistic results.

John Kraus: From what I have seen, Kraus was mostly interested in analyzing the helical antenna operating in the axial mode. For helical antennas operating in the normal mode, he mostly deferred to the previous work by Wheeler. To simplify analysis, Kraus assumed additional end loading, or top loading, external to the helix. The additional end (or top) loading changes the current distribution along the axis of the helix, and therefore the calculated radiation resistance. A top-loaded helix has about the same radiation resistance as a top-loaded rod.

 

[rfry]

Quoting from Antenna Engineering Handbook, 2nd Edition by Johnson and Jasik, page 13-18:

"For a normal-mode helix whose dimensions are small compared to a wavelength, the current distribution along the helix is approximately sinusoidal."

John Kraus also assumed sinusoidal current distribution along his Fig 8-72 (see clip). Therefore it is unclear as to the source of this belief of Mr Roos: "To simplify analysis, Kraus assumed additional end loading, or top loading, external to the helix."

Because the current at the top of the helix under discussion is not capacitively loaded with horizontal conductors, current at the top of the helix necessarily is zero -- as it is also for the linear monopole under discussion.

The current distribution along both of these forms of radiators in the NEC comparison has a sinusoidal shape. The current at the top of both of these radiators must be zero. The portion of a sinusoidal waveform at the operating frequency, beginning with zero current at the top, that can exist along these radiators that are physically short in terms of wavelength appears to be a straight line with zero current at the top and maximum current at the base of the radiator -- which Mr Roos describes as "triangular."

With essentially identical current distribution along the aperture of both radiators, it should be expected that the helix and linear monopoles in this discussion should have essentially identical radiation resistances and patterns.

This has been shown to be true in the NEC comparison in the OP, and is supported by the quoted statements from well-respected authors of antenna engineering textbooks.

 

[Ermi Roos]

When answering a post by Mr. Fry, one must be prepared for the long haul, because there is sure to be an extended spraying contest. The major difficulty with a debate with Fry is that it is hard to know in advance exactly what notions he has in in his mind. His various ideas gradually come to light as the debate progresses. It now appears that he thinks that an electically-short vertical rod over ground has a "sinusoidal" current distribution. The current distribution is actually a straight line with zero current on top and maximum current on the bottom. I called this distribution "triangular." A sinusoidal distribution (which I prefer to call "cosinusoidal") is a convex curve with zero current on top and maximum current at the bottom, corresponding to a quarter-cycle cosine function.

Since Fry is fond of NEC (I like it too, primarily because of its very low cost compared to other simulation programs), he may see these current distibutions for himself by first modeling a 3-meter vertical rod over ground operating at any frequency in the AM broadcast band. The current distibution shown by NEC will be what I call, "triangular," i.e., a straight slanted line. The lenth of the vertical rod can then be increased to a quarter wavelength at the operating frequency. This time, the current waveform will no longer be a straight line, but a convex curve like the quarter-cycle cosine function.

The point I was trying to make in this thread is that a short helical self-resonant monopole does not have a triangular current distribution, but rather a cosinusoidal current distribution with the same shape as for a quarter-wave rod. A short helical monopole is a "slow-wave" structure that has the same-shape current distribution as a quater-wave monopole that is not continuously loaded. The different shapes of the current distibutions of the two different short vertical monopoles accounts for the 2dB gain of the short helical antenna compared to the rod.

Fry was unable to get the expected current distribution by modeling a small-diameter helix using NEC. As I suggested in my previous post, he should have success by modeling a larger diameter helix with less turns. This would avoid numerical problems caused by using segment lengths that are too short to be used with NEC.

 

[rfry]

It now appears that he thinks that an electically-short vertical rod over ground has a "sinusoidal" current distribution. The current distribution is actually a straight line with zero current on top and maximum current on the bottom. I called this distribution "triangular." A sinusoidal distribution (which I prefer to call "cosinusoidal") is a convex curve with zero current on top and maximum current at the bottom, corresponding to a quarter-cycle cosine function.

Although the current distribution along the apertures of BOTH a linear and a helical monopole is sinusoidal in form, the 6.12-degree heights used in my comparison are not long enough for a sine wave curve to depart from what essentially is a straight-line current distribution along their heights.

These points are developed in the link below.

http://i62.photobucket.com/albums/h85/rfry-100/Monopole_Current.gif

 

[Ermi Roos]

My point is that the current distribution of an electrically-short self-resonant helical vertical monopole DOES depart from a straight line, and has the same quarter-cycle cosinusoidal shape as for a rod monopole with 90 degrees height (but over the short distance of the monopole). This is the reason that the short helical monopole has 2 dB more gain than a short rod the same height.This fact has been well-known for several decades.

I have had the same experience previously when debating you. For some reason, you hold on to an erroneous opinion to the end. Is it so important for you to be right ALL of the time? Like anybody else, occasionally you are wrong.

Sugestion: Why don't you see what you find with Google?

 

[rfry]

My point is that the current distribution of an electrically-short self-resonant helical vertical monopole DOES depart from a straight line, and has the same quarter-cycle cosinusoidal shape as for a rod monopole with 90 degrees height (but over the short distance of the monopole). This is the reason that the short helical monopole has 2 dB more gain than a short rod the same height. This fact has been well-known for several decades.

I have posted and documented the published sources for my statements, the accuracy of which anyone could verify if they wished to do so.

Instead of sending readers to Google, would you be willing to post the references in engineering literature, or your own computer simulations that support your statements, as I have done?

 

[Ermi Roos]

The only one I want to send to Google is you. I'm pretty sure that there isn't any other reader interested in our squabble about 2 dB, although some may be entertained by our public tempest in a teapot. It would be useful for you to search Google yourself because then you would have the opportunity to discover the truth for yourself. This would be more convincing than someone telling you something.

I doubt the usefulness of engineering references in this particular argument, because we both have access to the work of John Kraus, and we reached completely different conclusions. I think that you misread Kraus, and you undoubtedly think the same about me.

So, as a service to you, I did a quick Google search. There were several references, mostly to IEEE publications. I chose the following:

http://strobbe.eu/on7yd/136ant/#Helical

The author of this reference says that the gain of the helical antenna over the rod antenna is 1.54, while I said it is 1.621. I said it is about 2 dB, while he says it is about 1.9 dB. It looks like we are both nearly on the same page, but there is a slight computational difference. I say 1.621, because that is (4/pi)^2. Who knows; maybe the author of the reference has more information about the exact current distribution than I do, or there was a slight error. Anyway, I left a little wiggle room so that Fry can continue arguing forever.

 

[rfry]

So, as a service to you, I did a quick Google search. There were several references, mostly to IEEE publications. I chose the following: http://strobbe.eu/on7yd/136ant/#Helical

An interesting choice, compared to the citations I posted earlier from Kraus and from Johnson/Jasik -- whose textbooks are used in the coursework of respected engineering colleges, and which do not support the contention that a normal-mode helix has even 1.9 dB more gain than a linear monopole of the same end-end length, on the same frequency.

The same is shown by a well-constructed NEC study.

At this point probably most readers of this thread have been given enough information from both of us to determine the truth of this matter for themselves.

 

[Ermi Roos]

Kraus does not say what you claim, and your simulation is not well-constructed.

 

[Ermi Roos]

I was going to correct the errors in Fry's "well constructed" NEC study myself, but I will first give him the opportunity to fix it himself. Here are the problems with his work:

1. The first and foremost problem is that Fry's coil is not self-resonant. The cosinusoidal current distribution I talked about in this thread occurs only at resonance.

2. Closely related to # 1 above, the segments are not long enough for the analysis. When analyzing a helical antenna using NEC, overly-short segments cause an error in the analysis that causes the imaginary portion of the input impedance to be negative imaginary. Increase the diameter of the helix to increase the segment length so that no segmentation error message occurs. Set the pitch for resonance at the operating frequency (1.7 MHz).


Alternatively, leave the NEC model exactly the way it is now, and set the operating frequency upward until resonance occurs (no imaginarty component to the input impedance). Because the wavelength will be shorter, the segmentation error will disappear. Read the radiation resistance.

Now, apply the resonant frequency of the coil to the rod antenna model, and find the radiation resistance. Compare the radiation resistance of the resonant helical antenna to the radiation resistance ofthe rod antenna. The ratio of the two radiation resistances should be about 1.6.

 

[Tom Wells]

No tempest in a teapot, determining a real 2 db of gain is worth extended analysis.

I give points to both parties for an excellent presentation of how we can agree and disagree,
given imperfect and non-uniform measurements, models, applications, practices, etc.

Engineers regularly get pinched on semantics, because they are analog descriptors.

If we take the hypotenuese of a right trangle and bow it "outward" we achieve the
sinusoidal current distribution which is still essentially triangular, but "non-linear".

To the extent the radiated field "doesn't care" whether it emanated from a "strictly physically" reasonant structure,
there is every reason to use such a trick for 2 db at part 15 levels.

To the extent that the length is SO abbreviated at 3 m that any sinusoidal characteristic might be irrelevant is
also easily believable.

1 db is allegedly the smallest difference audible, 2db should be quite noticable, and 3db starts to mean real gain in a system.


My follow-up ruminations would be wondering whether all the same ground plane considerations apply,
and or whether elevated, axial installation of a helix might be useful at some elevation.

It would seem easy to feed with a twisted pair and not at all hard to build.

 

[Ermi Roos]

Thanks for your comments, Tom.

My own interest in studying self-loaded antennas is to understand the function of loading coils in general, to find the configuration that gives the best results. The 2 dB gain difference is significant only for understand why it occurs, not for the 2 dB itself. Of the three passive circuit components, the inductor is the least well understood. For example, textbooks usually only deal with magnetic fields when explaining inductor theory, but the electric fields of inductors are equally important for RF.

As for NEC simulation, I already mentioned overly-short segments, but there is also a concern that very small loop antennas (less than .05 wavelength in circumfurence) can't be simulated accurately by NEC-2 at all. NEC-4 supposedly does better. Also, the double-precision versions are said to be better. The guidelines are pretty vague for loop size, and also for spacing between turns.