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Log-periodic antenna construction and design

Short answer

An LPDA has dipoles whose lengths and spacings scale by τ, fed by a transposed line. Only elements near half-wave resonance form the active region, radiating toward the apex; as frequency changes, this region shifts. Design uses τ, σ, and α to give constant gain and impedance over a wide band.

Explain the construction, working principle and design of log-periodic antenna.

A log-periodic antenna is a frequency-independent antenna whose geometry repeats in a logarithmic manner, so its impedance and pattern repeat periodically with the logarithm of frequency. The most common form is the log-periodic dipole array (LPDA).

Construction

         apex angle 2α
   <----- direction of beam ------
      Ln ...  L3    L2     L1 (longest)
       |  |   |     |      |
       |  |   |     |      |
  feed>X--X---X-----X------X     ← crossed (transposed)
       |  |   |     |      |       feed line
       |  |   |     |      |
       <-dn-> R3    R2     R1   distances from apex
  • A series of dipoles of different lengths placed side by side; lengths, spacings and distances from the apex all scale by a constant ratio τ (< 1):
τ = Lₙ₊₁/Lₙ = Rₙ₊₁/Rₙ = dₙ₊₁/dₙ
  • Ends of the dipoles lie on two straight lines meeting at the apex with half-angle α.
  • All elements are fed by a transposed (crisscrossed) two-wire line, energised at the short (front) end; adjacent elements are 180° apart in feed.

Working principle

  1. At any frequency, only the few elements near λ/2 long (the active region) radiate strongly.
  2. Elements just behind the active region (longer, inductive) act as reflectors; shorter ones in front act as directors, as in a Yagi. Crossed feeding gives the progressive phase for end-fire radiation towards the apex (shorter elements).
  3. Elements much longer than λ/2 receive little energy because the active region radiates it first; shorter ones are off-resonance and carry little current.
  4. As frequency changes, the active region simply moves along the structure. Properties repeat when f changes by τ: f₂/f₁ = 1/τ, i.e. periodic in ln f.
  5. Bandwidth limits: lowest frequency when L₁ ≈ λ_max/2, highest when Lₙ ≈ λ_min/2.

Design (Carrel method)

1. Choose directivity D -> optimum τ and σ (Carrel chart)
   σ = dₙ/(2Lₙ)   spacing factor
2. Apex half angle: α = tan⁻¹[(1 - τ)/(4σ)]
3. Active-region bandwidth:
   Bar = 1.1 + 7.7(1 - τ)² cot α
4. Structure bandwidth: Bs = B × Bar, B = f_max/f_min
5. Number of elements: N = 1 + ln(Bs)/ln(1/τ)
6. Longest element: L₁ = λ_max/2;  then Lₙ₊₁ = τLₙ
7. Spacing: d₁ = 2σL₁;  dₙ₊₁ = τdₙ
8. Boom length: L = (λ_max/4)(1 - 1/Bs) cot α

Example: τ = 0.9, σ = 0.16 → α = tan⁻¹(0.1/0.64) ≈ 8.9°.

Characteristics

  • Bandwidth up to 10:1 or more; nearly constant gain (≈ 6–10 dBi), pattern and input impedance over band.
  • Unidirectional end-fire beam towards the apex; linear polarization in the plane of the elements.
  • Lower gain than a Yagi of the same length.

Applications: all-channel VHF/UHF TV reception, HF communication, EMC and spectrum measurements, wideband radar.

✓ Answer checked by Claude Opus 5.5 (high effort)

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