A Fundamental Study on Circularly Polarized Double-Loop Antennas with Quasi-Two Sources

Abstract

Two concentric double-loop antennas were analyzed using the moment method to increase the 3 dB axial ratio bandwidth. Each antenna has a driven loop connected to a branched feedline that is vertical to the ground plane. First, a parasitic loop was added outside of the driven one with a spacing of S. It was found that the axial ratio bandwidth has a maximum value of 23% for S = 0.02 wavelengths. Next, we moved a parasitic loop inside of the driven one. It was revealed that the antenna shows an axial ratio bandwidth of 40%, which is three times as wide as that of a single-loop antenna. The analysis results were verified with experimental work.

1. Introduction

A circularly polarized (CP) antenna [1] has two main advantages: it alleviates signal fading due to multipath propagation, and provides signal insensitivity to the orientation between the transmitting and receiving antennas [2]. These advantages have been leading to modern communication systems, such as mobile, navigation, and satellite applications [3]. Antennas used in the applications are designed based on several fundamental studies, and this study concerns a wideband CP antenna [4] with a simple and compact configuration.

It is known that a loop antenna radiates a CP wave with the help of a perturbation gap [5,6], segment [7], or loop deformation [8]. A recent study has shown that CP radiation can be obtained for a square-loop antenna with quasi-two sources [9], where two loop corners are excited with the same amplitudes and a phase difference of 90°, using a branched feedline vertical to the ground plane.

This study is a sequel to the previous one [9] and demonstrates the newest findings with respect to a square-loop antenna with quasi-two sources. Special attention was paid to the increased bandwidth of CP radiation. For this, we investigated two concentric double-loop antennas using the moment method [10].

Several studies have attempted to increase the CP wave bandwidth of a loop antenna [5,6,7,11,12,13,14]. The studies are classified into three groups by their loop types: annular single [11,12], separate dual [5,6,13], and concentric double loops [6,7,14]. The double-loop type has an advantage over the others due to its compact and simple antenna configuration.

Herein, a double-loop antenna has been constructed using driven and parasitic elements, each requiring a perturbation gap [6] or segment [7] for CP radiation. In contrast, the present loops require neither a perturbation gap nor a segment. Instead, pairs of loop corners are connected by lines F_n–C_n (n = 1 and 2), as shown in Figure 1, leading to a more straightforward design for CP radiation than a conventional one. Note that there are recent studies [15,16] whose titles include double loops, but CP radiation is generated by four slots [15] or two probes [16] instead of using CP loops. In addition, recent studies have focused on antenna size reduction at the cost of configuration complexity, while CP loops have simple configurations.

A motivation for this study comes from the fact that an array antenna composed of single loops with quasi-two sources exhibits a wider axial ratio bandwidth than non-resonant antenna arrays, such as a compact spiral or curl [17]. If the single loops in the array were replaced with double loops, we could expect a much wider bandwidth than that of the single-loop array. With this expectation, we investigated the use of a double-loop antenna with quasi-two sources in this fundamental study to increase the axial ratio bandwidth compared to that of a single-loop antenna with quasi-two sources.

This study is improved compared to the previous related studies [7,9], as summarized in

Table 1. Improvement of the present study compared to previous ones.

Study	Top View of Antenna Configuration	Location of Parasitic Loop	Method for Circular Polarization	Number of Loop Corner Connections	Spacing between Two Loops, S	3 dB Axial Ratio Bandwidth (%)
[7]		inner	perturbation segments	4	Fixed (S = 0.02λ0)	3
[9]		— 1	quasi-two sources	— 1	— 1	12
present		outer	quasi-two sources	2	optimized (S = 0.02λ0)	23
		inner	quasi-two sources	2	optimized (0.02λ0 < S < 0.05λ0)	40

¹ Not applicable.

. It is emphasized that the novelty of the present study is to clarify the effects of parasitic loop location on CP wave bandwidth for the first time. Furthermore, the present study optimizes the spacing S between loops for wideband CP radiation. In contrast, the previous study [7] fixed the spacing S and investigated only the case of an inner parasitic loop. As a result, the present study can attain a 3 dB axial ratio bandwidth of 40%, which is 13 times as wide as that in [7]. Note that the present study uses fewer loop corner connections than the previous one, leading to a simpler configuration.

After describing the design mechanism, this paper first analyze an antenna whose driven loop has an outer parasitic one. Next, we analyze a parasitic loop inside of a driven one and reveal the effects of parasite locations on radiation characteristics. Lastly, we present experimental work that was performed to validate the simulated results.

2. Design Mechanism

This section describes the design mechanism based on three antennas [7]. They are single-, discrete double-, and connected double-loop antennas, which are shown in the insets of Figure 2a, Figure 2b, and Figure 2c, respectively. Each antenna has a single feed at a corner F with the same perimeter 4L and spacing S at the same height H above the ground plane. The antenna was analyzed using our computer program that was developed based on the moment method [10] at a test frequency of f₀ = 3 GHz.

The discrete and connected double-loop antennas have double and wideband characteristics, as shown in Figure 2b,c. This fact means that the wideband can be attributed to the double bands. In other words, double bands merge to form a wideband once two loops are connected, which is the design mechanism of this study. Note that the wideband in [7] is 3% when using loops with a perturbation segment (a stub of the loop side). In contrast, the wideband in this study reaches 31% in Section 5 when using loops with quasi-two sources.

3. Antennas with an Outer Parasitic Loop

Figure 1 shows the antenna configuration. Two concentric square loops with a spacing S are located at height h above the ground plane. The outer and inner loops are parasitic and driven, respectively, and the driven loop’s perimeter is designated as P.

The driven loop has adjacent corners F_n, which are excited by a branched feedline F_n–B–F₂′ that is vertical to the ground plane, where the branch point B is at height h_B, as shown in Figure 1c. The driven loop corners F_n are connected to the parasitic loop corners C_n by lines F_n–C_n, as shown in Figure 1b. The antenna is made of wires with a radius ρ [9].

We analyzed the antenna using the moment method [10]. The ground plane size was assumed to be infinite, and image theory was applied to the analysis. The antenna was designed to radiate a CP beam in a direction that was normal to the antenna plane in the z-axis direction. For this, the loop perimeter was initially set to be P = 1λ₀ (λ₀: the free-space wavelength at f₀), so that the traveling wave-type current distributes along the loop arm, which is necessary for the CP beam. Taking this into consideration, we selected the loop perimeter and feedline branch height (P, h_B) as a function of loop spacing S. The other configurations are the same as those in [9]: (h, ρ) = (λ₀/4, λ₀/200).

The lower part of Figure 3 shows the simulated 3 dB axial ratio bandwidth versus loop spacing S. At each value of S, the parameters (P, h_B) were selected to maximize the bandwidth. The selected loop perimeter P versus S is shown in the upper part of the figure. It was found that as S increases, the bandwidth increases and reaches a maximum value. This maximum value is 23% at S = 0.02λ₀ with (P, h_B) = (0.96λ₀, 0.06λ₀).

The simulated gain and axial ratio versus frequency for S = 0.02λ₀ are shown with solid lines in Figure 4. The gain was found to be more than 5.1 dBi in the abovementioned CP wave bandwidth. For reference, the dotted lines show the results of a single-loop antenna [9]. The single-loop antenna has an axial ratio bandwidth of 12%. It can be said that the present antenna’s bandwidth is two times as wide as that of the single-loop antenna. The wider bandwidth is because the parasitic loop corners C_n are connected to the driven loop corners F_n, which are excited by the same amplitudes with a phase difference of 90° [9]. In other words, a double-loop antenna without an F_n–C_n connection does not show an increased axial ratio bandwidth.

The radiation patterns for S = 0.02λ₀ are shown in Figure 5. The radiation is decomposed into right- and left-hand CP wave components. It can be seen that the antenna radiates a CP beam that is normal to the antenna plane. The half-power beam widths (HPBWs) are 85° and 81° in the ϕ = 0° and 90° planes, respectively. The gain is 7.2 dBi. The corresponding HPBWs and gain for the single-loop antenna are 89°, 81°, and 7.4 dBi [9].

4. Antennas with an Inner Parasitic Loop

Thus far, we have studied an antenna with an outer parasitic loop. This section further considers the case of a parasitic loop inside a driven one. The effects of parasite location on radiation characteristics are discussed.

Figure 6 shows the antenna configuration. A parasitic loop is inside the driven loop, and the parasitic loop corners C_n are connected to the driven loop corners F_n by lines F_n–C_n. The other configurations are the same as those in Section 3.

The loop perimeter and feedline branch height (P, h_B) were again selected for wideband CP radiation as a function of loop spacing S. The simulated results are shown in the lower part of Figure 7, together with the selected loop perimeter P in the upper part. It was found that an increased axial ratio bandwidth of 40% is obtained in an S range from 0.02λ₀ to 0.05λ₀. The bandwidth increases threefold compared with that (12%) of the single-loop antenna.

The simulated gain and axial ratio versus frequency are shown with solid lines in Figure 8. The loop spacing is S = 0.03λ₀ with (P, h_B) = (0.98λ₀, 0.10λ₀). It was found that the bandwidth of the 3 dB gain drop from the peak value is 34%, whereas the axial ratio is less than 3 dB.

For comparison, the frequency responses for an outer parasitic loop (Outer-PL) in Section 3 are again shown with dotted lines in Figure 8. The CP wave frequency range for an inner parasitic loop (Inner-PL) was observed to extend towards upper frequencies. A reason for this upper-frequency extension is that the Inner-PL has a smaller perimeter (0.74λ₀ = P − 8S) than the Outer-PL (1.12λ₀ = P + 8S). A smaller loop mainly operates at an upper frequency, where the perimeter becomes one wavelength.

Figure 9 shows the radiation patterns for the Inner-PL with S = 0.03λ₀. It was observed that the antenna radiates a CP beam like that of the Outer-PL (see Figure 5). The HPBWs are 101° and 89° in the ϕ = 0° and 90° planes, respectively. The gain is 6.7 dBi. The corresponding HPBWs and gain of the Outer-PL are 85°, 81°, and 7.2 dBi.

5. Experimental Work

Up to this point, we have discussed an antenna with a straight feedline B–F₂′, as shown in Figure 6b. This section modifies the straight feedline into a crank one for impedance matching.

Figure 10 shows the antenna configuration with the crank feedline B–F₂′, specified by parameters ($\mathcal{l}$₁, $\mathcal{l}$₂) [9]. We selected the crank parameters for a VSWR of less than 2. The other configuration parameters were held at the same values as those for the straight feedline B–F₂′ in Section 4.

The simulated frequency response of the VSWR for ($\mathcal{l}$₁, $\mathcal{l}$₂) = (0.02λ₀, 0.24λ₀) is shown with a solid line in Figure 11, together with the axial ratio and gain. The VSWR was evaluated for a 50 Ω coaxial line. It was found that the VSWR and axial ratio are less than 2 and 3 dB, respectively, in a 3 dB gain drop bandwidth of 31% with a peak gain of 7.1 dBi. The simulated radiation patterns are shown with solid and dotted lines in Figure 12. The antenna radiates a CP beam like that of the straight feedline B–F₂′ (see Figure 9).

The abovementioned simulated results were verified by experimental work. An antenna was fabricated at f₀ = 3 GHz using a ground plane of 5λ₀ × 5λ₀. Figure 13 shows photographs of a prototype. The experimental results are shown with small circles and dots in Figure 11 and Figure 12. An agreement was observed to exist between the experimental and simulated results. Note that the radiation efficiency may theoretically be 100%, since there are only conductor losses that are known to be negligible up to a 12 GHz band. Also, note that the experimental work was performed at f₀ = 3 GHz, where we can make a prototype by hand, and our experimental equipment works well to verify the simulated results. As seen in Figure 13, the wires used in the prototype may be thick since we took the wire radius to be the same as that in [9] to facilitate a comparison.

6. Discussion

This section discusses our results compared to those of similar studies. The comparisons are summarized in

Table 2. Comparisons with similar studies.

Study	Loop Type	Method for Circularly Polarized Radiation	3 dB Axial Ratio Bandwidth (%)	ZinBW 1 (%)	Gain (dBi)	Operating Frequency (GHz)	Antenna Size x × y × z (λ03) z: Height
[11]	annular single	pins and slot	19.1	8 3	- 2	2.4	0.13 × 0.13 × 0.01
[12]		two probes	38	38	8	1.8	0.46 × 0.46 × 0.12
[5]	separate dual	perturbation gap	50	50	8	6	0.62 × 0.62 × 0.3
[6]		perturbation gap	32	43	10	6	0.74 × 0.74 × 0.26
[13]		quasi-two sources	43	- 2	9.1	3	0.5 × 0.65 × 0.25
[6]	concentric double	perturbation gap	25	- 2	8	5.75	0.44 × 0.44 × 0.25
[7]		perturbation segment	3.2	18	9	3	0.25 × 0.25 × 0.1
[14]		four apertures	23	23	7.5	1.4	0.25 × 0.25 × 0.04
present		quasi-two sources	31	45	7.1	3	0.25 × 0.25 × 0.25
previous [9]	wire single	quasi-two sources	12	>12	7.6	3	0.25 × 0.25 × 0.25

¹ Bandwidth of VSWR < 2, ² Not described, ³ Return loss < −10 dB.

. It is emphasized that the present axial ratio bandwidth is the widest among concentric double-loop antennas. Separate dual-loop antennas have wider bandwidths than the present antenna, which uses a larger configuration of side-by-side loops. It can also be seen that an annular single-loop antenna shows a comparable bandwidth of 38% using a complicated feeding system of two probes when compared to the present one.

Table 2 incorporates the previous study [9] in the last row. A comparison between the previous and present studies reveals that (1) the previous study proposed a new method for CP radiation (quasi-two sources). In contrast, the present study with quasi-two sources increases the axial ratio bandwidth using a concentric double loop, characterized by a more straightforward design than a conventional one, as mentioned in the Introduction. (2) Since the present study is a sequel to the previous one, the operating frequency and antenna size are the same, but the axial ratio bandwidth is increased to 31% from 12%.

It is necessary to explain the advantages of the present antenna over a reference one [13], which has a wider axial ratio bandwidth and a higher gain than the present one at the same operating frequency, as seen in Table 2. The advantages are as follows:

• The present antenna size is 0.25 × 0.25 × 0.25λ₀³, which is one-fifth as large as the reference one (0.5 × 0.65 × 0.25λ₀³);
• The present antenna has an unbalanced feed and can be directly excited using a coaxial line. In contrast, the reference antenna has a balanced feed and requires a complicated balun circuit design for the excitation using a coaxial line.

Before the conclusion, some questions will arise: (1) How do readers know which modes are responsible for the CP radiation? (2) Why is a decrease in the gain for the Inner-PL more appreciable than that for the Outer-PL (see Figure 8)? These answers are:

• When explaining the radiation mechanism of a wire antenna in free space, it is expected to use current distribution along the antenna arm instead of the electromagnetic field distributions (modes). The present antenna is made of wires in free space. The wire radius is ρ = λ₀/200, and the loops with a spacing of S < λ₀/30 are located at h = λ₀/4 above the ground plane. These values of (ρ, S, h) are not chosen for a conventional patch antenna design, where the radiation mechanism is often explained using the modes;
• A reason for the decrease in the gain is that the CP wave frequency range for the Inner-PL extends towards the upper frequencies, as mentioned in Figure 8. As the frequency increases from f₀, the loop height electrically becomes more than a quarter of the wavelength, decreasing the gain since the physical height is a quarter of the wavelength at f₀. Note that the antenna gain decreases as the antenna height above the ground plane increases from a quarter of the wavelength.

7. Conclusions

We have studied two concentric double-loop antennas with a spacing S between the driven and parasitic ones. The antennas with outer and inner parasitic loops showed 3 dB axial ratio bandwidths of 23% and 40% for S = 0.02λ₀ and 0.02λ₀ < S < 0.05λ₀, respectively. Subsequently, we modified the antenna’s straight feedline into a crank one for impedance matching. It was found numerically and experimentally that the antenna had a 3 dB gain drop bandwidth of 31%, where the axial ratio and VSWR are less than 3 dB and 2, respectively.

The antenna is made of wires with a fixed radius. The effects of the wire radius on the antenna characteristics have yet to be investigated.