What Are Log Periodic Antennas?

Log periodic antennas are a class of broadband, directional antennas whose electrical characteristics repeat periodically as a function of the logarithm of frequency. Because each complete log-frequency cycle restores the antenna's geometry to a self-similar scaled version of itself, the impedance and radiation patterns remain essentially constant over operating bandwidths exceeding ten to one. The concept was first described in the late 1950s and formalized in foundational IEEE publications that laid out the mathematical conditions for frequency-independent behavior.

The underlying principle distinguishes log periodic antennas from single-resonance designs such as the dipole or Yagi-Uda array. Where a Yagi achieves gain only over a narrow band, a log periodic structure distributes the active radiating region across successive elements as frequency changes, keeping electrical performance uniform without mechanical retuning.

Operating Principles and Self-Similarity

Log periodic behavior arises from self-similarity in the antenna's geometry. If each successive physical dimension of the structure (element length, element spacing, feed-point position) is scaled by a constant ratio called tau, the structure satisfies the condition for frequency independence. When frequency is multiplied by that same ratio, the antenna's electrical behavior repeats exactly. The ratio tau and the apex half-angle alpha of the array together determine the gain, beamwidth, and element count needed to cover a specified frequency range. Research on broadband logarithmically periodic antenna structures published by IEEE established the core analytical framework used in subsequent designs.

Log-Periodic Dipole Arrays

The log-periodic dipole array (LPDA) is the most widely used form. It consists of a sequence of parallel half-wave dipoles of gradually increasing length and spacing, fed by a balanced transmission line that crosses between each successive dipole pair. This alternating feed reverses the current phase at each element, which is necessary to maintain constructive interference toward the shorter-element end of the array (the high-frequency end). At any given operating frequency, only a subset of elements near resonance, called the active region, contributes significantly to radiation; elements outside this region act as parasitic reflectors or directors. The detailed mathematical treatment of mutual coupling in LPDAs, which accounts for the interactions among all elements rather than treating each as isolated, is documented in the IEEE publication on the design of log-periodic dipole antennas.

Design Parameters and Frequency Scaling

Practical LPDA design begins with specifying the lower and upper frequency limits. The longest element must resonate at or below the lowest frequency, and the shortest element must resonate at or above the highest. Tau governs how many elements are required: values close to 1.0 (nearly equal element sizes) produce high gain and smooth patterns but require many elements and a long boom, while lower tau values yield compact arrays with less gain. A value of tau between 0.7 and 0.95 covers most practical designs.

Beyond element dimensions, the characteristic impedance of the feed line, the balun design, and the boom material all affect impedance flatness and front-to-back ratio across the operating band. Modern implementations use printed circuit or planar forms, which allow integration with low-noise amplifiers for receiving applications. Work on wideband log-periodic meandered dipole arrays with artificial magnetic conductor structures demonstrates how substrate-integrated designs extend performance at higher frequencies.

Applications

Log periodic antennas have applications across a wide range of fields, including:

• HF and VHF communications requiring coverage of multiple amateur or military bands
• Electromagnetic compatibility (EMC) testing using calibrated receiving antennas across wide frequency sweeps
• Television and FM broadcast reception where multiple frequency bands must be covered by a single antenna
• Radio direction finding and signal intelligence systems
• Ultra-wideband radar and electronic warfare receivers