Help understanding input impedance of a patch antenna

Hi,
there is something i don't understand about microstrip antennas.
suppose that i'm designing a patch antenna with a resonant frequency of 2.4 GHZ, does it mean that input impedance of that antenna should be PURELY real at 2.4 GHZ at the edge?
i tried simulating this using a single patch using ADS and the simulation doesn't agree with the theory, i get that impedance isn't purely real at the edge (attached a picture), how could it be?

i've read this page - http://www.emtalk.com/mwt_mpa.htm and they wrote that the edge impedance is 343 Ω, how did they calculated it?
is their a formula for calculating the edge impedance of a patch antenna?

THANKS!

when you have substrate dielectric constant, substrate thickness and loss tan, it can use to calculate microstrip feedline
width of feedline can be matched to how you are using input impedance, usually for lab measurement it's use 50ohm Zin
so the easy way you can use a software like Txline, PCAAD etc(https://www.edaboard.com/thread255826.html) to calculate Wf for Zin 50 ohm with input your data substrate, or coversely calculate Zin with ur Wf+data substrate

The transition from the port width (=feedline width) to the patch width does not look right in your model.

In practice, there is always a location on the patch where impedance at F resonance will be purely real and 50 Ohms.
The wider is the crossection of the patch the closer this point is to the edge of the patch.
For suspended plate-type patch, to find exactly where is this point I cut narrow slot in the patch, install connector from the bottom of Ground plane and slide the patch along the connector to find this sweet spot. fast and gives accurate results. Just do not forget to fill the slot with solder.