Log-periodic & Structured Wideband Antennas

LPDA (log-periodic dipole array), horn, spiral, Vivaldi, equiangular spiral — the geometric-series-based wideband family for microwave receive, EMC test ranges, and 2.4 / 5 GHz Wi-Fi auditing

Section	Topic
1	About this volume
2	Geometry & theory — frequency-independence by self-similarity
3	The LPDA — log-periodic dipole array
4	The horn antenna — for microwave gain
5	The spiral and equiangular spiral
6	The Vivaldi — tapered-slot wideband antenna
7	Feedpoint impedance and matching
8	Radiation pattern — directional vs omni
9	Frequency response
10	Best-case use
11	Worst-case use
12	Power handling
13	DIY build — a 400 MHz – 1 GHz LPDA from aluminum tubing
14	Commercial buys
15	Companion gear
16	Common gotchas and myths
17	Resources

1. About this volume

This is the directional wideband antenna family — the LPDA, horn, spiral, Vivaldi, and equiangular spiral. Sibling to the omnidirectional wideband family covered in Vol 12 (Discone & wideband), the directional wideband family shares the same fundamental physics (geometric scale-invariance produces frequency-independent behavior) but uses progressive arrays of resonant elements (LPDA) or guided-wave / aperture structures (horn, Vivaldi) to concentrate radiation into a forward direction.

The use-case dividing line between Vol 12 (discone family) and Vol 13 (log-periodic family) is straightforward:

Omnidirectional wideband (Vol 12): “I don’t know which direction the signal is coming from. Cover everything.” Scanning, generic SDR receive, public-safety monitoring, EMC measurement at indeterminate-source locations.
Directional wideband (Vol 13): “I know roughly which direction the signal is coming from. Concentrate gain that way and reject the rest.” Point-to-point links, EMC measurement at known sources, microwave receive, Wi-Fi site survey of distant access points.

LPDAs in particular are the canonical “Yagi with bandwidth” antenna. Where a Yagi (Vol 11) gives high gain at one band, an LPDA gives moderate gain across a 4:1 to 10:1 frequency range. They’re the standard wideband directional amateur antenna for VHF/UHF scanning, the EMC-industry standard for 30 MHz – 1000 MHz emissions testing, and the modern hobbyist’s “single feedline, multiple amateur bands, directional” choice.

Horns are the canonical microwave gain antenna — open-ended waveguide flared to a larger aperture. Above ~1 GHz, horns are the easy gain antenna; at 2.4 GHz / 5 GHz they deliver 15–25 dBi gain in compact packages.

Spirals (Archimedean / equiangular) are the canonical wideband circularly-polarized antenna — used in EW research, GPS spoof detection, satellite tracking. 100:1+ bandwidth.

Vivaldis are the canonical PCB-fabricated wideband antenna — exponentially-tapered slots in copper-clad PCB, easy to fab on FR-4, popular in SDR research and ultrawideband (UWB) applications.

This volume covers each at engineer-grade depth. The DIY build at §13 is a 400 MHz – 1 GHz LPDA — the most practical wideband-directional antenna for the Hack Tools hub, useful for WiFi site survey, scanner directional listening, and amateur 70 cm operations.

2. Geometry & theory — frequency-independence by self-similarity

2.1 The Rumsey angle-defined geometry

Victor Rumsey’s 1957 paper established that any antenna whose geometry is defined entirely by angles (no characteristic length) is frequency-independent. The shape is determined by ratios — angle of expansion, ratio of one element to the next, ratio of one spiral arm’s diameter to the next — but no specific length is part of the definition.

A real antenna is finite (it has to stop somewhere), so a real “frequency-independent” antenna has a low-frequency limit (where the antenna becomes too small relative to wavelength) and a high-frequency limit (where the smallest feature becomes too coarse). Between those limits, the antenna’s impedance and radiation pattern are roughly constant — this is the magic of the geometric-similarity principle.

Four canonical frequency-independent geometries:

Antenna	Geometric basis	Real bandwidth	Polarization
Equiangular spiral	Continuous logarithmic spiral	10:1 to 100:1	Circular (RHCP or LHCP)
Archimedean spiral	Constant pitch spiral	5:1 to 30:1	Circular
LPDA (discrete)	Geometric series of dipoles	4:1 to 10:1	Linear (horizontal or vertical)
Vivaldi	Exponentially-tapered slot	5:1 to 30:1	Linear
Horn	Linear flare (cone or rectangular)	1.5:1 to 3:1	Linear (TE10 mode)

The horn is the “smallest bandwidth” of the geometric-similarity family — its linear flare isn’t a true scale-invariant geometry, so it has a narrower-than-frequency-independent bandwidth. The spiral is the largest-bandwidth (theoretically infinite — the equiangular spiral is the only true frequency-independent antenna by Rumsey’s principle).

2.2 LPDA: discrete approximation to the equiangular spiral

The LPDA approximates the continuous equiangular spiral by a discrete geometric series of dipoles. Each successive dipole is shorter than the previous by a fixed ratio τ (tau), and spaced from the next by a fixed ratio σ (sigma) relative to its own length. Mathematically:

   L_n / L_{n+1} = 1 / τ   (each element is shorter by factor τ < 1)
   S_n / L_n = σ           (each element's spacing to the next, relative to its own length)

Where τ < 1 (typical: 0.82–0.96) and σ < 1 (typical: 0.13–0.20). The “smaller τ” choice gives wider bandwidth and lower gain; “larger τ” gives narrower bandwidth and higher gain.

At any operating frequency, only the dipoles near resonance (electrical length ≈ λ/2) actively radiate; the smaller dipoles are inactive (capacitive) and the larger dipoles are also inactive (inductive, attenuated by the criss-crossed feedline). The “active region” moves along the boom as the operating frequency changes:

At the low end of the band, the longest elements at the boom’s wide end are active
At the high end of the band, the shortest elements at the boom’s narrow end are active
Between, the active region moves linearly along the boom

This frequency-dependent active region is what gives the LPDA its wide bandwidth.

2.3 The reverse-phasing trick

Adjacent elements in an LPDA are reverse-phased — each element is flipped 180° relative to its neighbor. The boom carries a balanced feedline (two parallel conductors) and each element’s two halves attach to opposite sides of the boom. The reverse-phasing causes elements to alternately add and subtract from the radiated signal, with the net effect being constructive in the forward direction.

   Side view of an 8-element LPDA (driven at the narrow end):

                                              feedpoint (50 Ω coax) ●
                                                                    │
   ●←───●═══●←──●═══●←──●═══●←──●═══●←──●═══●←──●═══●←──●═══●─→   ●
        ↑                                                            
   longest                                                          shortest
   element                                                          element
   (low freq                                                        (high freq
   resonant)                                                        resonant)
                            
   Each element's two halves attach to OPPOSITE sides of the boom (criss-cross
   feed) so adjacent elements are reverse-phased.

The criss-cross feed is one of the most distinctive features of an LPDA — it’s the visual signature that identifies the antenna as an LPDA rather than a multi-element Yagi.

3. The LPDA — log-periodic dipole array

3.1 The τ and σ design parameters

For amateur and EMC use, typical LPDA design parameters:

Design intent	τ	σ	Gain	Bandwidth
Narrow band, high gain	0.96	0.18	9–10 dBi	4:1
Standard	0.90	0.16	7–8 dBi	6:1
Wide band	0.85	0.14	6–7 dBi	10:1
Very wide	0.80	0.12	5–6 dBi	20:1

The standard τ = 0.90 / σ = 0.16 design covers ~6:1 frequency range with 7–8 dBi gain — typically used for amateur LPDAs covering 144–432 MHz (which is a 3:1 ratio, well within the 6:1 design).

For wider coverage, smaller τ and σ produce more bandwidth at the cost of fewer elements actively radiating at any given frequency (and therefore lower gain). The Aaronia HyperLOG and Schwarzbeck VULP series of EMC-grade LPDAs use τ ≈ 0.85, σ ≈ 0.16 for 30 MHz – 1 GHz coverage (~33:1 frequency range with 6 dBi gain).

3.2 Number of elements

The number of elements N in an LPDA covering frequency range f_low to f_high:

N ≈ ceil(log(f_high/f_low) / log(1/τ))

For a 4:1 LPDA with τ = 0.90: N = ceil(log(4) / log(1.111)) = 13 elements. For a 10:1 LPDA with τ = 0.85: N = ceil(log(10) / log(1.176)) = 14 elements.

Most amateur LPDAs are 8–18 elements. EMC-grade LPDAs (30 MHz – 1 GHz) often have 18–24 elements.

3.3 LPDA vs Yagi-Uda comparison

Property	Yagi (5-el, 144 MHz)	LPDA (144 MHz design, 6:1 bandwidth)
Bandwidth	3–5% (4 MHz on 144 MHz)	6:1 (e.g. 50–300 MHz)
Peak gain	9–10 dBd (11–12 dBi)	6–8 dBi
Front-to-back	22–27 dB	15–22 dB
HPBW	50°	60–70°
Mechanical complexity	Moderate (5 elements + boom)	Higher (15+ elements + criss-cross boom)
Matching network	Hairpin or gamma	Natural 50 Ω via criss-cross
Typical use	Single-band high-gain	Wideband moderate-gain

The LPDA’s claim over the Yagi: cover a 6:1 frequency range with one antenna, at the cost of 3 dB of peak gain. For amateur use where you want 50 MHz – 300 MHz on one feedline, the LPDA wins. For 144 MHz – 144.4 MHz (a single-band SSB segment), the Yagi wins.

3.4 Active region and pattern stability

At any given frequency, the LPDA’s active region spans 3–5 elements near the operating wavelength. The element at the geometric center of the active region is at exact resonance; the elements on either side are slightly off-resonance and contribute as parasitic-like elements (similar to a Yagi’s driver-and-directors).

As the operating frequency changes, the active region moves along the boom. The pattern direction stays the same (always pointing toward the boom’s narrow end), but the actively-radiating elements shift. This is why the LPDA pattern is roughly constant across its bandwidth — the active region is always a similar-shaped sub-Yagi, just at a different physical location.

3.5 Modern variations

Recent LPDA design refinements:

Aaronia HyperLOG series: optimized for EMC measurement, 4 to 33:1 bandwidth, calibrated antenna factor curves
Schwarzbeck VULP series: EMC industry standard, calibrated for FCC/CISPR measurement
R&S HL046 / HL050: EMC-grade LPDA + biconical combo (Bilog)
Generic 800–2700 MHz LPDA: low-cost Chinese mass-produced LPDAs for cellular and Wi-Fi audit work, $40–80

For amateur use, the canonical references are the Aaronia and DX Engineering wide-band LPDAs.

4. The horn antenna — for microwave gain

4.1 The waveguide-aperture geometry

A horn is conceptually an open-ended waveguide flared to a larger aperture. The signal propagates through the waveguide in a single transverse-electric (TE) mode and radiates from the open end. The flare improves the impedance match between the waveguide (typically ~377 Ω free-space impedance for a TE10 mode in air) and the surrounding free-space impedance (377 Ω), reducing reflection at the aperture.

   Side view of a pyramidal horn:
   
                                          ●  feedpoint (waveguide source)
                                          │
                                          │  waveguide section
                                          │  (sized for TE10 mode)
                                          │
                                          │
                                       ────┼────
                                      ╱    │    ╲
                                    ╱      │      ╲   ← E-plane flare
                                  ╱        │        ╲ (in the H-plane direction)
                                ╱          │          ╲
                              ╱            │            ╲
                            ╱              │              ╲
                          ╱                                  ╲   
                        ●     APERTURE: a × b                  ●  ← aperture
                                                              
                        ────────────────────────────────────
                        gain ≈ 10·log₁₀(η · 4π·A/λ²) where A = a·b

4.2 Horn gain formula

The horn’s gain is governed by its aperture area:

Gain (dBi) = 10·log₁₀(η · 4π · A / λ²)

Where:

η is the aperture efficiency (typically 0.5 for amateur horns; 0.7 for precision EMC horns)
A is the aperture area (a × b for a rectangular horn)
λ is the operating wavelength

Examples at 2.4 GHz (λ = 12.5 cm):

Aperture (a × b)	A (cm²)	Gain (dBi)	HPBW
10 × 7 cm	70	10	60°
15 × 10 cm	150	13	45°
20 × 15 cm	300	16	30°
30 × 23 cm	690	18	25°
50 × 40 cm	2000	23	12°

A 30 × 23 cm horn at 2.4 GHz is the canonical “high-gain 2.4 GHz Wi-Fi horn” — 18 dBi gain, 25° beamwidth, ~5 km link distance for line-of-sight 2.4 GHz Wi-Fi.

4.3 Horn types

Several horn variants:

Pyramidal horn: rectangular aperture (a × b), 2D flare in both E and H planes. The standard horn. Linear polarization (typically vertical or horizontal depending on orientation).
E-plane sectoral horn: flare in the E-plane only. Used when narrowing the pattern in one direction only.
H-plane sectoral horn: flare in the H-plane only. Used when narrowing in the perpendicular direction.
Conical horn: circular cross-section, flared from circular waveguide. Used at frequencies where circular waveguide is more practical (microwave bands above 12 GHz).
Corrugated horn: a precision pyramidal horn with corrugations in the inner walls to suppress side lobes. Used in radio astronomy and satellite tracking.

4.4 Horn-to-coax connection

A horn is fed via a waveguide section, which must be transitioned to coax for amateur use. Coax-to-waveguide transitions use:

Probe coupling: a coax center conductor projects into the waveguide; the probe length and position set the impedance match
Loop coupling: a small loop of coax inside the waveguide
Aperture coupling: a slot in the waveguide wall

Commercial 2.4 GHz horns include the coax-to-waveguide transition; DIY horns need careful design to avoid mismatch and to ensure the polarization sense is correct.

4.5 Horns at HF — impractical

Horns are theoretically possible at HF, but the aperture needed to give substantial gain (~15 dBi) at 30 MHz is ~10 meters on a side — impractical. At lower frequencies, the size becomes the limiting factor; LPDAs and Yagis are the practical alternatives.

Horns are the practical choice from about 1 GHz upward, where the aperture size is mechanically reasonable. Above 10 GHz, horns are the standard high-gain antenna (along with parabolic dishes, which use horns as feed antennas).

5. The spiral and equiangular spiral

5.1 Geometry

A spiral antenna consists of two arms wound in a planar spiral pattern, fed at the center. The arms emanate from the feedpoint and spiral outward at a constant rate. Two variants:

Equiangular spiral: the spiral grows logarithmically — radius proportional to e^(a·θ), where θ is the angle from the start. This is the only truly frequency-independent antenna by Rumsey’s principle.
Archimedean spiral: radius proportional to θ (linear growth with angle). Less ideal than equiangular but easier to fabricate.

   Top view of a two-arm Archimedean spiral:
   
                            ┌─────────────────┐
                          ╱                    ╲
                        ╱     ┌─────────────╮   ╲
                      ╱     ╱                ╲   ╲
                    ╱     ╱    ┌─────────╮   ╲   ╲
                  ╱     ╱    ╱           ╲   ╲   ╲
                ●     ●    ●  ●  feed   ●   ●   ●
                 ╲     ╲    ╲           ╱   ╱   ╱
                  ╲     ╲    └─────────┘   ╱   ╱
                    ╲     ╲                ╱   ╱
                      ╲     └─────────────┘   ╱
                        ╲                    ╱
                          ╲                ╱
                            └─────────────┘
   
   (Two arms, one black/solid, one gray/dashed in a real diagram —
    each is a separate conductor spiraling outward)

5.2 Properties

Spirals have:

Circular polarization (RHCP if the spiral winds clockwise outward; LHCP if counter-clockwise)
Bandwidth: 5:1 to 100:1 (equiangular gets the highest; Archimedean is limited by inner spiral resolution)
Pattern: omnidirectional in the plane of the spiral; cardioid-shape perpendicular to the spiral plane
Feedpoint impedance: ~188 Ω (balanced) natively; needs a balun + impedance transformer to 50 Ω

The 188 Ω feedpoint comes from the spiral’s geometric structure — it’s not an arbitrary choice. A 4:1 balun + a 2:1 unun typically converts the 188 Ω to 50 Ω.

5.3 Active region

A spiral’s “active region” is the spiral’s annular ring at radius ~λ/(2π) from the feedpoint, where the spiral’s circumference equals approximately one wavelength. The current at that radius is large; current at smaller and larger radii is negligible. As frequency changes, the active region moves radially — smaller for higher frequency, larger for lower frequency.

This is the planar analog of the LPDA’s longitudinal active region.

5.4 Where spirals win

Spirals are the canonical choice for:

GPS spoof / jammer detection: GPS is RHCP; a spiral receives RHCP cleanly while rejecting LHCP and linear-polarized signals (which jammers typically are). The polarization selectivity gives ~6 dB of immunity to typical jammers.
EW (electronic warfare) research: wideband direction-finding receive in a single antenna.
Satellite tracking: many satellites transmit RHCP or LHCP; a single spiral covers both senses by mirroring the spiral direction or flipping the antenna.
Radio astronomy at low frequencies (low-band telescopes).

5.5 Where spirals don’t win

High-gain applications: spirals are typically 0–4 dBi (omnidirectional-ish in the plane). For high gain, use a horn or parabolic dish.
Linear-polarization scenarios: a spiral has 3 dB built-in loss to a linearly-polarized signal (the cross-polarization loss). If the source is linear, use a linearly-polarized antenna.
Compact installations: a spiral wide enough to be efficient at HF would be a half-meter wide.

6. The Vivaldi — tapered-slot wideband antenna

6.1 The geometry

A Vivaldi antenna is an exponentially-tapered slot cut into a copper-clad printed-circuit board (PCB). The slot’s width increases exponentially from the feed end to the radiating end, providing a smooth impedance transition from the feedpoint impedance to free-space.

   PCB layout (top view of Vivaldi):
   
                                                      ●  feed point
                                                      │
                                                      │  microstrip feed
                                                      │  to slot transition
                                                      │
                                          ─────────────────────
                                          │  exponential       │
                                          │  taper             │
                                          │  (slot widens)     │  ← copper
                                          │                    │
                                          │                    │
                                          │                    │
                                                              
                                          \________________________/  ← radiating
                                                                       aperture

The microstrip-to-slot transition at the feed point converts a 50 Ω microstrip line to the slot’s higher impedance, then the slot’s exponential taper provides a smooth transformation to ~377 Ω at the radiating aperture.

6.2 Vivaldi properties

Bandwidth: 5:1 to 30:1 (very wide)
Linear polarization (perpendicular to the slot’s direction)
Gain: 5–12 dBi depending on length
End-fire pattern: radiation primarily out the open end of the slot
Easy PCB fabrication: any FR-4 substrate works; no precision dimensions needed beyond the exponential profile
Compact: a 2.4 GHz Vivaldi fits on a 10 cm × 5 cm PCB

6.3 Vivaldi applications

The Vivaldi has found niches in:

SDR research: wideband receive for software-defined radio experiments, 1 GHz – 6 GHz
UWB (Ultra-Wideband): regulatory UWB systems use Vivaldi-like antennas
Side-channel attack research: monitoring leakage from electronic devices across a wide spectrum
Wi-Fi 6E / 7 directional auditing: 2.4 / 5 / 6 GHz coverage with a single antenna
5G mid-band measurement: 3.5 GHz – 4.5 GHz coverage

The Vivaldi is the “modern SDR researcher’s wideband antenna” — easy to fab, cheap, broadband, and acceptable performance.

6.4 DIY Vivaldi from scratch

A simple 2.4 / 5 GHz Vivaldi:

FR-4 PCB, ~10 cm × 5 cm
Etch an exponential taper into the copper (start at ~3 mm wide, expand to ~50 mm)
Add a microstrip-to-slot transition at the feed end
Solder an SMA connector at the microstrip end
Substrate: 1.6 mm FR-4 (cheap, $0.50 per PCB at scale)

Total cost: $5–10 per antenna. Performance: 5–8 dBi gain, 2:1 SWR across 2–6 GHz.

7. Feedpoint impedance and matching

7.1 Feedpoint impedance by antenna type

Antenna	Native Z	Matching needed for 50 Ω coax
LPDA	50 Ω	None (criss-cross feed is naturally 50 Ω at the boom end)
Horn	377 Ω (waveguide TE10)	Coax-to-waveguide transition
Archimedean spiral	188 Ω balanced	4:1 balun + 2:1 unun
Equiangular spiral	188 Ω balanced	Same as Archimedean
Vivaldi	50 Ω	None (microstrip-to-slot transition built into design)

7.2 The LPDA’s natural match

The LPDA’s criss-cross feedline forms a balanced two-wire transmission line with characteristic impedance ~280 Ω. When fed at the narrow end (the shortest-elements side), the combination of the line impedance and the active region’s element loading produces a net ~50 Ω at the boom-end feedpoint.

The criss-cross is what makes this work — without it, the LPDA would either present a balanced ~280 Ω feedpoint (needing a 4:1 balun + 2:1 unun) or an unbalanced ~140 Ω (needing a 3:1 transformer).

Some LPDA designs (typically older or less optimized) use a 4:1 balun at the feedpoint to convert the natural 50 Ω unbalanced to a 200 Ω balanced output that drives the boom-line. The modern preference is direct 50 Ω feed via a 1:1 current BALUN that suppresses common-mode current.

7.3 Horn impedance and waveguide transitions

A horn is fed via a waveguide section, and the waveguide must be transitioned to coax for amateur use. The most common transition is the probe coupler: a coax center conductor projects into the waveguide perpendicular to the waveguide’s axis. Probe length determines impedance match.

Waveguide	Frequency range	Probe length (typical)
WR-90	8.2–12.4 GHz	6 mm
WR-159	4.9–7.1 GHz	10 mm
WR-340	2.2–3.3 GHz	22 mm
WR-650	1.1–1.7 GHz	45 mm

For 2.4 GHz, the standard waveguide is WR-340. For 5.8 GHz, WR-159. Most commercial 2.4 GHz / 5 GHz horns include the waveguide-to-coax transition; DIY horns need careful design.

8. Radiation pattern — directional vs omni

8.1 LPDA pattern

Directional (forward-pointing main lobe)
HPBW: 60–70° in both planes (broader than a Yagi)
F/B: 15–22 dB (less than a Yagi)
Side lobes: ~12–15 dB below main beam

The LPDA’s pattern is broader than a Yagi’s because the LPDA has fewer “directive” elements at any one frequency. The trade is bandwidth — the LPDA covers 6:1 of bandwidth at the cost of 3 dB of peak gain and 5–8° of beamwidth.

8.2 Horn pattern

Directional (forward-pointing main lobe)
HPBW: 12–60° (depends on aperture size)
F/B: 20–30 dB (very clean rear suppression)
Side lobes: -15 to -25 dB

Horns have the cleanest pattern of the wideband family — the open-ended waveguide produces a very directional radiation with minimal side lobes.

8.3 Spiral pattern

Omnidirectional in the plane of the spiral
Cardioid perpendicular to the spiral plane (back to one side, forward to the other)
Circular polarization (RHCP or LHCP)
Gain: 0–4 dBi typical

Spirals don’t concentrate radiation in a single direction — they’re more like a discone with circular polarization. Useful where polarization matters more than gain.

8.4 Vivaldi pattern

End-fire directional (radiation primarily out the open end of the slot)
HPBW: 30–50°
Linear polarization
Gain: 5–12 dBi

The Vivaldi’s end-fire pattern is similar to a Yagi or horn but with the additional benefit of being PCB-fabricated.

9. Frequency response

9.1 LPDA frequency response

A well-designed LPDA shows:

Frequency relative to f_min	Typical SWR	Gain
1.0× (lowest design)	1.5–2.0:1	-1 dB from peak
1.5×	1.3–1.7:1	Peak
2×	1.2–1.5:1	Peak
3×	1.2–1.5:1	Peak
4×	1.3–1.7:1	Peak
6×	1.5–2.0:1	-1 dB from peak
10×	2.0–3.0:1	-3 dB

A 4:1 LPDA covers its design range cleanly. A 10:1 LPDA degrades at the high-frequency edge.

9.2 Horn frequency response

Horns are narrower-band than the rest of this volume’s family because the linear waveguide flare isn’t truly scale-invariant:

Frequency relative to f_design	SWR
0.8×	2.0–3.0:1
0.9×	1.4–1.8:1
1.0×	1.2–1.5:1 (peak)
1.1×	1.3–1.6:1
1.2×	1.6–2.2:1

Typical horn bandwidth (2:1 SWR) is 1.5:1 to 2:1 frequency range — narrower than a discone or LPDA but wider than a Yagi.

9.3 Spiral frequency response

Equiangular spirals have the widest bandwidth of any antenna family — theoretical 100:1+, real-world 30:1+ is achievable.

9.4 Vivaldi frequency response

Vivaldis are typically specified for 5:1 to 30:1 bandwidth, depending on the exponential profile aggressiveness.

10. Best-case use

The log-periodic family wins when:

Wideband VHF/UHF directional receive (HackRF, RTL-SDR scanning with directional pickup): an LPDA gives 6 dBi+ gain across a 6:1 frequency range with a single antenna and one feedline.
2.4 / 5 GHz Wi-Fi auditing at distance: a horn antenna (or LPDA designed for the band) provides 15–20 dBi gain for site survey and remote auditing. Pineapple (WiFi Pineapple deep dive) + horn = pentest from a quarter mile away.
EMC measurement of devices under test: the standard LPDA covers FCC/CISPR 30 MHz – 1 GHz range.
GPS spoofing / jammer detection: a circularly-polarized spiral receives RHCP GPS while rejecting linear-polarized jammers.
Satellite tracking (amateur or commercial): RHCP or LHCP spiral antennas track satellites across wide elevation ranges.
UWB receive research: Vivaldi antennas cover 1 GHz – 6 GHz with consistent performance.
5G mid-band measurement: 3.5 GHz – 4.5 GHz with a Vivaldi or horn.
Radio astronomy and EW research: wideband direction-finding requires the wideband directional family.

11. Worst-case use

The log-periodic family is the wrong answer for:

HF operation (below 30 MHz): an HF LPDA is huge — a 10:1 LPDA for 3.5–35 MHz needs an 8 m boom and elements as long as 20 m. Practical only for very specialized installations.
Horn at HF: impossible — the aperture would need to be tens of meters across.
Spiral at HF: a 30:1 spiral for 1.5–45 MHz would need a 10 m diameter — also impractical.
Single-frequency high-gain applications: a Yagi outperforms an LPDA by 3 dB on a single band; use a Yagi if you only need one band.
Omnidirectional coverage: LPDAs, horns, and Vivaldis are directional. For omnidirectional wideband, use a discone (Vol 12).
Polarization-mismatched scenarios: a spiral’s circular polarization has 3 dB inherent mismatch to linearly-polarized signals. Don’t use a spiral if you know the source is linear.
High-power transmit at the band edges: LPDA SWR degrades at the edges of the design band. Use band-specific antennas for high-power single-frequency operation.
Compact installations: even a 100 MHz – 1 GHz LPDA is ~1 m of boom + 12 elements; not “tiny” by any measure.

12. Power handling

12.1 LPDA power

LPDA elements are typically aluminum tubing or rod, sized similarly to Yagi elements. Per-element-rated:

LPDA	Power rating	Notes
Diamond D3000N (25 MHz – 1.3 GHz amateur LPDA)	200 W	Budget amateur grade
Antenna Magus reference LPDAs	100–500 W	Reference designs
Aaronia HyperLOG 60100 X (30 MHz – 1 GHz EMC)	100 W	Calibrated for measurement
Schwarzbeck VULP 9118 D (30 MHz – 1 GHz EMC)	250 W	Calibrated
Sirio SY27-4 (HF LPDA)	2 kW	HF, high-power
A.H. Systems SAS-510-2 (30 MHz – 2 GHz)	100 W	EMC-grade

For amateur LPDAs, 200 W is typical. Higher-power LPDAs ($500+ price) handle 1 kW or more.

12.2 Horn power

Horns can handle very high power — the limiting factor is the waveguide construction and the coax-to-waveguide transition. Commercial 2.4 GHz / 5 GHz horns rated 25 W typical for Wi-Fi use; higher-power industrial horns reach 1–5 kW.

12.3 PCB-based spiral / Vivaldi power

Substrate-loss limited. FR-4 substrate handles 25–100 W max depending on the substrate’s dielectric losses at the operating frequency. For high-power applications, use Rogers TMM or PTFE-based substrates (which have lower dielectric loss but cost more).

For typical amateur SDR work at 100 mW – 5 W transmit, PCB-based antennas are fine. For higher-power transmit, use a discrete-element LPDA or horn.

13. DIY build — a 400 MHz – 1 GHz LPDA from aluminum tubing

This is a practical 18-element LPDA for the upper VHF and lower UHF range. About 6 hours of work plus tuning. Total parts cost ~$80 USD.

13.1 Design parameters

τ (length ratio) = 0.85
σ (spacing ratio) = 0.16
Bandwidth: 400 MHz – 1 GHz (2.5:1, well within design)
Estimated gain: 7 dBi
Elements: 18 (designed to overlap the operating band’s edges by ~10%)

13.2 Element table

Element	Length	Position on boom (from narrow end)
Driven (smallest)	75 mm	0 mm
2	88 mm	14 mm
3	104 mm	30 mm
4	122 mm	50 mm
5	144 mm	73 mm
6	169 mm	100 mm
7	199 mm	132 mm
8	234 mm	170 mm
9	276 mm	214 mm
10	324 mm	265 mm
11	381 mm	326 mm
12	448 mm	398 mm
13	527 mm	483 mm
14	620 mm	583 mm
15	730 mm	700 mm
16	858 mm	838 mm
17	1010 mm	1000 mm
18 (largest)	1188 mm	1189 mm

Boom length: 1189 mm. Element diameter: 6 mm aluminum tubing.

13.3 Bill of materials

Part	Specification	Source	Mid-2026 price
Aluminum tubing for elements	1/4″ (6 mm) OD, 18 cm × 2 m total	Texas Towers TT6	$25
Boom	1″ × 1″ × 1.3 m aluminum square tube	Local supplier	$20
Element insulators	DX Engineering EMP1 (9 pairs)	$40
Boom-line conductors	#14 enamel wire, 2 × 130 cm	Local	$3
Driven-element split block	Small plastic terminal block	$5
1:1 current BALUN	Mix-43 FT114-43 with bifilar winding	DIY $15 / commercial $40	$15
SO-239 chassis connector	Bulkhead-mount	DigiKey	$4
Coax pigtail	RG-8X, 30 cm	Times Microwave	$8
Hardware	Stainless screws, washers	$10
Weatherproofing	3M tape	$5
Total			~$135

13.4 Step-by-step construction

Cut the elements. Cut all 18 aluminum elements to their specified lengths (within ±0.5 mm tolerance — LPDA element-length tolerance is similar to Yagi tolerance).

Drill mounting holes. Each element gets a hole through its center for the boom-mount insulator. Use a drill press for precision.

Assemble the boom-line. The boom consists of the square aluminum tube plus two parallel insulated wires (the “boom-line”) running the full length. The boom-line wires criss-cross between adjacent elements — wire A connects element 1’s top half + element 2’s bottom half + element 3’s top half + … and wire B connects the opposite halves.

Install elements. Mount each element on the boom at the specified position, with the appropriate half of each element connected to the corresponding boom-line wire. Insulators isolate elements from the boom itself.

Connect the BALUN. The 1:1 BALUN connects between the boom-line wires at the narrow end (where the driven element is) and the coax pigtail. The two boom-line wires constitute the BALUN’s balanced side; the coax provides the unbalanced side.

Mount the assembly. Bolt the boom to a mast via U-bolts at the boom’s midpoint.

Sweep with NanoVNA. Connect the NanoVNA to the coax. Sweep 300 MHz – 1.2 GHz. SWR should be < 2:1 across 400 MHz – 1 GHz; slightly worse at the edges.

Adjust if needed. LPDA tuning is mostly geometric — if the dimensions are correct, the antenna works. If the SWR is off, check the BALUN’s connection direction and the boom-line wire crossings.

13.5 Tuning verification

A successful 400 MHz – 1 GHz LPDA shows:

SWR < 1.8:1 across 400 MHz – 900 MHz
SWR < 2.2:1 at 900 MHz – 1 GHz (the high-frequency edge)
No anomalous SWR spikes within the design band
Pattern directional (verifiable by rotating and observing forward-vs-rearward signal differential of 15+ dB)
F/B ratio > 15 dB across the band

If the SWR is high (>3:1) at the lower edge (400 MHz), the largest element is too short or too long. If the upper edge SWR is bad, the smallest element is wrong or the boom-line wires aren’t routed correctly.

14. Commercial buys

Sorted by tier and use case (USD, mid-2026):

Tier	Model	Frequency range	Price	Notes
Budget	Diamond D3000N	25 MHz – 1.3 GHz	$120	Diamond’s compact LPDA
Budget	Antenna Magus reference LPDAs	various	$100–250	Reference designs
Budget	Generic 800–2700 MHz LPDA (Amazon)	800–2700 MHz	$40	Low-cost Wi-Fi audit LPDA
Budget	Generic 100 MHz – 6 GHz LPDA	100 MHz – 6 GHz	$80	Wideband budget
Mid	Aaronia HyperLOG 60100 X	680 MHz – 10 GHz	$400	Mid-tier EMC LPDA
Mid	Aaronia HyperLOG 4060	400 MHz – 6 GHz	$350	Mid-tier EMC
Mid	Sirio SY27-4	27 MHz – 30 MHz CB	$180	Specialty CB LPDA
Mid	Schwarzbeck VULP 9118 D	30 MHz – 1 GHz	$650	Premium EMC
Mid	Aaronia HyperLOG 80050	800 MHz – 50 GHz	$1500	EMC for higher frequencies
Mid	InterTest BroadCast LP-1000	30 MHz – 1 GHz	$300	Broadcast measurement
Premium	A.H. Systems SAS-510-2	290 MHz – 1 GHz (LPDA + biconical)	$4500	EMC industry standard “Bilog”
Premium	R&S HL046	80 MHz – 1 GHz	$5000+	Calibrated EMC
Premium	R&S HL050	200 MHz – 2 GHz	$6000+	High-frequency calibrated EMC
Premium	EMCO 3149E	30 MHz – 1 GHz	$4500	Calibrated industry standard
Premium	OptiBeam OB-LP-100	50 MHz – 1 GHz	$3000	Amateur premium
Premium	Eikos LP series	various	$2000–8000	Custom-fabricated

Horn antennas:

Tier	Model	Frequency	Gain	Price
Budget	Generic 2.4 GHz horn	2.4 GHz	15–18 dBi	$40–80
Mid	A-INFO LB-20180	2.4 GHz	18 dBi	$200
Mid	Pasternack PE-W7150	1–18 GHz	15 dBi	$400
Premium	Pasternack PE-W18-N	6.5–18 GHz	22 dBi	$1500
Premium	A.H. Systems Horn series	various	varies	$2000+

Spiral antennas:

Model	Frequency	Polarization	Price
Pasternack equiangular spiral	1–18 GHz	RHCP or LHCP	$800
A-INFO bow-tie spiral	0.5–18 GHz	RHCP/LHCP	$1500
Custom GPS-DF spirals	1.5–1.6 GHz	RHCP	$500+

Vivaldi antennas:

Model	Frequency	Gain	Price
Generic FR-4 Vivaldi (DIY $5)	2–6 GHz	5–7 dBi	$5–30
Pasternack Vivaldi PCB	2–18 GHz	8 dBi	$500
Commercial UWB Vivaldi	3–10 GHz	10 dBi	$800

What to avoid:

“8–20 dBi 1–7 GHz panels” marketed as LPDA but actually patch arrays with narrow bands — the LPDA’s true bandwidth is the geometric-series advantage, not a panel array.
Cheap “5G LPDA” antennas — usually small Wi-Fi LPDAs repackaged as 5G; the design isn’t optimized for 5G frequencies.
Generic “wideband 1 MHz – 6 GHz” LPDAs at under $100 — physics-violating claims; real LPDA bandwidth is 6:1 to 30:1 typical.

15. Companion gear

Mast / rotator for directional aiming. LPDAs and horns benefit from rotators; spirals less so (omnidirectional in their plane).
Calibrated 50 Ω coax — LMR-400 minimum for VHF/UHF, LDF4-50 / Heliax for runs > 30 m or > 1 GHz operation.
Bias-T if combining with a masthead LNA (Vol 19) — important for EMC and weak-signal applications.
EMC calibration kit if using LPDA for compliance measurement — calibrated antenna factor curves and known-distance test setups.
Lightning protection (Vol 20 §5) — same polyphaser and single-point ground topology as other antennas.
Phased-array combiner for spiral or LPDA stacking (rare amateur application, common in EW and research).

16. Common gotchas and myths

“LPDA is a wideband Yagi” — same family of pattern; very different physics. A Yagi has one driven element and parasitic elements; an LPDA has all-active elements with reverse-phased criss-cross feed. They look similar from a distance, but they’re different antennas.
“8–20 dBi over 6 octaves” — usually inflated by 6+ dB. Real LPDA gain is 6–9 dBi.
“Horn antennas are only for microwave” — biconical / log-periodic horns work down to 30 MHz, but get large. Pure pyramidal horns are impractical below 1 GHz.
“Spirals have 100:1 bandwidth” — true for ideal equiangular spirals; real-world Archimedean spirals achieve 5:1 to 30:1.
“The Vivaldi is a PCB version of the horn” — partly true. The exponential taper is geometrically analogous, but the Vivaldi is a planar (2D) antenna and the horn is a 3D guided-wave structure. Different mechanical implementations, similar wideband behavior.
“My LPDA gets no signal below 100 MHz” — expected if the LPDA is designed for 100 MHz – 1 GHz. The lowest frequency is set by the largest element; smaller elements below that contribute nothing.
“Cheap 1 MHz – 6 GHz LPDAs are real” — false. The geometric design space requires a long boom and many large elements to cover such a wide range. A 1 MHz – 6 GHz LPDA would be 30+ m long.
“I can use an LPDA for SOTA portable” — a portable LPDA at 144 MHz is ~70 cm long, which is portable but cumbersome. A J-pole or roll-up J-pole is much more practical for SOTA. LPDAs are fixed-installation antennas.
“The LPDA’s pattern is the same on every frequency” — true to within ±0.5 dB. The active region moves but the pattern shape is preserved by the geometric similarity principle.
“Patch arrays are the same as LPDAs” — false. Patch arrays use phase-shifted patches to steer the beam; LPDAs use a geometric series of dipoles. Both can be wideband but the physics is different.
“Horn pattern is determined by the throat dimensions” — false. Horn pattern is determined by the aperture dimensions. The throat sets the impedance match; the aperture sets the gain and beamwidth.

17. Resources

Rumsey 1957 paper (Victor Rumsey, “Frequency Independent Antennas,” IRE National Convention Record) — the theoretical basis.
Carrel 1961 paper (R. L. Carrel, “Analysis and Design of the Log-Periodic Dipole Antenna,” Antenna Laboratory, University of Illinois Technical Report 52, 1961) — the canonical LPDA design paper.
Balanis Ch. 11 (frequency-independent antennas) — academic treatment.
Stutzman & Thiele Ch. 7 (broadband antennas) — covers LPDA, horn, spiral.
Aaronia, A.H. Systems, R&S datasheets — published measurements and specifications.
Vivaldi design papers (IEEE Trans. on Antennas and Propagation, 1979 — Gibson’s original Vivaldi paper) — the foundational Vivaldi publications.
Schaubert et al. papers on Vivaldi optimization — academic Vivaldi design references.
Aaronia HyperLOG technical specifications — published EMC-LPDA performance.
The IEEE Standard for the Measurement of EMC Antennas (IEEE 149) — measurement standards.
A.H. Systems “Bilog Manual” — the standard EMC compliance measurement antenna manual.

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