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Patch Antenna Calculator (Balanis Transmission-Line Model)

Rectangular microstrip patch width, length, edge input resistance, and bandwidth from the Balanis 4e transmission-line model. Edge resistance uses the integral form of G1 plus the G12 mutual conductance.

Patch Antenna Calculator

Rectangular microstrip patch dimensions from the Balanis transmission-line model. Returns physical width and length, edge input resistance, and a quick bandwidth estimate.

Units
Length
Frequency

Inputs

Geometry
GHz
mm
W = 40.082 mmL = 31.578 mmtop viewh = 1.524 mmside viewεr = 3.66
Rectangular patch antenna
Patch width W
40.082mm
1578.02 mil
Patch length L
31.578mm
1243.22 mil

More

Effective eeff3.432
Length extension dL0.724 mm
Edge input resistance Rin292.6 Ω
Estimated bandwidth1.18 %
Free-space lambda_0122.36 mm

Analytical calculation

Every step the calculator runs, with the formula, your numbers plugged in, and the result.

Patch width
Balanis 14.2.2. Picks W for an efficient single-mode radiator.
Effective permittivity
Treats the patch as a wide microstrip.
Patch length
dL is the fringing extension at each radiating edge; L = lambdaG/2 minus 2 dL.
Edge input resistance
Balanis Eq. 14.20a with both slot self-conductance G1 (14.12) and mutual conductance G12 (14.18a). G1 and G12 are integrals over the radiation pattern; the engine evaluates them numerically.

Frequently asked

How do I match the patch to 50 ohm?

Edge resistance is typically 200-300 ohm. The two common options are a quarter-wave transformer (the calculator below) between the edge and the 50 ohm feedline, or an inset feed cut about 25-30 percent into L. The inset depth depends on edge currents that the closed-form transmission-line model only approximates, so tune the depth in a 3D solver.

Why does my measured resonance differ from this number?

The transmission-line model ignores higher-order fringing and assumes an infinite ground. Real boards land within a few percent of this prediction. Run the geometry through RayRF to see the actual S11 peak before you fabricate.

Patch is too big, what do I do?

Switch to a higher-er substrate to shrink the patch. A 2.4 GHz patch on RO6010 (er 10.2) is about 60 percent the size of the same design on RO4350B (er 3.66): W shrinks roughly as 1/sqrt((er + 1)/2), L roughly as 1/sqrt(eeff). The trade-off is bandwidth: higher er means narrower BW and tighter tolerance on the resonance.

References

  • PrimaryBalanis, C. A. Antenna Theory: Analysis and Design, 4th ed., Wiley 2016, Ch. 14 (rectangular patch transmission-line model). Patch width and length, Hammerstad fringing extension dL, slot self-conductance G1, mutual conductance G12, and edge input resistance Rin = 1/(2(G1 + G12)) are all from this chapter.
  • G1 / G12Balanis Ch. 14: slot self-conductance G1 (sin^2 / sin^3-theta integral form) and mutual conductance G12 with J0(k0 L sin theta). The engine evaluates both numerically via composite Simpson's rule on theta in [0, pi].
  • BandwidthBalanis Ch. 14: Hammerstad fractional-bandwidth approximation for VSWR < 2, BW ~ 3.77 (er - 1) / er^2 (W/L) (h/lambda_0). Loses accuracy past h/lambda_0 ~ 0.05 as surface waves and higher-order fringing become first-order.
  • ConceptMicrostrip antenna (overview)

Closed-form is just the start.

These calculators hand you the analytical starting point. RayRF takes you the rest of the way: antennas, filters, feedlines, and more, simulated on your real stackup with copper losses, dielectric loss, and finite ground. Roughly a second per iteration.

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