International Journal of Antennas and Propagation

Volume 2015, Article ID 673536, 11 pages

http://dx.doi.org/10.1155/2015/673536

## Smart Wireless Power Transfer Operated by Time-Modulated Arrays via a Two-Step Procedure

^{1}DEI, University of Bologna, Viale Risorgimento 2, Bologna, Italy^{2}DEI, University of Bologna, Via Venezia 52, Cesena, Italy

Received 7 May 2015; Revised 16 July 2015; Accepted 21 July 2015

Academic Editor: Toni Björninen

Copyright © 2015 Diego Masotti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The paper introduces a novel method for agile and precise wireless power transmission operated by a time-modulated array. The unique, almost real-time reconfiguration capability of these arrays is fully exploited by a two-step procedure: first, a two-element time-modulated subarray is used for localization of tagged sensors to be energized; the entire 16-element TMA then provides the power to the detected tags, by exploiting the fundamental and first-sideband harmonic radiation. An investigation on the best array architecture is carried out, showing the importance of the adopted nonlinear/full-wave computer-aided-design platform. Very promising simulated energy transfer performance of the entire nonlinear radiating system is demonstrated.

#### 1. Introduction

Time-modulated arrays (TMAs) are extremely versatile radiating systems due to the almost unlimited possible combinations of control sequences that can be applied to periodically switch on/off the array elements [1]. Many research groups have introduced interesting potential applications of TMAs, such as sideband suppression [2–4], adaptive nulling [5], harmonic beam-steering [6, 7], and direction finding [8–10]. These and other works [11–13] propose different optimization strategies for the control sequence optimization but almost invariably assume that the radiating elements are isotropic and the switches behave ideally, while it has been demonstrated that realistic antenna properties and switch nonlinearities should be taken into account for a reliable assessment of TMA performance [14]. Some of these applications deal with the need for reduction of the sideband radiation occurring at the harmonics () of the fundamental frequency () due to the switch modulation frequency () [2–5]. For the purpose of the present work the applications taking advantage of the additional sideband radiation [6–10] are more appealing, and we will make use of the optimized sequence taken from literature, even if suboptimal (as demonstrated in [14]).

In this paper we intend to exploit these properties by following the rigorous approach described in [14], in order to provide a new smart wireless power transfer (WPT) functionality operated by time-modulated arrays. In the authors’ opinion this could be a new promising field of application of such systems, because of the unrivaled reconfigurability offered by TMAs. It is worth noting that this is not the unique advantage of these radiating systems: they also have a much simpler architecture with respect to other available solutions, such as phased arrays and retrodirective arrays [15], since comparable scanning capabilities can be obtained without the need for phase-shifters.

The paper is organized as follows: a brief recall of TMA main features is provided in Section 2. The presence of nonlinear switches as well as of (possibly) unequally spaced radiating elements strongly suggests the use of a rigorous nonlinear/electromagnetic computer-aided-design (CAD) platform, as summarized in Section 3. The description of the whole radiating system within the CAD tool frame allows us to accurately predict the behavior of a linear TMA during the novel two-step WPT procedure, as explained in Section 4. Sections 5 and 6 provide a detailed illustration of each phase of the WPT activity, together with simulated results for different TMA architectures, showing the high potentiality of the proposed solution.

#### 2. Time-Modulated Array Operating Principles

In case of a linear array operating at the fundamental frequency , with elements aligned along the direction (), with interelement spacing , the insertion of an RF switch at each antenna port allows us to introduce time-dependency in the array radiation characteristics. If each switch is driven by a periodic sequence of rectangular pulses of period , the constant complex excitation coefficients of the individual elements of a traditional array are multiplied by , representing the normalized periodic waveform operating the generic (th) switch. The TMA far-field at the fundamental frequency , evaluated at the point , can thus be cast in the form:where the time-dependent array factor (AF) expression is put into evidence.

The periodicity of the sequences biasing the switches allows us to Fourier-transform the array factor at , according to the following expression:By inspection of (2) it is straightforward to infer an interesting feature of TMA; that is, radiation takes place not only at the fundamental frequency , but at sideband frequencies, , too. This phenomenon, known as sideband radiation, represented a limitation in the first applications of these arrays [1]. The recent research activity has provided solutions to this problem, by means of proper control sequences optimization, including sideband harmonic suppression [2–4, 11]. The use of time as a further degree of freedom has paved the way to a wider spectrum of applications for this agile radiating system [5–10], because of the almost unlimited number of control sequence combinations.

For the purpose of the present paper the TMA characteristic of sideband radiation is exploited from a twofold point of view. Indeed, in Section 4 we demonstrate for the first time that the direction finding capability [8–10] in conjunction with the harmonic beam synthesis [6, 7, 16] makes the TMA architecture suitable for achieving smart far-field WPT.

#### 3. Rigorous Simulation of Time-Modulated Arrays

As for any nonlinear system, the simulation of TMAs can be carried out by resorting to the Harmonic Balance (HB) technique [17]. According to the Piecewise HB (PHB) formulation, the circuit is divided into a linear and a nonlinear subnetwork, described in the frequency and time domains, respectively. In the TMA case these two networks are represented by the radiating array of elements and the nonlinear switches, respectively. Therefore, in the simple case of one-port antennas, also represents the number of ports connecting the two parts of the circuit. The PHB approach matches very well the TMA analysis needs, since a broadband full-wave analysis in the frequency domain is normally the best way to produce the rigorous description of the linear radiating portion which is essential in view of accurate simulated results [18]. On the other hand, the nonlinearities introduced by the driving diodes are easily and accurately modelled in time-domain and then Fourier-transformed into the frequency domain. The nonlinear solving system is then obtained by applying Kirchhoff’s current law at all the ports, for all the frequencies used in the description of the nonlinear circuit regime.

The nonlinear TMA system supports a two-tone regime consisting of the intermodulation products of the sinusoidal carrier (angular) frequency to be radiated and the switch modulation (angular) frequency . The situation is reported in Figure 1 where time- and frequency-domain descriptions of the regime are provided.