Microstrip Patch Antenna Calculator

Mode Given Frequency → Compute Dimensions Given Patch Length → Compute Resonant Frequency Dielectric Constant (ε_r) Substrate Thickness h (mm)

Top View of Rectangular Microstrip Patch

Key Design Formulas (TM₁₀ Rectangular Patch)

1. Width (for good radiation efficiency)

W = c / (2·f_r) · √(2 / (ε_r + 1))

2. Effective dielectric constant

ε_eff = (ε_r + 1)/2 + (ε_r − 1)/2 · 1/√(1 + 12·h/W)

3. Fringing field extension (per open edge)

ΔL = 0.412·h · ( (ε_eff + 0.3)(W/h + 0.264) / ((ε_eff − 0.258)(W/h + 0.8)) )

4. Effective electrical length and physical length

L_eff = c / (2·f_r·√ε_eff)

L = L_eff − 2·ΔL

5. Inverse: find f_r from a known length

f_r = c / (2·(L + 2·ΔL)·√ε_eff)

Symbol Glossary (for Students)

• c – speed of light in free space (≈ 3×10⁸ m/s)
• f_r – resonant frequency of the patch (Hz)
• ε_r – relative permittivity (dielectric constant) of the substrate
• ε_eff – effective permittivity seen by the patch due to fringing fields
• h – substrate thickness (m)
• W – patch width (m, or mm in the calculator output)
• L – physical patch length (m, or mm in the calculator output)
• L_eff – effective electrical length including fringing
• ΔL – additional length at each radiating edge due to fringing fields

Design Notes & Assumptions

• Calculator assumes the dominant TM₁₀ mode.
• Substrate is moderately thin: h ≪ λ₀ and W/h > 1.
• Feeding method (coax, inset, proximity, etc.) is not included in the geometry – this is for basic patch size estimation.
• Results are first-order approximations; full-wave EM simulation (CST, HFSS, FEKO, etc.) is recommended for final optimisation.