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Patch antenna calculator

How it works

A patch is a resonator about half a wavelength long in the substrate, radiating from its two open edges. The length sets the frequency, the width sets the impedance and the bandwidth, and the match is made by moving the feed point in from the edge. A simple structure with one unpleasant detail: on FR-4, half the power goes into heating the glass-epoxy.

WLsectionpatchεrground planeh 1.6 mm
Length L sets the frequency, width W the impedance and the bandwidth, the feedpoint the match
Frequency (MHz)
Substrate material
Relative permittivity εr
Substrate thickness (mm)
Patch dimensions
Width W
Length L
Effective permittivity εeff
Fringing extension ΔL
Wavelength in the substrate λg
Feed
Impedance at the patch edge
Feed point from the edge (for 50 Ω)
Approximate bandwidth at SWR 2

📐 The formulas​

Width:

W = (c / 2f) × √( 2 / (εr + 1) )

Effective permittivity:

εeff = (εr+1)/2 + (εr−1)/2 × (1 + 12h/W)^(−1/2)

Extension from the fringing field:

ΔL/h = 0.412 × (εeff + 0.3)(W/h + 0.264) / ((εeff − 0.258)(W/h + 0.8))

Length:

L = c / (2f·√εeff) − 2·ΔL

Feed point for 50 Ω:

R(y) = R(edge) × cos²( π·y / L )

Symbols:​

  • h — substrate thickness, c = 299,792.458 mm·MHz
  • y — distance from the patch edge to the feed point
Where this calculator stops:
  • FR-4 has tanδ ≈ 0.02: at 2.4 GHz the efficiency falls to 50–60 %, so instead of 6 dBi you get 2–3. The calculator warns you
  • εr = 4.4 for FR-4 is an average: in reality it is 4.2…4.8 and falls with frequency
  • The edge impedance comes from an approximate formula; in practice the feed point gets trimmed
  • Copper thickness and the effect of the coaxial transition are not accounted for
  • The ground plane must extend at least 3h beyond the patch on every side

🎯 In practice​

  • Wi-Fi and 2.4 GHz. A 37 × 29 mm patch on ordinary 1.6 mm FR-4.
  • A dish feed. A patch is more compact than a horn, though narrower in bandwidth.
  • An antenna for a GPS or ADS-B receiver — the patch has long been standard there.
Practical advice:
  1. Trim the frequency with the length: the width controls impedance, not resonance.
  2. For more than 3 % bandwidth you need a thicker substrate or a lower εr — thin FR-4 will not give you a wide band.
  3. Instead of moving the feed point inwards you can cut an inset feed: same effect, easier to etch.
  4. Circular polarisation comes from a truncated corner or two feeds 90° apart, and that is a different design.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Patch antenna calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/patch (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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