Ham Radio Log Periodic Antennas — Complete Guide
The log periodic dipole array (LPDA) is the antenna that eliminates the trade-off between bandwidth and directional gain. While a Yagi delivers maximum performance on a single band and a dipole covers multiple bands only with a tuner, the LPDA provides consistent directional gain across a wide frequency range — often spanning multiple amateur bands — from a single antenna and feedline. This guide covers the theory behind LPDA design, the tau and sigma design parameters, element dimensions, practical construction, and how the log periodic fits into a complete HF station.
HF LPDA — Multi-Band Coverage
The most common amateur radio LPDA application — covering 14–30 MHz (20m through 10m) or the full 7–30 MHz HF range from a single rotatable antenna. Delivers 4–7 dBd of gain across the entire coverage range with consistent pattern and SWR.
Log-Yagi Hybrid
A hybrid design that uses a log periodic driven array with additional Yagi directors forward of the LPDA section. Delivers higher gain than a pure LPDA with broader bandwidth than a pure Yagi — the best of both designs for HF contest station use.
VHF/UHF LPDA
A compact LPDA covering VHF and UHF frequencies — used for wideband scanning receivers, SDR antennas, and TV reception as well as amateur radio. A well-designed VHF/UHF LPDA covers 50–1300 MHz from a single small antenna.
Fixed-Direction LPDA
A non-rotatable LPDA pointed in one favored direction — typically toward Europe from the US east coast, or toward Asia from the west coast. Delivers consistent wideband gain on all bands toward the target region without the need for a rotator.
Wire LPDA
An LPDA constructed from wire rather than aluminum tubing — suspended between supports like a wire dipole but with multiple elements. Less mechanically precise than aluminum construction but achievable with basic tools at significantly lower cost for HF use.
Broadband LPDA (3–30 MHz)
A large LPDA designed to cover the entire 3–30 MHz HF range from a single antenna. Requires a long boom and many elements — typically used at military, government, and serious DX expedition stations. Not practical for most residential installations but worth understanding.
The Frequency-Independent Principle
A log periodic dipole array achieves its wideband performance through a clever geometric principle: the antenna's electrical properties repeat at frequencies that are logarithmically spaced. At any given operating frequency, only a subset of the elements — the "active region" — are actually near resonance and contributing significantly to radiation. As the operating frequency changes, the active region shifts to a different set of elements, but the electrical environment around those elements is always the same geometric structure scaled to the new wavelength.
This self-similarity at different scales is the key insight. The antenna looks the same electrically at every frequency within its design range because the element spacings and lengths always maintain the same ratios relative to the operating wavelength. The result is consistent gain, consistent pattern, and consistent feedpoint impedance across the full bandwidth.
- Active region: the 2–4 elements near resonance at any given frequency carry most of the current
- Elements shorter than λ/2 (forward elements) act as directors — similar to a Yagi
- Elements longer than λ/2 (rear elements) act as reflectors
- The feedline is transposed between each adjacent element pair — this phase reversal is essential to the LPDA's operation
- The overall forward gain is typically 4–7 dBd — less than a optimized single-band Yagi of similar boom length
Tau and Sigma — The Two Design Parameters
Every LPDA design is defined by two dimensionless parameters: tau (τ) and sigma (σ). These two numbers completely determine the antenna's performance characteristics and element layout.
Tau (τ) — the ratio of successive element lengths and spacings. If element N has length L_N, then element N+1 has length L_N × τ. Similarly for spacings. Tau is always less than 1.0 (typically 0.85–0.97). Higher tau means more elements per octave, more gain, longer boom.
Sigma (σ) — the relative spacing constant, defined as d_N / (2 × L_N) where d_N is the spacing between adjacent elements. Sigma controls gain and front-to-back ratio. Typical values: 0.05–0.25. Higher sigma gives more gain but requires a longer boom.
Element Count and Boom Length
The number of elements in an LPDA is determined by the desired frequency range (ratio of highest to lowest frequency) and the tau value. More elements per octave (higher tau) means more consistent performance and higher gain but a longer boom and more construction complexity.
The longest element should be approximately 5% longer than a half-wave at the lowest design frequency — this ensures the active region never reaches the rearmost element. Similarly, the shortest element should be approximately 5% shorter than a half-wave at the highest design frequency. This 5% margin on each end ensures clean performance within the design bandwidth.
Feed System and Boom Construction
The LPDA feedline is a transmission line that runs the length of the boom, with each adjacent element pair connected with reversed polarity — the transposed feedline is what makes the LPDA work. In practice this is implemented in two ways:
- Two-conductor boom — the boom is split into two parallel conductors (typically two aluminum tubes side by side) that serve as the transmission line. Each element connects across the two boom halves — automatically achieving the phase reversal at each step.
- Single boom with transposed feedline — a single structural boom with a separate two-conductor feedline (twisted pair or small ladder line) running through or along it, alternating which conductor connects to each element.
- The boom transmission line characteristic impedance should match the desired feedpoint impedance — typically 50–200Ω depending on the spacing between conductors.
- A 1:1 current choke at the feedpoint (rear of the antenna) prevents common-mode current from flowing back down the coax.
- The coax feedline connects at the rear of the antenna — the small end — where the shortest elements are located.
The feed impedance of a properly designed LPDA is relatively constant across its bandwidth — typically 50–100Ω. The mean impedance is set by the boom transmission line impedance, which is controlled by the physical spacing between the two boom conductors.
| Tau (τ) | Sigma (σ) | Approx Gain | F/B Ratio | Elements per octave | Boom length / λ_max | Best Application |
|---|---|---|---|---|---|---|
| 0.85 | 0.08 | ~4.5 dBd | ~15 dB | ~5 | Short | Compact low-gain wideband |
| 0.88 | 0.10 | ~5.0 dBd | ~17 dB | ~6 | Moderate | Space-limited HF install |
| 0.90 | 0.12 | ~5.5 dBd | ~19 dB | ~7 | Moderate | Good compromise design |
| 0.92 | 0.12 | ~6.0 dBd | ~20 dB | ~9 | Moderate-long | Typical amateur HF LPDA |
| 0.93 | 0.14 | ~6.5 dBd | ~21 dB | ~10 | Long | High performance HF |
| 0.95 | 0.16 | ~7.0 dBd | ~22 dB | ~13 | Very long | Maximum gain LPDA |
| 0.97 | 0.18 | ~7.5 dBd | ~23 dB | ~18 | Extreme | Research / government |
Gain figures are approximate and assume optimized design. Boom length expressed as a fraction of wavelength at the lowest design frequency. Higher tau and sigma both increase boom length — choose based on available space and desired performance trade-off.
Designing a 14–30 MHz Amateur LPDA
The 14–30 MHz range (20m through 10m) is the most popular HF LPDA application for amateur radio. It covers the primary DX and contest bands in a single rotatable antenna without any tuner. Using τ = 0.92 and σ = 0.12 as design parameters:
Element Spacings for the 14–30 MHz LPDA
Element spacings follow the same tau ratio as the lengths — each spacing is τ times the previous spacing. The first spacing (between rear and second elements) is determined by sigma:
This boom length of approximately 20 feet is manageable for a tower-mounted rotatable installation. At 10m and 15m where boom length is proportionally shorter relative to wavelength, the gain is slightly higher than at 20m — the design is a practical compromise that works well across all three bands.
Verify your LPDA design with NEC2 modeling →When to Choose a Yagi
A Yagi is the better choice when:
- You primarily operate on one or two bands and want maximum gain on those bands
- Space or budget limits boom length — a Yagi delivers more gain per unit boom length than an LPDA
- You are designing for VHF/UHF weak-signal work where every fraction of a dB matters
- You want the simplest possible construction — a single-band Yagi has fewer elements and less complex feed system
- You are already using a multi-band dipole or EFHW for off-peak bands and just want a beam for your primary operating band
A 3-element 20m Yagi delivers approximately 7 dBd on 20m — about 1–2 dBd more than an LPDA covering 14–30 MHz. For a dedicated 20m contest or DX station, the Yagi wins on gain. But it provides no coverage on 15m or 10m without a separate antenna or complex multi-band Yagi design.
Full Yagi antenna guide →When to Choose an LPDA
An LPDA is the better choice when:
- You want consistent directional performance across multiple bands without band-changing antenna configurations
- You want to eliminate the antenna tuner entirely from the station — the LPDA presents near-50Ω on every covered band
- Tower space or rotator load limits you to one antenna — the LPDA covers 20m, 17m, 15m, 12m, and 10m from a single installation
- You operate digital modes across multiple bands where consistent feedpoint impedance simplifies the station setup
- You want a fixed-direction antenna covering all HF high bands toward a specific target region
- You need wideband coverage for special event or contest operation where rapid band changes are routine
The 1–2 dBd gain trade-off compared to a dedicated single-band Yagi is often worth the operational convenience of one antenna covering five bands with consistent performance.
The Log-Yagi Concept
The Log-Yagi (LY) is a hybrid antenna that uses a log periodic array as the driven section and adds additional Yagi directors forward of the LPDA section. The LPDA provides the broadband driven array that the Yagi directors can work with across a wide frequency range, while the directors add gain that a pure LPDA cannot achieve.
The result is higher gain than a pure LPDA with broader bandwidth than a pure Yagi — typically 7–10 dBd across the design frequency range. The trade-off is design complexity and boom length. The Log-Yagi design must be modeled carefully using NEC2 — the interaction between the LPDA section and the directors requires full electromagnetic simulation to optimize correctly.
- Gain advantage over LPDA: +1 to +3 dBd depending on number of directors added
- Bandwidth advantage over Yagi: significantly wider usable SWR bandwidth
- Complexity: requires NEC2 modeling, more elements, longer boom than pure LPDA
- Feed system: same as pure LPDA — transposed boom feedline with coax at the rear
- Popular commercial examples: Force-12, M2 Antennas, and Hy-Gain use Log-Yagi principles in their multi-band HF beams
Designing a Log-Yagi
Log-Yagi design is not straightforward — it cannot be done by formula alone. The interaction between the LPDA active region and the Yagi directors is complex and frequency-dependent, requiring full NEC2 simulation. The general design process:
- Design and model the LPDA section first — verify gain, F/B, and SWR across the target bandwidth using 4NEC2
- Add directors one at a time, starting with the director immediately in front of the shortest LPDA element
- Optimize each director's length and spacing using the NEC2 optimizer — targeting maximum forward gain while maintaining SWR below 2:1 across the bandwidth
- Check that F/B ratio does not degrade unacceptably as directors are added — some designs sacrifice F/B for gain
- Model the complete structure at multiple frequencies across the bandwidth, not just at the center frequency
- Build and verify — compare NanoVNA measurements to modeled impedance predictions
Wideband VHF/UHF LPDA
At VHF and UHF frequencies, an LPDA can cover an enormous frequency range in a physically small structure. A well-designed LPDA covering 50–1300 MHz spans more than 4 octaves — covering 6m, 2m, 70cm, 33cm, and 23cm amateur bands plus VHF/UHF scanning, FM broadcast, weather satellites, and ADS-B from a single antenna.
VHF/UHF LPDAs are particularly popular for:
- SDR (software defined radio) receivers needing wideband coverage — one antenna feeds the RTL-SDR or SDRplay across all frequencies
- Amateur satellite monitoring — covering VHF and UHF downlinks simultaneously
- Scanner antennas — covering aircraft, marine, public safety, and amateur bands
- EME and weak-signal work on multiple bands from one fixed installation
- Radio astronomy and passive RF observation requiring flat gain across a wide range
Construction at VHF/UHF uses aluminum rod or tubing elements — the same materials as a Yagi but with more elements and the characteristic transposed feedline. Dimensional tolerances are tighter than at HF: a 1% length error on 2m shifts resonance by 1.4 MHz, so careful measurement is important.
VHF/UHF LPDA Dimensions — 144 to 450 MHz Example
An LPDA covering the 2m and 70cm amateur bands from a single antenna, using τ = 0.88 and σ = 0.10:
Building a 10-Element HF Log Periodic for 20m–10m
Aluminum tubing elements, two-tube boom transmission line, coax feed at the rear — approximately 6 dBd across 14–30 MHz.
Model First in 4NEC2
Enter all 10 element positions and lengths into 4NEC2 with your actual element diameter. Add the transposed feedline as a transmission line (TL card in NEC2). Sweep 13–32 MHz and verify gain, F/B ratio, and SWR across the target range before purchasing any materials. The model should show gain between 5 and 7 dBd and SWR below 2:1 across the full range.
Build the Dual-Tube Boom
The boom consists of two parallel aluminum tubes separated by a fixed distance — this gap between tubes sets the characteristic impedance of the boom transmission line. A spacing of 1.5" between 1" OD tubes gives approximately 100–120Ω characteristic impedance. Mount the tubes on insulating spacers (polycarbonate or PTFE rod) every 18–24 inches to maintain consistent separation. The spacers must be non-conductive — metal spacers short-circuit the transmission line.
Cut and Install Elements
Cut all 10 elements from 3/8" or 1/2" aluminum tubing to the calculated lengths — accounting for element diameter correction (slightly shorter than thin-wire formula). Each element passes through or clamps to one boom tube at its center point. The key requirement: alternate which boom tube each element connects to — element 1 connects left-right, element 2 connects right-left, and so on. This alternating connection is what creates the transposed feedline effect.
Install the Feedpoint
The coax feedpoint connects at the rear of the antenna — at the longest element end. The coax center conductor connects to one boom tube and the braid connects to the other. The boom transmission line impedance sets the feedpoint impedance — a 100Ω boom with 50Ω coax benefits from a 2:1 balun or a λ/4 matching section of 75Ω coax. Alternatively, adjust the boom tube spacing to achieve ~50Ω characteristic impedance for a direct coax match.
Install a Current Choke
Wind 8 turns of coax through an FT-240-31 toroid immediately at the feedpoint — before the coax runs along the boom or down the mast. Common-mode current is a significant issue with LPDAs because the coax runs along the active antenna structure. Without a choke, the coax pickup skews the pattern and introduces SWR variation with coax routing changes.
Initial SWR Sweep Across Full Range
Connect the NanoVNA and sweep 13–32 MHz. The SWR should stay below 2:1 across the entire range. If there are specific frequency regions with high SWR spikes, suspect incorrect element connections (a phase reversal error at one element creates a local resonance problem). Verify each element's connection to the correct boom tube systematically.
On-Air Verification
Use the Reverse Beacon Network to verify gain and F/B ratio in the real world. Transmit CW on 20m, 15m, and 10m in sequence, comparing spot strengths from stations in the forward direction versus the rearward direction. A 20 dB F/B ratio should be clearly visible in the spot reports — forward stations should appear 20 dB stronger than rearward stations at the same distance.
Is a log periodic better than a Yagi for HF?
Neither is universally better — they excel in different situations. A Yagi delivers more gain on its design frequency and is simpler to build. An LPDA delivers consistent gain across multiple bands without a tuner and covers more of the HF spectrum from a single antenna. For an operator who primarily works one band, a Yagi is the better choice. For an operator who moves across 20m, 17m, 15m, 12m, and 10m regularly and wants directional gain on all of them without band-change complexity, the LPDA wins on operational convenience despite its modest gain disadvantage per band.
Why is the coax connected at the rear (short element end) of the LPDA?
The forward direction of an LPDA is toward the short elements — the antenna radiates from front to back, with the shortest elements at the front. The feedpoint is at the rear because that is where the boom transmission line terminates. RF enters at the rear, travels along the transposed boom transmission line toward the front, and radiates from the active region elements near resonance. This is counterintuitive — the antenna points in the direction of its short elements, away from the feedpoint end. When mounting on a rotator, the long elements face backward and the coax exits from the rear of the structure.
What frequencies does a typical amateur HF LPDA cover?
The most common amateur HF LPDA covers 14–30 MHz — the 20m, 17m, 15m, 12m, and 10m bands. Some designs extend down to 7 MHz (40m) by adding longer rear elements, but this significantly increases boom length and antenna size. A 7–30 MHz LPDA with τ = 0.92 requires approximately 12 elements and a boom of around 35 feet — a substantial structure. Most operators use a separate 40m antenna (dipole or vertical) and an LPDA for the high bands.
Does an LPDA need a rotator?
A rotatable LPDA needs a rotator — the same as any other directional antenna. However, one attractive option is a fixed-direction LPDA pointed toward a primary target region. An operator on the US east coast might point a fixed LPDA toward Europe and use a separate omnidirectional antenna for other directions. This eliminates the rotator and its associated mechanical complexity while providing consistent high-band directional gain toward the most important DX target.
What is the transposed feedline and why is it necessary?
The transposed feedline is the two-conductor transmission line that runs the length of the LPDA boom, with each adjacent element pair connected with reversed polarity. Without the phase reversal at each step, adjacent elements would be driven in phase with each other and would simply cancel rather than produce a coherent directional beam. The phase reversal ensures that elements on opposite sides of the active region work together constructively in the forward direction. In practice it is implemented by alternating which conductor of the boom transmission line each element connects to — every element switches sides.
Can I build an LPDA from wire instead of aluminum tubing?
Yes — a wire LPDA suspended between supports performs essentially the same electrically as an aluminum tube version, with the trade-offs that wire is more susceptible to wind movement (which shifts resonance) and is harder to maintain precise element lengths over time as wire stretches. For a fixed non-rotatable HF installation, a wire LPDA is a practical and cost-effective option. The two-conductor feedline can be implemented using twin-lead or home-made ladder line running between the wire elements with appropriate polarity reversals at each element.
What tau and sigma values should I use for a typical amateur HF LPDA?
For a practical amateur HF LPDA covering 14–30 MHz, τ = 0.92 and σ = 0.12 is a well-established starting point. This combination delivers approximately 6 dBd of gain across the design range, a front-to-back ratio around 20 dB, and requires approximately 10 elements on a 20-foot boom — a manageable structure for most tower installations. If boom length is a constraint, reducing tau to 0.88–0.90 shortens the boom at the cost of 0.5–1 dBd of gain. If maximum gain is the priority and boom length is not a constraint, increasing tau to 0.94–0.95 and sigma to 0.14 provides 7+ dBd at the cost of 13+ elements and a longer boom.
How does an LPDA compare to a trap Yagi for multi-band use?
Both cover multiple HF bands from one antenna but through different mechanisms. A trap Yagi uses resonant traps to create multiple resonant element lengths in one physical element — it operates as a standard Yagi on each band. An LPDA uses many driven elements with a transposed feedline to create frequency-independent directional performance. The trap Yagi typically delivers slightly more gain per band (5–6 dBd) but has narrower bandwidth per band and introduces trap losses. The LPDA delivers slightly less gain (4–6 dBd) but provides truly consistent performance across the full design range without traps. Both are valid choices — the trap Yagi is simpler to mount and maintain; the LPDA provides more uniform wideband coverage.