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Helical Antenna Calculator

Design axial-mode helical antennas for circular polarisation. Compute turns, pitch angle, diameter, physical length, gain, half-power beamwidth, input impedance and ground plane size using Kraus design equations.

// Design Specifications
MHz
°
mm
Axial mode range: α = 12–15°, C/λ = 0.75–1.33. Best performance: C/λ ≈ 1 (circumference = one wavelength). Outside this range the antenna operates in normal mode (omnidirectional) rather than axial mode (end-fire, circularly polarised).
// Kraus Design Equations
Optimal circumference: C = λ  (C/λ ≈ 0.75–1.33)
Diameter: D = C/π
Pitch: S = C·tan(α)   (α ≈ 14°)
Total length: L = N·S
Turn length: Lturn = √(C²+S²)

Directivity (Kraus):
D = 12·C2·N·S/λ3 (numerical, not dB)
G(dBi) = 10·log(12·(C/λ)²·N·S/λ)

HPBW: θ3dB = 52λ1.5/(C·√(N·S)) degrees
Input impedance: Zin ≈ 140·C/λ Ω
Axial ratio: AR = (2N+1)/(2N) → 1 as N increases
// Helix Geometry (schematic)
// Physical Dimensions
Wavelength & Helix
Free-space wavelength λ—
Helix circumference C—
Helix diameter D—
Pitch S (per turn)—
Total axial length L—
Wire length per turn—
Total wire length—
C/λ ratio—
Electrical Performance
Gain G—
Directivity D—
Half-power beamwidth HPBW—
Input impedance Zin—
Axial ratio AR—
Polarisation sense—
Bandwidth (approx)—
Ground Plane
Min ground plane diameter—
Recommended GP diameter—
// 50Ω Matching Network

The helical antenna input impedance Zin ≈ 140·C/λ Ω naturally. For C/λ=1, Zin≈140Ω.
To match to 50Ω feedline, use a λ/4 transformer:

Quarter-wave transformer Z—
Quarter-wave length—
Alternative: L-network shunt C—
λ/4 transformer: Zq = √(Zin×50) Ω
Length = λ/4 on coax (VF×λ/4)

Tapering the first half-turn (common technique):
Gradually reduce the diameter from Dmatch≈D/4 to D over the first turn
This provides a wideband transition from ~50Ω coax to the helix impedance without a separate matching network
// Construction Notes
Ground plane: Use a circular aluminium or copper disc ≥λ/2 in diameter. Larger ground plane (up to λ) improves front-to-back ratio. The ground plane edge should be turned up (cavity) or covered with absorber to reduce back lobe.

Wire material: Use bare copper or silver-plated copper wire. Wire diameter d should be 0.005λ to 0.05λ for good efficiency — thinner wire increases resistive loss, especially for indoor or small antennas.

Polarisation: Wind in the direction the fingers curl when the right thumb points in the direction of radiation for RHCP. Reverse winding gives LHCP. RHCP is standard for GPS, GLONASS, Galileo.

Bandwidth: Axial mode helices are inherently wideband — typically 0.75C/λ to 1.33C/λ — giving ~52% fractional bandwidth. This exceeds all GPS/GNSS bands simultaneously with a single antenna tuned to 1.5 GHz.

Axial Mode Helical Antenna — Design Guide

The axial mode helical antenna, invented by John Kraus in 1946, produces a circularly polarised end-fire beam with high gain. It consists of a helix wound from wire, mounted above a flat circular ground plane, and fed coaxially through the ground plane centre. When the helix circumference is approximately one wavelength, the antenna operates in axial mode, producing a well-defined beam along the helix axis with circular polarisation.

Applications

Helical antennas are widely used for GNSS reception (GPS, GLONASS, Galileo, BeiDou) because satellite signals are right-hand circularly polarised (RHCP) and the helix naturally matches this. They are also used in amateur satellite work, LEO satellite ground stations, cubesat communication links, and wherever moderate gain (>10 dBic) with circular polarisation is needed without a large aperture.

Kraus Design Equations

John Kraus derived the fundamental design equations for axial-mode helices empirically from measurements. The key relationships are: gain G = 12(C/λ)²N(S/λ), HPBW ≈ 52λ^1.5/(C√(NS)) degrees, and input impedance Z_in ≈ 140(C/λ) ohms. These equations are accurate to within a few percent for 3 ≤ N ≤ 15 and 12° ≤ α ≤ 15°.

Axial Ratio and Circular Polarisation Quality

The axial ratio AR = (2N+1)/(2N) quantifies how circular the polarisation is — AR=1 is perfect circular, AR>3 dB is effectively elliptical. For a 4-turn helix AR=9/8=1.125 (1 dB) — already very good. As N increases, AR approaches 1 (pure circular). In practice, AR is also affected by the ground plane size, feed geometry and nearby objects.