The Impact of Reduced Conductivity on the Performance of Wire Antennas Morteza Shahpari, Member, IEEE, David V

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO.11, NOVEMBER 2015 4686 The impact of reduced conductivity on the performance of wire antennas Morteza Shahpari, Member, IEEE, David V. Thiel, Senior Member, IEEE, Abstract—Low cost methods of antenna production primarily There are some advantages in choosing wire rather planar aim to reduce the cost of metalization. This might lead to a structures for these investigations. First, wire antennas have reduction in conductivity. A systematic study on the impact of been studied extensively in the literature. Also, new materials conductivity is presented. The efficiency, gain and bandwidth of cylindrical wire meander line, dipole, and Yagi-Uda antennas like carbon nanotubes are emerging which show promising were compared for materials with conductivities in the range characteristics and naturally have circular cross sections. We 103 to 109 S/m. In this range, the absorption efficiency of performed simulations over 103 109S/m to cover materials − both the dipole and meander line changed little, however the like CNTs which have conductivities in the order of 104 − conductivity significantly impacts on radiation efficiency and 107S/m [2]. the absorption cross section of the antennas. The extinction cross section of the dipole and meander line antennas (antennas The key point in the success of any mass production process that Thevenin equivalent circuit is applicable) also vary with is low cost, that is, circuit manufacturing techniques tend to radiation efficiency. From the point of radiation efficiency, the minimize the total used materials. By tapering the wire in [10], dipole antenna performance is most robust under decreasing the same performance was achieved with a conductor volume conductivity. Antennas studied in this study were fabricated with reduction of more than 50%. brass and graphite. Radiation efficiency of the antennas were measured by improved Wheeler cap (IWC) method. Measure- In this paper, we illustrate the influence of the non perfect ment results showed a reasonable agreement with simulations. materials on the impedance and radiation properties of three We also measured the extinction cross section of the six fabricated wire antennas: a half-wave dipole, a four element Yagi-Uda, prototypes. and spiral meander line antennas. Such investigations have Index Terms—Conductivity, radiation efficiency, absorption not been reported previously. We also study that how ab- efficiency, receiving antenna, absorption cross section, extinction sorbed, scattered, and dissipated power in a receiving antenna cross section, power to volume ratio. changes with conductivity in section III. The study reveals the relationship between the absorption cross section of the antennas and the radiation efficiency. We demonstrate that I. INTRODUCTION the extinction cross section of the dipole and meander line ATERIALS like carbon nanotubes (CNT) [1], [2] , and antennas is directly related to the radiation efficiency of these printed conductor technologies like circuits in plastic antennas. Moreover, we show the impact of conductivity on (CiP)M [3], [4] are finding their way to telecommunications absorption efficiency, generalized absorption efficiency, and systems. These applications are in demand because of the absorbed power to volume ratio in section III with additional low cost of production and ability to produce light weight, data in section ??. Section IV shows the fabricated samples. recyclable and flexible circuits. However, the conductivity of Measurement results are discussed in section V. printed conductors is usually much lower than the conductivity of copper, aluminum and silver. The main aim of this paper is II. ANTENNA DESIGNS to study the performance of lossy transmitting and receiving antennas made from materials with lower conductivities. In this paper, we selected three test case antennas: a half- Some RFID designs with reduced conductivity are reported wave dipole, a spiral meander line, and a Yagi-Uda antenna. in [5], [6]. The effect of the conductor thickness on the radia- These three wire antennas were designed to resonate at the arXiv:1509.06709v2 [physics.gen-ph] 10 Nov 2015 tion efficiency and backscatter power of RFIDs are studied same frequency (f =1 GHz). The dipole antenna was selected in [7], [8]. Also, a cost study of the printed antennas is because directivity and absorption efficiency are available in available from [9] for dipole antenna with different conduc- the closed form. Meander line antennas are one of the most tivities. Despite the interesting results presented in [5]–[9], popular choices for small antenna designs. The Yagi-Uda a comprehensive study of the effects of conductivity on the antenna was included in this study because of their excep- various parameters of the antennas is missing. In this paper, tional absorption efficiency. The geometry of the meander we address this gap in the current literature by exploring the line and Yagi-Uda antenna are selected from the [11], [12], effects of the change in the conductivity of different antennas. respectively. The Yagi-Uda antenna was optimized in terms of gain, side lobe level (SLL), and voltage standing wave ratio M. Shahpari and D. Thiel are with Griffith School of Engineering, Griffith (VSWR). University, Nathan, Queensland 4111, Australia To make these three antennas comparable with each other, This work is partly funded by the grant number DP130102098 from Australian Research Council. we selected a wire radius of 0.00225λ for all antennas. The Manuscript contains supplementary material which are available online. three antenna designs are shown in Fig. 1. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO.11, NOVEMBER 2015 4687 126.5 141.5 139.1 131.9 10 32.31 143 14.42 ) 65.95 80.34 88.13 dBi ( 0 D DDipole ) D (a) (b) (c) Y agi dBi DMeander ( Fig. 1. Self resonant antenna design configurations at f0 =1 GHz (a) a G GDipole half wave dipole (b) a meander line antenna (c) a Yagi-Uda antenna with one 10 G reflector and two directors (all dimensions are in mm). − Y agi GMeander 103 104 105 106 107 108 109 0.8 σ(S/m) 0.6 0.4 Fig. 3. Directivity D (solid) and gain G (dashed) versus conductivity σ (subscripts D, Y , and M refer to dipole, Yagi-Uda, and meander line antennas 0.2 respectively). (a) PEC (b) σ = 103S/m Dipole Yagi Meander Fig. 2. Comparison of current distribution over the Yagi-Uda antenna made 1 of (a) lossless (b) lossy (σ = 103S/m) materials 0.8 III. NUMERICAL RESULTS 0.6 The antennas were simulated in free space using a com- ηr mercial method of moments (MoM) code [13] by changing 0.4 the conductivity over the range 103 109S/m. It should be − noted that the geometric parameters for each antenna over 0.2 the simulations were similar, while the material properties 0 (conductivity of the metal) are changed. 103 104 105 106 107 108 109 Fig. 2 shows a comparison of the current distribution of σ(S/m) lossy and lossless Yagi-Uda. In order to make a meaningful comparison, quantities are normalized to the values at the Fig. 4. Radiation efficiency ηr versus conductivity σ feed point of the antenna. Fig. 2 shows that the normalized magnitude of induced currents on the elements of Yagi-Uda are different for lossless and lossy cases. As an example, the (see Fig. 4). This is partly explained by the small radiation normalized magnitude of the current distribution is almost resistance of the meander line (about 2Ω for PEC). For the same for the driven element radiators but the induced example, ohmic resistance of the meander line with σ 107 current is significantly less (almost half) on the parasitic ≈ S/m is about 0.5Ω, which reduces η to 0.8. The dipole elements when the material is changed from PEC down to r and Yagi-Uda antennas are less sensitive because of their conductivity 103S/m. Current distribution of the dipole and higher radiation resistance which is 70, 50Ω, respectively. The meander line was not affected significantly with the reduction radiation efficiency η drops for all conductivities when the of the conductivity to 103S/m. For instance, lossy dipole still r radiating structure is changed from a dipole to a Yagi-Uda shows a sinusoidal current distribution though with a much antenna. This is because parasitic elements in a lossy Yagi-Uda lower magnitude. dissipate electromagnetic power while directing the radiation. The directivity and gain of the antennas are depicted in Some of the key results of the paper are illustrated in Fig. 3. The directivity of the dipole is 2.12dBi which is close Fig. 5 which shows the performance of lossy antennas in the to 2.15dBi, the analytical result. The directivity D of the dipole receiving mode. Absorbed, dissipated, and scattered powers remains unchanged while changes are observed for the Yagi- are stacked on top of each other and normalized to the Uda antenna for σ < 105(S/m). It is interesting to see the gain maximum extinct power for each antenna type made of PEC. of the dipole does not change much over this conductivity More power is absorbed and scattered if the radiating structure range, however, gain of the meander line falls to negative is made from materials with higher conductivities, and the values for σ 107S/m. dissipated power vanishes. The absorbed power by a lossy As G = η D, it is expected that G and η should decrease r r antenna is directly influenced by radiation efficiency η . This with the conductivity. 1 The value of η shows that the meander r r is illustrated by the dashed traces (η P ) in Fig. 5 where line antenna is more sensitive to less conductive materials r a,P EC Pa,P EC is the absorbed power by the same antenna made of 1 Relation G = ηrD is separately investigated in Fig.

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