| 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 |
FR-4 (( \varepsilon_r = 4.4 ), ( h = 1.6 , mm )). microstrip patch antenna calculator
# Fringing extension num = (ereff + 0.3) * (W_m / h + 0.264) den = (ereff - 0.258) * (W_m / h + 0.8) delta_L_m = 0.412 * h * (num / den) delta_L_mm = delta_L_m * 1000 | Step | Parameter | Formula/Value | Result
import math def microstrip_patch_calc(freq_GHz, er, h_mm): """ Calculate rectangular microstrip patch antenna dimensions. freq_GHz : resonant frequency in GHz er : relative permittivity of substrate h_mm : substrate height in mm Returns dict with width, length, eff_permittivity, delta_L, inset_50 """ c = 299792458 # speed of light m/s f = freq_GHz * 1e9 h = h_mm / 1000 # convert to meters W_m = (c / (2 * f)) * math.sqrt(2 / (er + 1)) W_mm = W_m * 1000 freq_GHz : resonant frequency in GHz er :
1. Introduction A microstrip patch antenna consists of a radiating metallic patch printed on a grounded dielectric substrate. It is widely used in wireless communication (Wi-Fi, GPS, 5G, RFID) due to its low profile, light weight, and ease of fabrication.
# Effective length and physical length Leff = c / (2 * f * math.sqrt(ereff)) L_m = Leff - 2 * delta_L_m L_mm = L_m * 1000