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How do you design a rectangular microstrip patch?

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A rectangular patch is designed by choosing width W = (c/2fr)√(2/(εr+1)), computing the effective permittivity εeff and fringing extension ΔL, then setting length L = c/(2fr√εeff) − 2ΔL. These transmission-line-model equations, presented by Balanis using Hammerstad’s ΔL expression, typically predict resonance within a few percent before full-wave optimization.[1][2]

What are the design equations?

  1. Width: W = (c/(2fr))·√(2/(εr+1)).
  2. Effective permittivity: εeff = (εr+1)/2 + ((εr−1)/2)(1 + 12h/W)−1/2.
  3. Length extension: ΔL/h = 0.412·(εeff+0.3)(W/h+0.264)/((εeff−0.258)(W/h+0.8)).[2]
  4. Length: L = c/(2fr√εeff) − 2ΔL.
  5. Inset feed depth for 50 Ω: y0 from Rin(y0) = Redgecos²(πy0/L).[1]

What does a worked example give at 2.45 GHz?

For εr = 3.55 and h = 1.524 mm (values representative of a low-loss hydrocarbon/ceramic laminate; use the manufacturer’s recommended design εr[3]): W ≈ 40.6 mm; εeff ≈ 3.33; ΔL ≈ 0.73 mm; L ≈ 32.1 mm. The edge resistance of such a patch is typically a couple of hundred ohms, so an inset or probe feed is used to reach 50 Ω. Final dimensions should be tuned in a full-wave solver including the finite ground plane.

How accurate are the formulas?

The transmission-line model ignores mutual coupling between radiating edges and finite-ground effects; the cavity model is more accurate for impedance. Expect resonance errors of a few percent, more on thick substrates, so prototypes are typically built and trimmed.[1][4]

Frequently asked questions

Why use W from the formula?

It gives good radiation efficiency; other widths work but change impedance and bandwidth.

Does copper thickness matter?

Slightly at mmWave; it is usually neglected at low GHz.

What substrate height should I use?

Thicker gives more bandwidth; h of about 0.003–0.05λ0 is typical.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
  2. “Equations for Microstrip Circuit Design”. E. O. Hammerstad, Proceedings of the 5th European Microwave Conference, pp. 268-272. 1975.
  3. “RO4000 Series High Frequency Circuit Materials data sheet”. Rogers Corporation. current revision.
  4. “Microstrip Antenna Design Handbook”. R. Garg, P. Bhartia, I. Bahl and A. Ittipiboon, Artech House. 2001.
Categories: Antenna types