helix 4necerf

This article represents the revised andextended version of a lecture at theUKW conference 2010 in Bensheim.The article shows how a Helix antennacan be sketched with the 4NEC2 soft-ware. Followed by the construction ofa sample antenna, measuring its char-acteristics and comparison with thesimulation.

1.0Simulation of wire antennaswith NEC

NEC (Numerical Electric Code) was de-veloped in 1981 by the Lawrence Liver-more laboratory for the American Navyas a simulation method for wire antennas.The antenna is divided into very shortpieces (segments) where the current andvoltage change is almost linear. Amaz-ingly accurate simulations can be accom-plished, but naturally there are limits.Interestingly enough, a lower and anupper limit where the simulation be-comes ever more inaccurate.The lower frequency limit is defined bythe recommendation that there are ap-proximately 10 to 20 segments per wave-length but never more than 50 segments.If very low frequencies are used (e.g.

below 1MHz) the wavelength rises to300m and a segment becomes at least 6mlong. The program cannot react to anymore refinements of the environment (itapplies the rule of linear current on thesmallest segment) and the simulationquickly becomes senseless.With high and very high frequencies theconcept of an infinitely thin antenna wiredoes not work in the simulation anymore. A supplementary product forthicker wires, the Extended thin wirekernel can be used but as soon as therelationship between of the segmentlength to wire radius falls below 2.5, theprogram ends with an error message withwild warnings to the user about thisproblemNEC2 is the standard free applicationsoftware. Development has continuedand the weaknesses of NEC2 (e.g. incor-rect computation of structures that crossvery closely or wires buried in soil) wereonly corrected with NEC4. NEC4 wasrestricted for a long time and was consid-ered as secret. Today it is also availableoutside of the USA, but quite expensive(normally around the $2000).NEC2 can be downloaded from the Inter-net, but nothing can be done immedi-ately. It is a pure calculating machine thatwas originally written in FORTRAN andavailable as a compiled coded program.Therefore many people added extensive

An interesting program:Simulation and construction of aHelix antenna for 2.45GHz using4NEC2

Gunthard Kraus, DG8GB

VHF COMMUNICATIONS 2/2011

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operator interfaces and marketed these asWindows programs - some free of chargeand some with substantial prices. 4NEC2stands out by a long way because it isequipped with as many supplementaryproduct features and facilities that it isastonishing that it is free. Thereforepraise and thanks to the author of4NEC2, Mr. Arie Voors!Naturally such an enormous machine isnot completely free from small errors,but they do not disturb and fortunatelyonly express themselves in extreme cases(or contradictory commands e.g. movingsomething and forgetting the input). Thesoftware author requests that users in-form him of such things immediately byemail and then promptly investigatesthem.

2.0The Helix antenna

2.1. Some initial wordsIt is a quite an interesting construction

with just as interesting characteristics. Itis a spiral wire with turns a wavelengthlong at the operating frequency and atleast 3 turns. More turns increase the gainand make the beamwidth angle smaller.The typical upward gradient is about the wavelength and the reflector is ar-ranged at the beginning of the spiral witha diameter of a wavelength.The antenna is interesting: It supplies circularly polarised radia-

tion where the rotation of the spiralspecifies the polarisation.

It exhibits amazing constant data andcharacteristics within a range of ap-proximately 20% of a wavelength.

The radiation resistance is approxi-mately 150 theoretically (the practi-cal values are between 130 and200) and this changes only slowly.

Blind spots are present and are peri-odical, these must be considered dur-ing adjustment. They are clearlysmaller than the radiation resistanceand rarely exceed a value of 50

There is almost always no backwardradiation due to the metal reflectorand therefore an outstanding advan-tage.

Fig 1: An onlinecalculator like thismakes thedetermination ofthe mechanicalantenna datachild's play.


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Altogether this antenna is extremelygood-natured and forgives manyerrors during the mechanical conver-sion of the design.

Since there is usually no rose withoutthorns, here are the drawbacks: The mechanical dimensions are un-

fortunately not as delicate as withsome other antenna forms.

The directivity pattern can easily be-come baggy compared with otherantennas with similar gain.

The amazing wide bandwidth is paidfor with a decreased antenna gain thatcan be classified as not top classbut rather between centre zone andpoint.

2.2. DefaultsThe user only needs the intended operat-ing frequency (here: 2.45GHz) and thenumber of the turns to enter (with risingnumber of turns there is more gain and anarrower beamwidth, but also a longerantenna). Therefore for training a simple6 turns antenna is calculated, see Fig 1.Result: Wavelength = 122.4mm for a centre

frequency of 2.45GHz Internal diameter = 41.6mm

Gain = 10.85dBi Wire size = 2.4mm Upward gradient = 30.6mm Minimum reflector diameter =

75.9mm Entire antenna = 183.6mm = 6 x

length 30.6mm(In the result list the entire wire length isgiven as well as the information that thestructure was raised by 1.1mm to create aplace for the feed).For the practical construction copperwire with a diameter of 1.25mm wasselected because the connection at thebeginning of the spiral can be manufac-tured more easily to connect to an SMAplug without large diameter jumps. Toaccept this wire size NEC would like toknow the middle diameter of the spiral(using the on-line Calculators about41.6mm + 2.4mm = 44mm).This data was converted from the simula-tion into an experimental model. Thereflector was a square aluminium plate2mm thick and an edge length of 130mm(more than one wavelength as required).An SMA socket was screwed onto thelower surface of this plate with the innerpin through the reflector plate and sol-dered to the start of the spiral. It is

Fig 2: This is theend product, it isnot a finisheddesign but itserves as a sampleto check theaccuracy of thesimulation.


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important for the simulation that theHelix is raised by 5mm in order to copythis solder joint. The Helix is held by two 10mm polysty-rene strips stuck onto the reflector platewith UHU glue. Fig 2 shows this in gooddetail. Doubts about the polystyrene materialcan exist; it contains the insulation mate-rial polystyrene (Styroflex) useful at highfrequencies but it is 80% air. Because ofthe high fusing temperature of the poly-styrene at over 80C, no air humidity willbe enclosed in the large pores that couldcause additional absorption.

3.0Wire antenna simulation with4NEC2

3.1. Start and first simulationThe software can be downloaded inzipped form from different places on theInternet (see note at the end). The nu-cleus program 4NEC2 is installed andthen the supplementary products are in-stalled for 4NEC2X. However 4NEC2Xis always used because it gives the

coloured 3D diagrams of the simulationresults as well as the antenna structure.

3.2. Production NEC files and the firstsimulationA simple text editor is enough (e.g.Notepad) and all the necessary instruc-tions (Cards) are typed by hand. Natu-rally 4NEC2 contains other good editorswith easy operation but Notepad is fastestand experienced user eventually use thisinput method. Note that NEC measures all dimensionsentered in metres. If that is not desirable(e.g. working with inches), an additionalscaling map must be used for suitableconversion. The input for the Helix isshown in Table 1.Explanations: CM are comment cards and ig-

nored by the program. CE meansend of the comments.

GH (Geometry of Helix) specifiesthe form of the Helix; the line re-quired including the explanation isshown in Fig 3.

GM (Geometry Move card) pushesthe Helix upward by 5mm (Fig 4).

GW (Geometry of Wire) for theconnecting wire, see Fig 5. It repre-sents the interior leader of the SMAsocket and at the same time energizes

Table 1: The NEC file for the Helix antenna project.

CM Helix 2450MHz (6turns) over perfect groundCM Helix starts 5mm above groundCM Helix diameter = 44mm, spacing - 30.6mmCM Wire with a diameter of 1.25mm added between helix and groundCM Excitation at centre of this wireCEGH 1 120 0.0306 0.1836 0.022 0.022 0.022 0.022 0.0006125GM 0 0 0 0 0 0 0 0.005 0GW 150 1 .022 0 0 0.022 0 0.005 0.0006125GE 1 GN 1 EK EX 0 150 1 0 1. 0 FR 0 0 0 2450. 0


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the antenna. Its upper end is con-nected to the start of the Helix(coordinates of Helix and the upperend of the piece of wire the same).The lower end of the wire is put onthe Ground level that is formed bythe reflector. NEC automatically putsthe feed point into the centre seg-ment. Thus the upper end of the feedwire will meet the start of the Helixat a height of 5mm.

The next three entries; GE/GN/EKare all shown in Fig 6. They concernthe end of the geometry data, also

the Ground and the fact that theantenna wire is not infinitely thin.

From to Fig 7 the supply (Excitation)of the structure is programmed in thecentre section of the connecting wire.

... the conclusion (Fig 8), the indica-tion of frequency as well as markingthe end of the NEC file.

The NEC file is now saved in a suitableplace with the file extension .nec e.g.as helix_2450MHz.nec. 4NEC2X isstarted and the file loaded usingMain/file/open 4nec2 in/output file and

Fig 5: The innerpin of the SMAconnector becomesthis short piece ofwire 5mm long.

Fig 4: This raisesthe Helix by 5mmfro the SMAconnector.

Fig 3: Unbelievablythis short linecontains thecompletedescription for theHelix structure.

Fig 6: This definesthe groundcondition and theuse of a thick wirein the simulation.


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the path of this antenna file. Press F7 tostart the simulation after entering theattribute (Far Field pattern/fill/resolution= 5 degrees) as shown in Fig 9 andpressing Generate.The simulated far field radiation pattern(far field pattern) at a frequency of2450MHz is shown in Fig 10. Theazimuth angle Phi = zero degree(horizontal angle of rotation) is shown atthe bottom on the left. The elevationangle Theta is from 0 to 180 degrees orfrom 0 to -180 degrees is shown on thebottom right.

One of the most beautiful options of4NEC2 is the coloured 3D picture thatcan be opened with the key F9. The firstone (Fig 11) shows the antenna structure,it can easily be zoomed to show theindividual segments that the antenna di-vided into for the simulation. Unfortu-nately the pictures in VHF Communica-tions Magazine are in black and whitebut the program colours the feed point inviolet at the centre segment of the feedwire that makes it very easy to see. Thestructure can be moved and rotated usingthe mouse buttons.Changing over the menu to Multi Col-our shows the radiation pattern as well

Fig 7: The exitation takes place in themiddle of the wire.

Fig 8: There is no frequency sweep,the frequency is set to 2450MHz.

Fig 9: Pressing F7 displays thesesimulation parameters.

Fig 10: The simulated far field isdisplayed as a polar diagram.


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as the colours for the gain scale in dBi(Fig 12).

3.2. Simulation of gain, SWR andimpedanceStart the simulation menu by pressing thekey F7 (Fig 13); then adjusts the follow-ing:

Frequency sweep Gain (simply click to remove the

message No front/back ratio data isgenerated)

Resolution = 5 degrees Start = 2300MHz, Stop = 2600MHz, Step = 2 MHz

Fig 11: This is the3D representationshowing the feedpoint half wayalong the wire.This diagram is inglorious colour butVHF Communica-tions Magazine isonly printed inblack and white.The feed point isshown in violet onthe colour version.

Fig 12: This is avery good view ofthe structure. Itcan be moved inany direction usingthe mouse.


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(a maximum of 150 steps are possible,therefore the increment cannot be toolarge)Click Generate to start the NEC calcu-

lating machine. Following successfulsimulation the screen showing the SWRand reflection coefficient is displayed(Fig 14). SWR = 3.2 and S11 = -5.85dBis relatively bad at 2450MHz but thatdoes not have to be a bad indication:theoretically the radiation resistance isapproximately 150 and therefore suchvalues are to be expected.The feed impedance (Fig 15) can befound using the Show menu in the topleft hand corner. The theory is confirmedvery beautifully because the radiationresistance is maintained between 150and 190 over the entire frequencyrange from 2300 to 2600MHz. The im-aginary portion only increases to - j50at the lower end of the range. Fig 16 shows the antenna gain that is

Fig 13: The simulation parameter canbe set after pressing F7.

Fig 14: The SWR and reflectioncoefficient - see text.

Fig 15: The mystery of the helix is theradiation resistance of 150 that isthe cause of the large reflections. Fig 16: The gain is as promised verywide band.


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accessed using the Show menu. Thewide bandwidth of the antenna is shownbecause the gain rises from 10.5dBi at2300MHz to approximately 12dBi at2600MHz. At 2450MHz it is exactly11dBi. The lower diagram is empty be-cause the earlier message stated that nofront to back data would be calculated.A Smith chart can also be displayedusing the relevant button (Fig 17). Thisshows even better how the feed imped-

ance behaves if the frequency is changed.

3.3. Results of measurement of theexperimental model

3.3.1. Feed impedanceAn HP 8410 network analyser with amagnitude and phase display module wasused with a transmission reflectionbridge for 2 to 12.4GHz. An HP 8690sweeper supplied the excitation signalwith a module for 2 to 4GHz. The

Fig 17: There is aSmith Chart forthose who arefamiliar with thisrepresentation.

Fig 18: This showsthe measuredimpedance on aSmith Chart from2300 to 2600MHz.


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desired frequency range was carefullycontrolled from 2300 to 2600MHz by afrequency counter. This counter receivedits signal from the sweeper using a 10dBdirectional coupler.The measuring set was calibrated care-fully: Perfect adjustment using a Watkins John-son SMA termination with more than30dB reflection attenuation up to morethan 12GHz (the expert immediately rec-ognises these rare parts at the electronicsflea market by the blue lacquer finish).Thus the bright spot was centred care-fully in the centre of the magnitude andphase display.Now the termination was replaced by ashort piece of SMA semi rigid cable withthe same SMA connector as used on theHelix antenna fitted to the end. First100% reflection is exactly calibrated(bright curved path must be exactly onthe outside diameter of the magnitudeand phase display) AND the datum planeset by rotating the correct control on themeasuring bridge to the point of the innerpin of the SMA socket (the curve dimin-

ishes to a bright spot). This exactlymeasures at the beginning of the Helixspiral when the antenna is attached formeasurement. The result of the measure-ment can be seen in Fig 18 and thecomment: Not at all bad is surelydeserved.

3.3.2. Determining the antenna gainAn antenna measuring range would nor-mally be required to determine the gainof this antenna. Unfortunately this ismissing in the domestic cellar workshop.Thus the following cheat was used:The wavelength is 122.4mm for a fre-quency of 2450MHz. If a transmissioncircuit consisting of transmitter, receiverand two identical antennas is developedwith a path distance between the trans-mitting and receiving antenna of 120cmthat corresponds to a distance of approxi-mately 10 wavelengths and thus genu-ine far field propagation. But the fol-lowing applies:Since the radiated energy distributes overan ever-increasing solid angles whenmoving away from the transmitting an-tenna the energy per unit area decreases

Fig 19: This showshow to determinethe additionalattenuation causedby the reflection.


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according to the Friis transmission equa-tion at the receiving antenna. This is thefamous formula for free space path loss.If the gain of transmitting and receivingantenna is included it reads:

d is the distance between sending andreceiving antennas and is the wave-length that will be used for the calcula-tion being the speed of light divided bythe transmitter frequency. Using two completely identically manu-factured patch antennas with a resonantfrequency of 2.45GHz and an input re-flection of less than 3% at this frequency,in the measuring position. An advantageof the patch antenna is their affiliation tothe family of the planar array antennas.That means that the patch surface is atthe starting point for the radiation leavingthe antenna (technically the phase cen-tre).Using logarithmic representation in dB(with gain in dBm) for this arrangement:

in dBRe-arranging for the gain:

in dB

With a level of 0dBm and the antennadistance of 120cm the result is:

With a measurement of -29dBm at thereceiver (Spectrum Analyser calibrated at2.45GHz) gives an antenna gain of6.4dBi for the patch antenna that is aboutthe value in the textbooks (usually: 6.5 to7dBi, depending upon form, material andlosses).With the transmitting antenna replacedby the Helix antenna the level measuredat the receiver rose to around +2dB. Theinput impedance of the Helix must beconsidered, this is approximately 150therefore a large part of the availablepower (0dBm = 1mW) is reflected backinto the generator. Calculating the addi-tional attenuation is therefore childsplay, because on the left of the Smithdiagram of the 4NEC2-Simulation thereare some nomograms (Fig 19). The twolower ones are important and they will beconsidered more closely:For the point on the curve for 2450MHzthere is a point on the right hand scalereturn loss of approximately 5.5dB thatcorresponds to the negative value of S11.The left scale gives (by the reflectionscausing auxiliary absorption = reflectionloss) the value of approximately 1.5dBand thus a measured gain for the Helixantenna of 6.4dBi + 2dB +1.5dB =9.9dBi.

Fig 20: A block diagram of the antenna test setup.

2

ReRe 4

= dGGPP antennaceiveantennaTransmitrTransmitteceiver

++= dinxAntennagawerTransmitpoceivepower

4

log202Re

28.41

2120424.12log20

dBinTransmitgacmcminTransmitga

nAntennagai +=

=

24

log20Re

= d

werTransmitpoceivepowernAntennagai


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That is approximately 1dB less than thesimulation stated (11 dBi) but not too faraway. 1dB deviation correspond to 10%change of the voltage or approximately20% of gain and the losses in thepolystyrene and the mounting plate havenot been considered and the skin effectat this frequencyThe layout of the measuring setup isshown in Fig 20. The principle is quiteclear: A counter is connected via a directionalcoupler to indicate the frequency of thetransmitter signal. After an attenuator (toimprove adjustment) there is a coaxrelay. In the lower switch position thetransmit level can be measured and ad-justed to 0dBm. In the upper switchposition this output of 1mW goes to thetransmitting antenna. The inputs to thewattmeter and the patch antenna are twoidentical, equal lengths but as short aspossible, low-loss, SMA semi rigid ca-bles. The accurately measured level of0dBm = 1mW is fed to the antenna and isradiated. On the receive side the patchantenna is screwed directly onto theanalyser input. The two antennas areaccurately aligned at a distance 1.2mapart in poor reflection environment.(Note: The connection between the gen-erator and the antenna was made as shortas possible otherwise the mismatch (ithas a radiation resistance of 150) maycause further unexpected attenuations.The reflections lead too standingwaves in the cable and each maximumcauses losses in the cable (because thevoltage and current amplitudes are in-creased there) with this increase the SWRwill raise substantial. They can increasethe overall attenuation by over 4dB. Evenif the cable attenuation is only 1dB withcorrect adjustment. A gain (in this caseunfortunately energy dissipation) unfor-tunately always rises as a square of thecurrent or voltage amplitude. This effectis described in the chapter Additionalpower Loss due to SWR in [2], there arealso formulas and arithmetical examples

as well as a beautiful auxiliary attenua-tion diagram for the consideration of thisunpleasant effect.

4.0Conclusion

NEC is also useful for wire antennas; noblind tests are necessary, because theNEC simulation decreases the largestpart of the work and supplies, as shown,useful results. However the learning effort is substantialand pitfalls lurk everywhere that lead tosimulation errors. Often NEC or 4NEC2does not warn of these and specialknowledge of the user is required.Also only a tiny fraction of this tremen-dously efficient program with its possi-bilities could be presented. A constantlygrowing 4NEC2 tutorial can be down-loaded from [3] with all possible simula-tion examples and appropriate practicalreferences. However if all possibilitiesand refinement of the program were to bediscussed it would take more than 1000sides.Designing wire antennas with 4NEC2makes for much joy and increases yourpersonal knowledge. Much fun is due tomy friend and 4NEC2 specialist, HardyLau of the Dualen University BadenWrttemberg in Friedrichshafen. Withouthis knowledge and patient help withproblems or questions and his notes oncritical cases when the author was notsure or made incorrect assumptions thisantenna would not work probably yet.

5.0Literature

[1] John D. Kraus and Ronald J. Marhe-fka: Antennas for all Applications.


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McGraw Hill Higher Education. ISBNNo.: 0-07-232103-2[2] The ARRL Antenna Book, 21st edi-tion. Page 24-10

[3] Homepage of the authorwww.elektronikschule.de/~krausg.Download address for 4NEC2:http://home.ict.nl/~arivoors/Home.htm


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helix 4necerf

Documents

simulation method

antenna wiredoes

free of chargeand

spiral wire

construction of ahelix

interesting constructionwith

shortpieces segments

interesting characteristics