A New Observation in Decoupling and Sequential Rotation Array Configurations Using Loop Radiation Elements

Abstract

Using the method of moments, we analyze three array antennas for low cross-polarized radiation. Each antenna comprises two dual-loop elements connected to a feedline horizontal to the ground plane. First, a feedline end is excited with an unbalanced source as a reference antenna. Next, the feedline center is excited with a balanced source, after the transformation of a decoupling array configuration. It is found that the antenna exhibits a cross-polarized radiation lower by 12 dB than the reference antenna. Last, the decoupling antenna is modified to have an unbalanced source without a complicated balun circuit design. It is pointed out that the modified antenna is an array of four loop elements, sequentially rotated by 90º.

1. Introduction

A circularly polarized (CP) antenna has unique characteristics, such as reduced polarization mismatching and multipath interference [1,2]. These characteristics have led to many applications in modern communication systems [3]. This paper concerns a CP antenna array [4,5,6,7,8,9] composed of dual-wire elements.

A dual-wire element above the ground plane has been investigated for CP radiation [10,11,12,13]. The antenna is characterized by a simple feed system, where two elements are excited with a single feed. Recently, a novel antenna using a resonant loop element with quasi-two sources [14] has been proposed to exhibit a wider CP wave bandwidth than an antenna using a non-resonant element [15].

This study is a continuation of the previous one [14] and presents new findings regarding a dual-loop antenna with quasi-two sources. We apply the dual loop in an array antenna for the first time. The array is composed of two dual-loop elements, connected to a feedline horizontal to the ground plane. The radiation characteristics are evaluated using the method of moments (MoM) [16].

Special attention is paid to a reduction in cross-polarized radiation. Three arrays are investigated: the reference, present, and modified antennas. The reference antenna has a horizontal feedline F–T, whose end F is excited with an unbalanced source (see Figure 1). In contrast, the present antenna’s feedline is excited at the center C with a balanced source (see Figure 2) after the transformation into a decoupling configuration to reduce cross-polarized radiation [17]. The modified antenna is excited at the feedline end F with an unbalanced source (see Figure 3) to simplify the feed system without a complicated balun-circuit design.

The contribution of this study lies in replacing a balanced source required for a decoupling array antenna with an unbalanced source. The replacement is performed by shifting the excitation point from the center, along the horizontal feedline, by a quarter wavelength. Furthermore, a technical novelty is in a new observation: the modified antenna is an array of four single-loop elements, sequentially rotated by 90º. In other words, a conventional sequential rotation array antenna, with four single-loop elements, shown in Figure 3, has a quasi-decoupling array configuration, with two dual-loop elements (an authentic-decoupling array configuration is shown in Figure 2, where the array has a balanced source at the array center C). This new observation aids the understanding of decoupling and sequential rotation array configurations, serving as the groundwork for new ideas in antenna design in future work.

In this paper, we first present the radiation characteristics of the reference antenna. Next, we investigate the present antenna for CP radiation, paying attention to cross-polarized radiation. Lastly, the present antenna is modified for a simple feed system.

2. Reference Antenna

Figure 1 shows the configuration and coordinate system of the reference antenna. Two dual-loop elements are arrayed in the x-axis direction, with a distance of L_f and located at height H above the ground plane. Each dual-loop element comprises two square loops of perimeter P with a distance of d.

For CP radiation, each loop has adjacent corners α_n and β_n (n = 1, 2, 3, and 4) connected to a branched feedline α_n/β_n–B_n–γ_n vertical to the ground plane [14], as shown in Figure 1a,c. The branch point B_n and bottom end γ_n are at heights of h_B and h_L above the ground plane, respectively.

In each dual-loop element, the bottom end γ_m (m = 1 and 3) of the vertical, branched feedline is connected to another end γ_m+1 by a combining line γ_m–γ_m+1 in the y-axis direction, as shown in Figure 1a. Points F and T of the combining lines are connected by a horizontal feedline F-T in the x-axis direction, whose end F is excited by a coaxial line through a vertical wire F–F′ of length h_L.

For wideband CP radiation, each dual-loop element has a sequential rotation array configuration [13,18]: one loop of #m is rotated by 90° and excited with a phase difference of 90° for the other loop of #m + 1. The excitation phase difference is made by an excitation point shift of λ₀/8 along the combining line γ_m–γ_m+1 from the center, as shown in Figure 1b, where λ₀ is the free-space wavelength at a test frequency f₀. The antenna is made of wires with a radius ρ [13,14].

We analyze the antenna using our coded software based on the MoM [16]. The ground plane is assumed to have an infinite extent, and image theory is used in the analysis. The antenna is designed to radiate a CP wave in the direction normal to the antenna plane, in the z-axis direction. The loop parameters (P, h_B) are selected for a horizontal feedline length of L_f = 1λ₀. The other configuration parameters are fixed throughout the paper at the same values as those in [13,14] to facilitate the comparison: (d, H, h_L, ρ) = (λ₀/2, λ₀/4, λ₀/50, λ₀/200).

Figure 4 shows the simulated radiation patterns for (P, h_B) = (0.88λ₀, 0.08λ₀). The radiation is decomposed into right (E_R) and left-hand (E_L) CP wave components, which are shown with dotted and solid lines, respectively. The antenna radiates a left-hand CP beam in the z-axis direction. The half-power beam widths (HPBWs) are 27° and 36° in the ϕ = 0° and 90° planes, respectively. The gain is 12.3 dBi.

It is observed in Figure 4 that the cross-polarized radiation E_R is appreciable in the ϕ = 90° plane. The maximum E_R level is −7.0 dB at θ = −41°. This cross-polarized radiation is reduced using a decoupling array configuration in the next section.

3. Present Antenna

The antenna configuration is shown in Figure 2. The decoupling array described in [17] has a symmetrical configuration concerning the array center and is excited at the center with the same amplitudes and a phase difference of 180°. This is accomplished in the present antenna as follows.

• Points T and F of the combining lines γ_m–γ_m+1 are symmetrical with respect to the center C of the horizontal feedline T–F, and the center is excited with a balanced source (emphasized with + and – in Figure 2);
• Loops #3 and #4 are rotated by 90° around their vertical lines β₃–γ₃ and β₄–γ₄, respectively, for the two dual-loop elements to become symmetrical concerning the configuration center C′, at height H, above the horizontal line center C, as shown in Figure 2c. Note that the horizontal feedline has a length of L_f, as shown in Figure 2b.

Figure 5 shows the simulated radiation patterns for (P, h_B) = (0.92λ₀, 0.09λ₀) with L_f = λ₀/2. The cross-polarized radiation E_R shown with a dotted line in the ϕ = 90° plane is found to be reduced, compared to that of the reference antenna (see Figure 4). A reference antenna’s E_R level of −7.0 dB, in the direction of (ϕ, θ) = (90°, −41°), is reduced by 11.9 dB compared to the present antenna in the same direction. It is also found that the maximum cross-polarized radiation is −12.8 dB at θ = ±90° in the ϕ = 0° plane. The HPBWs are 38°and 36° in the ϕ = 0° and 90° planes, respectively. The gain is 12.2 dBi.

The simulated gain and axial ratio versus frequency are presented with solid lines in Figure 6. The gain has a peak value of 12.8 dBi, and drops from the peak by 3 dB at frequencies of 0.86f₀ and 1.38f₀, corresponding to a bandwidth of 46%. In this bandwidth, the axial ratio is less than 3 dB. For comparison, the results of the reference antenna are shown with dotted lines. The 3 dB gain drop bandwidth is 30%, where the axial ratio is less than 3 dB.

4. Modified Antenna

Up to this point, we have discussed the reference and present antennas to reduce cross-polarized radiation. The present antenna is excited with a balanced source, which involves a complicated balun-circuit design for a coaxial line feed. In this section, we modify the present antenna so that the antenna can be excited with an unbalanced source.

Figure 3 shows the modified antenna. The excitation point C in the previous section is shifted along the horizontal line F–T by λ₀/4 to the end F, at which the modified antenna is excited by a coaxial line via a vertical wire F–F′. This is the only difference between the antennas in the present and previous sections. We select the loop parameters (P, h_B) for CP radiation, holding the other configuration parameters at the same values as those in the previous section.

The solid and dotted lines in Figure 7 show the simulated radiation patterns for (P, h_B) = (0.91λ₀, 0.08λ₀). It is found that the antenna radiates a CP beam similar to that of the antenna in the previous section (see Figure 5). The maximum cross-polarized radiation is −12.0 dB at θ = −90° in the ϕ = 90° planes. The HPBWs are 38° and 36° in the ϕ = 0° and 90° planes, respectively. The gain is 12.5 dBi.

The simulated gain and axial ratio versus frequency are shown with solid lines in the lower part of Figure 8. It is found that the 3 dB gain drop bandwidth is 39%, where the axial ratio is less than 3 dB. The reference antenna’s results are again presented with dotted lines. The modified antenna has a wider 3 dB gain drop bandwidth than the reference antenna (30%). Further calculations reveal that the modified antenna has a 3 dB axial ratio bandwidth of 57%, which is almost the same as that (54%) of the reference antenna.

The solid line in the upper part of Figure 8 shows the simulated frequency response of the VSWR of the modified antenna. The VSWR is evaluated for a 50 Ω coaxial line. It is observed that the antenna has a VSWR of less than 2 in the 3 dB gain drop bandwidth.

When comparing the 3 dB axial ratio bandwidths of the modified (57%) and reference (54%) antennas, a question arises. Why are the bandwidths of the modified and reference antennas almost the same? The answer is that the modified antenna is also regarded as a sequential rotation array composed of four loops, i.e.,

• Referring to the loops shown in Figure 3a, we see that loops #2, #1, #3, and #4, are sequentially rotated 90° clockwise around their vertical lines β_n–γ_n. The clockwise rotation makes the phase of partial radiation from each loop progress by 90°, since the antenna radiates a left-hand (E_L) CP beam, as shown in Figure 7;
• Referring to a feed network composed of the horizontal feedline F–T of length L_f and combining lines γ_m–γ_m+1 of length d, shown in Figure 3b, we recognize that the excitation phases of loops #2, #1, #3, and #4, in turn, are sequentially delayed by 90° (to compensate for a radiation phase progress of 90°), since the line lengths are L_f = d = λ₀/2, leading to a sequential increase of λ₀/4 in the path length to each loop from the excitation point F.

Thus far, the simulated results have been discussed using the MoM. To verify the results, we reproduce them using a finite integration technique (FIT), i.e., commercial software called CST Studio Suite [19]. The results are shown with small circles and dots in Figure 7 and Figure 8. The FIT results agree with the MoM results.

Finally, we compare our results with those of similar studies. The comparisons are summarized in

Table 1. Comparison with similar studies.

Study	Array Type	Array Feed	Radiation Element	3 dB Axial Ratio Bandwidth (%)	Gain (dBi)	Operating Frequency (GHz)
[4]	2 × 2	multi-layer H-figured FL 1	magnetoelectric dipole	21.9	12.4	21
[5]	2 × 2	coplanar C-figured FL 1	patch	8.3	10.8	8.25
[6]	2 × 2	coplanar O-figured FL 1	patch	20.2	13.8	28
[7]	2 × 2	back cavities	patch	23.9	14.6	64
[8]	2 × 2	coplanar C-figured FL 1	patch	15	- 2	5.3
[9]	2 × 2	coplanar C-figured FL 1	patch	20.4	11.1	27
present	2 × 2	multi-layer H-figured FL 1	loop	39	12.5	3

¹ Feedline, ² Not described.

. It is emphasized that the modified antenna has the widest CP wave bandwidth. Note that all the studies deal with an array antenna composed of four resonant elements, sequentially rotated by 90°.

As additional data, photographs of an antenna fabricated at f₀ = 3 GHz are shown in Figure 9. In addition, Figure 10b and Figure 11 show tentative experimental results using the fabricated antenna. It is apparent that the experimental results are similar to the MoM results, which are identical to those in Figure 7 and Figure 8.

The following questions may arise before the conclusion:

(1)

Which antenna is a proposed one that significantly improves previous research results?

(2)

The modified antenna has no improvement in antenna characteristics and provides worse measured results than the simulated ones.

(3)

What does the quasi-decoupling mean and in what way can it be quantified?

(4)

The decoupling used in the title and the abstract is not obvious.

(5)

Dimensions and implementation details are not provided. Therefore, we cannot verify the presented results.

(6)

What is the parasitic radiation of relatively long feedlines?

(7)

How is the radius of the wire selected to satisfy the impedance matching requirement?

The answers to the above questions are:

(1)

We proposed the modified (sequential rotation) antenna with the widest CP wave bandwidth in previous studies, as shown in Table 1. The present (decoupling) antenna plays a role in finding a new observation in decoupling and sequential rotation array configurations, as in the title. This study claims a new observation as well as a new antenna proposition.

(2)

We compare the modified antenna to the reference one since the present antenna has a balanced feed that requires a complicated balun-circuit design for a coaxial-line feed. In addition, the measured results are considered additional data in this study because we verify the MoM results using the FIT ones.

(3)

The quasi-decoupling means that it reduces cross-polarized radiation, like authentic decoupling, but without a balanced feed. A reduction in cross-polarized radiation is used to quantify the quasi-decoupling.

(4)

The decoupling is used for the following [17]: The cross-polarized radiation is coupled to co-polarized radiation. If the coupling is released (this is called decoupling), the cross-polarized radiation is reduced. The reduction is performed via a cancelation of the cross-polarized, partial radiation from each antenna configuration part, where the antenna comprises two configuration parts symmetrical to the antenna center.

(5)

The dimensions and implementation are summarized in

Table 2. Antenna dimensions and implementation.

Implementation	Parameters		Antennas
	Antenna Part	Notation	Reference (λ0)	Present (λ0)	Modified (λ0)
optimization	loop perimeter	P	0.88	0.92	0.91
	branch height of vertical feedline αn/βn–Bn–γn	hB	0.08	0.09	0.08
precedent	length of horizontal feedline F–T	Lf	1	1/2
	loop distance in dual element	d	1/2
	loop height	H	1/4
	height of horizontal feedline F–T	hL	1/50
	wire radius	ρ	1/200

. It is shown that we can design the three antennas by optimizing just two parameters (P, h_B). This optimization makes it easy to verify the presented results.

(6)

The parasitic radiation from the feedline is smaller than the loop one, since the feedline height above the ground plane needs to be as small as possible, h_L = λ₀/50, compared to the loop height of H = λ₀/4, as shown in Table 2. This smaller parasitic radiation enables us to design the antennas using the loop parameters (P, h_B).

(7)

For the impedance matching, we do not choose the wire radius ρ but the horizontal feedline height: h_L = λ₀/50, giving a characteristic impedance of Z₀ = 125 Ω. This Z₀ matches both the coaxial feed and loop elements.

5. Conclusions

We have designed two dual-loop antenna arrays, each having a feedline horizontal to the ground plane. One end of the feedline of the reference antenna was excited with an unbalanced source. In contrast, the feedline center of the present antenna was excited with a balanced source for low cross-polarization. It was revealed that the present antenna exhibited a lower cross-polarization level by 12 dB, compared to that of the reference antenna. Subsequently, we modified the present antenna by replacing the balanced source with an unbalanced one for a simple feed system. The modified antenna still exhibited a low cross-polarization, having a 3 dB gain drop bandwidth of 39%, where the axial ratio and VSWR were less than 3 dB and two, respectively. We pointed out that the modified antenna is a sequential rotation array composed of four single-loop elements; simultaneously, the antenna has a quasi-decoupling array configuration comprising two dual-loop elements.