# Approximate edge resistance R_edge = 90 * (er**2 / (er - 1)) * (L_m / W_m)**2 if R_edge > 300: R_edge = 300 # practical limit
return "Width (mm)": round(W_mm, 2), "Length (mm)": round(L_mm, 2), "Effective permittivity": round(ereff, 3), "Delta L (mm)": round(delta_L_mm, 3), "Edge resistance (ohms)": round(R_edge, 1), "Inset from center for 50Ω (mm)": round(y0_mm, 2) if y0_mm else "N/A" microstrip patch antenna calculator
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 # Approximate edge resistance R_edge = 90 *
Designing a patch antenna manually requires solving several transmission-line equations. A automates these calculations, taking inputs like operating frequency, substrate permittivity, and height, and returning key dimensions: patch length (L), patch width (W), inset feed position, and input impedance. 2. Fundamental Design Equations The most common patch shape is rectangular. For a given resonant frequency ( f_r ), substrate relative permittivity ( \varepsilon_r ), and substrate height ( h ), the steps are: 2.1 Patch Width (W) [ W = \fracc2 f_r \sqrt\frac\varepsilon_r + 12 ] where ( c = 3 \times 10^8 , m/s ) (speed of light). 2.2 Effective Permittivity (( \varepsilon_reff )) Due to fringing fields: [ \varepsilon_reff = \frac\varepsilon_r + 12 + \frac\varepsilon_r - 12 \left[ 1 + 12 \frachW \right]^-1/2 ] 2.3 Fringing Extension ((\Delta L)) [ \frac\Delta Lh = 0.412 \frac(\varepsilon_reff + 0.3)(W/h + 0.264)(\varepsilon_reff - 0.258)(W/h + 0.8) ] 2.4 Actual Patch Length (L) [ L = \fracc2 f_r \sqrt\varepsilon_reff - 2\Delta L ] 2.5 Inset Feed Position (for 50Ω matching) The input resistance at the edge ((R_in)) is approximately: [ R_in(y=y_0) = R_in(0) \cos^2\left(\frac\pi y_0L\right) ] where (R_in(0)) is the edge resistance (typically 150–300 Ω). For 50Ω: [ y_0 = \fracL\pi \cos^-1\sqrt\frac50R_in(0) ] (y_0) is measured from the center toward the edge. 3. Example Calculation (Manual) Design goal: Rectangular patch antenna at ( f_r = 2.45 , GHz ) (Wi-Fi/Bluetooth). use other method
# Inset feed for 50 ohms target_Z = 50 if target_Z < R_edge: y0_m = (L_m / math.pi) * math.acos(math.sqrt(target_Z / R_edge)) y0_mm = y0_m * 1000 else: y0_mm = None # cannot match with inset; use other method