# Calculate wavelength wavelength = c / (frequency * 1e9)
import math
# 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: microstrip patch antenna calculator
# 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
# 3. Calculate Extension Length (delta_L) delta_L = 0.412 * substrate_height * (((epsilon_eff + 0.3) * (ratio + 0.264)) / ((epsilon_eff - 0.258) * (ratio + 0.8))) # Calculate wavelength wavelength = c / (frequency
if Rin_edge < 50: y0 = 0 else: # Calculating y0 using the transmission line model y0 = (L / math.pi) * math.acos(math.sqrt(50 / Rin_edge))
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). A common practical approximation for inset depth: #
Here are the step-by-step equations used to find the Width ($W$), Length ($L$), and the Inset Feed position.
# 2. Calculate Effective Dielectric Constant (epsilon_eff) # Use the ratio W/h for the formula ratio = W / substrate_height term = 1 + (12 / ratio) epsilon_eff = ((dielectric_constant + 1) / 2) + ((dielectric_constant - 1) / 2) * (term ** -0.5)
