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Helical antenna calculator

How it works

When the circumference of a turn approaches a wavelength, a helix stops being a coil and starts radiating along its own axis, circularly polarised. It is the simplest way to get circular polarisation with no phasing networks at all, which is why a helix sits on half the ground stations in satellite work.

reflector ≥ 0.8 λSD 60 mm
The circumference of a turn is close to λ and the pitch about λ/4: then the helix radiates along its axis
Frequency (MHz)
Helix diameter
Helix diameter (mm)
Number of turns
Takeoff angle (°)
Geometry
Turn length
Winding pitch
Overall antenna length
Reflector diameter (≥ 0.8 λ)
Characteristics
Gain
−3 dB beamwidth
Input impedance
Axial ratio

📐 The formulas​

Condition for axial mode:

0.75 λ < C < 1.33 λ          C = π × D — circumference of a turn
pitch angle α = 12…14°
S = C × tan α                winding pitch; at α = 14° this is ≈ λ/4

Performance (Kraus):

G[dBi] = 11.8 + 10 × log10( (C/λ)² × N × (S/λ) )
HPBW   = 52° / ( (C/λ) × √(N × S/λ) )
Z      ≈ 140 × (C/λ)    [Ω]
AR     = (2N + 1) / (2N)        axial ratio
Reflector diameter ≥ 0.8 λ

Symbols:​

  • N — number of turns, AR — axial ratio (1.0 is perfect circular polarisation)
Where this calculator stops:
  • Kraus's formula overstates the gain beyond about 14 turns, and the calculator warns you
  • Outside 0.75…1.33 λ the antenna is not in axial mode; the calculation is blocked with a warning
  • The 140·(C/λ) impedance is an approximation; the real figure depends on how the transition at the reflector is made
  • Wire diameter is not accounted for: thin wire gives a narrower bandwidth

🎯 In practice​

  • Receiving satellites. Circular polarisation removes the problem of the spacecraft tumbling in flight.
  • GPS and the L band. A small helix for 1575 MHz is a classic design.
  • Working through QO-100 and the like: a helix is easier to build than a patch with two feeds.
Practical advice:
  1. The winding direction decides RHCP or LHCP. Getting it wrong costs 20 dB — check which one you need.
  2. The reflector can be a flat disc or a cup: a cup lifts the gain slightly and cleans up the back lobe.
  3. Match with a strip over the first turn and a half — simpler than any transformer.
  4. A helix is wideband: one antenna covers a 1.7:1 frequency range with nothing changed.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Helical antenna calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/helical_antenna (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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