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Inverted-F Antenna Calculator (PCB IFA)

PCB inverted-F antenna sizing: arm length L from the CPW effective-permittivity closed form, feed offset W, ground cutout dimensions, and recommended ground plane extent. Tuning required.

Inverted-F Antenna Calculator

Arm length and feed offset for a PCB inverted-F antenna. The arm acts as a quarter-wave shorted resonator; its length L depends on the effective permittivity of the arm cross section, calculated from the CPW closed form using substrate thickness, trace width, and gap to the ground edge. The feed offset W is a typical L/6 tap; the exact W for a 50 ohm match comes from a simulator or VNA. L and W are a starting layout, not a final design.

Units
Length
Frequency

Inputs

Design frequency
GHz
Substrate
mm
Geometry
mm
mm
L = 20.726 mmW = 3.454 mmH = 3 mmground planecutout (no copper under antenna)open endshort to gndfeedstitching vias
PCB inverted-F antenna (IFA)
Arm length L
20.726mm
816.00 mil
Feed offset W (from short)
3.454mm
136.00 mil

More dimensions

Effective permittivity εeff (CPW model)2.178
Radiating section (feed to open end)17.272 mm
Free-space lambda_0122.364 mm
Antenna height H3.000 mm
H / lambda_00.0245

Ground plane and cutout

Cutout length (along arm, no copper)23.726 mm
Cutout width (perpendicular, no copper)7.000 mm
Min ground extension beyond antenna30.591 mm
Recommended ground extension beyond antenna61.182 mm

Analytical calculation

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

Free-space wavelength
Reference wavelength used by every length below.
CPW shape ratio
The IFA arm cross section is topologically a CPW: signal trace flanked by gaps of width H to the nearest ground edge on each side. k is the trace-to-pitch ratio. The factor 2H assumes the gap on the open-end side of the trace is also at least H wide, which is the case for a typical IFA layout.
CPW substrate ratio
k1 brings in the finite substrate thickness h_sub. When h_sub is large, k1 approaches k and the dielectric fills the lower half space (the Wen 1969 limit). When h_sub is small, k1 approaches zero and the substrate carries almost no field.
Effective permittivity
CPW quasi-TEM effective permittivity for the arm. The K(k)/K(k\prime) ratios come from the conformal map of the cross section and are evaluated via the Hilberg 1969 closed form (the same helper the CPW calculator uses).
Arm length
Quarter-wave shorted resonator length in the loaded medium.
Feed offset
Input resistance at the feed tap rises from zero at the short to the value at the open end. L/6 is a typical tap point that lands near 50 ohm on PCB IFA proportions; the exact W is set by sweeping S11.
Radiating section
Length from the feed tap to the open tip; this is the section that does most of the radiating.
Ground cutout
Clear all copper directly beneath the antenna outline, plus a small margin (about 1.5 mm) on each side, so the trace does not couple back to the cutout edge.
Ground plane extent
The ground plane is the counterpoise for the quarter-wave element. Extend it at least lambda_0/4 beyond the antenna footprint in every direction; lambda_0/2 gives a cleaner omnidirectional pattern.

Frequently asked

Why is there a cutout under the antenna?

A ground plane directly beneath the antenna trace acts as an image plane and cancels most of the radiation; you get a tightly coupled microstrip line that conducts well but does not radiate. Clearing the ground beneath the antenna lets the field expand into free space. The cutout should extend slightly past the antenna outline, about 1 to 2 mm on each side, so the trace does not couple back to the cutout edge.

How big does the ground plane need to be?

The ground plane is the counterpoise for the quarter-wave element. The radiation only behaves like a half-wave dipole when the ground extends far enough in every direction to support the image. As a starting point, keep at least lambda_0/4 of ground beyond the antenna footprint on every side. Going out to lambda_0/2 gives a noticeably cleaner omnidirectional pattern and a more stable resonance when the board is held or mounted close to other metal. Smaller ground planes still radiate, but the resonance shifts, the impedance match moves, and the pattern tilts toward the ground edges.

What height H above the ground should I pick?

Larger H gives wider bandwidth and slightly better efficiency, at the cost of board area. Practical values land in the lambda_0/100 to lambda_0/30 range; at 2.4 GHz that is roughly 1.2 mm to 4 mm. Below about lambda_0/200 the bandwidth gets very narrow and tuning becomes twitchy. Above about lambda_0/30 the structure stops behaving like a clean IFA.

References

  • IFA modelTaga, T. "Analysis of Planar Inverted F Antenna and Antenna Design for Portable Radio Equipment." Ch. 5 in Hirasawa, K. & Haneishi, M. (Eds.), Analysis, Design, and Measurement of Small and Low-Profile Antennas, Artech House 1992. Establishes the shorted-stub-with-tap model used here.
  • Effective permittivitySimons, R. N. Coplanar Waveguide Circuits, Components, and Systems, Wiley 2001, Sec. 4.2 (CPW with finite-thickness substrate). The IFA arm cross-section is topologically a CPW; eeff = 1 + ((er - 1)/2) * (K(k1)/K(k1')) / (K(k)/K(k')) with k = Wt/(Wt + 2H) and k1 = sinh(pi Wt / 4 h_sub) / sinh(pi (Wt + 2H) / 4 h_sub) is the formula used here.
  • Original CPWWen, C. P. "Coplanar Waveguide: A Surface Strip Transmission Line Suitable for Nonreciprocal Gyromagnetic Device Applications," IEEE Transactions on Microwave Theory and Techniques, vol. 17, no. 12, Dec. 1969, pp. 1087-1090.
  • ConceptInverted-F 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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