Most common mistakes in construction of diy ADS-B antennas

In forum articles and posts, we can read relevant info in proportion to the professionals' and experienced amateurs' activity. The rest is only partial or inaccurate information. (simply gossip of outsiders, half true or just inaccurate - perhaps acceptable in some circumstances)

Fact:
- For ADS-B reception, a resonant antenna at 1090 MHz must be used.
The higher the frequency at which we scale an antenna, the more accuracy is required. In our case, a deviation of some less than a millimeter can separate success from failure. For complex antennas, these errors not only add up, they can cause exponential deviation.

1. / Wavelength for 1090 MHz
If the inaccuracy given by rounding is allowed, the quarter wavelength is 68 mm. (If we want to be more accurate then 68.8 mm) But! This is only true when radio waves measured in the air. In different materials, radio waves travel different lengths in a given time. The ratio that shows the degree of deviation is the Velocity Factor (VF). This number must be multiplied by the calculated value to obtain the antenna parameter. For copper and aluminum this is 0.95 (95%). For the materials we use, this means 65.3 mm. We can look for the data of the coax cables on the manufacturer's data sheet, where we can also find the VF value for them. (There are antenna parts that often can be made of coaxial cable only. For example: balun --> BALanced-UNbalanced transformer)

Our antennas are always made of a material other than air, this is why we can never use a 68 or 69 mm lenght as a quarter wavelength for cutting!

The formula we use for getting the full wavelenght:
Speed of light / frequency in MHz multiplied by the Velocity Factor (VF)
300 / 1090 x 0.95

--> If you are not interested in details, skip this part and continue reading from the next paragraph.
VF equals the reciprocal of the square root of the dielectric constant (relative permittivity) of the material through which the signal passes. (Wikipedia)
-- In practice, remembering the above relation, the required conductor length and diameter for a lower frequency give a ratio to which, even taking into account the skin effect -> the Velocity Factor can be as high as 0.98.
In the case of microwaves, the skin effect only works up to a thickness of a few microns on the surface of the conductor, but the ratio between the length and diameter of the conductor is already significantly smaller. As I mentioned, in our case the VF value for copper is 0.95 (95%) which can decrease to about 0.94 at the highest frequencies even if using a thick conductor.
Careful work at higher frequencies is much more important than in other cases. Due to the skin effect, a high-gloss, preferably the perfectly smooth surface is necessary at the highest microwave frequencies. If we have an imperfect surface, parasitic phenomena may appear near the surface. Even really small gaps and scratches can detune the VF and other parameters.


2. / Quarter wave antenna (ground plane, cantenna and the like)
We clarified above that the quarter-wave radiator of the correct size is 65.3 mm (copper wire). The center of the Spider antennas are usually N or F connector - or something similar. The length of the driven element (pin in the middle) must be measured from the point where it emerges from the connector. Try to aim for an inaccuracy of less than one percent.
An important part of the antenna is the additional "pieces of wire" or sheet metal (whatever its shape) placed around the driven element - these wires also must be resonant at the given frequency. Do you remember? - **65.3 mm and 1090 MHz.
(**The full diameter of radials for a 50 ohm qwl antenna is a bit longer, because of the new properties made by bending the radials down. Best practice is measuring the full diameter from radial-tip to the other one's end even before bending down. Radials full diameter - including the connector itself - is 135 mm, before bending down.
Carefully cut, close to the aimed lenght but not over, then using a fine emery or nail file for the last tenths of millimeter.

Do not forget:
- Radiator (middle pin for qwl antenna) 65.3 mm (for both 50 and 75 ohm antennas)
- 50 ohm radials' full diameter 135 mm (measured before bending down, 50 ohm connector and cable)
- 75 ohm radials' diameter ~131 mm (always kept horizontally, using 75 ohm coax and connector).


Almost everyone makes mistakes here:
- If the metal shield of the connector is visible above the joints of the wires around, the visible part must also be included in lenght of gound plane elements. The shield seen there also an active part of the antenna! The threaded part of the F extensions are almost always visible, but this is not so bad, at all. (mainly when working without serious measuring devices) The visible part above the radials can also be considered as a temporarily adjustable element so that we can test the direction of change before deciding about cutting (or not) the next tiny part of the wires or the metal plate... Remember? Due to a 1-2% difference, things can go in the trash.

You could say: Mobil antenna owners never cut the roof of the car around the antenna! It is true, but they use antennas with hidden tuning elements in their antennas to tolerate the the differences of the given surface. Mobile antennas always have compromises and they are far from ideal.

- For Cantenna owners: I recommend the fact that from the protruding connector to the open end down below at the bottom of the antenna - "the entire lenght of the can plus the curved bottom from its center" - should be included in the measurement, not just the downward bent part! (Imagine a 1 meter circular plate where only the last millimeter is bent downwards ... Don't you think that only that 1 millimeter counts? :) From imagination back to the real world: --> The total electrical length affects the operation.

I should mention here that the input impedance of SDR receivers can be of two types. The older ones - still fitting the TV - are 75 ohms, the newer redesigned ones are the 50 ohms (with SMA or BNC connector). We'll get back to this subject soon.

The antenna rods of ground plane are always shown in the images when bent 45 degrees down. Not by accident, but it is not a mandatory rule for all. Amateur radios use 50-ohm input, auxilary devices, and feed lines to avoid signal loss and/or equipment failure. When feed line and antenna have other values than 50 ohm, operators use matching technics. (antenna tuner, balun, unun, choke, etc.) All the components have the same impedance - and where there is a discrepancy, they are made identical to the connected component by tuning or tricky fitting. Sometimes these methods have limitations and losses but in those circumstances they are acceptable and are within the safe value range...

- For owners of a 75-ohm SDR receiver, I recommend using standard 75-ohm coaxial cables - these have better parameters than the same-priced 50-ohm coaxial cables, and last but not least, the 75-ohm dongle fits this kind of cable. There is only one more thing that needs to be changed on the antenna. Bend the ground plane wires horizontally (90 degrees from the driven element) or use a flat, horizontal plate with 130.6 mm diameter instead. (131 is ok, since it is within 1%) Do not forget adding the visible part of the shield (height) of the connector above the plate. Now, you have a matching 75 ohm antenna.

By bending the wires 45 degrees down, the antenna will be 50 ohm. When fully folded down, it is about 32.5 ohm, but in our case it cannot be used.
The radials as ground plane serve and perform several functions. In addition to being a resonant part of the antenna due to its length, it matches the impedance to the cable at the set angle and performs the function of decoupling. (Explains to the antenna that the cable is no longer part of the antenna itself.) ... and also affects the radiation pattern.
Ground plane radials are actually elements converting capacitance to inductance and vica versa. This is already a topic in specialist books and quite boring ...

3. / Franklin collinear antenna - sometimes called vertical centerfed (2, 3 or) 4 half wave
Of the wire antennas, this can even be created without using expensive instruments. Franklin antennas usually have 2 or 4 half-wave radiators. The latter is already a hard nut to crack without at least an antenna-tester or a nano-VNA on the table - but possible to create with a mountain of patience.
The half-wave radiators are 131 mm long, and the phase-matching U-elements are also made of 131 mm wire. Squeezing the "legs" of the U little by little, the frequency decreases but the coupling strengthens. Radiation pattern and gain of the antenna depends also on distance of the neighbouring active elements. So, do not chose a too small distance between U legs! This construction does not allow you to pick the ideal distances (0.7-0.9 WL) between Imax points of halfwave elements for achieving the max gain, thus we have to get the antenna resonant at 1090 MHz with the proper phase delays between radiators, at least.

In the case of half-wavelength elements, the distance between the current-maximum points (the middle of the half-wavelength parts) can start from a minimum distance of 0.5 when the distance between the endpoints is Zero - because we can find a quarter-wave part both downstream and upstream of the center of the elements.
The bigger the distance than 0.5 -> the greater the distance between the endpoints of half-wave elements.

The common theory saying that by doubling the number of half-wave elements we will have an extra 3 dB gain is not always true. Most of the times it is NOT fulfilled. Gain is also a function of the antenna design, the distance from ground surface, and the conductivity of the ground.

You can read from the graph below that a Franklin 4 element antenna with its small endpoint distances - with a bit more than 0.5 value on the x axis - can have 7dBi omnidirectional gain, but it is far from the optimal 8.8 dBi gain.
...graph shows dBd - gain above a single dipole...
dipole spacing.jpg


Because of the sensitivity of the construction, take care of the radiators being in straight line by creating really precise bendings and fixing them to a common support stick (made of a neutral material like wood or fiber glass). The joints on the supporting stick shall not be fully fixed while you are still working on the antenna. (tune it really carefully since a part of a milimeter also counts)
The U element in the middle of the antenna is the feed point to join the coax cable. Using small "2-pin wire joint with tiny screws" on the legs of the feed point (do not forget sliding it onto the legs before bending the radiators) makes it possible to find the 50 or 75 ohm point without soldering again and again. Be patient, since you have to change the coax position little by little to find the optimal place. By tapping on different points on the stub, tuned frequency slightly changes as well. ...a little trick to make the process more comfortable: The factory made joint of the 2-pin connector must be cut and unnecessary parts removed to keep the ability of tuning the distance of the middle U legs.
For compensating the frequency shifts, all of the U parts should be finely and evenly tuned at the same time. In practice, the two phasing U on the sides have to be symmetrical, at least. So, you have to maintain the distance of the legs on 3 U elements and also the position of your coax on the center one. Any of the mentioned points on the antenna can mess up the final result. Make sure that the path of the coax leaves the antenna perpendicularly - do not lead it in parallel with the radiators and the matching stub (middle U element) before it is farther than a full wavelenght if possible. (from 28-30 cm, the distance is safe) Joining an extra wooden stick to the middle of the support stick already used for the radiators will help. They form a T.

/// I have a nano-VNA but it was still not so simple to match and tune this antenna. At the end, it had 50.23 ohm and 1.07:1 VSWR @1090 MHz, (29.4 dB return loss) ///

(note: PVC also detunes your antenna, avoid the use of it as material of suppport element)

4./ Loss of coaxial cable
There are ways to decrease or to get rid of cable losses. Use low loss coax at the impedance of your receiver and use Low Noise Amplifier (LNA) to compensate the expected loss. Amplifier shall be used at the antenna end, since the already lost or non existing signal can not be amplified at the receiver side. :) Use of LNA is more important if you want to use also a filter. These filters are good to keep the unwanted signals overdriving the receiver away - but filters have a so called insertion loss...
You can forget cable losses by not using the coax cable at all, or by use of a really short one (pigtail). Not a joke. :) These days, excelent USB extension cables are available.With a 10m lenght (30 feet) you do not necessarily have to insert extra power source for your dongle. The extension cable must be a USB2 compatible one. Beware of the ones for keyboards and mice only, because these cables have very low data rate, not like your dongle. (indoor, upstairs or attic) Connecting the antenna directly to the dongle is best. This way, you can forget bothering with coax cables. Cons: USB extension cables have the USB male plug and also an even bigger female end fixed on the cable. This is why you have to chose between drilling a huge hole - or cutting the factory-made cable to use a normal hole through the wall, and solder the previously cut cable back... I do not have to mention that this latest is against the garantie. :)


5./ CoCo (coaxial collinear) antennas
My opinion strictly... It is a time wasting faulty construction, mainly at 1090 MHz. There are too many cuts of elements for gathering the mistakes and almost impossible to set the necessary parameters even with Vector Network Analyzer. I have never seen a plan of coco antenna where both decoupling and matching were set correctly. There are really few documentation or study about coco antennas. Not by chance. It is really cheap and told to have so high gain, then why the hell we can not buy one in the shops? Let's see...

Intermezzo: Maniacs build them with 12 and 20 elements LOL

My opinion: Above 8 elements the extra gain is almost nothing compared to the problems we may get. Let's say, we can get it work as expected. A 8 or more element collinear has a really sharp plate-like radiation pattern, so we would lose the planes above us, plus any deviation of the antenna from the real vertical would cause even more losses. The round-plate-like pattern would cut into the ground too early - instead of catching planes in the air. The previously mentioned 1% tolerance is not acceptable here, since 1% shorter elements would down-tilt the lowest lobe of the radiating pattern, 3-4 degrees below the horizon. (it is ok if you run a repeater station on the top of a hill and you want to serve the ones in the walley. This down-tilt feature can be set easily at lower frequencies, dealing with longer elements)
So, this antenna tuned to either a bit lower or higher frequency would distort the radiating pattern. With the gain of 10+ elements you can not compensate the possibly distorted radiating pattern, the bad SWR and the mismatch of the antenna. Those who say the opposite tend to forget that the measured bad SWR at the antenna and/or the missing decoupling will always cause more loss at the other end of the coax, and the experienced loss is not linear.
(The values measured at the cable end seem to be more favorable than the real ones, but we cannot read the real properties of the antenna there. The loss of the cable also attenuates the amplitude of the reflected waves, so on a high loss and/or long cable we can see parameters close to perfect even if in reality the antenna is unusable.)

Note: Just pushing the coax pieces together is not antenna making, at all...
Assuming that the antenna is already matched correctly and the common currents of antenna and feedline are decoupled - we still have problems.
The phase shift calculated by the velocity factor of the coax cable is fine, this will force the outer surface of the adjacent antenna elements to radiate - even though they are NOT actually resonant at the calculated frequency due to their physical length. Braid radiates to air, so we should use another VF value here --> but we can not. The measured cable pieces can not be matched for both dielectric materials at the same time.
In summary: Though it can work after a lot of engineering job, but its effectiveness is questionable.

I admit, I also made some of this kind, but when I measured the parameters I would have liked to cry. I sent the final products to the trash.

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A really well made, 4 active element antenna will almost always work better at the same site, on the same position. You can achieve greater than 8 dBi gain, at 2° just above the horizon - so keeping the antenna vertically(!) is important, since 1-2 degree of inaccuracy may result in failure.

If you set the antenna to the side of a mast, you can "tune" the gain caracteristics by picking a side-distance from 1/4 to some more than 1/2 wavelenght. At 1/4, it is almost round-like with some loss towards the mast and some more gain in other directions. At half wl, you will get the maximum 9 dBd (~11dBi) gain towards the sides. This is more than enough for an omni antenna.
see: Stacked-phased antennas... You can expect 6dBd (8dBi) of average gain.

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By the way, collinear antennas are one of my favourites --> they deserve some attention mainly in vertical use.


...The whole paragraph about CoCo antennas is my personal opinion. You can still love them.


The commercially made, really good antennas are never coco-s, and collinear ADS-B antennas in the shops never have more than 4 driven elements.
(Only the ability of the reproducing proves that a plan is well engineered.)

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My words are not carved in stone, and far not all the necessary knowledge is covered by my experience and study - these sentences are for helping beginners with the first steps, not else...

The main rule is: Have fun!
Janos

PS: Sorry for my poor English
 
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Thanks ab cd :)

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Let's continue with extra tips:

After the GP antennas, we still have the opportunity to make an extremely simple wire antenna that works even better. Its gain is about 1-2 dB higher than that of Ground Plane antennas.

J-Pole antenna: -->DC shorted antenna, without amplifier you must switch the bias-t off !!!
As its name suggests, it is a J-shaped electrical conductor (e.g. Solid internal conductor of the coaxial cable).
Structurally, the lower part is identical to one of the U-elements of the Franklin antenna I mentioned in my previous post. One leg of this U-element is extended by a section equal to half-wavelength. Do you still remember? (required wavelength per 2 multiplied by Velocity Factor 0.95). This extended section is the radiating element of the antenna.
(Don't be fooled by the term "element" radiant. Antennas behave the same as receiving and transmitting antennas. See: Reciprocity )

I will now boldly describe: The U-shape under the half-wave radiator is actually a quarter-wave antenna feedline folded from a half-wave conductor. It is short-circuited at one end and electrically open at the other. If the U-shape resonates with the frequency used, for radio waves 0 ohms is one end and in practice the other end represents many thousands of ohms impedance. This allows us to find the right point for the coax.
On the shorter shank of the J-shape, 6-7 mm from the shorted end, we find the 50 ohm connection point for the coax shield braid, 75 ohms slightly higher. On the opposite side, symmetrically, the recommended connection point for the inner wire is on the longer shank. The antenna also works with a reverse connection, but the radiation pattern is less favorable.
qw_stub.jpg

It works right after almost every attempt to build, with at most a little tuning on it. If we’re content with a little compromise, just clip a “FairRite type 61 clip-on” near the antenna to the coax and you’re done. There is another solution ...
This antenna is my reference antenna, I use this while I repair or rebuild the other one.

Let's make things even better!
One more theoretical lesson - I promise, almost without math:
As I mentioned, the U-shaped feedline on the Franklin and J-Pole antenna is open on one side. What I didn’t mention is that it’s symmetrical or as it’s referred to in radio engineering: balanced. What is interesting about this? The fact that the coaxial cable that connects to it is unballanced (not symmetrical)
The currents of the antenna will also tend to travel on the outer surface of the coax, thus degrading the properties of the antenna. The FairRite clip mentioned above is listed as a choke on the antenna current on the outer braid of the coax. Decoupling of the antenna is more or less solved.
Why would we do this if there is an even cheaper and more elegant method? We need to ensure that the appropriate 50 (or 75) ohms are still connected to the receiver and the antenna is given a balanced connection at the other end of the coax. Everyone would be satisfied with that. The antenna, the receiver and ourselves - we are approaching the optimal solution!
The device to be placed between the coax and the antenna is the balun. (balanced-unbalanced transformer) It is also available in stores for VHF and UHF TV channels, but unfortunately this is not suitable for us - due to the frequency dependence. Don’t be sad, the solution is simpler than I will describe right away.
- This is important: Check the cable's VF (velocity factor) coefficient on the coax cable manufacturer's website. We will need the exact number.
Cut a piece a little longer than half a wavelength from the remaining cable you find at home. (300 per frequency in megahertz per 2 multiplied by the VF value obtained from the manufacturer) 300/1090/2 * vf
Cut the outer braid of the cable in the above length, keeping the inner conductor intact at both ends. (1-1 cm protruding wire at ends will be enough) Fold the sized piece in half so that the outer braid of the ends is aligned. Secure the cable with adhesive tape so that the cut ends remain next to each other. When bending, the loop is NOT sharply bent, this would damage the cable. Attach the cut ends of the prepared loop to the antenna side of the coaxial cable (now not attached to the antenna) and secure them together with adhesive tape or heat-shrinkable tube. By soldering or other method, electrically connect the outer shield braid of the loop and coax - near the cut surface. All three braid ends electrically form a single point. Solder one of the protruding middle conductors of the loop to the base of the protruding conductor of the coax. The 2 pin will be the connection point for the antenna - the outer shield braid will NOT be attached to the antenna! Now we have a 4: 1 balun adapter tuned to frequency like the pros!
Due to the small distance between the U-shaped legs, it is more practical to fasten the three cable ends in a triangular shape (the smallest distance). Also do not touch the bottom part of the U shaped wire on the antenna to the braid by chance!
4_1 balun.jpg

The 4: 1 ratio means that instead of the original 50 or 75 ohm impedance of the coax, we now have a 200 or 300 ohm balanced(!) interface. This higher value is not a problem since for any impedance we can find the right point on the U-shaped antenna element.
The point is that our antenna has a balanced connection, and after finding the right point on the legs, no unplanned current can flow on the outer braid, - thus our antenna has the planned radiation pattern and takes the energy radiated by the other antennas.
I could also have taught the 1: 1 balun so you don’t have to look for the connection point again, but we need the 4: 1 ratio more often.

- It is recommended to use "semi-rigid" cables to fit the antenna, so that we can do really precise measuring, cuts and soldering. On 1090 MHz, commonly used coax cables with the usual diameter are not always usable.

Always build a balun for the antennas where the connection is balanced, since a coaxial cable alone would distort the radiation pattern. Creating an antenna is a "step by step" procedure with strict rules. Antenna, connection interface, feedline and all the elements towards the receiver are parts of the system - so we have to match them properly.
A BALUN will preserve the benefits originally planned for the antenna. Last but not least, we learned that even a professional solution sometimes can be done without extra expenses!

Enjoy it :)
Janos
 
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Referring back to my suggestion above, I have just made a spare J-pole antenna. I show you the measured parameters to prove that making this antenna is soooooo easy.
On my nanoVNA-H:
Impedance is 49.935 ohm, SWR is 1.001:1 (return loss is -64dB)

See the red marker(s)

jpole_measurement.jpg

If you just hit the frequency and then close your eyes without looking at the other parameters, then you simply start using the antenna ->, you can still have a better product than the trendy quarter-wave GP and Cantenna versions. I would bet on most of the other, more complex antennas as well. (the more complex the less likely it is to work properly without the use of serious measuring and test instruments.)

The only thing to pay close attention to is that the presence of metal or other conductive materials in its environment (including the carbon fiber mast) are very destructive, they degrade its quality. Literally, a J-pole does not need "groundplane".
The last section of the antenna holder may be made of another neutral material. For example, a fiberglass or teflon rod. If not available, other materials are also acceptable, but by no means attach the antenna to the side of the support post. It is common for amateur use to put it on top of a metal mast (electrically connected to the lower part of the antenna). Don’t believe the plenty of such suggestions. I would have countless counter-arguments, but it would be very lengthy to explain and quite boring ...

Let's have fun!
 
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Great explanations. And I would love to see more pictures of your resulting and so perfectly matching antennas ;).

Some questions:
1) what is the distance between the 2 legs of the U-shape?
2) does the horizontal part of the U-shape adds up to the quater-wavelengths of the two legs? Or are they both or one only reduced by the length of the legs' horizontal connection? (btw, I always struggle with same question for the franklin phase delay U elements ...)
3) I read about some end-correction needed, that depends on the relation of wavelength to thickness of the wire used, e.g.
Doesn't this apply here, too, shouldn't one take this into account additionally?
 
Hi,

You can see the measurement result of one of my antennas above your post. ;) Of course, not all of them are "perfect". Accepting compromises possibly means the more likely healthy nerves for the rest of your lifetime. :)

Some answers:
1) and 2) leg distance is about 6 mm between closest surfaces. Most of the times the bottom part is not flat but rather curved to easily adjust the leg distance by straightening or further bending. I don't have an exact recipe for it. I do the refining while measuring. The total electrical length of the U element is equal to half the wavelength multiplied by VF. The top of the bend starting from the upper surface of the radiator is the starting point, and measured along the center line of the material - I also included the lower bent part of the U in the whole length ...
(Franklin antenna)

For J-pole, you cut a full vawelenght * VF piece of wire, then half of that shall be bent into half.

3)
The calculated value is "solely" multiplied by the VF for simplicity only. For materials of the usual thickness, the difference is insignificant, it is corrected for fine-tuning anyway. Compared to a more precise approach, there may be a difference of an extra three tenths of a millimeter at this frequency. (compared to the calculations with pure VF) We can't even cut exactly that way, so we leave a little extra material on the ends which we later carefully sand down as needed - if the measurements justify the operation
Please note that the linked material in your post is about a half-wave dipole antenna - but we have a half-wave radiator on both legs of the U.
(for J-pole, one half-vawe radiator) At the end of half-wave radiators, there is theoretically no current flowing but the voltage here is the highest - so the impedance here is thousands of ohms. Therefore, a U-shaped quarter-wave feed-line shorted at one end is required. Tap points can be found from zero (at the short circuit) to the open end of thousands of ohms - whatever impedance you may need.
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(a dipole you refer to other than the one I described above) The two halves of a half-wave dipole are each quarter-wave. In this case, the maximum current and the minimum voltage at the feed point, located in the middle - so low impedance can be measured here. In practice, this is already about 73 ohms. You can connect a coaxial cable directly to it but always use a 1: 1 balun. If the coaxial cable is 50 ohms, the half-wave dipole should be shortened by about 7-8%. (instead 5% comes from VF) This will get closer to the 50 ohm impedance and the phase state of the feedpoint will also be more balanced. (shows neither capacitive nor inductive nature)

If you want the antenna to cover more bandwidth, you can use thicker materials than usual, with a slightly shorter length. The skin effect has to do with the change needed. (I wrote about it at the top of my article in the dimmed paragraph)
I think, the skin effect is the root (origin) of the relationship between VF, the high-frequency conductivity, and also the Q factor.

There are also diagrams for the relationship between the thickness of material used and the shortening. We can forget the formulas.
1623851587318.png
1623851663692.png


I hope I could help..

Regards,
Janos
 
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I saw the measurement pictures. But I would be interested in pictures of the antennas you measured ;)

For 1+2 I'm done with the answer, thanks :). Hopefully I can reproduce your measurements with this as "recipe".

For 3) I wonder why you result in a 3/10th of a millimeter change. My calulation would look like this:
ratio of wavewlength to conductor diameter is 130,6mm/1,5mm = ~87
Checking the graph (see below) result in K = 0,9605
Applying to the length of the end section: 130,6mm * K = 125,5mm

Or what is wrong with my calculation?

1623853867343.png
 
While using the diagram, you do NOT have to use also VF !!
Use the original half vawelenght instead.

137.6 mm --> 130.6 by the original VF --> 130.0 to achieve the zero reactance
With 2.6 mm dia wire, the ratio is about 53, then the resistance at resonance is about 57 ohm. Cutting a bit more gets you to 52 ohm and zero reactance.

The multiplying factor (K) contains the VF

The original lenght would result a 73 ohm antenna with 43 ohm reactance. To cancel this reactance and get an antenna with pure resistance, we have to shorten the antenna - using the K value on the graph. To stay within the usable bandwidth at the desired frequency, we have to use a bit thicker wire.

In case of unusually thick or very thin material will cause real differences from the usual velocity factor... (0.95)

Once again: The diagram is for half-wave dipol. This is where we shall cut some more to get closer to 50 ohm and a nice reactance. Using 2.6 mm diameter will let you reaching the optimal values easier. The antenna will not be at the exact frequency, but it will not be so bad as long as the antenna has a proper bandwidth to let you cut more.. Reactance is more important than impedance in this case. Instead 1.1 you will measure max 1.3 SWR - but antenna can resonate at the frequency.
 
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Ah, I see, so the diagram is only valid for copper wire in air.

Actually I have only 1.5mm copper wire available, at the moment I will have to stick with this.

So calculation using this makes difference of ~1,1% remaining:
Half Wavelength with VF applied: 299.792.458m/s * 0,95/(2*1.090.000.000/s) = 130,6mm
Half wavelenght end section: 299.792.458m/s * 0,95/(2*1.090.000.000/s) = 132,1mm

So this should be the theory. I'm curious to see my practical results then :cool:
 
If you want to create a dipole, you shall use the second graph first.
- Read the lenght per dia rate at resonance and 0 ohm reactance first. (about 50, this gives you a wider bandwidth and the possibility to shorten the antenna so that the unwanted reactance can be cancelled. Detuning percent 7% as for the diagram. In my experiences it is a bit closer to 8)
Zero reactance means that the antenna works at the tuned frequency. Choosing a wavelenght alone is not enough.

- then calculate the real half wl per ratio. This is the usable dia of wire!
- Now check the first diagram.

That's all.

Of course, you HAVE TO use a 1:1 balun as a connecting interface and 50 ohm coax. I have already written about balun-s in another article.

Green text here: https://forum.planefinder.net/threads/franklin-antenna-for-those-who-have-a-75-ohm-receiver.1306/
 
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Sticking with 1.5mm wire:/
- When you get rid of unwanted reactance by shortening the antenna, the desired frequency will sneak out of the given bandwidth. This is why you have to use a bit "heavier" wire. Better bandwith will keep your antenna within the usable range.

This extra shortening problem is specific for half-wave dipoles.
- staying on resonance frequency and accepting the 43 ohm reactance (Inductive behaviour) would be a very bad compromise.
 
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Ah, I see, so the diagram is only valid for copper wire in air.

Actually I have only 1.5mm copper wire available, at the moment I will have to stick with this.

So calculation using this makes difference of ~1,1% remaining:
Half Wavelength with VF applied: 299.792.458m/s * 0,95/(2*1.090.000.000/s) = 130,6mm
Half wavelenght end section: 299.792.458m/s * 0,95/(2*1.090.000.000/s) = 132,1mm

So this should be the theory. I'm curious to see my practical results then :cool:
Practically, you can use this simplified format:
300 / 1090 /2 = half-wave = 137.6 mm

then

- lenght per dia ratio = 137.6 mm lenght / 1.5 mm dia = 91 (92 if you want)

- Check second graph at the target (zero) reactance and find the common point of zero line and the 91 rate value.
It is about 5.5% detuning ratio, and also means 94.5 K value on the other (first) graph.
Note that it means only 0.5% shorter wires than the usual VF would tell. It seems small, but it is a very important difference.

- On the first graph 52-53 ohm resistance belongs to the 94.5 K value. Perfect.
So, 137.6 * 0.945 = 130.032 ~130 mm

This 130 mm is the full lenght of the dipole, not the metal parts only!
The center of the half-wave dipole represents low impedance. If the connection point is not in the middle - or the gap between the quarter-wave parts is large - then the calculated impedance will not be true, the actual value may be much higher.
Make sure that the gap at the connection points does not exceed 1-2 millimeters. This is also included in the 130 mm size of the antenna.

To sum up:
Calculating only with VF, the impedance of the dipole is z = 72 ohm resistance + 43 ohm inductive reactance = ~ 115 ohm (very bad)
Reducing reactance by further shortening, resistance also decreases with it. When the reactance of the antenna reaches zero, pure 52 ohm resistance is obtained. Difference in lenght is about half a mm. This 0.5-0.6 mm will decide if antenna works well or it goes to the graveyard of other unfinished projects.

- Before you sand the ends of the elements, you can push the parts closer (half a mm or so) to test or measure the result of the next (targeted) lenght. Then set the gap back to the previous size and modify the lenght of elements equally. And so on, just small parts at a time.

(Always keep a bit more of lenght at calculations. It is easier to cut than making a wire longer again)
 
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