How does a log-periodic antenna work?

At any given frequency, only a subset of elements (the active region) is resonant and radiates effectively. The active region consists of elements whose length is approximately lambda/2. Elements shorter than resonant act as directors, elements longer act as reflectors, similar to a Yagi-Uda array. As frequency changes, the active region shifts along the boom to a different set of elements. The log-periodic principle means the antenna's electrical properties repeat at frequencies that are related by the ratio tau: if the antenna has gain G at frequency f, it has the same gain G at frequency f/tau, f/tau^2, and so on. This gives the antenna its broadband characteristic.

What are the key LPDA design parameters?

Tau (scale factor): ratio of adjacent element lengths, L(n+1)/L(n), typically 0.85 to 0.95. Higher tau gives more elements, higher gain, but larger antenna. Sigma (spacing factor): ratio of element spacing to element length, d(n)/2L(n), typically 0.05 to 0.18. Optimal sigma for maximum gain is approximately 0.058 times tau plus 0.148. Number of elements: N = 1 plus log(f_max/f_min) / log(1/tau). For 200 to 2000 MHz with tau = 0.9: N = 1 plus log(10)/log(1.111) = 23 elements. Longest element: lambda/2 at the lowest frequency. Boom length: L_boom = lambda_max/4 times (1 minus tau^N) / (1 minus tau). Feed: connected at the short element end (high frequency) for best pattern and impedance.

What are typical LPDA applications?

EMC testing: 30 MHz to 1 GHz or 200 MHz to 3 GHz, calibrated LPDA with known antenna factor for emissions and immunity testing per CISPR 16, MIL-STD-461. Spectrum monitoring and direction finding: broadband coverage for signal intelligence and spectrum management. HF communications: military and maritime HF (2 to 30 MHz) LPDA arrays provide reliable communication over all HF frequencies without antenna tuning. Television reception: the classic TV antenna is a log-periodic or log-periodic Yagi hybrid covering VHF (54 to 216 MHz) and UHF (470 to 698 MHz). SIGINT: broadband surveillance receivers use LPDA for wideband coverage with directional capability.

Broadband Antenna

Log-Periodic Antenna

/lawg peer-ee-od-ik/ — LPDA

Broadband directional antenna: constant gain (6-10 dBi), impedance, and pattern over 10:1+ bandwidth. Elements follow geometric ratio τ = L_n+1/L_n (0.85-0.95). Active region shifts along boom with frequency. At any f, λ/2 elements radiate; shorter = directors, longer = reflectors. EMC testing (30 MHz-3 GHz), spectrum monitoring, HF comms (2-30 MHz), TV reception, SIGINT.

Gain: 6-10 dBi

BW: 10:1+

τ: 0.85-0.95

Understanding Log-Periodic Antennas

The log-periodic dipole array is the workhorse broadband antenna of the RF industry. Where a single dipole operates at one frequency and a Yagi-Uda covers perhaps a 1.5:1 bandwidth, the LPDA achieves 10:1 or greater bandwidth with consistent gain and pattern. This makes it indispensable for applications that must cover wide frequency ranges: EMC testing, spectrum monitoring, signals intelligence, and HF communications.

The principle of frequency-independent antennas was established by Rumsey in 1957: if an antenna's shape is defined entirely by angles (not fixed dimensions), its properties are frequency-independent. The LPDA approximates this by using a discrete set of dipole elements whose dimensions scale by a constant factor, causing the antenna's properties to repeat periodically on a logarithmic frequency scale.

LPDA Design Equations

Scale factor:
τ = L_n+1/L_n = d_n+1/d_n
Typical: 0.85-0.95

Spacing factor:
σ = d_n/(2L_n)
Optimal: σ = 0.058τ + 0.148

Number of elements:
N = 1 + log(f_max/f_min)/log(1/τ)
200-2000 MHz, τ=0.9: N=23

Longest element:
L_max = λ_{min freq}/2
30 MHz: L_max = 5 m

LPDA vs. Other Broadband Antennas

Antenna	Bandwidth	Gain	Directional	Application
LPDA	10:1+	6-10 dBi	Yes	EMC, monitoring
Biconical	10:1	0-3 dBi	Omni	EMC testing
Horn	2:1	10-25 dBi	Yes	Measurement
Yagi-Uda	1.5:1	10-15 dBi	Yes	Point-to-point
Discone	10:1	0-2 dBi	Omni	Scanner, VHF

Common Questions

Frequently Asked Questions

How does it work?

At each frequency, only λ/2 elements (active region) radiate. Shorter elements = directors, longer = reflectors (like Yagi). As frequency changes, active region shifts along boom. Properties repeat at frequencies related by τ: same gain at f, f/τ, f/τ². Broadband behavior from geometric scaling principle.

Design parameters?

τ = L(n+1)/L(n), 0.85-0.95. Higher τ = more elements, higher gain, larger. σ = d/(2L), optimal = 0.058τ+0.148. N = 1+log(fmax/fmin)/log(1/τ). Longest element = λ/2 at lowest freq. Feed at short-element end. Typical VSWR <2:1 across band.

Applications?

EMC: 30 MHz-3 GHz, calibrated with antenna factor, CISPR 16/MIL-STD-461. Monitoring: broadband spectrum surveillance, direction finding. HF: 2-30 MHz military/maritime without tuning. TV: VHF/UHF reception. SIGINT: wideband coverage with directional capability.

Related Terms

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