Antennas › Log-Periodic Dipole Array

Log-Periodic Dipole Array (LPDA) Designer

Give it the frequency range and the gain you want, and it returns the scale factor, spacing factor, number of elements and a complete cut list: every element length and boom position, using Carrel's design procedure.

Inputs
Presets
Frequency range
Lowest frequency
Highest frequency
Design from
Target gain
dBi
Elements
Longest element diameter
mm
Element lengths are the theoretical half-wave values for thin elements. Real tubing makes elements resonate lower, so shorten them by a few per cent and verify with a full-wave simulation before building. The gain shown is an estimate from published Carrel design curves, good to roughly ±1 dB.
Results
Schematic and element resonances
Left: element lengths and positions along the boom, with the apex angle. Right: the half-wave resonant frequency of each element against the operating band.
Cut list
Related antenna tools
Yagi-Uda Antenna → Dipole Calculator → Gain & Beamwidth → Antenna Unit Converter →

How a log-periodic dipole array works

A log-periodic dipole array (LPDA) is a row of dipoles of increasing length, fed by a common transmission line that reverses the connection between neighbouring elements. At any frequency only a few elements near the half-wave length are strongly excited; they form the active region and radiate a unidirectional beam towards the short elements. As the frequency changes the active region slides along the boom, so the gain, pattern and input impedance repeat periodically with the logarithm of frequency. That is why one LPDA can cover a bandwidth of 4:1 or more with nearly constant gain.

Scale factor τ and spacing factor σ

Each element is τ times as long as the one before it, and the spacing between two elements is σ times twice the length of the longer one. A larger τ means more elements and higher gain; the best σ for a given τ is σ ≈ 0.243·τ − 0.051. The apex half-angle follows from α = atan[(1 − τ)/(4σ)]. Carrel's bandwidth of the active region, Bar = 1.1 + 7.7·(1 − τ)²·cot α, extends the structure beyond the operating band, so the number of elements is N = 1 + ln(B·Bar)/ln(1/τ).

Practical notes

Typical LPDAs reach 6 to 10 dBi of gain, less than a Yagi of the same size but over a far wider band. The feeder is usually two parallel booms with the dipole halves attached alternately, and the shortest element is the feed end. Use the cut list as a starting point and refine the result in a simulator such as NEC before cutting metal.