Characteristic Mode Analysis of Circular Microstrip Patch Antenna and Its Application to Pattern Diversity Design

In this paper, a highly-isolated microstrip patch antenna (MPA) is presented for pattern diversity applications. The physical insight of MPA is investigated without the influence of external exciter by using the theory of characteristic modes (TCMs). Shorting pins are added to manipulate the resonant frequencies of eigenmodes. TM11, TM01, and TM02 modes are clearly tracked and identified. For the first time, all the three modes are simultaneously utilized to enhance the performances of MPA. To be specific, TM01 and TM02 modes have conical pattern, thus are combined to increase the bandwidth, while TM11 mode has broadside pattern, and is used to provide pattern diversity. A two-port feed network, consisting of probe feed and aperture coupling, is designed to excite the three modes. The measured −10 dB bandwidth of the two ports is 720 MHz and 130 MHz. The simulated port isolation reaches 42 dB, and the measured value is higher than 27 dB. The proposed MPA has the advantages of clear operating principle, flexible mode tuning and high port isolation, thus is attractive in MIMO systems.


I. INTRODUCTION
Microstrip patch antennas (MPAs) are popular in various wireless applications due to the merits of low profile, low cost, and planar structure [1]. There are rich resonating modes available in this kind of antennas. It is easy to excite the TM modes of MPA to produce broadside or conical (or omnidirectional) radiation patterns. For example, the TM 10 mode of rectangular patch and the TM 01 mode of circular patch are often used to generate broadside and conical radiation patterns [2], [3]. Apart from single mode, two or more modes are merged to achieve multiple functions, such as dual-band [4], wideband [5], circular polarization [6], dual polarization [7], and pattern diversity [8]. The combination of multiple modes is very cost-effective to improve the performances of MPA.
Adding shorting pins between the microstrip radiator and the ground plane attracts great interest, since it introduces additional degree of freedom to tune the modes of MPA. One widely used application is shifting the resonant frequencies of modes, so that two modes with similar radiation patterns can The associate editor coordinating the review of this manuscript and approving it for publication was Shah Nawaz Burokur . be combined to increase the bandwidth [9]- [12]. For instance, in [9], both the TM 01 and TM 02 modes of circular patch are used to produce conical radiation patterns. The resonant frequencies of the two modes are pulled close by introducing shorting pins. Other applications of the shorting pins include enhancing the peak gain [13], [14], reducing the cross polarization [15], [16], increasing the beamwidth [17], suppressing the harmonic radiation [18], steering the null [19], and achieving pattern diversity [20]. For example, in [20], broadside and conical patterns are generated by the TM 11 and TM 01 modes. Shorting pins are introduced to make sure the two modes have the same frequency band.
Cavity model is widely adopted to analyze the modes of MPA [21], [22]. In this model, the open boundary is assumed to be perfect magnetic conductor (PMC). So the electric field in the cavity is perpendicular with the cavity. This method provides a simple way to observe the mode behavior of MPA, but has difficulty in analyzing shorting pins, because the number of shorting pins in practical model is discrete. In [14], the equivalent circuit of shorting pins in circular patch cavity is studied, and the mechanism for gain enhancement is revealed. However, it uses continuous annular metallic wall to represent the shorting pins. Thin-wire shortcircuited wall is used in [23] to increase the accuracy, but the shorting pins still need to be densely arranged. The calculation error will be large when the number of shorting pins is small.
The theory of characteristic mode (TCM) provides another straightforward way to observe the modes of MPA. This theory is based on the Method of Moments (MoM), thus is universal for all kinds of antennas [24]. One big advantage of this method is that the internal eigenmode of the radiator can be analyzed without the influence of external exciter. The physical insight of mode behavior is clear. In addition, the orthogonality of eigenmodes is useful to achieve multi-inputmulti-output (MIMO) function. In the last decade, TCM has been widely used in smartphone antenna designs. Multiple chassis modes of the smartphone are excited to broaden the bandwidth or provide MIMO operation [25]- [27]. Recently, TCM has been used in microstrip antenna designs [28]- [35]. For example, the eigenmodes of E-shaped patch and U-slot patch are depicted in [28]- [31]. The influence of the exciter on eigenmodes is analyzed in detail. What's more, discrete number of shorting pins can also be evaluated. For instance, in [33], the effect of shorting pins on reducing out-of-band mutual coupling is presented. In [35], a dual-polarized patch antenna is proposed with eigenmode analysis. Finite number of shorting pins is used to enhance the bandwidth of higher order modes. However, to the best of the authors' knowledge, the effect of shorting pins on circular patch model has not been analyzed with TCM.
Pattern diversity, also known as angle diversity, is widely used in MIMO communications, which is usually achieved by generating broadside and conical patterns at the same time. High port isolation is preferred to provide unrelated wireless channels. In this paper, multiple eigenmodes of circular patch are used to design wideband highly-isolated pattern diversity antenna. Based on TCM, the resonances of TM 01 , TM 02 , and TM 11 modes are tracked in a wide frequency range without the influence of external exciter. Here, the concept of mode merging refers to the fact that multiple modes are utilized simultaneously to improve the performances of antenna. To be specific, TM 01 and TM 02 modes are merged to produce conical radiation patterns, while TM 11 mode is utilized to produce broadside radiation patterns. Hybrid feed technique, including probe feed and aperture coupling, is designed to excite the two radiation patterns. The port isolation can achieve 40 dB. The rest of the contents are organized as follow. In Section II, the eigenmodes of the circular MPA with shorting pins are identified. The effect of the shorting pins on TM 01 , TM 02 , and TM 11 modes is analyzed in detail. In Section III, a compact two-port MPA is designed for pattern diversity. TM 01 , TM 02 , and TM 11 modes are simultaneously excited to generate broadside and conical radiation patterns. Two feed schemes are compared to achieve high port isolation. In Section IV, a practical prototype is fabricated and measured. Finally, the conclusion is drawn in Section V.

II. EIGENMODES OF MPA WITH SHORING PINS
In order to analyze the internal modes of MPA, microstrip radiator without external exciter is discussed. Fig. 1 shows the geometry of the MPA. It consists of a circular patch, an annular column of shorting pins, a ground plane, and a single layer of substrate. The substrate is made of RO4003C (ε r = 3.55, tanδ = 0.002), with thickness of 1.524 mm. The circular patch and the ground plane are printed on the top and bottom sides of the substrate, respectively. There are 9 shorting pins that are uniformly placed with respect to the center. The fabrication of the model is easy, since standard PCB technique is adopted. Table 1 lists the parameters of the model. The radius of the circular patch, the offset distance between the shorting pins and the center of the circular patch, the diameter of the shorting pins, and the number of the shorting pins are four key parameters that determine the mode performance of the MPA.

A. EQUIVALENT CIRCUIT MODEL
The equivalent circuit model (ECM) of the proposed circular MPA is analyzed firstly. According to the transmission line theory, the ECM of circular MPA without shorting pins has been derived in [36]. However, the ECM becomes complex when discrete shorting pins are annularly placed. In order to evaluate the effect of the shorting pins, the ECM of the MPA model has been modified, as shown in Fig. 2. Considering that the shorting pins are located between the center and the edge of the circular patch, an additional RLC circuit is added to represent the loading effect of the shorting pins [14]. Then, the resonant frequency of the circular MPA with n shorting pins can be calculated using equation (1).
2400 VOLUME 10, 2022 where L a and C a are obtained from L 1 ||L 2 and C 1 ||C 2 . L p , L c , C p , and C m are determined by the physical parameters of the shorting pins. ECM provides a straightforward way to analyze the effect of the shorting pins on MPA. However, the calculation of the parameters is difficult, especially for multiple modes, since the shorting pins are discretely distributed.

B. EIGENMODE IDENTIFICATION
Comparing with ECM, TCM is simpler and more accurate to analyze the loading effect of finite number of shorting pins. The theory of this method has been presented in many literatures [37], thus is not shown in this paper for brevity. Here, only one quantity, namely the modal significance (MS), is considered to evaluate the mode performance. The definition of MS is as follows: where λ n is the eigenvalue of the n-th mode. λ n represents the ratio of stored energy to radiated energy of the n-th mode. λ n will be zero when all the energy is radiated. As is shown in Equation (1), MS maps the [−∞, +∞] value range of λ n into the normalized range of [0, 1]. MS equals to 1 when all the energy is radiated, and equals to 0 when all the energy is stored. The maximal value of MS determines the resonant frequency of the mode. It provides a convenient way to evaluate the eigenmode performance. The more the value approaches to 1, the stronger the radiating ability is. In practical engineering applications, we usually use MS ≥ 1/ √ 2 to define the available bandwidth. Therefore, MS represents not only the radiating ability, but also the bandwidth potential of the mode.
Full wave simulation software CST ver. 2019 is applied to calculate the eigenmodes of the circular patch model, where CM analysis has been integrated in the Multilayer Solver. The size of the ground plane is assumed to be infinite in the calculation. The MS of the microstrip circular patch model with shorting pins is analyzed in wide frequency band. Fig. 3 shows the first three eigenmodes that can be resonant in the concerned frequency band. According to the peak value of MS, the resonant frequencies of the three modes are at 3.42 GHz, 4.44 GHz, 5.25 GHz, respectively. The bandwidth of the mode increases, as frequency increases. It is noted that there is a degenerate mode at the second resonance.  This mode has orthogonal polarization with mode 2, and is not discussed for brevity.
The eigencurrents are observed to identify the eigenmodes of the radiator. Fig. 4 shows the currents distribution on the circular patch at the three resonances. In Fig. 4(a), it is seen that the currents are along the radial axis, and the directions of the currents at the inner side and outside of the shorting pins are opposite. This distribution indicates that mode 1 is the TM 01 mode. In Fig. 4(b), the currents are mainly along the horizontal direction, and the currents at the left edge and right edge have the same direction. It implies that mode 2 is the TM 11 mode. In Fig. 4(c), the currents are along the radial axis, which is similar with mode 1. However, the directions at the inner and outer sides of the shorting pins are the same, rather than opposite. It indicates that mode 3 is the TM 02 mode. By observing the eigencurrents distribution, all the three eigenmodes are clearly identified.
The far fields of the three modes are analyzed to further verify the mode identification. Fig. 5 shows the 3-D radiation VOLUME 10, 2022  patterns of the three modes at their resonant frequencies. It is shown that TM 01 and TM 02 modes have conical radiation patterns, while TM 11 mode has broadside radiation patterns. The peak gains of the three modes are 5.0 dBi, 9.8 dBi, and 4.8 dBi, respectively. These observations also verify the identification of the three modes.

C. PARAMETER ANALYSIS
The unit cell of the proposed MPA is analyzed by sweeping the key parameters. As listed in Table 1, there are four parameters that affect the structure of the model. The effect of these parameters on MS is studied to tune the resonant frequencies of TM 01 TM 02 and TM 11 modes. Fig. 6 shows the effect of the radius of the circular patch (r o ) on the MS of the three modes. It is seen that increasing r o can effectively decrease the resonant frequencies of all the three modes. Figs. 7-9 analyzed the influence of the shorting pins in detail. As shown in Fig. 7, when the shorting pins move towards the center of the circular patch, the resonant frequencies of TM 11 mode and TM 02 mode shift downward, while the resonant frequency of TM 01 mode   stays stable. In Fig. 8, the influence of the diameter of the shorting pins (D) is studied. It is shown that decreasing D can effectively decrease the resonant frequencies of TM 11 mode and TM 01 mode, while has little effect on TM 02 mode. Fig. 9 discusses the number of shorting pins (N ). As N increases, the resonant frequencies of both the TM 11 mode and TM 01 mode shift upward, while the resonant frequencies of TM 02 mode stays stable.
From the parameter analysis above, it is concluded that the resonant frequencies of the three modes can be effectively shifted by changing the parameters of the shorting pins. Although each mode cannot be tuned independently, the multiple parameters provide sufficient degrees of freedom to control the resonant frequencies of the modes. For example, r s only affects TM 11 and TM 02 modes, N only affects TM 01 and TM 11 modes. In the following sub-section, the multiple modes will be manipulated so that they can enhance the antenna performance.

D. COOPERATION OF MULTIPLE EIGENMODES
Considering that TM 01 and TM 02 modes have conical pattern, and TM 11 mode has broadside pattern, the possible idea of mode cooperation can be: (i) Wideband by merging TM 01 and TM 02 modes; (ii) Pattern diversity by merging TM 11 and TM 01 (or TM 02 ) modes; (iii) Wideband and pattern diversity by merging TM 01 , TM 02 and TM 11 modes. Obviously, the third type has the best performances.
It is necessary to move the resonating frequencies of the multiple modes so that they will be close to each other. Based on the parameter analysis, the number of the shorting pins is further investigated. Fig. 10 shows the resonant frequencies of TM 11 , TM 01 , TM 02 modes with different number of shorting pins. As N increases, the resonant frequencies of TM 11 mode and TM 01 mode increases rapidly, while the frequency increase of TM 02 mode is insignificant. The resonant frequencies of TM 11 mode and TM 01 mode are close to each other, when the number is near 18. The frequencies of all the modes become stable when the number is higher than 21. Because the dense arrangement of shorting pins resembles continuous metallic wall. It is also shown that the resonant frequency of TM 01 mode is always lower than that of TM 11 mode. Thus, it is impossible to utilize the two modes to achieve pattern diversity at the same frequency.
After loading proper number of shorting pins, the TM 01 , TM 02 and TM 11 modes can be utilized simultaneously. Fig. 11 depicts the cooperation process of the three modes. On the one hand, the bandwidths of TM 01 and TM 02 modes are merged to obtain wideband operation. Both modes can generate conical radiation patterns. On the other hand, the resonant frequency of the TM 11 mode is designated to be the same as that of the TM 02 mode. Considering that TM 11 mode can generate broadside radiation patterns, pattern diversity function can be achieved when the two patterns are excited independently. Such kinds of pattern diversity can provide signals in half hemisphere. The wide angle coverage ability is promising for indoor WLAN applications. Fig. 12 illustrates the algorithm for the proposed antenna design. In the beginning, conventional MPA without shorting pins is studied. The eigenmodes of the model are calculated based on CM analysis. If the resonant frequencies of TM 01 , TM 02 , and TM 11 modes are not close to each other, it will increase the number of shorting pins and carry out iteration. If the three modes can be merged, it will design a twoport feed network for the three modes to achieve pattern diversity.

III. PATTERN DIVERSITY ANTENNA DESIGN
As shown in Fig. 4, the eigcurrents of TM 01 and TM 02 modes are along the radial axis. To obtain conical radiation pattern, the proper feed location for the two modes should be at the center of the circular patch. The eigcurrents of TM 11 mode are along the horizontal direction. To obtain broadside radiation pattern, the proper feed location for this mode should have some offset distance from the center point. With this scheme, a two-port feed network can be designed to excite the three modes simultaneously.
Probe feed is a simple way to excite the modes of microstrip antenna. In the beginning, two probe feeders are  directly added to achieve two-port design. Fig. 13(a) shows the geometry of the circular patch model with two probe feeders. One probe feeder is located at the center of the circular patch, and the other probe feeder is placed in the y-axis. Fullwave simulation software HFSS ver. 2019 is used to optimize the parameters. In the simulation, the boundaries are open space and have a distance of λ/4 from the model. The minimal far field distance is 0.22 m. The offset distance, s, is 13.8 mm. The number of shorting pins is 18. The ground plane has finite size, which is 56 × 56 mm 2 . Some parameters of the MPA model are slightly changed. That is, r s = 12.4 mm, D = 0.5 mm, r o = 18 mm. Fig. 14 shows the simulated S parameters of the two-port antenna. The impedance bandwidth of Port 1 is wide. There are two resonances at 4.75 GHz and 5.15 GHz, which are generated by TM 01 mode and TM 02 mode. For Port 2 excitation, there is only one resonance generated by TM 11 mode. Considering that the bandwidth of a single mode is limited, the bandwidth of Port 2 is relatively narrow. In this way, three modes are effectively excited. However, the port isolation is poor, which is merely 11 dB in the overlapping bandwidth. It is known that the eigenmodes are naturally orthogonal, so the mutual coupling is attributed to the introduction of the two feeders. Port 2 is offset from the center, which deteriorates the symmetry of the structure. Further effort is needed to improve the port isolation.
Aperture coupling is another typical way to excite the modes of microstrip antenna. It has more degrees of freedom than probe feed, so the impedance matching is easier. The influence of this feeder on antenna symmetry might be low, since the feed line does not contact with the circular patch directly. Fig. 13(b) shows the modified geometry of the microstrip antenna. The probe feeder of Port 2 is replaced by aperture coupling feeder. The two feeders consist of a probeaperture hybrid feed scheme. The H-shaped aperture is etched on the ground plane. A small piece of substrate is added below the ground plane, where an L-shaped microstrip line is printed on the bottom of the substrate. The substrate is made of 0.508-mm-thick RO4003C. The characteristic impedance of the feed line is 50 . The optimized parameters are as follows: p = 11 mm, l 1 = 8.4 mm, l 2 = 5 mm, l 3 = 1.6 mm, w = 0.8 mm. The other parameters are the same as those of the antenna with two probe feeders.
As shown in Fig. 14, the port isolation is quite different, when aperture coupling feeder is used. The value is above 40 dB in the overlapping bandwidth, which is greatly larger than the 11 dB in two-probe feed scheme. The comparison implies that using aperture coupling to replace the probe for Port 2 is effective to improve the port isolation. The hybrid feed scheme will be adopted in the final design.
The merging process of TM 01 and TM 02 modes is shown in Fig. 15. The resonant frequency of TM 01 mode increases, while that of TM 02 mode stays stable, when the number of shorting pins (N ) increases. The resonant depth of both modes also becomes deeper. Using the −10 dB criterion, the bandwidths provided by the two modes can be merged, thus achieving wide bandwidth. Fig. 16 shows the simulated surface currents on the circular patch. Two modes will be excited when Port 1 works. The corresponding currents are shown in Fig. 16(a) and Fig. 16(b). Comparing with the eigencurrents in Fig. 4, the two modes have similar currents distribution with TM 01 and TM 02 modes, where the currents are along the radial axis, and are out of phase and in phase at the inner and outer sides of the shoring pins, respectively. One mode will be excited when Port 2 works. The currents in Fig. 16(c) resemble the eigencurrents of TM 11 mode, where the currents are along the vertical direction. Observing from the currents distribution, the identification of the three modes are further verified.
By adding a column of shorting pins and adopting probeaperture hybrid feeding structure, the proposed antenna has  significant advantages over the traditional microstrip antenna in utilizing the number of modes and port isolation.

IV. EXPERIMENTAL RESULTS
The prototype of the two-port MPA is fabricated and measured. Fig. 17 shows the photograph of the prototype. It has two layers of RO4003C substrate, with sizes of 56 × 56 mm 2 and 20 × 20 mm 2 , respectively. Four plastic screws are used to assemble the two layers together. Two SMA connectors are soldered at the bottom and edge of the board. Fig. 18 shows the simulated and measured S parameters of the two-port MPA prototype. The simulated and measured reflection coefficients show reasonable agreement. There are two resonances for Port 1 excitation, and one resonance for Port 2 excitation. The measured −10 dB bandwidth of the two ports is 720 MHz (4.53-5.25 GHz) and 130 MHz (5.09-5.21 GHz) respectively. The measured port isolation is worse than the simulated value. It may be caused by fabrication error and assembling error. However, the measured port isolation is still higher than 27 dB, which is sufficiently high.  The radiation patterns of the antenna are measured in a far field chamber. During the measurement, when one port is connected with the VNA, the other port is terminated with 50 load. The simulated and measured normalized radiation patterns with Port 1 and Port 2 excitations are shown in Fig. 19. Good agreement can be observed from the simulated and measured results. The radiation patterns have conical shape, when Port 1 is excited. The main beam is up tilted due to the influence of the ground plane On the other hand, broadside radiation patterns are observed in the two principal planes when Port 2 is excited. It is also shown that the measured cross polarizations are worse than the simulated ones, but are still below −18 dB in both planes. Fig. 20 shows the simulated and measured peak gains with frequency variation. For Port 1 excitation, the beam direction is at about 40 • . It is seen that the peak gain is 4.8 dBi, and the gain variation is within 1 dB across the bandwidth. For Port 2 excitation, the gain at the broadside direction is 9.5 dBi.    This value is larger than that of conventional patch antenna without shorting pins. It implies that the shorting pins can also increase the gain of MPA, since the radiating aperture is enlarged. Fig. 21 shows the simulated radiation efficiency of the two ports. In the −10 dB impedance bandwidth, the radiation efficiency of Port 1 and Port 2 is higher than 81% and 77%, respectively. The different values of radiation efficiency with the two port excitations are caused by the fact that different modes have different radiating ability. Table 2 compares the proposed antenna with other circular MPAs that have annular column of shorting pins. Comparing with the referenced designs, the proposed antenna can excite the maximal number of modes simultaneously, and multiple functions of wideband and pattern diversity. Although [18] can also excite 3 modes, it needs 3 radiators, thus the antenna structure is bulky.

V. CONCLUSION
In this paper, multiple eigenmodes of circular MPA with shorting pins are analyzed based on characteristic mode analysis. Key parameters of the shorting pins are studied in detail. Three modes, namely TM 11 , TM 01 , TM 02 modes, are simultaneously utilized to enhance the performances of the MPA. The bandwidth of TM 01 and TM 02 modes are merged to provide wide bandwidth with conical radiation patterns, while TM 11 mode is used to generate broadside radiation patterns, thus achieving pattern diversity. A simple two-port feed network is designed to excite the three modes simultaneously. High port isolation is achieved by using probe-aperture hybrid feed. The measured bandwidth is 720 MHz for conical pattern, and is 130 MHz for broadside pattern. The measured port isolation is above 27 dB. With the advantages of flexible mode tuning, wide bandwidth, high port isolation, and pattern diversity, the proposed MPA has great potential in MIMO communications.