# Effective permittivity ereff = (er + 1)/2 + ((er - 1)/2) * (1 / math.sqrt(1 + 12 * h / W_m))
| Step | Parameter | Formula/Value | Result | |------|-----------|---------------|--------| | 1 | Width W | ( \frac3e82 \times 2.45e9 \times \sqrt(4.4+1)/2 ) | ≈ 37.26 mm | | 2 | ( \varepsilon_reff ) | ( \frac4.4+12 + \frac4.4-12 (1 + 12 \times 1.6/37.26)^-0.5 ) | ≈ 3.74 | | 3 | ΔL | ( 0.412 \times 1.6 \times \frac(3.74+0.3)(37.26/1.6+0.264)(3.74-0.258)(37.26/1.6+0.8) ) | ≈ 0.729 mm | | 4 | Length L | ( \frac3e82 \times 2.45e9 \times \sqrt3.74 - 2 \times 0.729 ) | ≈ 29.06 mm | | 5 | Edge resistance (R_in(0)) | Approx. formula | ≈ 220 Ω | | 6 | Inset (y_0) for 50Ω | ( \frac29.06\pi \cos^-1\sqrt50/220 ) | ≈ 8.4 mm from center | microstrip patch antenna calculator
FR-4 (( \varepsilon_r = 4.4 ), ( h = 1.6 , mm )). # Effective permittivity ereff = (er + 1)/2
For a reliable design, combine calculator output with electromagnetic simulation and at least one physical iteration. Happy antenna designing! End of piece. Happy antenna designing
# Approximate edge resistance R_edge = 90 * (er**2 / (er - 1)) * (L_m / W_m)**2 if R_edge > 300: R_edge = 300 # practical limit