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Antenna design calculator

Six antennas with closed-form textbook designs: dipole, monopole, microstrip patch, PCB inverted-F, NFC loop and axial-mode helix. Type a frequency and the materials; the dimensions, feed impedance, gain, bandwidth, a dimensioned drawing and the radiation pattern appear as you type. Edit any dimension to see the resonant frequency move the other way.

Antenna type
Inputs
Design frequency
2.4500 GHz
λ = 12.24 cm
Dimensions — edit to solve backwards
W
Patch width (radiating edge)
37.23 mm
mm
L
Patch length (resonant)
28.81 mm
mm
y0
Inset depth for 50 Ω
10.69 mm
Balanis 14-20a
W0
Feed-line width (50 Ω microstrip)
3.059 mm
Pozar 3.197
napprox.
Inset notch gap (each side)
1.529 mm
0.2–0.5 W0
Gnd
Minimum ground plane (W+6h × L+6h)
56.43 mm
Balanis §14.2
h
Substrate thickness
1.600 mm
Dimensioned drawing
W = 37.23 mmL = 28.81 mmy0 = 10.69 mmW0 = 3.059 mm (50 Ω)ground ≥ 56.43 mm × 48.01 mm (W+6h × L+6h)notch n = 1.529 mmsectionh = 1.600 mmεr = 4.4, εeff = 4.081t = 35 µm copperΔL = 0.7386 mm per edgeR_in(0) = 321 Ω → 50 Ωtop view · inset microstrip feed · E-plane along L
Electrical parameters
QuantityValueSource
λ0Free-space wavelength12.24 cm
εeffEffective permittivity4.081Balanis 14-1
ΔLFringing extension (each edge)0.7386 mmBalanis 14-2
LeffEffective length L + 2ΔL30.29 mm
G1Slot conductance969.3 µSBalanis 14-12
G12Mutual slot conductance586.2 µSBalanis 14-18a
R_in(0)Edge input resistance321.4 ΩBalanis 14-17
R_in(y0)Resistance at the inset50 Ω
Zc,feedFeed-line impedance check50.23 Ω
BWVSWR 2:1 bandwidth≈1.12 %Bahl & Bhartia
D0Directivity (lossless, infinite ground)6.08 dBipattern integral
HPBW_EE-plane beamwidth180.2°
HPBW_HH-plane beamwidth82.0°
h/λ0Electrical substrate thickness0.01308
Radiation pattern (normalised, dB)
E-plane
0 dB-3 dB-10 dB-20 dB0°90°−90°±180°
0° = broadside (normal to the patch); ±90° = ground plane
E-plane (along L): two-slot cavity model, Balanis 14-40
H-plane
0 dB-3 dB-10 dB-20 dB0°90°−90°±180°
0° = broadside (normal to the patch); ±90° = ground plane
H-plane (along W): two-slot cavity model, Balanis 14-41
Notes
  • Transmission-line model (Balanis ch. 14): good to a few percent for thin, low-εr substrates. The notch capacitance shifts resonance by ~1 %; verify with a full-wave solver before fabrication.
  • Copper thickness t is used only as a reminder for etching tolerance here; it does not enter the TL formulas.
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SMA edge mount connector 2.45 GHz

How this is calculated

Rectangular microstrip patch (transmission-line model)

Formulas

W = c/(2f)·√(2/(εr+1))
εeff = (εr+1)/2 + (εr−1)/2·(1 + 12h/W)^−1/2
ΔL = 0.412·h·(εeff+0.3)(W/h+0.264) / ((εeff−0.258)(W/h+0.8))
L = c/(2f·√εeff) − 2ΔL · Leff = L + 2ΔL
G1 = 1/(120π²)·∫₀^π [sin(k0W/2·cosθ)/cosθ]² sin³θ dθ
G12 = 1/(120π²)·∫₀^π [sin(k0W/2·cosθ)/cosθ]²·J0(k0L·sinθ)·sin³θ dθ
R_in(0) = 1/(2(G1+G12)) · R_in(y0) = R_in(0)·cos²(πy0/L) → y0 = (L/π)·acos√(Z0/R_in(0))
W0/h from Z0: A = Z0/60·√((εr+1)/2) + (εr−1)/(εr+1)(0.23+0.11/εr); W0/h = 8e^A/(e^2A−2) (W0/h<2) else (2/π)[B−1−ln(2B−1)+(εr−1)/(2εr)(ln(B−1)+0.39−0.61/εr)], B = 377π/(2Z0√εr)
BW ≈ 3.77·(εr−1)/εr²·(W/L)·(h/λ0)
pattern: |√(1−sin²θ sin²φ)·sinc(k0h/2·cosθ)·sinc(k0W/2·sinθ sinφ)·cos(k0Leff/2·sinθ cosφ)|, D0 = 4π·max/∬ F² dΩ
reverse: f = c / (2·(L+2ΔL)·√εeff)

Assumptions & validity

  • Dominant TM010 mode, thin substrate (h ≪ λ0), infinite ground plane, no surface-wave or conductor loss (directivity = gain). Copper thickness is not in the model.
  • Locked to Balanis Example 14.1/14.2 (10 GHz, εr 2.2, h 0.1588 cm → W 1.186 cm, L 0.906 cm, G1 1.57 mS, G12 0.617 mS, Rin 228 Ω, y0 0.3126 cm).

Sources

  • Balanis 4th ed., ch. 14 (eqs. 14-1, 14-2, 14-6, 14-7, 14-12, 14-17, 14-18a, 14-20a, 14-40/41), Examples 14.1–14.2
  • SDSM&T EE483 notes "Microstrip Antennas — Rectangular Patch" (TL design procedure, feed-width design equations)
  • N. Nikolova, McMaster, Lecture 20/21 (εeff, Zc, resonance 21.4, patterns 21.55–21.57)
  • D. R. Jackson, Univ. of Houston, "Introduction to Microstrip Antennas" (bandwidth cross-check); Bahl & Bhartia bandwidth approximation via RayRF
  • D. M. Pozar, Microwave Engineering, eq. 3.196–3.197 (microstrip Zc and width)