[Paper Review] A Two-element Parasitic Antenna Approaching the Minimum Q-factor at a Given Directivity

Fabien Ferrero, Léonardo Lizzi+2 more|arXiv (Cornell University)|May 5, 2017

Antenna Design and Analysis29 references3 citations

TL;DR

This paper presents a two-element parasitic antenna with a circumscribing sphere of 0.2λ at 880 MHz, achieving 7.2 dBi directivity and -6.5 dB radiation efficiency at 876 MHz, approaching the theoretical minimum Q-factor for a given directivity. The design leverages stored energy bounds to optimize directivity and bandwidth, demonstrating robust performance in miniaturized, autonomous configurations suitable for spatial filtering.

ABSTRACT

In this paper we investigate a super-directive antenna based on a parasitic structure with a circumscribing sphere of diameter 69 mm corresponding to 0.2$λ$@880 MHz. The antenna is modeled, simulated, measured, and it is also evaluated against the new Q-factor bound for small antennas at a given total directivity. A maximum directivity of 7.2 dBi is measured with a radiation efficiency of -6.5 dB at 876 MHz. An intermediate directivity of 6.2 dBi is observed at 880 MHz with 20 dB front-to-back ratio and -7 dB radiation efficiency. The antenna performs well with respect to the developed fundamental bound. The results is promising for applications that require miniaturization and spatial filtering. The above antenna properties are robust and we show with measurements that the antenna preform well also when it is integrated as an autonomous unit.

Motivation & Objective

• To design a miniature, balanced parasitic antenna with high directivity and low Q-factor under size constraints.
• To evaluate the antenna’s performance against newly developed fundamental Q-factor bounds for a given directivity.
• To demonstrate robustness of superdirective properties when integrated into an autonomous system with PCB and battery.
• To quantify the trade-off between directivity, radiation efficiency, and bandwidth using stored energy-based Q-factor bounds.
• To validate simulation results with measurements, including effects of cables and connectors on radiation patterns.

Proposed method

• The antenna is modeled using full-wave electromagnetic simulation and fabricated as a two-element parasitic structure with integrated balun.
• Stored energy bounds are applied to derive a theoretical lower bound on the Q-factor for a given total directivity, using convex optimization techniques.
• The design operates at ka < 0.7, placing it in the superdirective regime where directivity exceeds classical limits.
• Measurements are performed with and without coaxial cables to isolate the impact of external components on radiation efficiency and pattern.
• The radiation pattern, front-to-back ratio, and realized gain are characterized across frequency bands to assess spatial filtering capability.
• Theoretical Q-factor bounds are compared with measured Q-factor to evaluate how close the design comes to fundamental limits.

Experimental results

Research questions

• RQ1 How close can a miniature parasitic antenna come to the theoretical minimum Q-factor for a given directivity?
• RQ2 What is the trade-off between directivity, radiation efficiency, and bandwidth in electrically small antennas?
• RQ3 How do conductive losses and external components like cables affect measured radiation performance?
• RQ4 Can superdirective properties be preserved when the antenna is integrated into an autonomous, compact system?
• RQ5 To what extent do stored energy-based Q-factor bounds predict the performance of realizable antennas?

Key findings

• A maximum directivity of 7.2 dBi was measured at 876 MHz with a radiation efficiency of -6.5 dB, indicating a trade-off between directivity and efficiency.
• At 880 MHz, the antenna achieved 6.2 dBi directivity, 20 dB front-to-back ratio, and -7 dB radiation efficiency, demonstrating effective spatial filtering.
• The measured Q-factor was 35 at 885 MHz, with a peak directivity of 5.5 dBi and -4 dB total efficiency, showing a favorable compromise for practical use.
• The 3D radiation pattern at 880 MHz showed a 10.7 dB power ratio between forward and backward hemispheres, confirming strong spatial filtering.
• Measurements with and without cable showed good agreement near resonance (0.88–0.9 GHz), validating the measurement setup and robustness.
• The antenna maintains superdirective behavior and key performance metrics when integrated on a PCB with a battery, confirming robustness in autonomous operation.