Calculate a microstrip patch antenna

Hello!

I try to simulate a microstrip patch antenna for GPS with cst, but I don't hit the right frequency.
I found some equations in books and a calculator in the internet, but none of the simulation results matches the calculation results.

This is the onlinecalculator
http://www.emtalk.com/mpacalc.php?er..._list=Wmm&Rin=

The equations of the books for the length and width of the antenna are:

L=y/2-dL //y = wavelength of the gps-signal; dL = 0.625mm
W=(c/2f)*sqrt(2/(E+1)) //E = dielectric Constant


I used 1.4mm as the thickness of the material and 4.3 as its dielectric Constant.

The width of both calculations is 58.49mm. The length of the internetcalculator is 45.9mm (~y/4), from the book 93.9mm (~y/2).

When I do a simulation with these results there is a peak in the s-parameter at 1.57GHz but it is always between -3 and -6db. There are some other frequencies with up to -30db but they are higher than 3GHz.

Now I don't know if I did a mistake in the calculation or the simulation.

Are the results from the equations realistic?

Thank you!

In this calculation, you need to use the effective wavelength with substrate - not the free space wavelength in air. The effective wavelength with substrate depends on the distribution of fields between substrate and air. If the fields would all be in substrate, the effective wavelength is free space wavelength divided by sqrt(eps_r)