You could start here. http://anlage.umd.edu/Microwave%20Measurements%20for%20Personal%20Web%20Site/Agilent%20NWA%20Basics%205965-7917E.pdf

or here

https://rfmw.em.keysight.com//webinar/Network-Analyzer-Fundamentals/Network-Analyzer-Fundamentals.html

or here

https://www.youtube.com/watch?v=AF0xEu9t4do

or this

https://www.youtube.com/watch?v=TbEK4v_3Xuo

The link given by Malcolm is already a good starting point. Anyway you should first do a coax calibration [open short load or electronic cal kit) (if you carry out S11 measurements from the coax side) from say 8 to 13 Ghz then make sure that you have a very good Rf waveguide load on the waveguide side.

I'm follower.

Fritz Caspers and Malcolm White Thank you very much

The dimensions of the ports of the coaxial to waveguide adapters in the X-band that I designed are as follows: 5.08 * 22.86 And 2.8 * 22.86 Now my questions are:

1- Do I just have to measure the adapters with a 50 ohm waveguide load a quarter of the wavelength?

2. For each of the adapters, should the size of the waveguide load port be the same as the adapter port?

3- Reference for designing 50 ohm waveguide load, please introduce because waveguide loads available in the market with dimensions of 11.16 * 22.86 are standard and are larger than my adapter ports.

Impedance of normal size waveguide is 300 ohms or more and varies with frequency. There are standard equations. See https://www.microwaves101.com/encyclopedias/waveguide-wave-impedance, but it is more complicated than this, so look at more references. There is (at least) one definition of impedance that depends on the height to width ratio, and one that doesn't. Even your smallest height waveguide will be more than 50 ohms. I don't think you will find a 50 ohm waveguide load. Your transition should look like 50 ohms from the coax end and like whatever impedance the waveguide is from the other end. If it has no or very small (-20dB?) reflection seen from the coax end, and small losses (it probably will have) then it will have a low reflection from the waveguide end too. Lossless components without ferrites in have th same match (S11=S22 S21=S12) from both directions.

answer to 3

If you put a horn with a gradual taper (and no step) on the end of the waveguide it will be a good load - it will radiate with low reflection. Also if you put a piece of absorber with a good point and a long taper in the guide, it will be a good load, if the taper is long enough. You can't get a good load by putting a different size waveguide on, there will be a reflection from the step in nearly every case. Reflection = bad load

I don't understand question 1

2 yes - with no step in the waveguide, or a taper between the two sizes, several wavelengths long.

Minimum VSWR is your goal. You can terminate one side with good load and tune the oter port VSWR. It all depends what equipment you have available.

Ilya Tchaplia & Malcolm White thank you...

I need a waveguide load to test and tune the adapters, how can I design or buy a waveguide this time?

I need to load a waveguide whose port dimensions are the same as the port dimensions of my adapters.

Buy some microwave absorber for the right frequency, maybe in a sheet. cut a triangle 10 wavelengths long with a base that fits in the waveguide. slide it into the waveguide point first all the way. It will probably be a good load. If you push it in or pull it out you should see no change in S11 if it is a good load. You won't find one to buy. Someone may design and make one for you for a lot of money.

The load depends on things changing slowly over a wavelength, so make sure the point is thin.

Buy one, with test data that you know the performance. The quality of the load will determine the performance that you can tune your transition to.

Ilya Tchaplia & Malcolm White thanks a lot.

Someone told me that I need a waveguide load and a quarter wavelength transmission line to test and tune the adapter.

1-That is correct? (If it is wrong, please introduce the method)

2- Please advise on how to make a load with an absorbent triangle piece.

3-The height of the port of the waveguide adapter (5.08 mm) must be connected to the height of the load port (10.16 mm). Can I use an interface waveguide where the port is 5.08 on one side and 10.16 mm on the other?

Thanks...

A quarter waveguide adaptor will transform the impedance from one value to the other with a good match at the design frequency. It needs to be a quarter wavelength long at the guide wavelength. The impedance needs to be the geometric mean of the two impedances, so the height needs to be the geometric mean of the two heights. There will be a correction to the length because the steps look like shunt capacitors and change the length a bit.

https://www.microwaves101.com/encyclopedias/quarter-wave-transformers

https://en.wikipedia.org/wiki/Quarter-wave_impedance_transformer

http://wcchew.ece.illinois.edu/chew/ece350/ee350-10.pdf

http://www.introni.it/pdf/10%20-%20Waveguide%20Handbook.pdf for the capacitance of the step

It is indeed a tricky situation when you try to measure a 2-port device with two different interfaces (and hence impedance). The VNA ports are coaxial interface where you have one end co-axial line and at the other port of your DUT in wave guide. An easy approximation will be to construct two equal such devices and to connect them back to back and use the co-axial ports to connect to VNA with proper cable/adapter calibration (co-ax). Also one can get two more such devices and use them as VNA ports (for eg. TRL calibration) and then use the calibrated wave guide ports to measure the back-to-back pair of adapters (only that this time, the adapters are having wave guide ports). Both these measurements approximate that the two adapters are equal in their performance. The best way to measure would be to use a VNA with adaptor removal feature but such VNA might not be readily available. Vahid Sh