Fig1.Structure of microstrip patch antenna [1]
The height of 0.003λ0 ≤ h ≤ 0.0λ0 and the dielectric constant of the substrate with the range of 2.2 ≤ εr ≤ 12 is usually chosen. Radiation occurs because of fringing field between patch edge and ground plate. While low dielectric constant with thick substrate makes more efficiency in expense of larger antenna size, in the case of a compact antenna design there is a need of higher dielectric constant. [3]
In this paper FR4 (thickness=1.6mm, dielectric constant=4.6) used as the substrate. Central operating frequency was 2.4GHz and The input impedance 50 ohm. Width of rectangular patch can be achieved from equation (1).
\(w=\frac{1}{2f_{r}\sqrt{\mu\cdot\varepsilon_{0}}}\sqrt{\frac{2}{\varepsilon_{r}+1}}\)(1)
The effective dielectric constant is important because of fringing effect and can be calculated from equation (2).This is important because some waves travel in the air and some in the substrate.
\(\varepsilon_{r_{\text{eff}}}\)=\(\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{\sigma}-1}{2}\left[1+12\frac{h}{w}\right]^{-\frac{1}{2}}\)\((2)\)
The patch length has greater effect on resonance frequency rather than the width and can be obtained from equation (3).
\(L=\frac{1}{2f_{r}\sqrt{\varepsilon_{r_{e}}}ff^{\sqrt{\mu_{0}\varepsilon}}\sigma}-2\Delta L\)\((3)\)
The additional line length because of fringing effect can be achieved from equation (4) (W/h>1).
\(\frac{\text{\ \ ΔL}}{h}=0\cdot 412\frac{\left(\varepsilon_{\text{reff}}+O\cdot 3\right)\left(\frac{w}{n}+O\cdot 264\right)}{\left(\varepsilon_{r_{\text{eff}}}-3.258\right)\left(\frac{w}{h}+3\cdot 8\right)}\)(4)
The effective patch length can be obtained from equation (5).
\(L_{e}=L+2\Delta L\) (5)
Based on the information gotten above, the effective patch length of 30.27mm and the width of 37.35mm were calculated. Among usual feeding techniques microstrip line feed was used. In this method a strip line connects to the edge of patch with smaller width than patch. The inset cut reduces the need of impedance matching. Increasing dielectric thickness causes increasing spurious feed radiation and also surface waves that makes undesired cross polarized radiation and deficiency in desired bandwidth. [3]