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Background Info Element Diameters and NEC Limitations Guiding numbers and Limits Scaling Frequency in Antenna Calc. Programms Scaling Frequency in 4nec2 and EZNEC Element Diam. Scaling per Formula by DL6WU / G3SEK Scaling Element Diameters using a Formula Element Diam. Scaling by Hand Scaling Element Diameters by Hand StepbyStep Example Scaling a 50 MHz 5 ele. from 15.875 (5/8 in) to 12.7 mm (1/2 in) Preface I am frequently being asked how I scale Yagis to other frequencies or element diameters ... or whether I could do that on a certain of my designs ... here is a little tutorial how to do that. Do not get me wrong here, I like to help but it is clear that I can not scale whatever design to whatever diameter and put it onto the website in the limited time I have ... So I prefere to give a good instruction to enable other hams to do needed scalings themselfs. If you would have Brian Brezelys Antenna Optimiser or YO full version it would do it automatically. But this program is not available anymore and would have to be licensed. And needs some skills to operate. News / Update 20150310 Below I show how to scale element by element to new diameter starting with the most far out directing D x. Recently I found out that with most Long Yagis I am happier starting at the rear end. Modify the reflector, spare the Driven Element and work towards the last out element seems to give a cleaner result with less effort to me. That is a subjective measure. Both ways work but I thought it worthwhile to be mentioned here. Element Diameters and NEC Limitations The NEC kernels formulas compute to best accuracy with relatively thin wires. Now what exactly is a thin wire? To give some dirction here I quote the essentail sentences from the NEC II Manual. The NEC II kernel is used in EZNEC up to the actual version v5.x and in 4nec2 (if no NEC4 kernel is mounted). Numerical Electromagnetics Code (NEC) . Method of Moments Part III: Users’s Guide, G. J. Burke, A J. Poggio, 1981, Lawrence Livermore Laboratory Section II, Structure Modeling Guidelines 1. wire modeling (1) “The main electrical consideration is segment length Δ relative to the wavelength λ. Generally, Δ should be less than about 0.1 λ at the desired frequency.“ λ = 2.079 m at 144,200 MHz 0.1 λ =0.1 * 2.079 m = 0.2079 m A typical 144 Mhz Yagi element may have a length of around 0.998 m; At a segmentation of 10 per wire the resulting segment length is 0.998 m / 10 = 0.0998 m. That leads to a minimum to chosen length factor of 0.2079 m / 0.0998 m = 2.08. In straight words a segmentation of only 10 segm./wire is better than double of the recommended minimum. As we continue to read down the manual we find the following: (2) “[...] while shorter segments, 0.05 λ or less may be needed in modelling critical regions of an antenna.” Taking into account the minimum to chosen length factor we are still on the side of recommended solution with just 10 segments per wire, even if say the DE to D1 zone of a Yagi should be considered a critical region. (3) “Small values of Δ / a may result in extraneous oscillations in the computed current near free wire ends […]. Extremely short segments, less than about 10E3 λ, should also be avoided […]”. 10E3 λ = 0.001 λ 0.001 * 2.079 m = 0.002079 m 2.079 m / 0.002079 m = 1000 segment length = Δ , wire radius = a “[…] Δ / a must be greater than about 8 for errors of less than 1%.” Choosing a common diameter for Yagi elements of 8 mm we arrive at a = 8 / 2 mm = 4 mm Δ / a = 8 gives us a minimum segment length of Δ = 8 * a = 8 * 4 mm = 32 mm. That equals a maximum segmentation of 998 mm / 32 mm = 31 “With the extended thinwire kernel, ? / a may be as small as 2 for the same accuracy.” Δ / a = 2 gives us a minimum segment length of Δ = 2 * a = 2 * 4 mm = 8 mm. That equals a maximum segmentation of 998 mm / 8 mm = 124 “Unless 2 π a / λ is much less than 1, the validity of these approximations should be considered.” 2 π a / λ = 2 π * 4 mm / 2079 mm = 0,0121 Finally lets have a look at how low numbers of segments are used in the NEC manuals examples themselfs. On the manuals pg. 125 we do find an example of a Yagi – like structure, take a look at the chosen segmentation: (4) “Example of a 12 elem. log peridoc antenna Total 78 segments, No of Seg/wire 9, 9 ,7 ,7 ,7, 7, 7,5 ,5 ,5 ,5 ,5 ” OTHER limitations NEC2 Manual, part III: User's Guide (WDBN version 0.92), pg. 9: "When wires are parallel and very close together, the segments should be aligned to avoid incorrect current perturbation from offset match point and segment junctions." EZNEC Manual, s. index for "Wire spacing" or "Closely Spaced Wires" "In all cases, wire spacing should be at least several wire diameters." With wires spaced as closely as 0.01 wl nec2 and nec4 based software produces bad Average Gain numbers. Numbers for gain and Antenna Temperatures produced with Average Gain numbers far from 1.000 for the lossless model must be processed through the Average Gain correction formulas, see here At a distance of 0.025 wl the convergence challenge seems to be cured for most designs. Guiding numbers and Limits • Making elements thicker we need to lessen their length. Thicker elements are SHORTER • Making elements thinner we need to extend their length. Thinner elements are LONGER • Elements are NOT prolonged / shortend in linear way or using fixed numbers over the whole YagiUda. While the far out elements need most adaption this flatens out around the driver cell. An example of what delta length to what element; note the progression as we move from Driver Cell to far end ... (50 MHz 5 ele. Yagi from 5/8 to 1/2 in) Ele.: Refl DE D1 D2 D3 [mm] 1 3 7 17 22 Exemplarily numbers (all strongly depending on actual design) Band 50 MHz 144 MHz 432 MHz Refl. / D5 Refl. / D10 Refl. / D10 4 mm <> 6 mm  4 mm / 10 mm 3 mm / 7 mm 6 mm <> 8 mm  4 mm / 8 mm 2 mm / 5 mm 8 mm <> 10 mm    4 mm <> 8 mm  5 mm / 24 mm  5/8 in  1/2 in 1 mm / 22 mm   It is clear that changing element diameters but leaving element positions as they are leads to slight changes in distances elementtoelement. Thus the Yagi 'never will be the same again' if we take a macroscopic view by looking at the 10th dB in F/B or F/R or side lobe magnitudes. Furthermore it is understood that thinner elements introduce more loss and vice versa. So that scaling down from 8 mm to 6 mm element diameter may cost us 0.05 dB. If it does not this will be on slight cost of other properties namely F/B or whatever side lobe supression or band width. Scaling Frequency in Antenna Calc. Programms • 4nec2 This is 4nec2 v5.8.14. The 4nec2 holds a scaling function in the Geometry Editor First select which wire shall be scaled. I assume all  so use CTRL + A windows shortcut for convenient marking of all wires. Selected wires turn from blue to red, s. screenshot below • EZNEC+ v5 EZNEC holds a scaling function that transfers a Yagi or whatever Antenna from given to new frequnecy. It does not leave the element diameter as it is though. The scaling function does a 100 percent scaling, including the element diameters. We are down from 1/2 in to 4.4158 mm which equals the ratio between 50.1 and 144.1 MHz. From here on we have to 'adjust' the element diameters to some feasible number like 4 mm, 5 mm or Imperial 3/16 in = 4.763 mm as shown below. Here click I give an overview on most common Imperial measures to millimeter. Element Diam. Scaling per Formula by DL6WU / G3SEK 20211010 Preface: The following shows a methode for scaling elements to new lengths with a wanted new diameter ar parameter. This methode is not new. It has been published in the well known VHF/UHF DX Book in 1995 and probably much earlier elsewhere. I did not introduce this methode on my web until now, since I was never happy with scaling to largly changes of diameters and in general for longer Yagis from around 10 elements on 70 cm onwards. Nevertheless I was frequently contacted and asked about this methode. Dan, AC6LA integrated it into his very capable AutoEZ for instance. Also recently Klaus, DL5AB showed me a quite fine scaling of just the sample design for hand scaling I show down this page. After a fruitful discussion with him, thanks to Klaus, I decided to not longer hold back this set of formulas and integrated this chapter. Hand scaling, if done right (hi) leads to better results, but for small changes of diameters on lower bands 144 MHz and below and less approx. 10 el. it delivers very usable results. Mind this correction only works for straight elements! A bent dipole, reflector or whatever might come closer if its straightened length is filled in but still the reactance would not be fully met. Not to mention folded dipoles, quad or LFA loops. (corrected formula, tnx to Robin, G1YFG, 20231008) in this
A Microsoft TM Excel which makes use of these formulas: Note that I do not feel responsible for any possible inconventience resulting by making use of this file. Use this file on your own risk. Link to download/open this MS Excel: This Microsoft TM Excel was created by DG7YBN and holds some of the ideas of the file that Klaus, DL5AB showed me. This Excel computes the impedance of the element as a first stage. This column D is masked. Of course you can demask it if you like to see those values. Scaling Element Diameters by Hand I do this by hand. As a preparation I write down three, four key numbers: Best Return Loss frequency and number in dB, like a Return Loss of 33.4 dB at 432.1 MHz. Then F/B and Gain. For adjusting element lengths to a new diameter I start with the farest out parasitic Element. Set this one to new diameter only. Modify length so that F/B and Return Loss are similar to before. Then modify next inner parasitic element moving toward the Driven Element. Same routine, next element, same routine ,....., DE, same routine, finally Refl., same routine Note: 1. The Refl. demands the least change in length of all (some have next to none change of length on the Refl, depending on design!), Farest out parasitic ele. or second farest have most change in length. From Farest out Dxx length change decreases until very little delta length for DE and Reflector only. 2. Gain will suffer by some 0.05 dB or so when moving to thinner elements due to higher losses. Some way gain will increase a little for thicker elements. 3. F/B can not stay absolutely same, for this is a close similar antenna now, but not absolutely identical. Why? The ratio of absolute distances between elements (i.e. ele. positions from ele. to ele. surface have changed slightly simply because they are thicker / thinner now.) 4. Thicker ele. are shorter / Thinner ones longer. Scaling a 50 MHz 5 ele. from 15.875 (5/8 in) to 12.7 mm (1/2 in) How to scale a Yagis elements onebyone by hand: Starting with the farest out parasitic element working towards the DE and finally adjusting the Refl. • 1. Writing down F/B, Gain and SWR at a distinctive point Elevation and SWR plot of our unscaled Yagi. Key properties of our starting point Yagi with 5/8 in elements are Forward Gain 9.91 dBi F/B 25.49 dB Return Loss 34.5 dB at 50.60 MHz as a distinctive point • Scaling D3 Modifying D3's diameter to 1/2 in leads to which leaves us with an F/B of 23.96 dB instead of original 25.49 dB Lengthening D3 millimeter by millimeter working towards same F/B as before leads to F/B of 25.46 dB at a new length of 1236 mm / side. Forward Gain is back from 9.86 dB to 9.91 dB too. Time to check in the SWR Plot window => With new D3 diameter we find a Return Loss of 34.5 dB at our mark of 50.60 MHz. Note that the only parameter I was adapting to was F/B and still the Return Loss and complete RL plot are fine now. Good enough ... , now up to next element in row • Scaling D2 Modifying D2's diameter to 1/2 in leads to which leaves us with an F/B of 26.25dB instead of original 25.49 dB Lengthening D2 millimeter by millimeter working towards same F/B as before we can see how the F/B lessens with every added millimeter until we arrive at same F/B as before. At a new length of 1328,4 mm oer side we find an F/B of 25.49 dB and Forward Gain is back to 9.91 dB too. and pattern as with all 5/8 in elements and finally verifying the SWR or Return Loss plot; yet again, our marker at 50.60 MHz shows almost same result: we started with an RL = 34.5 dB and now have a 35.2 dB. Yet again, all achieved by using the F/B as trimming param only. • Scaling D1 Modifying D1's diameter to 1/2 puts it all to a test since D1 is very responsibly for Z and the Return Loss plot .. and indeed we are not far off ... RL(50.60 MHz) = 32.0 dB against 34.5 dB at starting point and this is the point were we see the finite accuracy when scaling element diameters while element positions are fixed. With 0.2 mm less lenght on D1 we come closer to the RL as was but drift away slightly from the original F/B. With constant element positions there is no choice but to arrange an intermediate arrangement. So I draw back the lenght of D1 from the just found 1379.7 mm to 1379.5 mm. • Scaling the DE Modifying DE's diameter to 1/2 in we split from the 'tune it to similar F/B dogma' and adjust Z with an eye on the imaginary part jX in the Z = R + jX until Return Loss plot and our marker are quite close to the starting point once again I get an RL(50.60 MHz) = 33.4 dB for a new length of 1469.5 mm each side. • Scaling the Reflector Modifying the Reflectors diameter to 1/2 we find that it does not have to be modified at all. Finally check the pattern and SWR plot ... still same .. almost finished ... 73, Hartmut, DG7YBN 