Hi, sumit007:
Yes. It is affected by Er, Thickness (T) of the substrate, and width (W) of the patch antenna. Normally, Zin does not change much in the non-resonanting direction. It changes from slightly above 0 to about 250 ohms from the center to the edge when the location is changing in the resonating direction. The curve is dependent upon the Er, T and W. When W is bigger, the line between the X = 0 and X = L/2 is closer to a straight line. When W is small, the R will be increasing from 0 slowly and it will go to high value when it is close to the edge.
L
-------------------------
| |
| W -> | -> resonating direction
| |
------------------------ -> x
Best regards,