Understanding the radiation pattern of a log periodic dipole array
Simply put, the radiation pattern of a log periodic dipole array (LPDA) is directional, like a slightly fuzzy searchlight beam, with maximum power radiated outwards from the pointed front of the antenna (the direction of the shortest elements). This pattern is a direct result of its unique, scaled dipole design, which allows it to operate over a wide frequency range while maintaining consistent performance. Unlike a simple Yagi-Uda antenna whose pattern can degrade at band edges, the LPDA’s pattern remains remarkably stable across its entire operational bandwidth. The key characteristics of its radiation pattern are moderate to high gain, a relatively narrow beamwidth in the plane of the elements (the E-plane), and a wider beamwidth in the plane perpendicular to the elements (the H-plane).
The magic behind this consistent pattern lies in the antenna’s traveling wave operation. In an LPDA, the electromagnetic wave doesn’t just resonate locally at one dipole; it propagates along the antenna’s boom from the longest elements (the “back”) towards the shortest elements (the “front”). As the wave travels, it encounters dipoles that are progressively closer to resonance. The active region—the set of diples that are effectively radiating and receiving at a given frequency—moves along the structure. This ensures that the electrical distance from the active region to the feed point and the front of the antenna remains relatively constant, which is crucial for maintaining a stable phase front and, consequently, a stable radiation pattern. This is why the LPDA is considered a frequency-independent antenna.
Let’s break down the pattern into its two principal planes for a standard, horizontally-polarized LPDA mounted with its boom parallel to the ground:
E-Plane Pattern (Elevation Plane, parallel to the elements): This is the plane containing the axis of the dipoles. The pattern here is typically a single, main lobe with its maximum radiation at a right angle (broadside) to the boom. The beamwidth is defined as the angular separation between the two points where the power drops to half (-3 dB) of its maximum value. For a well-designed LPDA, the E-plane half-power beamwidth (HPBW) is usually in the range of 50 to 80 degrees. The pattern also features minor lobes, called side lobes, and a rear lobe, but these are typically suppressed by 10-15 dB or more relative to the main lobe, depending on the design parameters.
H-Plane Pattern (Azimuth Plane, perpendicular to the elements): This is the plane containing the boom. The pattern is fan-shaped; it’s narrower in the elevation angle but much wider in the azimuth. The H-plane HPBW is generally wider than the E-plane, often falling between 80 and 120 degrees. This fan-shaped pattern is useful for applications like television reception, where you want good coverage across a wide horizontal area.
The actual shape and performance of the radiation pattern are heavily influenced by several key design parameters. Adjusting these allows engineers to tailor the antenna for specific applications.
| Design Parameter | Typical Value Range | Impact on Radiation Pattern |
|---|---|---|
| Scalar Taper (τ) | 0.78 – 0.95 | A higher τ (closer to 1) increases boom length but improves pattern stability and front-to-back ratio. A lower τ makes the antenna more compact but can increase side lobe levels. |
| Relative Spacing (σ) | 0.04 – 0.06 | Affects the coupling between elements. A higher σ generally increases gain and improves impedance matching but also increases the overall size. |
| Number of Elements (N) | 8 – 20+ | More elements directly increase the antenna’s gain and sharpen the main lobe (reduce beamwidth). It also improves the front-to-back ratio. |
| Boom Length | Scales with τ and N | A longer boom accommodates more elements and a slower taper, directly correlating with higher gain and a more directional pattern. |
For a quantitative look, here is a typical gain and beamwidth specification for a commercial VHF/UHF Log periodic antenna designed for communication applications:
| Frequency Range | Average Gain | E-Plane HPBW | H-Plane HPBW | Front-to-Back Ratio |
|---|---|---|---|---|
| 100 – 200 MHz | 7.5 dBi | 75° | 110° | >15 dB |
| 200 – 400 MHz | 8.5 dBi | 65° | 100° | >18 dB |
| 400 – 800 MHz | 9.5 dBi | 55° | 90° | >20 dB |
Understanding the pattern is useless without knowing how it’s measured. In an anechoic chamber, which is a room designed to absorb reflections, the antenna is mounted on a rotating positioner. A reference antenna transmits a signal, and the LPDA under test rotates while a receiver records the signal strength at every angle. This data is then plotted to create the familiar radiation pattern diagrams. The front-to-back ratio is a critical metric derived from this measurement. It’s the ratio of power radiated in the intended forward direction to the power radiated in the exact opposite direction (180 degrees from the main lobe). A high front-to-back ratio, often 15 dB or more for a good LPDA, is desirable as it reduces sensitivity to interference coming from behind the antenna.
In real-world deployments, the theoretical pattern is modified by the antenna’s environment. Mounting the antenna over a ground plane, for instance, creates an image of the antenna below the ground. This interaction modifies the radiation pattern, especially at low elevation angles. For a horizontally polarized LPDA mounted at a height *h* above ground, the pattern can develop nulls at certain elevation angles due to destructive interference between the direct ray and the ray reflected from the ground. The elevation angle of the main lobe can be approximated by Δ = arcsin(λ/4h), where λ is the wavelength. This is crucial for maximizing signal strength in point-to-point communication links.
The polarization of the LPDA’s radiation pattern is determined by the orientation of its dipoles. Horizontal dipoles yield a horizontally polarized pattern, and vertical dipoles yield a vertically polarized pattern. While the basic pattern shape remains similar, the interaction with the environment differs significantly. Horizontal polarization is more susceptible to fading effects from ground reflections, while vertical polarization often provides better coverage for mobile applications near the ground. For complex signals, circular polarization can be achieved by using two crossed LPDAs fed with a 90-degree phase difference, resulting in a radiation pattern that can communicate effectively with antennas of any orientation.