Franklin antenna for those who have a 75 ohm receiver!

--> Feeders with 50 ohm system will also find useful ideas...

I recently made a Franklin antenna model whose most parameters can be changed.
Franklin.jpg

As I played with this, I realized that unreasonably many people were disappointed with this antenna, they had failed in construction. Now those with a 75-ohm system can breathe again. There is hope and simple solution to get rid of most problems!
...In addition, 75-ohm ADS-B antennas are not available in stores...

In fact, I could never see a photo about this antenna on flight feeder forums with the necessary 4:1 or 1:1 balun. No wonder they don’t work or just provide unacceptably bad reception. (comparison of a Franklin and a GP antenna is not even fair but I often read reports about a similar performance.)

Let's change this sad situation...

The most sensitive point of this antenna, in terms of construction, is the central bent element - the impedance adapter. If it is not made of the correct length of wire or you do not find the correct impedance points - the antenna will not work.

... What if we didn’t even use this component? The impedance at the end point of the half-wave antenna element is extremely high - thousands of ohms. This is too difficult to handle. ... it is better to use well-proven methods.
The impedance of half-wave dipole antennas is already very close to 75 ohms. (about 73 ohms and made of 2 quarter wl segments)
Why would we complicate our lives with a different solution?
Let's see.

It will be simple:
- forget the middle U-shape and cut the connected radiators in half
modifications.jpg


- connect the middle conductor of your 75-ohm coaxial cable and the shield braid directly to the endpoints (feed point) Do not use long wires!

There is only one step left. We have to prevent antenna currents from also using the outer conductor of the coax as an antenna component. It is the key movement of the construction.

- Cut a quarter wavelength long part from any remaining piece of coaxial cable -> a little longer one so that the middle conductor can protrude 1-1 cm. Now we are not using the Velocity Factor given by the manufacturer, but the ratio to be used in copper wire. (0.95 so 95%)
Don't even calculate, I'll tell you...
- For 1090 MHz keep the braid intact at a length of 65.3 mm and close it short to the middle conductor at the ends. If you did it right, now you hold a metal rod of the same cross-section as the original coaxial cable, with a spike at the ends. We need it now as a large-area electrical conductor, not as a coax.
- Bend one of the pins at the base by 90 degrees and fit the cable piece - parallel to the cable end attached to the antenna. Attach the straight pin to the center conductor of the coaxial cable (or to the point where it connects to the antenna). The other pin should point to the antenna coaxial cable. Where it touches, carefully remove the plastic insulation in a small area to gain access to the braid. Solder the bent pin there or hide it between the insulator and the braid. The two adjacent coaxies are parallel and have a 2 mm air gap between them.
The reason why we used the VF 0.95 is this air gap and the copper surface of the modified coax.

DC and RF currents both tend to choose the easier path. In our case it will be the braid instead the center conductor where just a smaller part will go through. Thanks to the connections and the resonant quarter wave lenght, we will have mutually neutralizing electric fields between the parallel surfaces of coax parts. Common currents of antenna and coax braid can not flow on the tuned frequency, so antenna elements will behave like an extra metalic object (coax to the receiver) would not be connected there...

Now, the antenna will surely fit the cable well, and the latter will not distort the radiation pattern of the antenna. Not to mention the fact that you just made successfully a 1:1 balanced-unbalanced transformer (BALUN)


- This kind of decoupling method with this 1:1 balun works well also for others with the central impedance tuner U element, either 50 or 75 ohms. This U section is for setting the proper impedance only, but you have to deal with the "common currents" as well. (it is decoupling)
In radio engineering, this 1:1 balun is called: "The Pawsey stub" or "EMI Stub Symmetrising Device". Technically they are identical if there is an air gap in both solutions...
If you stay with the U stub and pick a bit higher impedance, - 200 or 300 ohm depending on your 50 or 75 ohm coax cable (tap points are about at the lower third of the U) - you have to use a 4:1 balun. I have already written about it in another post.

The 1:1 balun shall be chosen for decoupling when you already have the same impedance on the antenna and the coaxial cable.
The 4:1 balun is for matching and decoupling at the same time.
(the ratio indicates the impedance transformation if there is)


Using this sizing in 75 ohm, and decoupling method with a balun in both 50 and 75 ohm systems, the functionality of the antenna is almost certain.

In the 75 ohm version, there are only 3 half-wave antenna parts instead of the original 4.
In return, we got rid of most problems. Keep in mind that the much-loved FlightAware 66cm antenna has a gain of 5.5 dBi.
The Franklin version we just made is 7-7.2 dBi - so we still have no reason to complain. :) Of course, the choice is yours but without antenna tester or VNA - I suggest the half wave dipol middle part for 75 ohm systems...
If you can not see a plane, not the 7dB gain is the problem but the shape of Earth or the position of the antenna, maybe the objects and buildings around it. An unnecessarily high gain antenna can cause problems as well...
Anyway, a well made lower gain antenna is always better to use than having a non working one with higher gain (according to its specs only).


For sure, I will also specify the other parameters:
- Radiators at the ends of the antenna 130.7 mm (including the curved part at the bendings)
- the quarter-wave elements forming the middle half-wave dipole are theoretically 65.3 mm long - in practice, a bit shorter to have a good resonance. The lenght includes the gap (feed point) between the dipole elements!
- Between the lowest point of the two phase-delay U-elements and the nearest point of the radiators (measured not from the center of the wire) ~65 mm. The distance between the stems of the U is 6 mm (between surfaces), which you can later compress slightly or open a bit more as needed, but the stems should remain parallel. In fact, it is a matter of straightening or further bending the already bent part at the bottom. (do not forget keeping the stems parallel) This allows you to fine-tune the length of U , ...just parts of a millimeter if necessary. Full electrical lenght of U is half-wave, 130,7 mm.
- You can attach the radiators to a wooden stick so that they do not move.
- It is best if the coaxial cable is routed at a steep angle from the antenna elements, including the phase delay U sections.
- Use a bare copper wire to make the antenna.

+1 tip for building antennas with more than one driven element or radiating parts:
Do not finish your antenna in a single workflow and hope that it will surely work. If possible, build the antenna's logical sections one by one. In case a Franklin antenna, create the matching section and the connected radiators first. When the "module" works fine, you have the perfect measured lenghts for the next module. Just copy the parameters and work with them, since the used materials and their properties are not always the same - so you can not trust your calculator or a recipe alone. Otherwise, you will get a W-like zigzag on your tester, and you will not be able to determine which element is not resonant at the designed frequency. Also keep in mind that getting an acceptable SWR sometimes means nothing about the quality of your antenna. My 50 ohm dummy load is "really wide-band antenna" with 1:1 VSWR everywhere, but it will never get a signal from outside... :)
So, check the units one by one and follow the well proven practices for the whole project.

...back to the Franklin antenna...
If you are satisfied with the result, seal the cut surfaces of the coax with hot glue for outdoor use. (better than two-component resins as they detune the antenna)
You can still use the wooden wand to mount the radiators. Apply several times a mixture of white spirit (or alcohol) and oil, using a piece of cotton wool then allow to dry. Then make it water repellent by waxing. In case of rain, the antenna will not become temporarily unusable or the chances will be lower.

Good luck with the construction! (maybe just a conversion)

Janos
 
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Trying to revive the thread :) Actually building a Franklin with 4 elements for 75 ohm antenna/cable/dongle/etc. 2.5mm cooper diameter wire. For rigidity reasons, I'm looking to make the original 50 ohm one and to feed the stub to a 4:1 balun. Hence looking for the 300 ohm stub position. Is there any way to calculate this position any other than trial and error? Found something about Smith charts but I'm not yet sure how to use them. Many thanks!
 
Trying to revive the thread :) Actually building a Franklin with 4 elements for 75 ohm antenna/cable/dongle/etc. 2.5mm cooper diameter wire. For rigidity reasons, I'm looking to make the original 50 ohm one and to feed the stub to a 4:1 balun. Hence looking for the 300 ohm stub position. Is there any way to calculate this position any other than trial and error? Found something about Smith charts but I'm not yet sure how to use them. Many thanks!
Hello!
Your solution would also work with appropriate technical development and the use of instruments, but I would like to draw your attention to the fact that:
- Feeding the end point of the half-wave (high-impedance) antenna element involves many problems and even more measurements/checks during construction.
- No stub is needed to power the half-wave dipole (2x 1/4 wl), the impedance is already around 72 ohms. Why would you increase the impedance if you would reduce it to the same value again?
- Good to know:
1689633887909.png

see: https://www.antenna-theory.com/antennas/halfwave.php

- Miniature baluns can also be bought ready-made. For the structure I recommend, only this - or a similar one - needs to be inserted between the antenna and the amplifier "1:1 (balun) 75 ohm
For example these:
https://cdn.macom.com/datasheets/MABA-011112.pdf

- For the 50 ohm system, we either trim the dipole and use thick material, or we use a 1.5:1 50 ohm balun.

I am convinced that the gain of the antenna would be sufficient with 3 elements instead of the original 4. The curvature of the earth causes problems before the distance itself.

- Do not forget:
The entire system must be uniform in impedance, from the antenna to the receiver itself - including everything in between. (cable, amplifier, filter, bias-t circuit and everything else)
75 ohm cables are usually ok, but inline TV amplifiers are usually noisy(!), since they are engineered for already strong signals getting through a very long cable.

You mentioned " Smith charts ".
Obviously, only the representation of your own measured values on Smith charts can be useful. Interpreting the diagram requires some preliminary studies, but some basic operations can be easily learned (with a little diligence) even if our original profession is far from radio and physics.
- Recommended videos: https://www.youtube.com/results?search_query=Smith+charts

The cheapest way to measure is to buy a NanoVNA device. (beware of fake ones, and keep an eye also on usable frequency range) The purchase is only really useful for those amateurs who want to own one for more than just building a single antenna.
 
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Dear Janos,

I'm very thankful for your post. I'm enjoying your posts, a lot, as you have the capability to summarize deep technical stuff into a easy-peasy understanding matter, in a very short time.

Right now I'm using a simple full-wave dipole, made by PY4ZBZ, (https://www.qsl.net/py4zbz/adsb.htm#e) with a matching stub. Reaching about 300km without amplifier. Matching is a headache, though...

You're right - makes no sense to self giving me, headaches, by using a stub. It was only for rigidity reasons, but I guess I can compensate that by mounting both ends soldered on a small PCB, etched accordingly. I will make your 75 ohm version of the antenna, with two half wave "stubbed" dipoles, and also planning to build a Pawsey 1:1 balun, as I have plenty of coax :) (I believe the Pawsey is exactly what you have described earlier in this post) I'm unsure about this phrase " I am convinced that the gain of the antenna would be sufficient with 3 elements instead of the original 4. " as I don't know how can it be made with 3 elements as they are not even. Moreover what should be the distance between the two inline dipoles at the connection point? Does not affect this the total length of the antenna, or each of the dipoles functions with no relation to the other? I mean can I have 2-3 mm at the connection point or 25 mm and is the same? Taking into account that there is no stub anymore, the coax should pe soldered also perpendicular on the dipole, or it can be soldered along the dipole?

Many thanks Janos! Looking forward to learn more :)
 
I'm glad to be useful, even though I'm just an amateur "hobbyist". :)

The term "full-wave dipole" made me smile a little. I wouldn't call this antenna as a "full-wave dipole", in terms of its operation, - though it is a dipole, I'd rather name it a colinear antenna, because just duplicating the antenna as a unit and connected via another "hairpin", it is already a Franklin. Kinda' special case.
(I would like to point out that the dimensions - in the drawing made by PY4ZBZ available on your link - are incorrect. 150 mm will never be resonant on 1090 MHz.
-->
The correct lenght for half wl dipole is around ~131 mm, and 1/4 wl stub is 65.3 mm.
Remember: Speed of RF wave in copper wire is 0.95 times the value of speed in free space) See my previous articles.
1689756935914.png

At the frequency we are interested in, tenths of millimeters (!) are also important when sizing the antenna. I must mention here that at least the most basic instruments are required. (Combination of antenna tester, NanoVNA, possibly white noise generator and receiver. The latter is not a calibrated procedure, but better than nothing.

- A stub is nothing more than a quarter-wave feedline with a short circuit at one end. As you know, we use it to feed the end point of a half-wave antenna element because we experience high impedance at the open end of the feed line. (Because of the open end, the resistance approaches infinity, therefore the current is close to the minimum, the voltage is close to the maximum)
Dipole antennas are most often connected to the feedline in the "low impedance, high current" part.
When we fit a half-wave element to just one leg of the stub, we see the well-known J-pole antenna in front of us. J-pole is not a dipole. This is a half-wave end-fed antenna.
When each leg of the stub has a half-wave element, it is still not necessarily a dipole. Technically, this is a vertical stacked-phased array with 2 half-wave elements. Of course, we won't argue about this, since you are at least partly right. (Refering back to "full-wave dipole") Let's move on.

3 or 4 elements?:
- Taking advantage of the fact that we have already reached this point, you can easily see how the 4-element Franklin antenna becomes a 3-element one. Because, although the middle element is connected to the antenna feed line in the middle, it is therefore physically in 2 parts, but at the same time it is considered a single part. (Half-wave dipol = 2 times quarter-wave, fed in the middle) So, this is a half-wave dipole. The other elements of the antenna are also half-wave, - connected with a phase matching (phase delay) stub. Together with the central dipole, there are a total of 3 active elements - they work in the same phase.
Examining the antenna in a different way: - The middle stub can be dropped from the system if both adjacent half-wave elements are cut in the middle - the two thus become a single half-wave dipole element.

You mentioned the physical stability concern and also the idea of soldering it to the PCB. It's a good idea, and develop your idea further with a box of the right size. This weatherproof and stiffening box should contain the PCB, antenna ends, coax cable and 1:1 balun and/or a ferrite core.

If you don't have instruments, it is very difficult to make the resonance of the antenna and the balun (both) exactly. The more tuned items in the system, the harder it is to make.

- Instead of the Pawsley stub, you can use - as a compromise - a split core ferrite (clap-on) to eliminate the flow of the common current between the antenna and the cable. In this way, the cable would no longer act as part of the antenna, it would not tune out its resonance and radiation (reception) characteristics.
You can even use two placed close to each other - to create as much resistance as possible for the high-frequency current that tends to flow through the cable's stockings.
I thought of something like this, of course, don't lose sight of the cable thickness and the upper frequency around 1GHz:

"Taking into account that there is no stub anymore, the coax should pe soldered also perpendicular on the dipole, or it can be soldered along the dipole?"
- When the antenna ends have high impedance (high voltage, low current) - the antenna is very sensitive, avoid the presence of nearby metal objects. (including the coax itself)
Short answer: - yes, perpendicular

- The feature of the Franklin antenna is the feeding of the half-wave element through the end point. Of course, connecting several half-wave radiating elements with quarter-wave phase-delay stub(s) makes it possible to connect the coax (feed line) anywhere. For example, the 4-element Franklin antenna can be fed either by inserting another stub at the very end (as in the case of the J-pole antenna), between the two adjacent half-wave elements at either end, or by feeding it at the center, which seems normal. By choosing the connection point, the energy distribution of the antenna can be "adjusted", thus also the radiation characteristic. If the feeding takes place near the lower element of a vertical, multi-element antenna, the characteristic will be flatter - but the more distant attached elements only receive about half of the supplied energy and the ones further away only a quarter compared to the directly fed element. This is the reason why the directly fed antenna element is always the most critical and more sensitive to accuracy.

Sometimes I mention a radiator as if I were talking about a transmitter antenna. It's not a mistake. The use of the antenna as a receiver requires the same parameters as the transmitting antenna, of course with the correction of the power limit.
See: https://www.tutorialspoint.com/antenna_theory/antenna_theory_reciprocity.htm

PS: Sorry for my bad English
 
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...what should be the distance between the two inline dipoles at the connection point? Does not affect this the total length of the antenna, or each of the dipoles functions with no relation to the other? I mean can I have 2-3 mm at the connection point or 25 mm and is the same? Taking into account that there is no stub anymore, the coax should pe soldered also perpendicular on the dipole, or it can be soldered along the dipole?
Very smart questions!

I mentioned above that the two metal parts (2 * 1/4 wl elements) are together make a single unit - it is called a 1/2 wl dipol

- The difference is that you could see a half wl part in one piece earlier - since it was fed at one end. (using stub)
- A half wl element can be fed not only at its end. Remember the ends and their high impedance (a few thousands of ohms)
As we tap the half wl element closer and closer to the center part, Voltage becomes lower and current gets higher. The middle of a half wl antenna part has the lowest impedance. Usually, the antenna need to be cut at this low impedance part - to join the coax, balun or anything else.

Calculated full lenght of a dipol consists also the gap in the middle. (You have to measure the distance between farther endpoints.)

Size of gap and symmetry may determines the available lowest impedance ~ from 54 to 85 ohm, but impedance depends also on other properties.
In practice, - depending on the mechanical stability - it is from 2-3 to 5 mm.
Having a very small gap makes it difficult to create good junctions without getting new problems, because of the appearing parasitic phenomena.
Wide gap may distort the receiving properties, but not a "lethal" problem. (note the connection of feed line) Spreading the wires of feedline towards the antenna elements (forming a V) will rise impedance. In the close areas of feed line and antenna, impedance might have a different value on them, the area can be considered as transition of antenna and feedline properties.
The area around the joint can be considered part of either the antenna or the feed line, or both. In practice, gap is the distance between braid and the closest surface of central wire of coax.
On lower frequencies, the "rules" above are somewhat less strict.
- Try to solder precisely, so consider the asymmetry of the coax cable to keep the connection distances (more or less) equal to the center line of antenna elements (even if the connection point is not on the centerline).
1689746765062.png

You can do a really precise job with the use of semi-rigid cable.
1689751125845.png
Of course, SMA connectors are 50 ohm - you may need another type
Semi-rigid cables are available with several kind of impedance value, not just 50 and 75 ohm. This type of cable is useful for creating "impedance transformers" or "tuned feed line"for a special frequency. Let it be another lesson.

Of course, unnecessary wires and the unplanned presence of materials with high frequency conductivity (carbon fiber box, synthetic resin not recommended for rf application, etc.) should be avoided.

Just to know something for the sake of knowledge itself:
- Half wave antennas - mainly wire ones - can be fed also in a non-usual way. Deciding the place of fed point other than one of ends or center part, may make an antenne resonant not only on the frequency belongs to the full lenght of the element. HAM operators use this phenomena often. Using this option, an antenna tuner is required for matching.

--------------

PS: See my refreshed remarks on your antenna currently in use. (a post earlier) I think, you should fix the original antenna first, then a franklin may come. A more complex antenna generates cumulative problems. For building a really working version of Franklin antenna, you need more than luck, a NanoVNA-H at least.
Making an antenna without an instrument is like driving blindfolded and relying on your intuition.
 
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Dear Janos,

As usual, a very complex and condensed knowledge. Pure joy! Your english is very good, BTW!

I still have to parse again and again, the last 2 posts, and to made a graphical representation of what have you explained, in order to fix it for good in my understanding. Meanwhile I'm reading Kraus's Antenna Book and also Volakis Antenna engineering book

About the PY4ZBZ antenna - someone said that the dimensions seems to be more of a 5/8 dipole, and if he made the antenna as a regular 130-131mm half-wave dipole it become reactive...I will test it tonight - cut the elements to dimension and see what can I obtain

The next step will be the 75 ohm Franklin exactly as you described it. I will follow here with the details

Many thanks for your explanations and guiding!
 
About the PY4ZBZ antenna - someone said that the dimensions seems to be more of a 5/8 dipole, and
Hi,

The PY4ZBZ antenna does not appear to be a close to 5/8 wavelength version. (rather, it may be a dimension taken to simplify cutting the wire)
At the 1090 MHz frequency we use, the 5/8 wavelength antenna is ~163.3 mm and not 150.

- Observing the current distribution of the antennas, we can make sure that at the usual feed point of antennas - antennas with longer than half a wavelength - there is no feed point in the center part corresponding to the current maximum, also the high impedance end-point is not guaranteed. ...so a part of the antenna will be out of phase / or tends to resonate on another frequency.
It is more like a random-wire antenna. Consider that this is not necessarily a bad thing, but here it unnecessarily complicates the implementation aspects - without bringing a significant result. If all technical conditions are optimal, the gain of the 5/8 antenna is 3.2 dBi - only according to the plan drawings. This gain is so close to the gain of a real half-wave antenna (element) that it can be considered the same.
The added next radiator of the designed antenna does not double the gain either, but only adds 2-2.2 dBi.
(From now on, instead "first element 3dBi+second one 2.2dBi = ~5.2 dBi" --> we should rather use 2.2 dBd ( it means 2.2 dB over a dipole, as a reference. I have to mention that the initial ~3 dBi is a special case. In practise it is always less.)

Many people make wild calculations, but they pay less attention to feasibility.

Imagining the "mirrored pair" of the 5/8 antenna in the drawing, we can see that the center of the antenna works against the other parts, making the efficiency worse.

1690314000225.png

By playing with the physical and electrical length of the sizing, it can be made resonant, taking into account - and consciously using - the parasitic capacitances in the nearby wires.
- How much does this bring us closer to our goal? So that we have a non-resonant length antenna that we make resonant with compromises? Compromise is always a price we pay by. What goods do we get for it? Worth it?
In my opinion, "keep it simple" is a much more practical motto. It is also easier to design, modify or maintain.

- Whatever antenna we want to match with a U-shaped feed line, the quarter-wave(!) stub itself also MUST be resonant at the given frequency. (the referenced antenna is not like this)
The construction of this part is as important as the dimensioning of the rest of the antenna. The bandwidth of the matching part is very narrow! As a result in the case of the smallest error, the antenna will not resonate at the desired frequency even if all other parts are perfect.

Modeling of antennas has another important part, effect of the ground. The design is not appropriate if we model free space and/or ideal ground. Vertical antennas behave quite differently if the distance between the base point and the ground is within 1 wavelength, or some fraction thereof. (they used to happen more often in broadcasting)
In our case, the base point (many meters high) is located at a height corresponding to a multiple of the wavelength, but the radiation characteristics can change even for a more modest change in height.

Even the most symmetrical antenna will not work as planned with vertical polarization, because the radiation characteristics will change due to the influence of the ground and the different distances of the antenna ends. (ideally to your advantage)

-----
note:
What Franklin antennas and their close relatives have in common is that they are very sensitive to objects around them (including the coax cable) and it is very difficult to make them permanently weatherproof.
- Anyway, it is just a hobby. A never-ending learning curve. Have fun!
 
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Antenna matcing L-network and Smith Chart
(in a more friendly way)

Remembering the need of measurements in antenna projects, maybe some of us already has an antenna analyzer or it is on his/her shopping list. Do not forget having a look at the antennas in the neighborhood. If you're lucky, there is a HAM operator who "wants" to lend his analyzer for you. ;)
As I mentioned, a NanoVNA is a real swiss-knife, but - though its price is not high - buying one is not surely worth for a single-time antenna constructor.

By measuring the properties of antenna, SWR and Impedance belonging to the planned frequency appears on the analyzer.

Impedance is shown, similar to this example:
Z= 62 ohm jX= -73 ohm
That is all we want to know first.
- I admit, I do some math sometimes but I am not a lover of that.
This time, we carefully avoid things like this:
1691838612025.png


Saving us from devil math, here comes - literally to your experienced fingertips - a mobile app for android.

- Do not run away from its name: "Smith Chart Matching Calc" (See the link at the end of this post)

This is a friendly app. It doesn't do everything(!) for you, but you really only have to play a bit to design the tiny L circuit that matches the newly completed antenna to the system impedance.

- You only need to enter the initial data, then you select the elements of the adapter L network one by one. You can swap components by dragging, or throw the unnecessary items away with a swipe of your finger.

- I think, you've already watched the video in my previous post, then we can get on with it.
Pay close attention to the "Ying-Yang" and the "eLevate" parts!
- for your comfort, it is practical to make snapshots (screen-capture) of the most important parts of the explanation in the video.
Here is the video again:

When the system impedance (usually 50 ohms) and the data provided by the antenna analyzer (you know, the Z and the jX things) have been entered correctly, the cursor will appear on the Smith chart. You don't need to know anything else about it, other than that you are doing well - if that point makes its curved track(s) to the very center of the chart.

We select an LC combination from the options explained in the video above and place their symbols on the screen of our phone. They can be highlighted by touching to change their value using the (strange) arrows at the top of the chart, also you can swap the elements' positions simply by a drag movement.

We can observe the result of the modeled change on the drawings made by modifying the parts. You can refine the order and properties of the components until the cursor is in the middle of the chart. You have matched the antenna to the system. :)
...that way we can avoid the use of terrifying mathematical formulas.

The app also helps to adjust the parameter of the part to the nearest standard value. They're usually available in stores - so that your solution is not just theoretical. For selecting an "E" standard for the parts' value-series, the related options are available under "NVP Tuning Mode".
"E24 series" or a similar menu item can be selected.

Well, based on what has been described, we CAN use the Smith Chart without immersing ourselves in mathematics or acquiring the NanoVNA mentioned several times.

Additional information:

An L-matching network built with discrete elements are not just for correcting/transforming impedance, but -first of all for making the antenna resonant where physical size has a hard compromise. A resonant antenna (on the planned frequency) has a clean, resistive behaviour - but the optimal (V)SWR is not surely at the (pre)calculated resonance point. Several times, it is too complicated to finetune a multi-element antenna by altering the parts. Sometimes, adapting thesystem impedance to the antenna by using a VERY cheap adapter in between them is more logical. (...and comfortable... You know, lazy people improve the world by getting ideas about how we can do things with less effort ;))

In some cases, the correction is handled directly by an antenna tuner between the antenna and the transmitter.

For impedance transformation and/or symmetrical/asymmetrical conversion, we use BALUN and UNUN





1691841564493.png
 
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HI Janos!

Excellent antenna matching theory!

Now - it's something i do not get - If i'm looking at the beggining of the thread, where we adapt the antenna to 75 ohm, transforming it in a "half wave dipole - we have λ/2 at the end dipole arms, followed by another λ/2 (in the phasing stub) and then suddenly we have λ/4 at the center arms of the dipole, where is to be feed by the coax. In the below image I found somewhere on the net, see it below, we have λ/2 all over till the coax. I know that you told me that two metal parts (2 * 1/4 wl elements) are together make a single unit - it is called a 1/2 wl dipole, but here in the center we have a virtual full λ which is confusing me. Should not have been cut also to λ/4?. Or this is a feed point not for coax but for an impedance matching stub?

If so - why 2 arms ended in λ/4 gives us 75 ohm and the below arms ended in λ/2 are giving us a MUCH higher impedance?

Thank you!

franklincollinear.jpg


P.S Also on this site they have also a dipole made of two arms in peculiar way as they use always λ/4 even in phasing stub and not λ/2 https://www.dataero.fr/fabriquer-une-antenne-pour-ads-b/

Thank you Janos for your time and patience!
 
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The diagram above doesn't make much sense from our point of view.
"Not all that glitters is gold!"

- We don't need 6 half-wave radiators and 4 phase-delay quarter-wave feed-lines. Moreover, the figure does not explain how the high-impedance end points of the half-wave elements will connect with the coax cable in the middle of the antenna.
It's incomplete and gross.
We had cut the half wl elements in the middle with a reason. So that we do not have to deal with proper size of tuned feed-line and also we can forget guessing if we have the right impedance tap-point... and so on.
Please accept the idea of counting the high-current points only. Though - in theory, - we can feed a half wl element anywhere we want, but we have to deal with phase and impedance too. Also with the capacitive and inductive behavior of the antenna. So, try to keep an eye on my view of point, "keep it simple!"


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Go step by step (starting with a single dipole) to understand how it works. Believe me, you can experiment a lot with two short pieces of wire and the coax cable.
- What does the antenna do if you use a thicker wire? (thinking of Q-factor, velocity factor and skin effect -- logical relations and rules)
- Is the frequency out of tune? Does it remain resonant or are we experiencing reactance?
- What about the bandwidth of the antenna?
- Does the radiation characteristic change? (environmental factors, antenna physical parameters, etc.)
- Connecting the antenna to the coax: RF choke (coil/rf bead), Balun (Voltage balun, Current balun), UnUn, RF transformers, L-Matching Network.
- Measurement technique
- ...etc.

Always stick to the simplest suggested solution. Because of the frequency we use, a construction with an accuracy of a tenth of a millimeter is necessary anyway. Therefore, we must first guarantee that our antenna really behaves like a tuned antenna, hopefully better than a wire of arbitrary length...
Then you can deal with more complex tasks. I always do it the same way.

- There is no universal recipe! We may use different alloyed copper that can be used with or without enamel insulation, with a silver-plated surface to improve high-frequency properties, etc.
The cross-section of the wires in different countries is not the same either!
- Success / or failure also depends on these small things.
(a 1-2% difference in size may result in the project being thrown in the trash)

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A half-wave dipole consists of two quarter-wave "halves". Of course, it still forms a single unit. It can be fed through its low impedance point, so the quarter-wave impedance matching can be omitted here. Stick to THIS solution if you want to implement it.


... The half-wave radiators of the well-known Franklin antenna - which I modified so that it can be used with a 75-ohm system (without the central quarter-wave feed line) - are fed at their endpoints via the much-discussed quarter-wave adapter, and the more distant half-wave radiators are fed by the elements of the same design - but already phase-delayed in function fed through.
 
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Forget it!
69 mm is not resonant lenght in copper wire!
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Loops, coils, U-shaped tuned feed lines, or U-shaped feed lines wound bifilarly, and many other solutions are possible, but just because someone posted it - doesn't mean it will work that way in our case. (Thick wire can not have a sharp enough bending for all the solutions, not to mention the parasitic capacitance... )
These wire folds actually deprive the antenna's "opposite phase" elements of the possibility of radiation. This way, the "useful" surface of antenna can work for what it is designed. Take (see) these parts as collapsing sections of the conductor in such a way that the currents within the sections cancel each other out, but "resonant electrical lenght" keeps the matching phase transition points exactly at their endpoints for the connected radiators. (it tells to the active element where the radiator ends are.)

Again: 69mm is NOT RESONANT at 1090MHz.
Our antenna is not made of air!

See: https://forum.planefinder.net/threa...s-in-construction-of-diy-ads-b-antennas.1285/
 
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If so - why 2 arms ended in λ/4 gives us 75 ohm and the below arms ended in λ/2 are giving us a MUCH higher impedance?

The wavelength at a given frequency means - following the sinusoidally varying current - that the entire cycle during its journey in a single period:
- The current occurs at the zero transition first, then it draws the positive half-wave while covering a distance of "half a wavelength", then it covers the other half-wave distance during the current change of the negative half-wave.
- Examining the events belonging to the half-wavelength, we can see that the current reaches its maximum at the quarter-wave, and then decreases to zero during another quarter-wave lenght of journey.
We experience the maximum current at the quarter-wave points of the alternating periods in the middle of the half-wave(s) - so we can assume the minimum resistance here (low impedance).
- The current and the voltage alternate in an inverse way compared to each other. As we get closer and closer to the ends of the half-wave conductor, we can measure an ever-decreasing current but an ever-increasing voltage. The voltage maximum will be at the ends of the half-wave wire, where the current drops to a minimum. Based on the simple formula learned in lower school, if R=U/I, low current even with high voltage means high resistance. In the case of alternating current with high frequency, we are talking about impedance, but the principle is the "same".
- At the center of the resonant half-wave conductor(!), where there is a point of maximum current, the voltage is at its minimum - hence the low resistance/low impedance.

You may want to watch this video:

...and this is the less entertaining one, but it contains the hardcore answer with tons of math (for mazochists only) :)
 
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