Table 2 Design equations for inset-fed rectangular patch antenna^16,17.

Feed length

\({L}_{f} = (2R + 1)\frac{\lambda }{4}\)

R-design parameter, \(\lambda\)-wavelength

(1)

Feed width

\({W}_{f}=\frac{7.457h}{\mathit{exp}\left({Z}_{0}\sqrt{\frac{{\varepsilon }_{r}+1.41}{87}}\right)}\)

\({Z}_{0}\)– characteristics impedance, h-substrate height, \({\varepsilon }_{r}\) -dielectric constant

(2)

Inset feed distance

\({d}_{0}=\frac{L}{\pi }{\mathit{cos}}^{-1}\left(\sqrt{\frac{{Z}_{\text{in}}\left({y}_{0}\right)}{{R}_{\text{in}}\left({\text{edge}}\right)}}\right)\)

L-actual length of the patch

\({Z}_{\text{in}}\)-input impedance

\({R}_{\text{in}}\left({\text{edge}}\right)\)-input impedance at edge of the patch

(3)

Actual length of the patch

\(L=\frac{c}{2{f}_{r}\sqrt{{\varepsilon }_{e}}}-2\Delta L\)

\({L}_{e}=\frac{c}{2{f}_{r}\sqrt{{\varepsilon }_{e}}}\)

\({L}_{e}\)-Effective length

(4)

Residual length

\(\Delta L=0.412h\times \frac{\left({\varepsilon }_{e} + 0.30\right)(\frac{W}{h} + 0.264)}{\left({\varepsilon }_{e} - 0.258\right)(\frac{W}{h} + 0.8)}\)

h-substrate height

(5)

Effective dielectric constant

\({\varepsilon }_{e} =\frac{{\varepsilon }_{r}+1}{2}+\frac{{\varepsilon }_{r}-1}{2}{\left(1+\frac{12h}{W}\right)}^{-\frac{1}{2}}\)

\({\varepsilon }_{r}\)-dielectric constant

(6)

Width of the patch

\(W= \frac{c}{2{f}_{r}}\sqrt{\frac{2}{{\varepsilon }_{r}+1}}\)

c-speed of light

(7)

Resonating frequency

\({f}_{r}\) \(=\frac{c}{2{L}_{e}\sqrt{{\varepsilon }_{e}}}\)

c-speed of light

(8)