Rectangular Patch Antenna Designer

A rectangular microstrip patch antenna is a metal rectangle on a dielectric substrate above a ground plane. It resonates when its length ≈ λ/2 in the substrate. Gain ≈ 6–8 dBi, bandwidth ≈ 1–5%. Uses transmission line model (Bahl-Trivedi closed form).

Equations & Parameters ▸

\(W=\dfrac{c}{2f}\sqrt{\dfrac{2}{\varepsilon_r+1}},\quad L=\dfrac{c}{2f\sqrt{\varepsilon_{eff}}}-2\Delta L,\quad \Delta L=0.412h\dfrac{(\varepsilon_{eff}+0.3)(W/h+0.264)}{(\varepsilon_{eff}-0.258)(W/h+0.8)}\)

f	Design frequency (resonant frequency).
εᵣ	Substrate dielectric constant. FR4 ≈ 4.4, Rogers 4003C ≈ 3.55.
h	Substrate thickness (mm). Thicker → wider bandwidth, larger patch.
W	Patch width (mm) — determines input impedance; set to minimise excitation of higher modes.
L	Resonant patch length (mm) = λ/(2√εeff) − 2ΔL.
εeff	Effective permittivity. Fields extend partly into air above patch.

Physical constants used

c	Speed of light = 2.998×10⁸ m/s
µ₀	Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m
ε₀	Permittivity of free space = 8.854×10⁻¹² F/m

Inputs

Design frequency, f

Dielectric constant, εᵣ

FR4≈4.4, Rogers4003≈3.55

Substrate thickness, h

1.6 mm standard FR4

Results

Patch Dimensions

Patch width, W—

Patch length, L—

Length extension, ΔL—

Substrate

Effective εᵣ—

Diagram

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