LPDA Antenna Array: Design & Applications

• LPDA antenna arrays are broadband antennas comprising systematically varying dipoles that deliver scalable performance over a wide frequency range.
• They employ geometric scaling factors and controlled apex angles to achieve optimal impedance matching, moderate gain, and minimal VSWR.
• Practical designs are validated through full-wave simulations and in-situ calibrations, ensuring reliable performance in radio astronomy and cosmic-ray detection.

A log-periodic dipole antenna array (LPDA) is a broadband, frequency-scalable antenna realized as a sequence of half-wave dipoles of systematically varying length and spacing. Each element is mounted parallel on one or more conducting booms, with the lengths and spacings scaled by a fixed factor to achieve stable impedance, directivity, and pattern characteristics over an octave or larger frequency ratio. LPDAs are widely employed for applications ranging from radio astronomy and cosmic-ray detection to electromagnetic compatibility testing, leveraging their wideband impedance match, moderate gain, and controllable polarization properties (Briechle, 2016, Acedo et al., 2020, Seikh et al., 20 Jan 2026).

1. Geometric Parameters and Design Laws

LPDA design is governed by the log-periodic principle, wherein the n-th dipole element possesses length $L_n=L_1\tau^{n-1}$ and spacing $S_n=S_1\tau^{n-1}$, with $L_1$ and $S_1$ being the largest element parameters, $\tau<1$ a constant scale factor, and $n=1\ldots N$ (Seikh et al., 20 Jan 2026, Acedo et al., 2020). $L_1$ is typically set by the lowest design frequency ($L_1\approx c/(2f_\text{min})$), and $N$ is calculated to provide the needed bandwidth, $N=1+\log(f_{\max}/f_{\min})/\log(1/\tau)$.

The apex angle $\alpha$ regulates the mechanical spread and pattern envelope, typically set by $\tan\alpha\approx(L_1-L_N)/(2L_\text{boom})$ for $L_\text{boom}=\sum_{n=1}^N S_n$ (Acedo et al., 2020). Typical parameters, as realized in the SKALA4 (SKA1-LOW) element, include $\tau=0.85$, $N=12$, $L_1=3.0$ m, $L_\text{boom}\simeq4.2$ m, and $\alpha\approx 37^\circ$ for 50–350 MHz performance (Acedo et al., 2020). The AERA LPDA at Pierre Auger Observatory uses $\tau\approx0.85-0.90$, $N=9$, and covers 30–80 MHz with element lengths from $\sim$1 m to 5.3 m (Briechle, 2016). Optimal element diameter is selected for bandwidth and structural integrity, typically 10–15 mm for tubular conductors at these frequencies (Acedo et al., 2020, Seikh et al., 20 Jan 2026).

2. Impedance Matching and Feeding Structure

Consistent impedance is a signature LPDA feature. The input impedance $Z_\mathrm{A}\simeq50\,\Omega$ is achieved using a wideband balanced/unbalanced (balun) transformer, either via coaxial sleeves (SKALA4 design) or other transmission line structures. The design aims for VSWR $<2:1$ over most of the operational frequency range, with reactance kept below $\pm j15\,\Omega$ and often improved by minor capacitive tuning ($C_\text{match}=2$–4 pF) (Acedo et al., 2020).

Reflection coefficient $\Gamma(f)$, return loss $RL(f) = -20\log_{10}|\Gamma(f)|$ dB, and Smith chart loci are extracted from measured or simulated S-parameters, with a typical design goal of $RL<-10$ dB across the band for robust matching (Seikh et al., 20 Jan 2026). AAFIYA [Editor’s term] provides reference Python workflow for automated S-parameter extraction, impedance analysis, and publication-quality visualization, supporting validation against simulation data (Seikh et al., 20 Jan 2026).

3. Radiation Characteristics and Polarization Properties

The directional response of an LPDA is described by its vector effective length (VEL) $\vec{H}(f,\theta,\phi)$, which yields the open-circuit voltage $$U(f,\theta,\phi)=\vec{H}(f,\theta,\phi)\cdot\vec{E}(f,\theta,\phi)$$ (Briechle, 2016). The gain $G(f,\theta,\phi)$ relates to the effective height $h_\mathrm{eff}$ via

$$G(f,\theta,\phi) = \frac{4\pi}{\lambda^2}|h_\mathrm{eff}(f,\theta,\phi)|^2 \frac{\operatorname{Re}\{Z_\mathrm{A}\}}{Z_0},$$

with $Z_0=120\pi\,\Omega$.

Single-element realized gain for LPDAs of $\sim$5–8.5 dBi is achieved over octave bandwidths, with beamwidths narrowing from $\sim$90° at the low end to $\sim$70° at the upper frequency for E-plane, and typically $<-20$ dB cross-polarization at boresight (Acedo et al., 2020, Seikh et al., 20 Jan 2026).

Polarization isolation is quantified by cross-polarization ratio (XPR) and purity metrics, e.g., $$XPR(f,\theta)=10\log_{10}[P_\mathrm{co}(f,\theta)/P_\mathrm{cross}(f,\theta)]$$ and $$PP(f,\theta)=[P_\mathrm{co}-P_\mathrm{cross}]/[P_\mathrm{co}+P_\mathrm{cross}]$$ (Seikh et al., 20 Jan 2026). These parameters are validated through anechoic chamber measurements and full-wave simulation (e.g., HFSS, WIPL-D or NEC-4.2), yielding $>$95% agreement in amplitude and beam structure over 100–850 MHz (Seikh et al., 20 Jan 2026).

4. Calibration, Yield, and Validation Workflows

Absolute pattern calibration is critical for high-precision science applications. At AERA, an in-situ far-field calibration campaign employed an octocopter-drone to position a reference emitter above the array, measuring received power at known $(f,\theta,\phi)$ values to derive $|\vec{H}_i(f,\theta,\phi)|$ using a Friis-derivative relation (Briechle, 2016):

$$|\vec{H}_i(f,\theta,\phi)| = \sqrt{\frac{4\pi\,Z_\mathrm{A}}{Z_0}\,R^2\,\frac{P_{r,i}(f)}{G_t(f)\,P_t(f)}}$$

where $R$ is source-to-antenna range, $P_{r,i}$ received power, $G_t$ transmitter gain, $P_t$ transmit power. The achieved absolute amplitude uncertainty was 9.3%.

Workflow validation is performed by overlaying measured and simulated $|\vec{H}_\phi(\theta)|$ patterns (as in AERA, $|\vec{H}_\phi|$ at $\theta=45^\circ$ is $\approx0.8$ m, with $<10\%$ residual to simulation across the scan) (Briechle, 2016). AAFIYA enables automated impedance, realized gain, and beam pattern validation, with yield estimation via Monte Carlo tolerancing of $L_n$ and $S_n$, supporting robust design under fabrication uncertainty. Standard metrics include pass/fail RL$<-10$ dB and specified minimum realized gain (Seikh et al., 20 Jan 2026).

5. Array Configuration and Mutual Coupling

Large-aperture LPDA arrays (e.g., SKA1-LOW) consist of quasi-random distributions (Halton or jittered-spiral) of $N_e$ LPDAs (e.g., $N_e=256$ per 35 m station). Mutual coupling is mitigated by >1.5 m minimum element spacing, randomized placement, and use of ground-screens beneath elements to reduce surface wave propagation (Acedo et al., 2020).

The total array pattern is given by $$E_\mathrm{tot}(\theta,\phi)=a(\theta,\phi)\cdot AF(\theta,\phi)$$ with array factor $$AF(\theta,\phi)=\sum_{n=1}^{N_e} w_n\,a(\theta,\phi)\,e^{-j\boldsymbol{k}\cdot\boldsymbol{r}_nu(\theta,\phi)}$$, where $w_n$ are complex weights, and $a(\theta,\phi)$ the element response (Acedo et al., 2020). Spacing $d$ is chosen to balance grating lobe suppression (prefer $d<\lambda_\text{min}/2$) and manageable coupling/costs ($d\sim$1.5–2 m is typical for 50–350 MHz) (Acedo et al., 2020).

6. Scientific Applications and Impact

LPDA stations are deployed in radio detection of cosmic-ray air showers, where absolute calibration of the vector effective length is required to reconstruct incident electric field amplitudes with systematics below $10\%$. At AERA, such calibration improved primary energy reconstruction uncertainty from $\sim$14% to $\lesssim$10%, with a $\sim$10–15 g/cm$^2$ improvement in $X_{\max}$ resolution (Briechle, 2016).

SKALA4 LPDAs, as used in the SKA1-LOW array, provide wideband sky coverage matched to contemporary requirements in radio astronomy. Accurate impedance and beam control, together with validated cross-polarization and yield, are necessary for reliable signal extraction amid complex environments (Acedo et al., 2020). AAFIYA automation extends to future data-driven LPDA optimization and rapid prototyping workflows for coherent large-scale experiments (Seikh et al., 20 Jan 2026).

7. Practical Design Recommendations

Key design choices are summarized:

Parameter	Typical Range	Source
Scaling factor $\tau$	0.85 (SKA4, AERA); 0.85–0.90 (general)	(Acedo et al., 2020, Briechle, 2016, Seikh et al., 20 Jan 2026)
Apex angle $\alpha$	12°–15° (AAFIYA); 37° (SKALA4)	(Seikh et al., 20 Jan 2026, Acedo et al., 2020)
# of elements $N$	9 (AERA), 12 (SKA4), 16–20 (100–850 MHz)	(Briechle, 2016, Acedo et al., 2020, Seikh et al., 20 Jan 2026)
VSWR	$<$2:1 (full band)	(Briechle, 2016, Acedo et al., 2020, Seikh et al., 20 Jan 2026)
Boresight gain	5–8.5 dBi	(Acedo et al., 2020, Seikh et al., 20 Jan 2026)
Cross-pol ratio	$<$–20 dB (boresight)	(Acedo et al., 2020, Seikh et al., 20 Jan 2026)

For validation, cross-calibration with full-wave simulation (HFSS, WIPL-D, NEC), Friis-based realized gain in anechoic conditions, and systematic tolerance-and-yield estimation are recommended for ensuring reproducible, publication-grade LPDA performance (Briechle, 2016, Seikh et al., 20 Jan 2026). All critical workflow steps can be encoded in reproducible scripts as demonstrated by AAFIYA’s minimal analysis template (Seikh et al., 20 Jan 2026).