If ( R_\textin(0) ) is not known from the exact formula, use the approximation: [ R_\textin(0) \approx 90\frac\varepsilon_r^2\varepsilon_r - 1\left(\fracLW\right)^2 \quad (\textfor thin substrates) ] Given: ( f_r = 2.45 \text GHz ) ( \varepsilon_r = 4.4 ) (FR4) ( h = 1.6 \text mm ) ( Z_0 = 50\ \Omega )
[ \varepsilon_\textreff = \frac4.4+12 + \frac4.4-12\left(1+12\frac1.637.3\right)^-0.5 \approx 4.18 ]
[ y_0 = \frac28.4\pi \cos^-1\sqrt\frac50297 \approx 9.04 \times \cos^-1(0.41) \approx 9.04 \times 1.148 \approx 10.4 \text mm ] inset fed patch antenna calculator
Use these equations to build your own calculator in Excel, Python, or MATLAB.
[ \Delta L = 0.412 \times 1.6 \frac(4.18+0.3)(37.3/1.6+0.264)(4.18-0.258)(37.3/1.6+0.8) \approx 0.74 \text mm ] If ( R_\textin(0) ) is not known from
(using simpler formula for demonstration) [ R_\textin(0) \approx 90\frac4.4^24.4-1\left(\frac28.437.3\right)^2 \approx 90\times\frac19.363.4\times0.58 \approx 297\ \Omega ]
1. Introduction A rectangular microstrip patch antenna is one of the most common planar antennas. Feeding it directly with a microstrip line creates an impedance mismatch because the patch edge has high impedance (typically 150–300 Ω), while the feed line is usually 50 Ω. The inset fed (or recessed microstrip line feed) technique solves this by placing the feed point inside the patch, where the input resistance drops to 50 Ω at a specific inset depth. Feeding it directly with a microstrip line creates
[ W = \frac3e82(2.45e9)\sqrt\frac4.4+12 \approx 37.3 \text mm ]
To match the feed line impedance ( Z_0 ) (e.g., 50 Ω): [ Z_0 = R_\textin(0) \cos^2\left(\frac\piLy_0\right) ] [ y_0 = \fracL\pi \cos^-1\sqrt\fracZ_0R_\textin(0) ]