Single stub matching of loop antenna at 4.2 GHz

Question

I am trying to match a loop antenna using the single stub matching technique.

Operation frequency: 4.2 GHz
Vacuum wavelength: 7.2 cm

Cable:
Impedance: 50 Ω
Velocity factor: 0.66

The antenna impedance is unknown, but it is approximately a full wavelength and I think it should be around 100 Ω at 4.2 GHz.

My theoretical matching procedure (see picture below): I have a VNA, which I calibrate at a certain plane without connecting the antenna. Then I connect the antenna via a straight BNC connector and a given number of small connectors to get the real part of the admittance measured by the VNA to be 1/50 Ω. After that, I change the straight BNC connector with a BNC tee which has the same length. Then I connect a BNC cable to the free end of the BNC tee and I trim this cable to get rid of the imaginary part of the admittance. I am then left with a real admittance =1/50 Ω. My antenna is now matched.

Empirical problems:

1. I can never get the real part of the admittance to be 1/50 Ohm, when adding the small length connectors, it always behaves kind of weirdly, not very continuous with the length of the transmission line...

2. The open stub which should have a purely imaginary impedance also changes the real part of the impedance read by the VNA...

Experimental questions:
Do you have any advice for the practical implementation of single stub matching?
Should I use another kind of matching? What is the best kind of matching at these frequencies? The signal going to the antenna will maybe be a few watts in the end.

Theoretical question:
As it is when I do the matching, even if I get it right and the VNA measures 50 Ohm impedance at the plane of calibration, how do I know that the power is actually being radiated by the antenna and not the stub part?

Answer 1

What does the "BNC Tee" do? Aside from the fact that 4.2 GHz and BNC are not usually combined, on this hinges the whole idea. Also, note that most BNC tees that exist in the world are from TV cabling or old coax Ethernet cabling, and not 50 Ω, but 75 Ω.

Is it a power combiner that isolates the port going to your antenna and going to your stub? Then, this won't help. Is it something else? If so, what are its port properties? Something that can be used at 4.2 GHz will come with some documentation or at the very least clear labelling! Again, 4.2 GHz and BNC is an unusual combination: Aside from frighteningly expensive BNC connectors at measurement devices, very few BNC things are actually tested and specified up to 4.2 GHz. That is a direct consequence of the large diameter of BNC, which lends itself to large-diameter coax, and that tends to have low cutoff frequency.

I think you forgot here that someone who builds a Tee already needs to make a decision on what kind of microwave device they are building.

Furthermore, that stub will at most be half a wavelength (probably more in the range of a quarter wavelength.

A wavelength in velocity factor 0.66, cable, would be around 47 mm, so half a wavelength would be maybe 24 mm. Now, subtract the non-zero length of the BNC tee and the BNC connector, and you're not left with much to trim at all – and, also, unlike a well-manufactured microstrip stub on a board, you really need make sure your "trimming" doesn't make that end of the cable an antenna, but an actual "open", electrically. (You can of course always add full multiples of wavelengths, but I'd fail to see how you'd then build anything reliable).

Furthermore, your antenna is not the folded part of the core, your antenna encompasses the mantle of your coax and the exposed core in this antenna design, so, this isn't even a matching problem alone.

So, I don't think this has any chance of working the way you want it to; wrong cabling, wrong components, approach doesn't transfer as well to coax whose diameter is not negligible compared to wavelength, as it becomes impossible to build a "pure" open stub.

Do you have any advice for the practical implementation of single stub matching?

Do it on PCB.

Should I use another kind of matching?

Yes; this is a classic antenna design problem, and your solution to match a simple antenna is a complex matching circuit. Instead, I'd probably consider making your whole antenna something on a PCB, add the 50 Ω matching to the same and then connect that to your measurement device.

What is the best kind of matching at these frequencies?

Depends 100% on what you need to do – bandwidths, mechanical properties, acceptability of losing power etc.

In your case, the proper method of matching is probably not trying to do ana unbalanced folded dipole with random properties due to mechanical inaccuracies.

The signal going to the antenna will maybe be a few watts in the end.

That's relatively much. If you have a microwave amplifier with that amount of output power, it's probably not going to be BNC-connected, so the question becomes why you're doing all this on BNC.