Circular Microstrip Patch Antenna Calculator

Mode Given Frequency → Compute Radius Given Radius → Compute Resonant Frequency Dielectric Constant (ε_r) Substrate Thickness h (mm)

Top View of Circular Microstrip Patch

Cavity Model (TM₁₁ Mode)

1. Effective radius a_eff from resonant frequency

a_eff = X₁₁ · c / (2·π·f_r·√ε_r)

(for TM₁₁, X₁₁ ≈ 1.84118)

2. Effective radius vs physical radius (fringing)

a_eff = a · √( 1 + F )

F = [2·h / (π·a·ε_r)] · [ln(π·a / (2·h)) + 1.7726]

3. Resonant frequency from a known radius

f_r = X₁₁ · c / (2·π·a_eff·√ε_r)

Symbol Glossary

• c – speed of light ≈ 3×10⁸ m/s
• f_r – resonant frequency (Hz)
• ε_r – relative permittivity (dielectric constant) of substrate
• a – physical radius of circular patch (m, or mm in calculator)
• a_eff – effective radius including fringing fields
• h – substrate thickness (m)
• X₁₁ – first root of J₁(x) (Bessel function) for TM₁₁

Design Notes & Assumptions

• Assumes dominant TM₁₁ mode of a circular patch on a grounded substrate.
• Substrate is thin: h ≪ λ₀, and patch radius is electrically small compared to free-space wavelength.
• The expressions are first-order closed-form results; full-wave simulation (CST, HFSS, FEKO, etc.) is recommended for final fine tuning.
• Feeding method (coax probe, aperture, proximity, etc.) is not modeled here; the calculator only estimates the resonant geometry.