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Impedance Matching of an Antenna

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I am reading about antenna design and have a few questions which I could not get clarified.

I read about "Stubs". I got to know that Stubs are used for impedance matching of an Antenna either by leaving it as an open circuit in one end or as an short circuit.

Question - How to find the input impedance of an Antenna of a particular length? Is there any method and how to calculate the stub length? Is there any formula?

Would really help me if someone could provide an example for calculating the input impedance of the antenna and the stub length for impedance matching
 

For patch antenna you can obtain input impedance using
1) formulas (https://www.antenna-theory.com/antennas/patches/patch3.php)
2) online calculators (https://www.emtalk.com/mpacalc.php)
3) em simulators (learn with free Sonnet lite)
Usually patch matching is done only for real part of impedance using quarterwave transformers or inset feed.
Stubs are sometimes used too, for general complex impedance matching you can start using program Smith V4.1 (https://www.fritz.dellsperger.net/smith.html), read some theory and try to do matching in this program to check your calculations. Or use some other online smith chart matching tool (https://www.will-kelsey.com/smith_chart/).
 

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