What is input impedance at the radiation edge of patch?

Why it differs from impedance of microstrip line? We can see at antenna as open stub with length L and width W. What is the idea behind this "edge impedance"?

Here is patch antenna calculator:
http://www.emtalk.com/mpacalc.php

It seems that it uses formula: z=90*(Er^2/(Er-1))*(L/W)^2
https://www.edaboard.com/thread278673.html

When using simulation, must we measure this impedance at point, or over whole edge?

Previously, I think somebody already answered to this question. The simulation is looking for a defined port width, which usually is smaller than the whole edge length of the patch, otherwise you would simulate the patch as an an open ended line stub. I know that some EM simulators don't have option for defining the port width, and in this case have to add some short transmission lines to narrow the port connection.

Why we would use one port width or another?

If we use this formula: z=90*(Er^2/(Er-1))*(L/W)^2
there is no feeding size, and for rectangular patch we have Z=90*(Er^2/(Er-1))
Isn't it implies that edge impedance is the same regardless port width?

In simple case i thought we have three impedances: patch edge, matching line, 50 ohm line
1) calculate edge impedance Z=90*(Er^2/(Er-1))
2) calculate quaterwave matching line as sqrt(Z*50)
3) connect edge through matching line to 50 ohm line.

If edge impedance depends on port width, then using formula 1) is wrong?

If the port width is not specified, the equation is good for defining the impedance of an open ended stub.
For a patch antenna knowing the entire edge length impedance is useless, from the moment that for various port widths the impedance changes.

No, for two reasons:

1. The patch antenna requires an open end on both sides. Think of it as a radiating resonator. If we have feedline on one side that covers the entire edge, this changes the currents on the antenna and we have an open ended stub.
2. The port width can't be lambda/2. The requirement for a simulation port is that it is electrically small (< lambda/10). Electrically large ports are impossible by definition, because we have constant voltage at the port, and that would be unphysical if the port is lambda/4 or lambda/2 wide.