Firstly, S21 is a two port analysis not a single port reflected energy analysis as you would use for an antenna,
With a VNA you have these four analysis situations:
1) S11
2) S12
3) S21
4) S22
For single port analysis the first and last are used while for two port analysis the middle two are used.
Two port is used for looking at any two port device - could be an amplifier, filter, lead line (like coaxial cable) or an unknown "black box" with two ports, etc.
Single port would be for looking at a single port device, like an antenna or some kind of load OR a two port device with the opposite port terminated in a load that the VNA is calibrated for (usually 50 ohms for most non-cable or non-broadcast TV RF or 75 ohms for TV or broadcast related equipment).
I have no experience with tha "NanoVNA" but a lot of experience with HP/Agilent lab desktop VNA's so I can only go by what I have experience with and knowledge of; nevertheless, all two port VNA's should be arranged pretty similarly, at least for the basics.
Typically, as you look at the front of the VNA, the left most port (your left) is referred to as the S1 port while the right most port (again, your right) is referred to as the S2 port.
So a S11 measurement is looking at the transmitted versus received energy as presented to the S1 port of the VNA. It is looking at the magnitude AND the phase of the reflected energy relative to the presented transmitted energy so as to use the results to compute and present a "picture" of the quality of the load as seen by the VNA's S1 port.
That's the nice thing about VNA's - VECTOR Network Analyzers! They look at not just the magnitude ("strength" or amplitude) of the reflected energy but its phase (angle relative to a calibrated resistive load). That "angle" shows you how capacitive (negative angle) or inductive (positive angle) the resulting reflected energy is. A scalar-only analyzer, SCALER Network Analyzer, can only show you the magnitude of the reflected energy. A typical SWR meter is a very specific abbreviated form of a single port Scalar Network Analyzer.
When designing matching circuits, for example, it really helps to know the phase angle of the reflected energy so as to know which matching components to use, inductors, capacitors, and in which arrangement. You want to shoot for nulling out the reactive component as much as possible so for a +j-something you want to throw in a compensating -j-something which would be a capacitance and vice-versa for the opposite situation (inductance to compensate for a capacitive reactive load or -j-something). Then you want to bring the resistive part as close to the desired system impedance (usually 50 ohms or 75 ohms as explained above) as possible.
Google S-Parameter Network Analysis to read up on this and get a feel for the proper care and feeding of your VNA. Yes, a fair amount of math is involved but even skimming over the math portions and at least reading the descriptions, in a good tutorial, can give you a decent overall picture and really open your eyes about the bigger picture of impedance and gain/loss network analysis.
By the way, yes, you can show impedance on that VNA based on the choices I saw that you listed. It would be the absolute value of Z or |Z|. Again, Googling S Parameter Analysis would explain this to you.
So, getting back to the basic use of a VNA; for single port impedance analysis of an antenna you would typically use just the left most S1 port on the VNA and switch the VNA to single port S1 analysis mode. This would correctly be termed a "S11" device analysis. Think of the two numbers following the capital "S" as references to the port of the analyzer and think of it as "S parameters relative to those sourced from the VNA's S1 port and reflected back to the VNA's S1 port" - or, put another way, "Port #1 sourced to the attached load/device versus port #1 reflected from the attached load/device" - "S11", in short.
So, the title for your thread SHOULD have been antenna S11 analysis. S21 for an antenna doesn't really make much sense when only using a VNA in single port mode and only one antenna. By itself, an antenna is, in effect, a "single port device" (from the point of view of a typical VNA) as you don't have a second "port" on the antenna that you can easily connect to the S2 port of the VNA. You could, I think, use a second test antenna of known quality at the test frequencies attached to the second, S2 port of the VNA, and then do a gain/loss S12 analysis (energy sourced from the S1 port relative to energy received by the S2 port) as well as a S21 analysis (energy sourced from the S2 port relative to energy recieved by the S1 port) and, assuming the second test reference antenna is very well calibrated for (all relavant qualities of the test antenna are known and calibrated for in the VNA) then, conceivably get a picture of the radiated energy from the antenna under test (S12) and recieved energy by the antenna under test (S21) that you want to look at in terms of its effectiveness at the test frequencies. This is not something I have ever done so I cannot give much intelligent guidance about this based on actual practical experience. I think PRC Guy on here has done this, however, and he would be the best source of advice concerning using a VNA to test antenna patterns and gain/loss measurements. Pretty much I differ to him for all things antenna in depth.
In terms of calibration and test leads - as others have said, you need to calibrate out the effects that the test leads have on the Device Under Test or "DUT". You ONLY want to see what the DUT looks like electrically and NOT the entire system of the DUT plus test leads. So you have to make the test leads (the coax cable between the VNA and the DUT) invisible to the final results. You typically do this by calibrating your VNA at the test frequencies and using the calibration standards (your "open", "short", and "load") attached to the end of your test coax where they would attach to the DUT rather than only at the VNA connectors. Think of the DUT and test leads as a "reference plane" and you want to move that reference plane as close to the DUT connectors as possible. The idea, again, is to see how the DUT looks like as compared to a "perfect resistive 50 ohm load" (as "perfect" as practically possible, of course - just use your provided standards). The closer it is to that standard at the frequencies of interest the better as far as impedance measurements are concerned.
Of course, this single port impedance test shows absolutely nothing about how effective the antenna is in terms of radiating and receiving energy, gain/loss, patterns, etc. As mentioned above, you need to perform different tests to look at these characteristics of antennas and, again, I think PRC Guy is a great source of knowledge, both practical and theoretical, in this area and I trust his guidance for such things.
As to testing presented impedance of 1/4 wave antennas (like most portable and mobile antennas) - be aware that they really should have a ground plane to work against when looking at their impedance. 1/4 wave antennas and others requiring ground planes, need to have the shield of the test coax right where they attach to the antenna's connector connected to a ground plane with a cross section appropriate for the frequencies under test. In general, for quick and dirty tests, you could use a sheet of metal as large as possible under the antenna and have a connector in the middle to attach the antenna to with the coax running underneath and back to the VNA. The sheet of metal will be attached to the shield of the thru coax connector and hence the coax itself while the center conductor would be attached to the primary element of the antenna. A metal folding table with a hole drilled through the exact center and a suitable through coax connector (like a female to female bulkhead connector, SMA, BNC, or whatever you need) mounted in the drilled hole could be a good testing setup for this as long as you know that, as you go beyond the lowest frequency that the ground plane is effective for your measurement error will get worse.
This is one reason why this phenomenon occurs - you look at a simple 1/4 wave antenna that likes to have a ground plane with a VNA and you see bad results until you touch the connector's outer shield and they then seem to improve. Your body when "connected" to the coax connector shield, becomes a form of ground plane for the antenna.
Also, all antennas will be affected by objects around them that have some opacity at RF, including all metal, your body, trees, etc. You really want to test antennas in a nice open space with nothing around them.
You want to see as little reflected energy as possible meaning most or, ideally all, of it is absorbed, and in the case of antennas, then, ideally, radiated by, the antenna. It's symmetrical which means that good radiation characteristics should mean (in the majority of cases, at least) that the receive quality of the antenna is also good.
For half wave antennas like that TV dipole of yours that you like so much, when tuned to the frequency of choice, they do not require a ground plane as the second "half" of the antenna is present in the form of the other 1/4 wave element. So this type of antenna can be connected to the VNA without needing a ground plane but it should still be kept in as open a testing space not near any metal, etc., as possible.
But just having a good impedance does not necessarily mean the antenna is effective. Your test 50 ohm standard or "dummy load" looks really good to the VNA, of course, but it makes a really bad antenna! Again, you need to look at other types of measurements to use to test antennas in addition to S11 impedance.
The above is also why you can be "faked" into believing that the antenna is "good" when you don't properly calibrate out the test setup including leads and any intervening connectors, etc.
There's a lot to this and I've only touched on some of the basics. Read up on it on-line and listen to advice from guys like PRC Guy.
-Mike
