Issue 
EPJ Appl. Metamat.
Volume 6, 2019
Metamaterials Research and Development in Japan



Article Number  3  
Number of page(s)  5  
DOI  https://doi.org/10.1051/epjam/2018010  
Published online  18 January 2019 
https://doi.org/10.1051/epjam/2018010
Research Article
Balanced gain for a square metaloop antenna
Science and Engineering, Hosei University, Koganei, Tokyo, Japan
^{*} email: hymat@hosei.ac.jp
Received:
29
August
2018
Accepted:
3
December
2018
Published online: 18 January 2019
A square loop antenna implemented using a metamaterial line, referred to as a metaloop, is discussed. The metaloop radiates a counter circularly polarized (CP) broadside beam when the loop circumference equals one guided wavelength. The frequency response of the gain shows two different maximum values: gain G _{Lmax} for a lefthanded CP wave at frequency f_{GLmax} and gain G_{Rmax} for a righthanded CP wave at frequency f_{GRmax}, where G_{Lmax} is smaller than G_{Rmax}. In order to increase G_{Lmax}, while not affecting the original G_{Rmax} as much as possible (i.e. balance the gain), a parasitic natural conducting loop (paraloop), whose circumference is one freespace wavelength at f_{GLmax}, is placed at height H_{para} above the metaloop. It is found that the difference in the gains can be reduced by choosing an appropriate H_{para}. The radiation pattern at f_{GLmax} is narrowed by the paraloop, while the VSWR is not remarkably affected.
Key words: Square metaloop antenna / circularly polarized radiation / gain balance
© H. Nakano et al., published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
A loop antenna radiates a linearly polarized (LP) wave [1]. When the circumference of the loop is one wavelength, the maximum LP radiation appears in the broadside direction. This broadside LP radiation can be changed to circularly polarized (CP) radiation by adding perturbation elements [2] to the loop, as shown in Figure 1. The rotational sense of the CP radiation, either a righthanded (RH) sense or a lefthanded (LH) sense, is uniquely determined by the location of the perturbation elements relative to feed point F: the loop in Figure 1 radiates an RHCP wave. In other words, the loop antenna radiates a CP wave with a single rotational sense.
The single rotational sense also holds true for a grid loop array in [3]. Although perturbation elements are not added to the loops, a traveling current is generated along the arrayed loops and radiates a CP wave. The rotational sense is determined by the winding sense of the loops.
It is often required that an antenna has dualband counter CP radiation to keep sufficient separation of signals, i.e., the LHCP and RHCP radiation in two different frequency bands, in order to avoid interfering with each other. When a pair of dualband counter CP antennas is adopted as a transmitting antenna and a receiving antenna, it is desirable for these antennas to have the same gain. If the LHCP and RHCP gains are different, the receiving antenna captures LHCP and RHCP waves with different receiving power levels. Therefore, a postprocess circuit connected to the receiving antenna needs additional amplification circuits to enhance the weak power. This complicates the postprocess circuit designs. To avoid such an issue, the same gain (balanced gain) is desired.
Recent study has shown that a metamaterial (MTM) loop antenna, referred to as a metaloop, is an antenna that meets the requirement of dualband counter CP radiation [4], where the loop is realized using the concept of a composite RH and LH transmission line [5–7], referred to as a metaline.
The maximum gain for the metaloop within the low frequency band (LoFB) in [4] is smaller than that within the high frequency band (HiFB). This is attributed to the antenna size relative to the freespace wavelength (electrical antenna size); the freespace wavelength within the LoFB is larger than that within the HiFB, and hence the electrical antenna size within the LoFB is smaller than that within the HiFB.
Thus, a question arises as to how the difference in the gains can be reduced. This paper presents a technique for reducing the band gain difference for a dualband counter CP metaloop antenna, where a parasitic loop (paraloop) is placed above the metaloop. Note that the metaloop antenna in this paper is analyzed using a full wave analysis tool, HFSS [8], and experimental work is performed in an anechoic chamber.
So far, other authors have designed MTMloaded and MTMinspired loop antennas. For example, the MTMloaded loop in reference [9] and MTMinspired loop [10] are designed as an LP antenna. An antenna using complementary capacitively loaded loop in reference [11] and loop antennas in [12–20] are also designed as an LP antenna. The design requirements for these antennas differ from ours, i.e., dualband counter CP radiation with balanced gain, while meeting two additional requirements: (1) broadside radiation and (2) simple feed system without balun circuits. To our best knowledge, there have not been such MTMrelated loop antennas.
Fig. 1 Natural loop antennas radiating a circularly polarized wave with a single feed point F. The loop has perturbation elements [2]. 
2 Metaloop structure
The metaloop antenna to be considered here is shown in Figure 2. The antenna arm is printed on a square dielectric substrate of side length S_{sub}, relative permittivity ε_{r} and thickness B. The substrate is backed by a square ground plane (GP) of side length S_{GP} (=S_{sub}). The antenna arm, symmetric with respect to the x–z plane, is composed of five straight metalines, whose lengths are L_{1} = L_{5} and L_{2} = L_{3} = L_{4}. Each metaline is made of numerous conducting subwavelength segments of width w and length p_{0}, where the gap between neighboring segments is denoted as Δg. Repeating arm sections, each having length 2(Δg + p_{0}) ≡ p, are designated as the arm unit cells. The central segment of the cell is shortcircuited to the GP through a chip inductor, L_{Y}. Neighboring segments are connected through a chip capacitor, 2C_{Z}. Point F is the feed point and point T is the terminal point connected to the GP through a resistive load, R_{B}, to suppress reflected currents from point T to point F.
Note that L_{Y} and 2C_{Z} are determined as follows. First, using HFSS [8], we obtain the frequency response of the scattering parameters (Sparameters) for the unit cell including L_{Y} and 2C_{Z}. Second, based on the obtained Sparameters, we draw the dispersion curve (phase constant β = ±2π/λ_{g} vs. frequency f [4], where λ_{g} is the guided wavelength). These two steps are repeated until the dispersion curve is balanced (smoothly connected at a preselected transition frequency f_{T}), changing L_{Y} and 2C_{Z}. The values for L_{Y} and 2C_{Z} when the dispersion curve is balanced are what we need.
The parameters used for the following discussion are summarized in Table 1; these parameters create a preselected transition frequency of f_{T} = 3 GHz, i.e., phase constant β is negative at frequencies below f_{T} and positive at frequencies above f_{T}. Figure 3 shows the loop peripheral length L_{1} + L_{2} + L_{3} + L_{4} + L_{5} normalized to the guided wave length, λ_{g}, as a function of frequency f. Note that the frequencydependent guided wavelength λ_{g} used in Figure 3 is derived from the dispersion curve explained in the previous paragraph.
Frequencies f_{L} and f_{U} in Figure 3 are the lower and upperedge frequencies for a fast wave region. The radiation occurs between f_{L} and f_{U}. A traveling wave current flows along the loop from point F to point T, with guided wave length λ_{g}, which varies with frequency f. The propagation phase constant is β = −2π/λ_{g} < 0 at f < f_{T}, β = 0 at f = f_{T}, and β = 2π/λ_{g} > 0 at f > f_{T}. In order to obtain a broadside beam at two different frequencies where the loop length is 1λ_{g}, the inphase condition (β = 0) is not used.
Fig. 2 Metaloop antenna. (a) Perspective view. (b) Side view. (c) Arm unit cell. 
Parameters.
Fig. 3 Loop length L_{1} + L_{2} + L_{3} + L_{4} + L_{5} normalized to guided wavelength λ_{g}, as a function of frequency. β < 0 at f < f_{T}, β = 0 at f_{T}, and β > 0 at f > f_{T}. 
3 Frequency response of the gain
By resistive load R_{B}, a traveling wave current flows along the loop from point F to point T, with frequencydependent guided wavelength λ_{g}. In other words, the metaline acts as a leaky wave antenna. Generally, the radiation efficiency of the leaky wave antenna is not high due to absorption of the power input to the antenna by R_{B}. If R_{B} is removed, the input impedance (and hence Voltage Standing Wave Ratio (VSWR)) becomes unstable and CP radiation is not obtained by a reflected current from point T.
The current at frequency f < f_{T} has a progressive phase distribution from point F to point T due to a negative phase constant (β = −2π/λ_{g} < 0). Hence, the current behaves as if it travels from point T to point F (clockwise). This results in LHCP radiation in the broadside direction at a frequency where the loop length is one guided wave length (1λ_{g}). Conversely, the current at f > f_{T} has a regressive phase distribution from point F to point T due to a positive phase constant (β = 2π/λ_{g} > 0). Hence, the current flows from point F to point T (counter clockwise), resulting in RHCP radiation in the broadside direction at a frequency satisfying a 1λ_{g}loop length. Thus, dualband counter CP radiation in the broadside direction is obtained.
From Figure 3, it is expected that CP broadside radiation will be obtained around frequencies 2.60 GHz ≡ f_{N} and 3.50 GHz ≡ f_{H}, because the loop length normalized to guided wavelength λ_{g} is one at f_{N} and f_{H}: (L_{1} + L_{2} +…+L_{5})/λ_{g} = 1. For the remainder of the paper, f_{N} and f_{H} are referred to as the Nion frequency and Hion frequency, respectively. Figure 4 shows the gain as a function of frequency, where G_{L} denotes the gain for an LHCP wave, called the LHCP gain, and G_{R} denotes the gain for an RHCP wave, called the RHCP gain. It is found that G_{L} is dominant at frequencies below f_{T} = 3 GHz, because the current flows with a negative phase constant (β < 0). Conversely, G_{R} is dominant at frequencies above transition frequency f_{T} due to β > 0. Maximum gain G_{L} appears at a frequency near Nion frequency f_{N} and maximum gain G_{R} appears at a frequency near Hion frequency f_{H}. These frequencies are denoted as f_{GLmax} and f_{GRmax}, respectively. The difference in the maximum gains, G_{Lmax} at 2.58 GHz ≡ f_{GLmax} (close to f_{N}) and G_{Rmax} at 3.51 GHz ≡ f_{GRmax} (close to f_{H}), is approximately 5.5 dB.
Fig. 4 Frequency response of the gain. 
4 Reduction in the gain difference
In this section, the difference in maximum gains G_{Lmax} and G_{Rmax} is reduced as much as possible. For this, the antenna system shown in Figure 5 is considered, where a parasitic natural conducting strip loop of width w_{para} and peripheral length L_{para} is located at height H_{para} above the metaloop. The parasitic loop is designed such that only the smaller gain, G_{Lmax} at f_{GLmax}, is increased, without reducing the larger gain, G_{Rmax} at f_{GRmax}.
The CP radiation from the metaloop excites the parasitic loop and generates a rotating/traveling current along the loop.
The parasitic loop acts as a director for the driven meta loop, like Yagi–Uda antenna. If the radiation from the para sitic loop at f_{GLmax} is constructively superimposed onto the radiation from the metaloop in the broadside direction, gain G_{Lmax} increases. For this to occur, parasitic loop length L_{para} is chosen to be one freespace wavelength (1λ_{0}) at f_{GLmax}: L_{para} = 116.7 mm. The remaining task is to optimize loop height H_{para}.
Figure 6 shows G_{L} at f_{GLmax} = 2.58 GHz and G_{R} at f_{GRmax} = 3.51 GHz in the broadside direction (zdirection) as a function of parasitic loop height H_{para}. It is found that there is an optimum antenna height for G_{Lmax} ≈ G_{Rmax}.
Based on the result shown in Figure 6, the loop height is determined to be H_{para} = 11 mm, corresponding to 0.09 wavelength at f_{GLmax} = 2.58 GHz. Figure 7 shows the frequency response of the gain. The bandwidth (BW) for a 3dB gain drop criterion for G_{L}, denoted as G_{L}BW, is 13.5% and the BW for a 3dB gain drop criterion for G_{R}, denoted as G_{R}BW, is 14.6%. For confirmation of the analysis/simulation results, measured/experimental results are also presented (see fabricated antenna in Fig. 5b).
Fig. 5 Metaloop with a parasitic natural conducting loop. (a) Perspective view. (b) Fabricated metaloop. 
Fig. 6 G_{L} at f = 2.58 GHz and G_{R} at 3.51 GHz as a function of parasitic loop (paraloop) height H_{para}, where w_{para} = 2 mm and L_{para} = 116.7 mm (≈1λ_{0} at 2.58 GHz) are used. 
Fig. 7 Frequency response of the gain with a parasitic loop (paraloop), where H_{para} = 11 mm = 0.09 wavelength at f_{GLmax} = 2.58 GHz. 
5 Radiation pattern and VSWR
Figure 8a shows the analysis/simulation results of the radiation patterns at the maximumgain low frequency f_{GLmax} = 2.58 GHz (radiation efficiency of η ≈ 69%) and high frequency f_{GRmax} = 3.51 GHz (η ≈ 60%), together with experimental results, where E_{L} and E_{R} denote the LHCP wave component and the RHCP wave component, respectively. For comparison, the analysis/simulation results in the absence of a parasitic loop are also shown in Figure 8b. It is clearly seen that the radiation pattern at low frequency f_{GLmax} is narrowed by virtue of the presence of the parasitic loop, while the radiation pattern at high frequency f_{GRmax} is less affected by the parasitic loop, as desired. Figure 9 shows the frequency response of the VSWR, which remains almost unchanged in the presence of the parasitic loop. Discrepancy between the analysis and experiment results is attributed to the fact that soldering the capacitive chips to the subwavelength segments is not uniform due to handwork.
Finally, the following comments are added. The metaloop antenna in this paper could be operated as a dualband CP element with the same rotational sense (dualband monoCP radiation), although this is not our objective. Such dualband monoCP radiation is performed by introducing switching circuits to points F and T so that each point can be chosen to be either a feed point or a terminal point. (1) For dualband monoLHCP radiation, set points F and T to be the feed (fd) and terminal (trmnl) points, respectively, at low frequency f_{low} < f_{T}, which is expressed as . And at a high frequency f_{high} > f_{T}, change the role of points F and T by using switching circuits: . (2) For dualband monoRHCP radiation, set at f_{low} and at f_{high} by using switchcircuits.
Fig. 8 Normalized radiation patterns at f_{GLmax} = 2.58 GHz and f_{GRmax} = 3.51 GHz. (a) In the presence of a parasitic loop. (b) In the absence of a parasitic loop. 
Fig. 9 Frequency response of the VSWRs in the presence and absence of a parasitic loop (paraloop). The 3dB gaindrop bandwidths for G_{L} and G_{R} are denoted as G_{L}BW and G_{R}BW, respectively. 
6 Conclusions
The dualband counter CP wave radiated by a square metaloop antenna has a maximum gain of G_{Lmax} at frequency f_{GLmax} that is different from maximum gain G_{Rmax} at frequency f_{GRmax}, where G_{Lmax} < G_{Rmax}. To reduce the difference in these gains, a square parasitic natural conducting loop of one freespace wavelength at f_{GLmax} is placed at height H_{para} above the metaloop. It is found that there is an antenna height where the parasitic loop increases gain G_{L}, while not remarkably affecting gain G_{R}. Thus, the gain difference can be reduced, i.e., G_{Lmax} ≈ G_{Rmax}, with the VSWR remaining almost unchanged in the presence of the parasitic loop.
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Cite this article as: Hisamatsu Nakano, Ittoku Yoshino, Tomoki Abe, Junji Yamauchi, Balanced gain for a square metaloop antenna, EPJ Appl. Metamat. 6, 3 (2019)
All Tables
All Figures
Fig. 1 Natural loop antennas radiating a circularly polarized wave with a single feed point F. The loop has perturbation elements [2]. 

In the text 
Fig. 2 Metaloop antenna. (a) Perspective view. (b) Side view. (c) Arm unit cell. 

In the text 
Fig. 3 Loop length L_{1} + L_{2} + L_{3} + L_{4} + L_{5} normalized to guided wavelength λ_{g}, as a function of frequency. β < 0 at f < f_{T}, β = 0 at f_{T}, and β > 0 at f > f_{T}. 

In the text 
Fig. 4 Frequency response of the gain. 

In the text 
Fig. 5 Metaloop with a parasitic natural conducting loop. (a) Perspective view. (b) Fabricated metaloop. 

In the text 
Fig. 6 G_{L} at f = 2.58 GHz and G_{R} at 3.51 GHz as a function of parasitic loop (paraloop) height H_{para}, where w_{para} = 2 mm and L_{para} = 116.7 mm (≈1λ_{0} at 2.58 GHz) are used. 

In the text 
Fig. 7 Frequency response of the gain with a parasitic loop (paraloop), where H_{para} = 11 mm = 0.09 wavelength at f_{GLmax} = 2.58 GHz. 

In the text 
Fig. 8 Normalized radiation patterns at f_{GLmax} = 2.58 GHz and f_{GRmax} = 3.51 GHz. (a) In the presence of a parasitic loop. (b) In the absence of a parasitic loop. 

In the text 
Fig. 9 Frequency response of the VSWRs in the presence and absence of a parasitic loop (paraloop). The 3dB gaindrop bandwidths for G_{L} and G_{R} are denoted as G_{L}BW and G_{R}BW, respectively. 

In the text 
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