Short note: Logarithmic antenna

A log-periodic (logarithmic) antenna is a frequency-independent antenna whose structure is scaled by a constant ratio, so its impedance and radiation pattern repeat periodically with the logarithm of frequency. The usual form is the log-periodic dipole array (LPDA).

  beam <-- short end              long end
          Ln .. L3   L2     L1
          |  |  |    |      |
  feed -> X--X--X----X------X   crossed feeder
          |  |  |    |      |
   τ = Lₙ₊₁/Lₙ = Rₙ₊₁/Rₙ = dₙ₊₁/dₙ < 1

Design parameters

• Scale factor τ (≈ 0.8–0.95), spacing factor σ = dₙ/(2Lₙ), apex half-angle α with tan α = (1 − τ)/(4σ).
• Frequency period: properties repeat when f changes by 1/τ, i.e. ln f₂ − ln f₁ = ln(1/τ).
• Lowest frequency: L₁ ≈ λ_max/2; highest: Lₙ ≈ λ_min/2.

Working: dipoles are fed by a transposed line from the short end. At each frequency only the elements near λ/2 (the active region) radiate; longer ones behind act as reflectors and shorter ones as directors, so the beam points towards the short end (apex). As frequency changes, the active region slides along the structure.

Characteristics: very wide bandwidth (up to 10:1), nearly constant input impedance and pattern, gain ≈ 6–10 dBi, linear polarization.

Applications: all-channel TV reception, HF/VHF communication, EMC testing and spectrum monitoring.