Helical antenna axial and normal modes

A helical antenna is a conductor wound into a helix (like a spring), fed at one end by a coaxial cable whose outer conductor is connected to a ground plane. Depending on its size relative to λ, it works in the normal mode or the axial mode.

Structural design

          _____
         /     \    D  = helix diameter
         \_____/    C  = πD (circumference)
         /     \    S  = spacing (pitch) between turns
         \_____/    α  = pitch angle = tan⁻¹(S/C)
         /     \    N  = number of turns
         \_____/    L  = NS = axial length
  ===============   ground plane ≥ 0.5λ
         |
       coax feed
 one turn unrolled:  L₀ = √(C² + S²)

Special cases: α = 0° → loop; α = 90° → straight wire (monopole).

Normal (broadside) mode

• Condition: helix dimensions ≪ λ (NL₀ ≪ λ, D ≪ λ).
• Working: each turn behaves like a small loop (gives E_φ) plus a short dipole of length S (gives E_θ). Both have the same doughnut pattern, so radiation is maximum normal to the helix axis, null along the axis.
• Polarization: elliptical; axial ratio AR = 2Sλ/C². It becomes circular when C = √(2Sλ).
• Merits: very compact; can replace a long whip (shortened monopole).
• Demerits: narrow bandwidth, low radiation resistance and efficiency; circular polarization only at one frequency.
• Applications: compact "rubber-ducky" antennas in walkie-talkies and handsets.

 Normal mode            Axial mode
   <==  |||  ==>           |||  ====>
   max ⊥ axis              max along axis

Axial (end-fire) mode

• Condition: 3/4 λ < C < 4/3 λ (C ≈ λ), S ≈ λ/4, pitch angle 12°–14°, N > 3.
• Working: the wave travels along the helix as a travelling wave; with one wavelength per turn, the fields of successive turns add along the axis. The current rotates around the axis, so the radiated field is circularly polarized (sense same as winding), giving a single main lobe along the axis away from the ground plane.
• Formulas (Kraus):

HPBW ≈ 52 λ^(3/2) / (C √(NS))   degrees
FNBW ≈ 115 λ^(3/2) / (C √(NS))  degrees
D    ≈ 15 N C² S / λ³
Zin  ≈ 140 (C/λ) Ω    (≈ 100-200 Ω)
AR   ≈ (2N + 1)/(2N)

• Merits: circular polarization, wide bandwidth (≈ 1.7:1), moderate to high gain (10–15 dBi), simple and robust, almost resistive input impedance.
• Demerits: bulky at low frequencies, needs a ground plane and matching from ≈ 140 Ω to 50 Ω.
• Applications: satellite and space-probe telemetry, GPS, radio astronomy, feed for parabolic reflectors.