How a log periodic works
An LPDA is a row of dipoles, each shorter than the last by the factor τ, connected to a feeder that crosses over between every element. At any frequency, only the two or three elements close to a half wavelength are active, with the longer ones behind acting as reflectors. As the frequency changes, the active region slides along the boom, so the gain and impedance stay much the same over the whole range. That's why LPDAs are used for wideband receiving, EMC testing and TV.
Choosing τ and σ
τ sets how quickly the elements shrink and σ the spacing relative to element length. A higher τ, near 0.95, gives more gain but needs more elements. For each τ there's an optimum σ for the most gain, about 0.243τ − 0.051, which the calculator shows. Typical designs give 6 to 8 dBi. The method is R. L. Carrel's 1961 design procedure, as used in the ARRL Antenna Book.
Building tips
- Use two parallel booms as the feeder, with alternate half-elements on each boom, which gives the crossover automatically.
- Feed at the short end with coax run through one boom, and short the booms together behind the longest element, or terminate them.
- The feed impedance is usually 50 to 100 Ω depending on boom spacing. A 1:1 or 2:1 balun suits most designs.
For a single-band beam with more gain, use the Yagi calculator.
Questions
How much gain does a log periodic have?
Usually 6 to 8 dBi, steady across its whole frequency range. A Yagi of the same length has more gain, but only on one band.
What τ should I use?
Around 0.9 is a good balance. Higher values give a little more gain but need many more elements.
Why does the feeder cross over between elements?
It reverses the phase between neighbouring elements, which makes the array fire towards the short end.
Can I use an LPDA for transmitting?
Yes, with elements and a balun that handle your power. Many HF LPDAs cover 13 to 30 MHz.