Microstrip antenna on a thick substrate with high dielectric constant problem.

Hello all! I have used calculators, such as
http://www.emtalk.com/mpacalc.php?er...=93.1506262859
and
http://www.everythingrf.com/rf-calcu...nna-calculator
And some formulas from papers on patch antenna. It worked nice for 2.4GHz, and simulation gived the same center frequency.

Now trying to simulate log-periodic patch array, but at high frequencies (10 to 20GHz) i have problem to calculate center frequency using formulas/calculators. Is it true, that for thick substrates, for example 2mm and Er=4, this formulas are not very accurate? Simulation and formula sizes differs for few mm! Not even 0.1 of mm.