L
Admin
The log-periodic dipole array is the workhorse for EMC test, spectrum monitoring and wideband TV/LTE reception: moderate gain (typically 6 to 8 dBi), a stable pattern and impedance across a decade or more. The design rules are old (Carrel, 1961) but the details still trip people up.
1. The two parameters
- tau (scale factor) is the ratio of successive element lengths and spacings, usually 0.8 to 0.95. Larger tau means more elements, higher gain and smoother impedance.
- sigma (relative spacing) is the spacing divided by twice the longer element length. For a given tau there is an optimum sigma that maximises gain; the classic Carrel curves were later corrected (Butson and Thompson) and are about 1 dB optimistic, so do not promise the chart value.
- The apex half-angle alpha follows from tau and sigma: tan(alpha) = (1 - tau) / (4 sigma).
2. Sizing to the band
The active region is the group of 2 to 4 dipoles near half a wavelength long. The longest element should be noticeably longer than lambda/2 at fmin and the shortest noticeably shorter than lambda/2 at fmax, otherwise gain and match collapse at the band edges. The usual fix is a bandwidth of structure factor Bs = B * Bar, where Bar = 1.1 + 7.7 (1 - tau)^2 cot(alpha) widens the design band.
3. Feeding
Each dipole is fed from a two-wire (or twin-boom) line with a 180 degree transposition between successive elements. On a twin-boom design the alternating halves achieve that crossing mechanically. Feed from the short-element end; terminate the long end with a short stub or a load to soak up energy that leaks past the active region at fmin.
4. Impedance
The input impedance is set mostly by the feeder characteristic impedance and the average dipole impedance. Twin-boom LPDAs naturally land between 50 and 100 ohm. If you need 50 ohm, run coax inside one boom to the front (infinite balun), which also keeps common-mode current off the outside of the cable.
5. PCB LPDAs
Printed LPDAs put alternating dipole halves on opposite sides of the substrate. They are compact and repeatable, but the substrate shortens elements and adds loss; re-tune lengths in EM rather than scaling by sqrt(Dk).
6. What to check on the bench
- S11 across the whole band, especially the bottom 10 percent.
- Gain and front-to-back versus frequency; a ripple usually points to too small a tau.
- Phase-centre movement if the antenna is used for EMC distance-corrected measurements.
For the board: what tau do you use for EMC-grade LPDAs, and how do you handle the phase-centre correction in your test reports?
1. The two parameters
- tau (scale factor) is the ratio of successive element lengths and spacings, usually 0.8 to 0.95. Larger tau means more elements, higher gain and smoother impedance.
- sigma (relative spacing) is the spacing divided by twice the longer element length. For a given tau there is an optimum sigma that maximises gain; the classic Carrel curves were later corrected (Butson and Thompson) and are about 1 dB optimistic, so do not promise the chart value.
- The apex half-angle alpha follows from tau and sigma: tan(alpha) = (1 - tau) / (4 sigma).
2. Sizing to the band
The active region is the group of 2 to 4 dipoles near half a wavelength long. The longest element should be noticeably longer than lambda/2 at fmin and the shortest noticeably shorter than lambda/2 at fmax, otherwise gain and match collapse at the band edges. The usual fix is a bandwidth of structure factor Bs = B * Bar, where Bar = 1.1 + 7.7 (1 - tau)^2 cot(alpha) widens the design band.
3. Feeding
Each dipole is fed from a two-wire (or twin-boom) line with a 180 degree transposition between successive elements. On a twin-boom design the alternating halves achieve that crossing mechanically. Feed from the short-element end; terminate the long end with a short stub or a load to soak up energy that leaks past the active region at fmin.
4. Impedance
The input impedance is set mostly by the feeder characteristic impedance and the average dipole impedance. Twin-boom LPDAs naturally land between 50 and 100 ohm. If you need 50 ohm, run coax inside one boom to the front (infinite balun), which also keeps common-mode current off the outside of the cable.
5. PCB LPDAs
Printed LPDAs put alternating dipole halves on opposite sides of the substrate. They are compact and repeatable, but the substrate shortens elements and adds loss; re-tune lengths in EM rather than scaling by sqrt(Dk).
6. What to check on the bench
- S11 across the whole band, especially the bottom 10 percent.
- Gain and front-to-back versus frequency; a ripple usually points to too small a tau.
- Phase-centre movement if the antenna is used for EMC distance-corrected measurements.
For the board: what tau do you use for EMC-grade LPDAs, and how do you handle the phase-centre correction in your test reports?