The inset feed ($y_0$) introduces a capacitive loading. If the antenna match is not perfect, adjust the inset depth slightly. A deeper inset generally lowers the input impedance; a shallower inset raises it.
Theoretical calculations are a starting point. Real-world factors like connector soldering, substrate impurities, and copper roughness usually shift the frequency downward (making the antenna electrically larger).
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. microstrip patch antenna calculator
# Example usage frequency = 2.4 # GHz substrate_thickness = 1.6 # mm substrate_permittivity = 4.4
): The permittivity of the substrate material. For common FR4 boards, this value is typically around . Substrate Height ( The inset feed ($y_0$) introduces a capacitive loading
W = 37.3 mm, L = 29.1 mm, Feed inset = 8.4 mm from patch center.
import math
Due to fringing fields: [ \varepsilon_reff = \frac\varepsilon_r + 12 + \frac\varepsilon_r - 12 \left[ 1 + 12 \frachW \right]^-1/2 ]
A simplified approximation for the inset depth to achieve 50$\Omega$ is: $$y_0 \approx \fracL\pi \cos^-1\left( \sqrt\frac50R_in(y=0) \right)$$ (Note: $R_in(y=0)$ is the input impedance at the edge of the patch, typically 100-300 Ohms depending on geometry. The inset cuts into the patch by distance $y_0$). Theoretical calculations are a starting point
[ L = \fracc2 f_r \sqrt\varepsilon_reff - 2\Delta L ]
# 5. Calculate Inset Feed Position (y0) for 50 Ohms # First, calculate edge impedance (approximate method) # G = W / (120 * lambda_0) is a simplification, here we use a standard empirical approximation for Rin # Rin_edge is typically calculated via radiation conductance G1 # Simplified standard formula for Rin at edge: lambda_0 = c / frequency_hz G1 = (W / (120 * lambda_0)) * (1 - ( (k0 * substrate_height) ** 2 ) / 24 ) # Approx conductance # k0 is wave number. For simplification in this text calculator, we use a standard approximation: Rin_edge = 90 * (dielectric_constant**2) / (dielectric_constant - 1) * (W/L) # Note: Rin_edge varies heavily. A common practical approximation for inset depth: