$$f_r = \frac12\pi\sqrt\epsilon_r\mu_0\epsilon_0\frac1L\sqrt\frac1\epsilon_r + 1.393 + 0.267\fracWL$$
The calculator output is as follows:
The diagram below illustrates how the effective dielectric constant ( ϵreffepsilon sub r e f f end-sub ) and field extensions ( ΔLcap delta cap L ) manifest structurally at the patch edges. 4. Substrate Selection Considerations patch antenna calculator
ΔL=0.412h(ϵeff+0.3)(Wh+0.264)(ϵeff−0.258)(Wh+0.8)cap delta cap L equals 0.412 h the fraction with numerator open paren epsilon sub e f f end-sub plus 0.3 close paren open paren the fraction with numerator cap W and denominator h end-fraction plus 0.264 close paren and denominator open paren epsilon sub e f f end-sub minus 0.258 close paren open paren the fraction with numerator cap W and denominator h end-fraction plus 0.8 close paren end-fraction 4. Calculate Final Patch Length ( Calculate Final Patch Length (