Microstrip patch input impedance

hi ,
I have question about the rectangular microstrip antenna input impedance at edge. I find the following firmula refernced to Balanis antenna theory and design(but still not found it in Balanis as written below ),

Z = 90(εr2/(εr-1))(L/W)2

where W and L are the respective width and length of the patch.
my question :1-is there someone who already used this formula.
2- is there any other formula calculating directly the input impedance at Edge? I used the steps in Balanis(antenna theory and design,
page 821)

Zin = 1/Yin = 1/2G1 where G1 = (W/120λ)[1-1/24(k0h)2]

and found different results of the input impedance.

Thanks in advance.