A Log periodic antenna achieves its remarkable wide bandwidth capability primarily through a clever geometric design where the dimensions of its elements increase logarithmically from the front to the back. This structure ensures that different groups of elements are responsible for resonating at different frequencies. As the operating frequency changes, the active region—the set of elements that are effectively radiating and receiving—shifts smoothly along the antenna’s structure. This “traveling wave” effect allows the antenna to maintain consistent performance, including a stable input impedance and radiation pattern, across a very wide frequency range, often exceeding a 10:1 ratio.
The Core Principle: Scaling and the Active Region
The magic of the log periodic antenna lies in its adherence to a precise scaling law. The entire antenna is defined by a set of geometric parameters that remain constant. The most critical is the scaling factor (τ), which is always less than 1. This factor determines the ratio of the lengths and spacings of adjacent elements. For example, if the longest dipole element is 1 meter long and τ is 0.9, the next element will be 0.9 meters long, the one after that 0.81 meters, and so on. The spacing between elements follows the same rule. This self-similar, logarithmic scaling is the direct reason for the antenna’s broadband nature.
At any given frequency, only a small cluster of elements around the one that is half a wavelength long are actively participating in radiation. This cluster is the active region. Elements significantly shorter than the resonant length act as capacitive loads, while much longer elements act as inductive loads; both are largely inactive. As the frequency increases, the active region moves forward toward the shorter elements. Conversely, as the frequency decreases, it shifts backward toward the longer elements. This seamless handoff from one set of elements to another is what prevents the narrowband resonance behavior typical of a simple dipole and creates a continuous broadband response.
| Parameter | Typical Value Range | Impact on Bandwidth & Performance |
|---|---|---|
| Scaling Factor (τ) | 0.78 – 0.95 | A lower τ (e.g., 0.8) results in fewer elements for a given bandwidth but slightly lower gain. A higher τ (e.g., 0.95) provides smoother performance and higher gain but requires more elements. |
| Relative Spacing Constant (σ) | 0.08 – 0.15 | This defines the spacing between elements relative to their length. A higher σ can improve gain but if too high, can cause grating lobes (unwanted radiation patterns) at higher frequencies. |
| Number of Elements (N) | 10 – 20+ | More elements allow for a wider bandwidth and a more stable input impedance across the band. The bandwidth is roughly proportional to τ^(-N). |
| Boom Length | Varies with lowest frequency | Determined by the longest element (for the lowest frequency) and the scaling factor. A 100 MHz low-frequency limit with τ=0.9 can require a boom over 3 meters long. |
Electrical and Mechanical Design Synergy
The electrical performance is inextricably linked to the mechanical design. The elements are mounted on a central metallic boom, but unlike a Yagi-Uda antenna, the boom is not continuous for DC. The elements on opposite sides of the boom are electrically connected, typically by alternating which side of the boom they are attached to or by using a feed line that crisscrosses. This is crucial because it creates a 180-degree phase shift, ensuring the elements radiate in phase for a end-fire radiation pattern (direction off the front of the antenna).
The feed mechanism is also key to wideband impedance matching. The antenna is fed at the front (the shortest element end) with a balanced transmission line, like a twin-lead cable. The characteristic impedance of this feed line is carefully chosen, often between 50 and 100 ohms, to match the active region’s impedance. Because the active region’s size and distance from the feed point change with frequency, its impedance naturally varies. However, the scaling principle ensures this variation is minimal and periodic with the logarithm of the frequency, hence the name “log-periodic.” This results in a input impedance that stays relatively constant, often within a 2:1 SWR (Standing Wave Ratio) across the entire band, which is a hallmark of a good broadband antenna.
Radiation Pattern Stability
For many antennas, as frequency changes, the radiation pattern can distort dramatically—becoming omnidirectional at one frequency and multi-lobed at another. The log periodic antenna maintains a consistent directional pattern. The forward-directed gain, front-to-back ratio, and beamwidth remain fairly stable because the active region always comprises a similar number of elements (typically 3-4) with similar relative lengths and spacings. The larger, inactive elements behind the active region act as reflectors, while the smaller, inactive elements in front act as directors, much like in a Yagi antenna, but this function is frequency-dependent and shifts along the structure. This dynamic reflector-director system is fundamental to the pattern stability.
The following table compares the bandwidth and pattern stability of a log periodic antenna with other common antenna types, highlighting its unique advantage.
| Antenna Type | Typical Bandwidth | Radiation Pattern Stability | Primary Use Case |
|---|---|---|---|
| Half-Wave Dipole | Narrowband (~10-15% of center freq) | Pattern stable within its narrow band | Fixed-frequency communications |
| Yagi-Uda Antenna | Very Narrowband (~2-5% of center freq) | High gain, but pattern degrades quickly outside design freq | Directional TV, amateur radio bands |
| Discone Antenna | Extremely Wideband (up to 10:1) | Omnidirectional pattern, but gain is very low (~2 dBi) | Scanning, wideband reception |
| Log Periodic Dipole Array | Very Wideband (commonly 10:1 or more) | Directional pattern and gain remain stable across the band | TV reception, EMC testing, spectrum monitoring |
Practical Considerations and Performance Trade-offs
While the bandwidth is impressive, it’s not without trade-offs. The primary trade-off is physical size. To cover lower frequencies, the longest element must be approximately a half-wavelength at that lowest frequency. A log periodic antenna designed to cover 100 MHz to 1 GHz would still need a boom long enough to accommodate the element for 100 MHz (about 1.5 meters long), plus all the scaled elements in front of it, resulting in a sizable structure.
Another trade-off is gain relative to size. While the gain is stable, it is typically moderate, ranging from 6 to 12 dBi. This is lower than a similarly sized Yagi-Uda antenna designed for a single frequency because the Yagi concentrates all its elements to optimize performance at one point. The log periodic spreads its elements out to cover a wide spectrum, so its gain for a given size is inherently lower. Furthermore, the efficiency can be slightly reduced at the band edges due to the increasing influence of the inactive elements.
Designers must carefully balance the scaling factor (τ), the spacing constant (σ), and the number of elements (N) to meet specific requirements for bandwidth, gain, size, and cost. For instance, in critical applications like electromagnetic compatibility (EMC) testing, where precise, repeatable measurements from 30 MHz to 1 GHz or beyond are needed, the design prioritizes pattern purity and impedance stability, often leading to antennas with a high τ and many elements. In contrast, a consumer TV antenna might use a lower τ and fewer elements to reduce cost and size, accepting a slight performance compromise.
Material and Construction Impact
The choice of materials directly affects the realizable bandwidth, especially at higher frequencies. The elements must be constructed from materials with high conductivity, like aluminum or copper, to minimize resistive losses. At VHF and UHF frequencies, even a thin aluminum tube is sufficient as the skin depth is small. However, for antennas covering into the microwave range (several GHz), the elements become very thin and may be made from stamped metal or printed circuit board (PCB) traces. The mechanical tolerance becomes critical; a small imperfection in the length or spacing of a small element can detune its resonant frequency significantly. The boom must also be rigid to maintain the precise element spacing, as sagging or bending would distort the scaling law and degrade performance across the band.