# Mutual Coupling Reduction between Two Closely Spaced Antennas with a General PMC Symmetry Plane for Mobile Terminals

Authors: Yijiao Fang; Jiangwei Zhong; Yao Nie; Maosheng Fu
Journal: International Journal of Antennas and Propagation
 (2023)

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## Abstract

In this paper, an artificial general perfect magnetic conductor (PMC) decoupling structure is proposed to improve the isolation between two-element closely spaced antenna arrays with an operating frequency around 2.4 GHz. This kind of PMC structure can effectively activate the in-phase coupling current and cancel the antiphase coupling current raised by the original perfect electric conductor (PEC) equivalent interface, thereby blocking the energy coupling from one antenna input port to another. The proposed design is composed of a transmission line and a lumped element in the neutral position of a pair of electrically small antennas. To validate the utility of this approach, we analyze the current/field distribution of this structure and the mode superposition mechanism in the present paper. The results show that, with a close center-to-center distance of 5 mm, the isolation between the arrays is improved from −5 dB to −20 dB at around 2.4 GHz. Furthermore, to validate the feature that this special in-phase coupling current distribution is insensitive to frequency, we analyze the decoupling performance in a frequency reconfiguration or a dual-frequencytwo-element antenna array. The decoupling feature emerges in the proposed structure over a larger frequency range (2.2–2.6 GHz) than the previous design. A sample of this two-element frequency reconfiguration antenna system is fabricated and measured in this paper. We also realized a dual-frequency antenna system with expected isolation. Through the above discussion, we can know that these decoupling geometrical parameters can be worked in the whole range of 2.2–2.6 GHz with the same decoupling structural parameters. Good performance and compact structures make the proposed structure suitable for mobile communication applications.


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## Body

## 1. Introduction

To satisfy more pressing needs for wireless channel capacity without increasing RF spectrum resources, multiple antennas were employed and widely used on the transmit or receive sides in mobile terminals [1–3]. Multiple antennas can be widely applied in diversity and multiple-input or multiple-output systems to provide multiple signal paths, thereby increasing the performance of mobile terminals. However, there is a serious impediment to this technology, which is the strong mutual coupling between these closely spaced antennas limited to the small size of mobile terminal devices. Strong mutual coupling can bring a series of problems, like the deterioration of the antenna efficiency and signal interference with each other.Recently, the decoupling technique has been given a lot of attention, and a wide range of approaches were proposed to suppress this closely spaced same-frequency interference. One of the primary solutions is proposed by employing metamaterial/metasurface structures [4–9] or PBG/EBG (photonic/electric bandgap) structures [10–14], which have band-stop characteristics. Another is to eliminate the original coupling surface current by introducing a balancing reverse current. It can be induced by a neutralization microstrip line [15], a parasitic element [16], or a decoupling network [17–24]. Apart from that, there are many other solutions used to eliminate coupling, for instance, self-decoupled elements [25] and high-order modes [26]. Lately, a simple and effective design guideline has also been proposed to provide an intuitive explanation of the decoupling phenomenon [27]. Furthermore, dual-band decoupling mechanisms have also been studied in a series of literature [28–30].Consulting the previous research, the mutual coupling reduction between two even more closely spaced antennas can be obtained with an excellent decoupling performance. However, most of the decoupling structures are designed in the order of half a specific wavelength, which can make the new branch of the coupling current have an extra 180-degree phase difference with the original one. From another perspective, the decoupling structure is an inverter efficient in a specific frequency. At the same time, a lot of efforts have also been made to realize a multiple-band decoupling system. For example, in the earliest study, superposition of single-band decoupling structures at different operating frequencies is introduced to achieve the multiple-band decoupling system [28], and beyond that, some optimized designs are proposed to realize a dual-band decoupling system in two discrete frequency bands [29, 30]. In this paper, we propose an efficient decoupling structure in which decoupling occurs over a continuous frequency range (2.2–2.6 GHz). It is suitably applied to the two-element frequency reconfiguration or multifrequency decoupling antenna system. In this paper, we realized a two-element frequency reconfiguration and a dual-frequency decoupling antenna system with expected isolation by using this mechanism.


## 2. Materials and Methods

The geometry of a conventional two-element antenna array and a proposed general PMC equivalent structure is shown in Figures1(a) and 1(b), respectively. This two-element antenna array consists of two symmetrical closely spaced electrically small antennas. When port 1 is excited as the input port, mutual coupling occurs and electromagnetic power flows along this PEC coupling path to the output port 2. The proposed PMC structure in Figure 1(b) is built by a symmetrical microstrip line structure with a grounded capacitor C or inductor L. Both of them can be considered two-port networks. However, the electromagnetic features of them are opposite.Figure 1
(a) The symmetric plane of the conventional antenna model without decoupling elements, which is equivalent to a perfect electric conductor (PEC). (b) The symmetric plane of the proposed general PMC equivalent structure, which is equivalent to a perfect magnetic conductor (PMC).
(a)(b)To briefly explain the different electromagnetic features between them, the surface current density distributions and theE-field/H-field distributions around the symmetric plane of these two structures are displayed in Figures 1(a) and 1(b), respectively. As we know, the dual case of the PEC boundary is as follows [31]:(1)n∧×E=0,andn∧•B=0.From Figure1(a), we can note that the E-field is perpendicular and that the H-field is parallel to the symmetric plane of the antenna array. It is obvious that the proposed structure satisfies the PEC boundary condition. Moreover, we can note that the currents on either side are in opposite directions.On the contrary, for the proposed PMC structure in Figure1(b), the E-field is parallel and the H-field is perpendicular to the symmetric plane. As we know, the dual case of the PMC boundary is as follows:(2)n∧×H=0,andn∧•D=0.It means that the symmetric plane in Figure1(b) can be considered a PMC plane. Moreover, we can note that the currents on either side are in the same direction.When the coupling path is a PMC surface, the surface current in the output side (right) moves in the same direction of the input side (left) without a phase change, in contrast to a 180 deg phase change from the PEC coupling path.To further understand the characteristics of the proposed PMC decoupling structure, the surface current density and electric field distributions are shown in Figures2(a) and 2(b) at around 2.4 GHz, respectively. Figures 2(a) and 2(b) represent the electromagnetic properties when the PMC decoupling structure has a grounded capacitor C = 3 pF or inductor L = 11 nH in the neutral position, respectively. The equivalent circuit model corresponding to the proposed PMC decoupling structure is also shown in Figures 2(a) and 2(b). From the above results, we can know that the proposed structure is a transformation of the microstrip line. The lumped elements C or L in the center ensure the mirror symmetry of the current.Figure 2
Surface current density and electric field distribution of the proposed artificial PMC decoupling structure. (a)C = 3 pF. (b) L = 11 nH.
(a)(b)Based on the previous studies [28], a 2-port network can be transformed into a combination of a common mode and differential mode. The common mode has the symmetrical current distribution which corresponds to the PMC structure in Figure 1(b). The differential mode has the antisymmetrical current distribution which corresponds to the PEC structure in Figure 1(a). The S-parameter relation is as follows [31]:(3)S11=Sc11+Sd112,(4)S21=Sc11−Sd112.In the above formula,Sc represents the S parameter of the common mode and Sd represents the S parameter of the differential mode. It can be seen from formula (4) that the proposed general PMC equivalent structure in Figure 1(b) can be introduced as a new path of coupling. Hence, the original coupling (shown in Figure 1(a)) can be canceled by the reverse current from the new path, and the isolation between the left and right antennas is improved.The geometry of a coupling reduction antenna system with the proposed PMC structure is shown in Figure3. The total antenna system is printed on a lossy FR4 dielectric substrate with a thickness of 0.6 mm. The ground plane is on the top surface, and the size is about 20 × 24 mm. Radiation elements and the decoupling structure of the proposed antenna system are also printed in the top half of the FR4 substrate. Each metal portion, including the ground and the antenna itself, is shown as a dark gray portion in Figure 3. The whole system comprises two closely spaced conventional planar antennas with d1 = 10 mm, d2 = 7 mm, d4 = 4 mm, w1 = 1 mm, w2 = 2 mm, and a decoupling structure. This decoupling structure is a composition of a microstrip line with length d3 = 5 mm, a grounded capacitor C or inductor L, and two impedance-matching inductors L1 = L2. The two antenna-feeding ports are all loaded with a 50 ohms load for impedance matching.In Figure 3, we can note that it is a left-right symmetric structure along the central plane. The microstrip line and grounded lumped elements C or L are all placed at the center of the two antennas. The width of the microstrip line is about 0.5 mm, and the height above the ground plane is also 0.5 mm. The simulated and measured results are shown and discussed in the following.Figure 3
Geometry of a coupling reduction antenna system with the proposed PMC structure.


## 3. Results and Discussion

For the geometry in Figure3, these simulated S-parameters corresponding to C = 3 pF and L = 11 nH are presented by full lines and dot lines in Figure 4, respectively. By comparison, S-parameters of the conventional two-element antenna system (shown in Figure 1(a)) are also studied and presented by the dot lines with a circle pattern in Figure 4(a). The S11/S22 results show a deep resonance frequency band around 2.4 GHz. We can see that, without a decoupling structure, the isolation between port 1 and port 2 (magnitude S21/S12) is around 5 dB. To improve the isolation between these two closely spaced antennas, we inserted a decoupling model in it. It can be observed that the isolation around a center frequency of 2.4 GHz is improved from 5 dB to better than 20 dB. Meanwhile, the corresponding return loss S11/S22 also has good performance.Figure 4
(a) SimulatedS-parameters of the conventional antenna model without the decoupling elements (dot lines with a circle) and the proposed isolation improvement system with the decoupling structure and C = 3 pF (full line) or L = 11 nH (dot line). (b) Isolation (S12/S21) at different L from 11 nH to 27 nH.
(a)(b)Isolation (S12/S21) at different L from 11 nH to 27 nH is also investigated and shown in Figure 4(b).Input-resistant matching is all improved byL1 and L2. For the grounded capacitor C, L1 = L2 = 1 nH. For the inductor L, L1 and L2 are equal to infinity. In this case, L1 and L2 can be removed.Generally, for a previous decoupling model, the center decoupling frequency is sensitive to the resonance frequency of the decoupling structure. This operating frequency is always a one-to-one match with certain dimensions of the decoupling structure and certain values of the lumped elements. In the present paper, this type of transmission line structure has obvious decoupling properties and is insensitive to frequency variations. This feature shows that the method is effective and has potential applications in the decoupling of frequency reconfiguration (or multifrequency) two-element antenna arrays.A sample of a frequency reconfiguration isolation improvement system is fabricated and shown in Figure5, and a comparison of the simulated and measured S-parameters of the proposed system is displayed in Figure 6. It could be seen that both the theoretical and experimental results confirm our expectations. As shown in Figure 6(a), for a closely spaced two-element frequency reconfiguration antenna system, we insert a fixed-parameter decoupling structure with the parameters same as above Figure 3 with C = 3 pF. These frequency reconfiguration antennas can operate from 2.3 GHz to 2.5 GHz by changing the length D at the end of the antenna branch. It is interesting to observe that the isolation improvement occurs at different operating frequencies but with the same decoupling parameters. This means that the proposed decoupling model keeps the same in phase. Current distribution in this range of frequencies canceled the original coupling current. The decoupling mechanism is effective.Figure 5
Photograph of the proposed frequency-reconfiguration decoupling antenna system.Figure 6
(a)S-parameters of the proposed frequency-reconfiguration decoupling antenna with different D (simulated and measured). (b) Antenna efficiency (measured). (c) 2D radiation gain (simulated). (d) ECC (simulated) at 2.44 GHz for D = 10 mm.
(a)(b)(c)(d)Furthermore, the efficiency, 2D radiation gain, and ECC for the frequency reconfiguration antenna system are shown in Figures6(b) and 6(d). The antenna efficiency is around 50%. In Figure 6(c), we note the 2D radiation gain before and after inserting the decoupling structure. The radiation patterns with the decoupling structure have a stronger forward radiation pattern. It means that mutual coupling is weakened by the decoupling structure. Besides this, it is observed that the main lobe of the 2D radiation pattern of port 1 is perpendicular to the one of port 2.To further reveal the general decoupling characteristics of the proposed isolation improvement system, a dual-frequencytwo-element antenna array is also designed and analyzed in Figures7 and 8. The antenna radiation elements consist of two meandered branches with different lengths. Therefore, the two antenna radiation resonances occur at around 2.2 GHz and 2.6 GHz, respectively. A coupling structure with L1 = L2 = 1 nH and C = 3 pF is inserted at the central area of these two symmetric dual-frequency antennas and then makes an improvement of S21/S12 values to a high level as low as −25 dB. In the meantime, the values of S11/S22 around these two resonance frequencies can also maintain original radiation performance. In conclusion, this dual-frequencytwo-element antenna array has expected high isolation in all two bands.Figure 7
Geometry of the proposed dual-frequency decoupling antenna system.Figure 8
S-parameters versus frequency for dual-frequency decoupling antennas.Based on the abovementioned results, we can conclude that, in the proposed transmission line-like decoupling structure, the surface current andE-field distributions are central symmetry. When the lumped element is a capacitor C, the E-field reaches the maximum value at the center of the symmetry structure. On the contrary, when the lumped element is an inductor L, the E-field reaches the minimum value at the center of the symmetry structure. The electric field direction is along the symmetry plane. The vertical component of the electric field is zero. In either case, the symmetry plane of part one can be regarded as a PMC equivalent interface. This PMC interface is shown to have a property of frequency insensitivity. So in conclusion, the proposed prototype has the characteristics of an equivalent PMC interface and the symmetrical field distribution and in-phase surface current. This means that this structure has many potential Internet applications in multifrequency applications.


### 3.1. Comparison

Table1 compares the proposed decoupling structure with other decoupling methods. By comparison with different decoupling methods in the recent literature, such as EBG, decoupling networks, and parasitic elements, proposed decoupling has obvious advantages in operating bandwidth and center-to-center distance. Moreover, Table 1 also shows that this method has a great contribution to isolation improvement.Table 1
Comparisons of the decoupling performance between antenna arrays.
RefDecoupling schemesBW (%)IsolationMax. gainCenter-to-center distance[12]EBG∼2>20 dB—∼0.50λ0[15]Neutralization line∼5>20 dB2.1 dB∼0.50λ0[25]High-order modes∼3>20 dB7 dB∼0.50λ0[27]Extra coupling path∼5.5>15 dB7.8 dB∼0.44λ0ProposedExtra coupling path∼5>20 dB1.6 dB∼0.3λ0


## 3.1. Comparison

Table1 compares the proposed decoupling structure with other decoupling methods. By comparison with different decoupling methods in the recent literature, such as EBG, decoupling networks, and parasitic elements, proposed decoupling has obvious advantages in operating bandwidth and center-to-center distance. Moreover, Table 1 also shows that this method has a great contribution to isolation improvement.Table 1
Comparisons of the decoupling performance between antenna arrays.
RefDecoupling schemesBW (%)IsolationMax. gainCenter-to-center distance[12]EBG∼2>20 dB—∼0.50λ0[15]Neutralization line∼5>20 dB2.1 dB∼0.50λ0[25]High-order modes∼3>20 dB7 dB∼0.50λ0[27]Extra coupling path∼5.5>15 dB7.8 dB∼0.44λ0ProposedExtra coupling path∼5>20 dB1.6 dB∼0.3λ0


## 4. Conclusion

In this paper, we proposed a novel decoupling structure by using a PMC equivalent interface. We analyze its special in-phase coupling current at around 2.4 GHz. Isolation is improved by this kind of reversed coupling current against the original coupling current. Besides this, this special in-phase coupling current can also be excited over a continuous frequency range (in the condition ofd3 = 5 mm L = 11 nH, the frequency range is about 2.2–2.6 GHz). To prove this, we realized a two-element frequency reconfiguration antenna system and a two-elementdual-frequency antenna system to explore more applications.To summarize, the most obvious advantages of the proposed approach are simple to implement, excellent isolation (>20 dB), and larger bandwidth (∼5%). The measured antenna efficiency is about 50%, and the measured ECC is less than 0.005. It has also shown great potential for applications in multiband antenna arrays or frequency reconfiguration antenna arrays. This new approach is an attractive solution for suppressing antenna mutual interference. The simple and efficient decoupling structure makes it applicable to the electrically small antenna design of compact and miniaturized devices such as mobile terminal devices.



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*Source: 2343818-2023-02-24.xml*