On end‐fire super directivity of arrays of two elementary dipoles and isotropic radiators

Abstract

The concept of source currents of a radiating source can be employed to express its directivity in some particular cases analytically. For an antenna array, this concept can be extended to the concept of a generalised directivity based on self‐ and mutual radiation intensities, self‐ and mutual radiated powers and excitation currents of array elements. These approaches were applied to examples of the array of two elementary dipoles and the array of two isotropic radiators. Particularly, the evaluation of the directivity of the end‐fire arrays, which are of special attention due to superdirective properties, was treated. Novel closed‐form expressions for the directivity of these arrays with out‐of‐phase excitation were derived. It was observed that the end‐fire directivity can be further enhanced by optimising the excitation currents of the arrays. Their optimal phase difference and corresponding increased directivity were also found analytically. The results were validated by a full‐wave simulator.

The Statistics of Superdirective Beam Patterns

“…, where (6) is the ABP, a complex function containing 5 RVs (i.e.,  x,l ,  y,l ,  z,l ,  g,l ,  ,l ) for each array element. In view of subsequent developments, it is convenient to rewrite the ABP as (7) where (10) If all the errors are zeroed, for each l,   0…”

“…The possibility of considerably increasing the directivity makes superdirectivity a topic of great interest and current research [8][9][10][11], in view of numerous applications, including microphone array [12,13], sonar [14,15], radar [5,16] and radio communication [6,17]. The main research aim is to combine the increase in directivity with the reduction in robustness against spatially uncorrelated noise and random errors.…”

“…Assumptions 1 and 2 and adopting the notation in(22), the term R in (17) can be rewritten as and, applying(10) and Assumption 3, it is straightforward to show that Assumption 1 the expectations in (90) do not depend on l, introducing the notation in(24) the expectation in (89) can finally be rewritten as…”

Optimization of Super-Directive Linear Arrays with Differential Evolution for High Realized Gain

“…While the maximum directivity is directly proportional to the number of elements in a classical array consisting of isotropic sources (D ∝ N ), it was theoretically shown in the seminal work of Uzkov [3] that if the distance between the elements converges to zero, the directivity of the array can reach up to the square of antenna elements number (D ∝ N 2 ) towards the end-fire direction. However, for a considerable number of years, these systems, known as super-directive arrays (which can be broadly defined as antennas whose end-fire directivity exceeds that of uniformly excited apertures [4]), have been deemed impractical due to their susceptibility to sensitive feeding currents and limited efficiency resulting from feed line impedance mismatch [5], [6]. Thus, there is a significant need to develop optimization frameworks to realize these antenna arrays and provide practical excitation topologies to make super-directive arrays a feasible technology.…”

Finding Optimal Total Active Reflection Coefficient and Realized Gain for Multi-port Lossy Antennas

“…Optimal excitation for maximal realized gain is established via a simple analytical formula and, similarly as for TARC, the conditions for its optimality are provided in terms of feeding, matching, and characteristic impedance. The understanding provided by the method updates the knowledge about optimal excitation of antenna arrays [17], [20], [21], [22], [23].…”