--- title: "Log-periodic antenna construction and design" subject: "Propagation and Antenna" chapter: 3 key: "semester_6/propagation_and_antenna:log-periodic-antenna" source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/log-periodic-antenna site: BCT Engineering --- # Log-periodic antenna construction and design Propagation and Antenna · Chapter 3: Antenna Classification - Asked in: 2073 Magh, 7 marks; 2070 Magh, 8 marks; 2070 Bhadra, 10 marks (asked 3 times) - Video: [Log Periodic Antenna (Basics, Log Periodic Dipole Array, Applications & Advantages) Explained](https://www.youtube.com/watch?v=JhcdmMsPhv8) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/log-periodic-antenna - Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-3 ## Question Explain the construction, working principle and design of log-periodic antenna. ## 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. ## Answer 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 ```text 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): ```text 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) ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the LPDA, tau is defined as A. L(n+1)/Ln = R(n+1)/Rn = d(n+1)/dn, less than 1 B. f_max/f_min C. the apex angle D. Ln/R(n) Answer: A. Lengths, spacings and distances from the apex all scale by the same ratio tau. (Key point: Scaling ratio) 2. At any frequency, which elements radiate strongly? A. Only the longest element B. The few elements about lambda/2 long C. All elements equally D. Only the shortest element Answer: B. This active region moves along the structure as frequency changes. (Key point: Active region) 3. The beam of the LPDA points A. towards the longest elements B. broadside to the boom C. towards the apex (shorter elements) D. straight up Answer: C. Crossed feed gives end-fire radiation toward the short end. (Key point: Beam direction) 4. Adjacent elements are fed A. in phase by a straight line B. by separate transmitters C. through parasitic coupling only D. 180° apart by a transposed two-wire line Answer: D. The crisscrossed feeder gives the phase needed for end-fire radiation. 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