[ \varepsilon_\textreff = \frac4.4+12 + \frac4.4-12\left(1+12\frac1.637.3\right)^-0.5 \approx 4.18 ]
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. inset fed patch antenna calculator
[ \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 ] [ \varepsilon_\textreff = \frac4
(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 ] The inset fed (or recessed microstrip line feed)
Use these equations to build your own calculator in Excel, Python, or MATLAB.
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 )
[ 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 ]