A Printed Hybrid-Mode Antenna for Dual-Band Circular Polarization with Flexible Frequency Ratio

Abstract

In this paper, a printed hybrid-mode antenna for dual-band circular polarization (CP) is proposed. In the proposed antenna, one T-shaped element is fed by a coplanar waveguide and one L-shaped element is loaded to the ground plane. The relationship between the antenna’s geometric parameters and the circular polarization characteristic (axial ratio) is examined through electric current distribution and radiation field components. In addition, the antenna’s resonant modes are investigated through characteristic mode analysis (CMA). Through parametric studies, the range of two frequency ratios is explored, revealing that the antenna operates as a dual-band single-sense CP antenna, even in ranges where the two frequency ratios (the ratio of high frequency to low frequency) are smaller compared to antennas in other studies. The proposed antenna has a frequency ratio of less than 1.5 between the two frequencies and can be flexibly designed. The proposed antenna is designed for the 2.5 GHz band and 3.5 GHz band. The measured bandwidths of 10 dB impedance with a 3 dB axial ratio are 2.35–2.52 GHz and 3.36–3.71 GHz, respectively.

1. Introduction

Many applications such as Sub-6 GHz 5G, IoT communication, and those in IMS bands are used in the frequency band below 6 GHz. In this context, dual-band antennas are very effective in ensuring wide coverage and compatibility with different communication standards, as well as in reducing the size and cost of antennas. In addition, the use of circularly polarized waves allows greater freedom in antenna installation orientation, and from the perspective of improving communication quality in multipath environments, dual-band circularly polarized antennas are expected to play an important role in future mobile communication systems.

In dual-band printed antennas for CP, there are two types of polarization sense, single sense [1,2,3,4,5,6,7,8,9,10] and dual sense [11,12,13,14,15,16,17,18,19,20,21,22]. Dual-sense CP has the advantage of improving reliability in fading environments due to its different polarization characteristics. Single sense has the benefit of enabling the simplification of signal processing circuits. In addition, while the frequency ratio between the two bands is a very important characteristic in dual-band antennas, single-sense CP antennas are relatively easier to design for applications where the two frequency ratios are close. Antennas with two low-frequency ratios were also designed in [1,2,4,5,8,10].

Based on radiation patterns, dual-band CP antennas can be classified into two types: bidirectional radiation pattern [1,2,3,4,5,11,12,13,14,15,16,17] and unidirectional radiation pattern [6,7,8,9,10,18,19,20,21,22]. Antennas with bidirectional radiation patterns enable compact and wideband designs but have the disadvantage of low gain. Antennas with unidirectional radiation patterns require a large ground plane, resulting in a larger antenna size and generally narrow bandwidth. However, they have the advantage of high gain. Thus, the characteristics of antennas with unidirectional and bidirectional radiation patterns differ significantly.

The authors of [23] proposed a printed dual-band dual-sense antenna for CP using a hybrid mode. Its radiation pattern is bidirectional. The antenna consists of an L-shaped element and a loop element. The two elements are fed by a coplanar waveguide. The vertical feeding element and ground plane are shared for both elements. The left-hand circular polarization (LHCP) is produced mainly by the vertical part of the L-shaped element and the horizontal part of the loop element in the low-frequency band. The right-hand circular polarization (RHCP) is generated mainly by the horizontal part of the L-shaped element and the vertical part of the loop element in the high-frequency band.

In this paper, a printed dual-band single-sense antenna for CP using a hybrid mode is proposed based on the results of [23]. In order to compare it with the antenna in [23], the antenna was similarly designed for the 2.45 GHz band and 3.5 GHz band. Furthermore, the antenna was fabricated and compared with the measured results. Additionally, the fabricated antenna is shown to be advantageous in terms of antenna size and frequency bandwidth compared to other studies. The operational principle of the hybrid mode for dual-band single-sense CP is elucidated by the relationship between each element and the radiated electric field and electric current distribution. The parts of the antenna contributing to resonance are discussed and undergo characteristic mode analysis (CMA). In recent years, within the rapidly spreading technology of Sub-6 GHz 5G, parts of frequency bands n77 (3.3–4.2 GHz), n78 (3.3–3.8 GHz), and n79 (4.4–5.0 GHz) have been utilized. Since the ratio between these frequency bands is small, dual-frequency circular polarization antennas with small frequency ratios are effective for Sub-6 GHz 5G. Through simulation, the controllable range of the ratio between the two frequencies was investigated herein.

For the simulations, the simulation software package Altair Unit FEKO v2024.1, which is based on the Method of Moments, was used. The antenna characteristics were measured by using an Anritsu MS46122B (Anritsu Corporation, Atsugi, Japan) vector network analyzer in an anechoic chamber.

2. Antenna Design

Figure 1 shows a proposed hybrid-mode antenna. The antenna consists of one T-shaped antenna and one L-shaped element. The T-shaped antenna is fed by a coplanar waveguide. The L-shaped element is loaded on the ground plane. The relative dielectric constant, the thickness, and the loss tangent of the dielectric substrate are ε_r = 3.6, h = 1.6 mm, and tanδ = 0.022, respectively. The antenna is excited by a coaxial feed from the back of the dielectric substrate. In both reference [23] and this study, the T-shaped element is placed at the center of the antenna. However, the L-shaped element in this study is positioned on the opposite side of the T-shaped element compared to the loop element in [23] to create a dual-band single-sense CP. Figure 2 shows the main radiating components which contribute to the hybrid mode. The hybrid mode for CP in the low-frequency band is produced mainly by the vertical part of the T-shaped element and the horizontal part of the L-shaped element. The hybrid mode for CP in the high-frequency band is generated mainly by the horizontal part of the T-shaped element and the vertical part of the L-shaped element. As shown in Figure 2a, in the low-frequency band, the length of the T-shaped element (the sum of the solid and dashed green lines) and the length of the L-shaped element (the sum of the solid and dashed blue lines) are approximately a quarter wavelength. In the high-frequency band, the length of the T-shaped element (the sum of the solid and dashed blue lines) and the length of the L-shaped element (the sum of the solid and dashed green lines) are approximately a half wavelength, as shown in Figure 2b. The relationship between the element length and wavelength is presented in Section 4.2.

Since the size of the proposed antenna is small, the size of the sub-miniature A (SMA) receptacle is relatively large compared with the antenna. For side-mounting feeding, the receptacle and cable influence the measurement of the axial ratio. Therefore, the SMA receptacle is inserted from the bottom of the dielectric substrate. The positions of the center of the feed point and the shorting pins W_c and L_c were chosen so that the whole body of the SMA connector would not protrude from the ground plane [23].

Input impedances were tuned by varying the width F_s of the feed line and the gaps g_a between the feed line and the ground plane [23]. As shown in Section 5.2, the simulations revealed the relationship between the geometric parameters and the axial ratio, as a result of which the axial ratios were adjusted mainly by the length W_d and L_b of the L-shaped element and the length L_f and the position W_j of the horizontal element of the T-shaped element. The ratio of the two frequencies was adjusted due to L_b and L_e. The discussion on the two frequency ratios is conducted in Section 5. The geometric parameters of the final designed antenna for the 2.45 GHz band and the 3.5 GHz band are as follows: L_a = 53.0, L_b = 17.5, L_c = 5.5, L_d = 1.0, L_e = 5.0, L_f = 20.5, L_gg^L = 28.5, L_g^R = 19.5, L_h = 27.5, W_a = 28.2, W_b = 3.5, W_c = 3.0, W_d = 8.7, W_e = 14.2, W_f = 1.5, W_gg^L = 13.0, W_gg^R = 12.5, W_j = 5.6, F_s = 3.0 (unit: mm). Figure 3 shows a photograph of the fabricated antenna. The antenna was made on FR-4 substrate.

3. Antenna Characteristics

This section presents the simulated and measured results of the reflection coefficient (|S₁₁|), axial ratio, radiation pattern, and gain of the proposed antenna and compares them. Simulations were performed using FEKO’s Method of Moments with Automesh functionality, with the highest frequency set to 5 GHz for mesh optimization. For the measurements, the frequency range was set from 1 GHz to 5 GHz with 401 measurement points, and the IFBW was set to 1 kHz. The distance between the transmitting and receiving antennas was 2 m.

Figure 4a,b show the simulated |S₁₁| and the axial ratio. Good impedance matching and axial ratio were achieved simultaneously in the 2.45 GHz band and the 3.5 GHz band. The simulated bandwidths of 10 dB impedance with a 3 dB axis ratio are 6.98% (2.35–2.52 GHz) in the low-frequency band and 7.73% (3.36–3.63 GHz) in the high-frequency band. The measured results are also shown for comparison. The measured results agree well with the simulated ones. The measured bandwidths are 5.30% (2.39–2.52 GHz) in the low-frequency band and 9.90% (3.36–3.71 GHz) in the high-frequency band. The simulated and measured results satisfy the design specifications of the 2.45 GHz band (2.41–2.50 GHz) and the 3.5 GHz band (3.40–3.60 GHz). In the 2.45 GHz band, the dimension of the designed antenna is 0.10 λ_2.45² (0.231 λ_2.45 $\times$ 0.433 λ_2.45). In the 3.5 GHz band, the dimension of the designed antenna is 0.21 λ_3.5² (0.332 λ_3.5 $\times$ 0.625 λ_3.5).

Figure 5a,b show the radiation patterns at center frequencies of 2.45 GHz and 3.5 GHz. The radiation patterns are normalized by the maximum values in the xz-, yz-, and xy-planes. The figure shows that RHCP radiates to the +z direction and LHCP radiates to the -z direction in both frequency bands. It is confirmed that the proposed antenna radiates single-sense CP at two different frequency bands. The measured results agree reasonably well with the simulated results in the forward space of the antenna ($0°\le \theta \le 90°$). However, in the backward space ($90°\le \theta \le 180°$), there is a significant discrepancy between the measured results and simulated results. This is due to the influence of the stand used to secure the antenna.

The total gain G_T of a circularly polarized antenna can be expressed as follows [24,25]:

G_T = 10 log₁₀(G_TV + G_TH)  [dBic]

(1)

where G_TV and G_TH are the partial power gains for vertical linear polarization and horizontal linear polarization, respectively. In the measurements, G_TV and G_TH were obtained using a linearly polarized standard gain horn antenna. Figure 6 shows the simulated and measured absolute gains. A ±0.5 dB ribbon is attached to show the overall uncertainty of the gain measurements. The simulated absolute gains at 2.45 GHz and 3.5 GHz are 2.39 dBic and 0.89 dBic, respectively. The measured absolute gains at 2.45 GHz and 3.5 GHz are 3.3 dBic and 2.4 dBic, respectively. The simulated radiation efficiencies are 93.0–93.8% in the 2.45 GHz band and 92.9–93.2% in the 3.5 GHz band.

Table 1. Comparison of the bandwidth, the antenna size, and the frequency ratio in our work and in other previous studies in the literature.

	BW (Low Band) [%]	BW (High Band) [%]	Size [λL2]	Size [λH2]	fH/fL	Gain (Low Band) [dBic]	Gain (High Band) [dBic]	Single/Dual (Sense)
[1]	0.98	1.08	0.06	0.087	1.21	1.35	3.5	single
[2]	6.87	0.57	0.221	0.365	1.27	$\ge 5$		single
[3]	7.13	3.25	1.440	8.649	2.45	3.7	3.2	single
[4]	9.09	11.11	0.129	0.213	1.29	2.5–4		single
[5]	2.84	2.10	0.754	2.599	1.86	4.79	4.27	single
[5]	3.88	1.38	0.805	1.309	1.28	4.47	4.23	single
[23]	7.32	9.04	0.0741	0.151	1.44	1.5	5.2	dual
This work	5.30	9.90	0.100	0.208	1.44	3.3	2.4	single

shows references from the literature that pertain to dual-band single-sense antennas for CP, excluding reference [23]. For all of the studies, the data in the table represents the size of the fabricated antenna and its measurement results. All antennas in Table 1 have a bidirectional radiation pattern. BW in Table 1 is the 10 dB impedance bandwidth with a 3 dB axial ratio. Since the 10 dB impedance bandwidth covers the 3 dB axial ratio frequency band in all references and the proposed antenna, BW in Table 1 also corresponds to the 3 dB axial ratio bandwidth. Only references [1,4] achieve antenna sizes below 0.25 wavelength squared at both frequencies. In terms of frequency bandwidth versus size, the antenna in reference [4] performs the best. However, due to the complex structure, it appears difficult to change the two frequency ratios. Since the proposed antenna has a very simple structure (just combining T-shaped and L-shaped elements), the two frequency ratios can be adjusted very easily over a wide range, as shown in Section 5. Furthermore, the proposed antenna has a relatively broad bandwidth at the two frequencies and is compact in size. Reference [1] has an antenna size smaller than 0.1 wavelength squared at both frequencies, but its frequency bandwidth is very small. The proposed antenna has better frequency bandwidth characteristics relative to the antenna size compared to other antennas. Compared to the dual-sense antenna [23] designed by the authors, the antenna in this work is slightly larger in size but exhibits similar performance characteristics.

4. Operational Principles

In this section, the operational principles of dual-band single-sense CP and resonant modes in the frequency bands for CP are examined.

4.1. Dual-Band Single-Sense CP

In order to investigate the effects of the L-shaped element on |S₁₁|, the axial ratio, and absolute gain, four different configurations shown in Figure 7a–d are considered. Type A is an antenna for linear polarization. Type B has an asymmetric structure with respect to the feed line. In Type C, the T- and L-shaped elements are connected to form a loop. In Type D, the L-shaped element is loaded on Type B, which is the type of the proposed antenna. Figure 8a–c show the |S₁₁|, axial ratio, and absolute gain of the four types of antennas. While Type A has a peak of |S₁₁| around 3.0 GHz, Type B has peaks at 2.1 GHz and 3.5 GHz. Furthermore, Type D has a new resonance around 2.6 GHz in addition to the resonance of Type B. It is found that the L-shaped element influences the impedance matching in both frequency bands.

The minimum axial ratio for Type B is 5.92 dB at 1.92 GHz in the low-frequency band and 3.76 dB at 3.55 GHz in the high-frequency band. However, when the L-shaped element is loaded on the ground (Type D), the axial ratio achieves less than 3 dB in both the low- and high-frequency bands. When the L-shaped element is connected to the T-shaped element (Type C), the minimum axial ratio is less than 1 dB in the low-frequency band, similar to the proposed antenna. However, the minimum peak of the axial ratio does not appear in the high-frequency band. To radiate circular polarization at two frequencies, it is important not to connect the L-shaped element and the T-shaped element to form a loop.

From Figure 8c, it can be confirmed that Type B radiates LHCP in the low-frequency band and RHCP in the high-frequency band. However, the proposed antenna radiates RHCP in both frequency bands. It can be seen that the radiated field in the low-frequency band is reversed by the L-shaped element. Thus, the L-shaped element contributes significantly to the radiation characteristics (the sense of the circularly polarized wave, axial ratio, and gain).

Table 2. E_θ and E_ϕ in the low-frequency band.

	Min. AR [dB]	Freq. [GHz]	$\left|{\mathit{E}}_{\mathit{\theta }}\right|-\left|{\mathit{E}}_{\mathit{\varphi }}\right|$ [dB]	$\mathit{\angle }{\mathit{E}}_{\mathit{\theta }}-\mathit{\angle }{\mathit{E}}_{\mathit{\varphi }}$ [°]
Type B	5.92	1.92	4.66 (−7.64, −12.3)	−67 (118.0, −175.0)
Proposed (Type D)	0.44	2.45	0.35 (−2.77, −3.12)	87.7 (−85.3, −173.0)

shows the magnitude and the phase of E_θ and E_ϕ at θ = 0° in the xz plane at the frequency, giving the minimum axial ratio in the low-frequency band of Type B and Type D. In Type B, |E_θ| is 4.66 dB larger than |E_ϕ|. In Type D, however, the difference between |E_θ| and |E_ϕ| is very small (0.35 dB). Both |E_θ| and |E_ϕ| of Type D increase away from those of Type B. The phases of E_θ and E_ϕ in Type B are 118° and −175°, and those in Type D are −85° and −173°. The phase of E_ϕ in Type B changes little when the L-shaped element is loaded, but the phase of E_θ changes significantly.

Table 3. E_θ and E_ϕ in the high-frequency band.

	Min. AR [dB]	Freq. [GHz]	$\left|{\mathit{E}}_{\mathit{\theta }}\right|-\left|{\mathit{E}}_{\mathit{\varphi }}\right|$ [dB]	$\mathit{\angle }{\mathit{E}}_{\mathit{\theta }}-\mathit{\angle }{\mathit{E}}_{\mathit{\varphi }}$ [°]
Type B	3.97	3.54	3.05 (−3.63, −6.68)	77.0 (178.0, 101.0)
Proposed (Type D)	1.85	3.47	1.11 (−3.22, −4.33)	78.5 (177.0, 98.50)

shows the magnitude and the phase of E_θ and E_ϕ at θ = 0° in the xz plane for Type B and Type D in the high-frequency band. The |E_ϕ| of Type D is also higher than that of Type B. However, the increase is smaller than that in the low-frequency band. |E_θ| is almost unchanged between Types B and D. The phase change is very small for both E_ϕ and E_θ. These suggest that the horizontal element of the L-shaped element does not have much effect on the E_θ in the high-frequency band. The axial ratio is adjusted by a slight increase in |E_ϕ|.

Figure 9a shows the time average of the electric current distribution at the minimum axial ratio at 2.45 GHz in the low-frequency band. This frequency is the same as the calculated frequency in Table 2. Electric currents with large magnitude occur in the T-shaped element and in the L-shaped element. Based on Figure 9b, when ωt = 0°, the x component of the electric current (J_x) flows in the same direction on the horizontal elements of both the L-shaped element and the T-shaped element. Additionally, the y component of the electric current (J_y) also flows in the same direction on the vertical elements of both T- and L-shaped elements. When ωt = 90°, however, J_x on the L-shaped element flows in the opposite direction to J_x on the T-shaped element, and its intensity is great. For this reason, the phase of E_θ differs by around 180° between Type B and Type D (Table 2), resulting in opposite rotation directions, as shown in Figure 8. |E_ϕ| increases with radiation due to J_y on the L-shaped element.

Figure 10 shows the electric current distribution at 3.5 GHz, which is the center frequency in the high-frequency band. In the high-frequency band, the directions of J_x on the T-shaped element and L-shaped element are the same for both ωt = 0° and 90°. Similarly, J_y is also the same. Therefore, the phase change of the electric fields between Type B and Type D is small. Although Type B does not radiate CP, it is close to 3 dB. As shown in Table 3, in Type B, |E_ϕ| is smaller compared to |E_θ|, but by adding the L-shaped element, |E_ϕ| is generated by J_y on the L-shaped element, achieving an improved axial ratio.

4.2. Resonant Mode of Dual Band

In the previous subsection, the principle of generating a dual-band single-sense circularly polarized wave was explained using the magnitude and phase of the two radiated electric field components E_θ and E_ϕ. In this subsection, the relationship between geometric parameters and resonant modes is investigated through characteristic mode analysis (CMA). The analysis clarifies which parts of the antenna operate as half-wavelength or quarter-wavelength antennas and contribute to resonance.

In CMA, the eigenmodes of the antenna structure are evaluated using Modal Significance (MS) and characteristic angle (CA). For CP realization, two orthogonal modes must have equal MS values and CA values of 180° ± 45°. When the MS value is large, resonance occurs; therefore, if the MS value is large and impedance matching is achieved, a minimum value of |S₁₁| will occur [26,27]. In this paper, the analysis conditions were set with a maximum mode number of 10, and the analysis was performed on the structure without any feed ports.

Figure 11 shows the MS. In the simulation software FEKO, mode numbers are automatically assigned based on eigenvalues, and all MS values > 0.3 are included up to mode 4. For mode 5 and beyond, the MS values are less than 0.1, so they are excluded from this analysis as their contribution to antenna characteristics is limited. The figure shows up to mode 7.

Table 4. Characteristic angle (CA).

	Mode 1	Mode 2	Mode 3	Mode 4
2.45 GHz	142.54° −37.46°	234.37° 54.37°	93.32° −86.68°	266.93° 86.93°
3.47 GHz	108.21° −71.79°	167.32° −12.68°	94.92° −85.08°	250.15° 70.15°

shows the CA. The upper row of the column shows the CA value, while the lower row indicates the difference from 180°. The simulation frequencies are 2.45 GHz and 3.47 GHz, which give the minimum axial ratio (Table 2 and Table 3).

At 2.45 GHz, mode 1 and mode 2 are dominant. At 2.45 GHz, the CA of mode 1 and mode 2 are 142.54° (=180 − 37.46°) and 234.37° (=180° + 54.37°), respectively, and they deviate from 180° by almost the same amount. Also, the phase difference between these two modes is approximately 90°. This means that mode 1 and mode 2 are orthogonal. The MS value for mode 1 is 0.98 at 2.2 GHz, and the MS value for mode 2 is 0.91 at 2.6 GHz, which causes |S₁₁| peaks around 2.2 GHz and 2.6 GHz, as shown in Figure 8a. At 2.45 GHz, the MS values of these two orthogonal modes (mode 1 and mode 2) are close, so these two orthogonal modes contribute to the radiation of a circularly polarized wave. Figure 12 shows the electric current distribution at 2.45 GHz of mode 1 and mode 2. The lengths L₁ in mode 1 and L₂ in mode 2 (shown in black), which indicate strong current intensity, are approximately 28.5 mm (0.23 λ_2.45) and 29.5 mm (0.24 λ_2.45), and the antenna operates as a quarter-wavelength antenna.

In Figure 11, at 3.47 GHz, mode 2’s MS value = 0.94, which is the largest. This is followed by mode 4 (MS = 0.35) and mode 1 (MS = 0.31), which have nearly identical values. Additionally, the CA value of mode 2 is 167.32° (Table 4), which is close to 180°. This means that mode 2 is the resonant mode. Figure 13 shows the electric current distribution at 3.47 GHz of mode 2 and mode 4. Since the electric current distribution of mode 1 is similar to that of mode 2, it has been omitted in this paper. At 3.47 GHz, a strong electric current of mode 2 occurs in the T-shaped element, and a slight electric current of mode 4 occurs in the L-shaped element. The addition of the L-shaped element generates mode 4. Although the MS value of mode 4 is low, the electric current in the vertical element contributes to the radiation of circular polarization, as shown in the previous subsection. The length L₃ in mode 2 (shown in black), which indicates strong current intensity, is approximately 35 mm (0.41 λ_3.47). This means the proposed antenna operates as a half-wavelength antenna.

5. Parametric Studies

The proposed antenna has a very small ground size compared to the wavelength $(L_a\times W_g^R=0$.44 λ_2.45 $\times$ 0.1 λ_2.45 = 0.62 λ_3.5 $\times$ 0.15 λ_3.5). Therefore, this section discusses the influence of ground plane size on antenna characteristics. Furthermore, a detailed investigation is conducted on the relationship between the geometric parameters of the L-shaped and T-shaped elements, which are the radiating elements, and the antenna characteristics.

5.1. Ground Plane

Figure 14 shows the simulated results of |S₁₁| and the axial ratio when the ground size is varied. The dielectric size is also changed to match the ground plane size ($W_g^R$, $W_g^L$, $L_g^R$, $L_g^L$). From the time-averaged current distribution in Figure 9 and Figure 10, it can be seen that the intensity of the electric current on the ground plane is smaller than that on the T-shaped and L-shaped elements. However, since the electric current is distributed over the entire ground plane, changing the ground plane size alters the electric current distribution on the ground plane, thus affecting |S₁₁| and the axial ratio. In the low-frequency band, the intensity of the electric current is strong on the ground plane near the connection between the L-shaped element and the ground plane (Figure 9a). Therefore, when $L_g^L$ is changed, the change in axial ratio at 2.5 GHz is larger than the change in the 3.5 GHz band.

5.2. L-Shaped and T-Shaped Elements

Figure 15, Figure 16 and Figure 17 show the simulated results of |S₁₁| and axial ratio characteristics when the geometric parameters L_b, W_d, and L_h of the L-shaped element are varied. The geometric parameters L_b, W_d, and L_h of the L-shaped element influence |S₁₁| in the low-frequency band. The impact on the axial ratio in the low-frequency band differs depending on the parameters. As described in Section 4.1, the L-shaped element radiates horizontal polarization in the low-frequency band. Therefore, the length L_b of the horizontal part of the L-shaped element controls the axial ratio in the low-frequency band and the frequency at minimum axial ratio. Furthermore, the vertical part of the L-shaped element affects the axial ratio in the high-frequency band. Figure 16b also confirms that the length W_d of the vertical part controls the axial ratio in the high-frequency band. When W_d increases, the gap length between the L-shaped and T-shaped elements increases. Due to this change in gap length, the currents on the horizontal elements of the L-shaped and T-shaped elements change, causing the horizontal component E_θ of the electric field to change, resulting in a change in axial ratio. The connection position L_h of the L-shaped element to the ground plane particularly affects |S₁₁| in the low-frequency band.

Figure 18, Figure 19 and Figure 20 show the simulated results of |S₁₁| and axial ratio characteristics when the geometric parameters L_e, L_f, and W_j of the T-shaped element are varied. The geometric parameters L_e, L_f, and W_j of the T-shaped element affect |S₁₁| and the axial ratio in the high-frequency band. It can be seen that L_e in particular enables frequency adjustment over a wide range in the high-frequency band. In the low-frequency band, the T-shaped element contributes to vertical polarization radiation. Therefore, the horizontal element length L_f has little influence on the axial ratio in the low-frequency band. Additionally, W_j controls the axial ratio in the low-frequency band. This is similar to the case when W_d of the L-shaped element is varied, where increasing W_j increases the gap length between the L-shaped and T-shaped elements. Similarly to Figure 16b, when the gap length is changed, only the axial ratio changes while maintaining the frequency at a minimum axial ratio in the low-frequency band. This indicates that the gap length is important for axial ratio adjustment in the low-frequency band.

For dual-band antennas, control of the ratio between the two frequencies is important. In particular, geometric parameters that allow the tuning of only one frequency while keeping the other frequency fixed are crucial in antenna design. As a result of the above discussion regarding Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20, it was confirmed that L_b and L_e are effective for controlling the low- and high-frequency bands, respectively. Next, the frequency ratio and frequency bandwidth controlled by L_b and L_e are investigated.

For circularly polarized antennas, the frequency band where the axial ratio is below 3 dB and |S₁₁| is below −10 dB is important. Therefore, Figure 21 and Figure 22 show the center frequencies, the ratio of the two center frequencies, and the frequency bandwidth where the axial ratio is below 3 dB and |S₁₁| is below −10 dB when L_b and L_e are varied.

It is found that the center frequency in the low-frequency band can be largely controlled by L_b, while the center frequency in the high-frequency band can be largely controlled by L_e. Within the range of L_b and L_e shown in Figure 21 and Figure 22, good impedance matching is achieved; the frequency bandwidth is also more than 4%. Additionally, f_H/f_L achieves dual-band single-sense CP in a wide range from 1.15 to 1.45. A value of f_H/f_L lower than 1.2 was not achieved in the references in Table 1, making the proposed antenna very effective compared to other references in terms of the variable range of f_H/f_L.

As shown above, the two frequency ratios can be reduced by L_b and L_e, and it is also possible to combine the two frequency bands into one by adjusting the combination of L_b and L_e. Figure 23 shows the simulated results at L_b = L_e = 8 mm. By merging the two frequency bands into one, the frequency bandwidth with a 10 dB impedance with a 3 dB axial ratio is 17.4% (2.76–3.29 GHz). The design of a wideband circularly polarized antenna is also possible.

6. Conclusions

A compact printed hybrid-mode antenna for dual-band single-sense CP was proposed in this study. The proposed antenna consists of a T-shaped element and an L-shaped element. The T-shaped element is connected to the feeding line and the L-shaped element is connected to the ground. The geometry of the antenna is very simple and the size of the antenna is compact. Through simulation, the hybrid mode for dual-band single-sense CP was elucidated. The proposed antenna has good circularly polarized performance. Using CMA, the relationship between the antenna components and resonance was clarified. As a result, it was shown that the antenna operates as a quarter-wavelength antenna in the low-frequency band and as a half-wavelength antenna in the high-frequency band. Through a parametric study, it was found the ratio between the center frequencies of the high- and low-frequency bands of the proposed antenna can be widely adjusted, even enabling the design of an antenna in the low-ratio region, where such a design was not possible in other research.

The simulated |S₁₁|, axial ratio, radiation pattern, and absolute gain were compared with the measurement results, and both showed good agreement. These results validate the present study.

The proposed antenna is not suitable for direct integration into handheld devices because nearby objects degrade the CP performance. Instead, it should be positioned away from the device using a coaxial cable. Due to its narrow CP radiation angle, the antenna has limitations for omnidirectional communication. However, it is well suited for fixed installations in open environments such as agricultural monitoring and environmental sensing, where high-quality directional communication is required. The dual-band characteristics enable efficient data collection from sensors at different frequencies, maximizing the antenna’s dual-band CP capabilities.