Microstrip Patch Antenna Formula
The Microstrip Patch Antenna conversion calculator estimates the width (W) and length (L) of a rectangular patch antenna based on dielectric properties, substrate height, and resonant frequency.
Width (W): W = (c / (2 × f₀)) × √(2 / (εᵣ + 1))
Effective dielectric constant: ε_eff = (εᵣ + 1)/2 + ((εᵣ – 1)/2) × (1 + 12(h/W))⁻⁰·⁵
Effective length: L_eff = c / (2 × f₀ × √ε_eff)
Length extension: ΔL = 0.412 × h × ((ε_eff + 0.3)(W/h + 0.264)) / ((ε_eff – 0.258)(W/h + 0.8))
Actual length: L = L_eff – 2 × ΔL
Formula Explanation
The width W determines the resonant frequency and radiation characteristics of the antenna. The effective dielectric constant ε_eff adjusts for fringing fields at the patch edges. L_eff calculates the electrical length, while ΔL accounts for the additional length due to fringing. Finally, the actual length L is derived by subtracting twice the fringing extension from L_eff.
Uses of Microstrip Patch Antenna conversion calculator
- Designing patch antennas for Wi-Fi, GPS, and satellite communications.
- Quickly estimating antenna dimensions during RF circuit prototyping.
- Educational purposes for understanding microstrip antenna theory.
- Testing and optimizing substrate materials and dielectric properties.
- Accelerating research and development in compact antenna designs.
Formula Example
Given: εᵣ = 4.4, h = 1.6 mm, f₀ = 2.4 GHz
Step 1: Calculate W = (3×10⁸ / (2 × 2.4×10⁹)) × √(2 / (4.4 + 1)) ≈ 38.9 mm
Step 2: Compute ε_eff ≈ 4.0
Step 3: L_eff = 3×10⁸ / (2 × 2.4×10⁹ × √4.0) ≈ 30.6 mm
Step 4: ΔL ≈ 0.8 mm
Step 5: Actual length L = 30.6 – 2 × 0.8 ≈ 29.0 mm
The patch antenna should therefore have dimensions W ≈ 38.9 mm and L ≈ 29.0 mm.