Metal-Frame Antenna for Big-Screen Smartphones Using Characteristic Mode Analysis

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I. INTRODUCTION
Smartphones are prevalent nowadays.They are increasingly intelligent and becoming convenient digital assistants in daily life.Ever since the iPhone 4 in 2010, the metal-frame antennas have been widely used in the smartphone design.This technique effectively expands the size of the antenna, making it no more confined to a small space inside the smartphone body [1].
However, in a recent couple of years, one clear trend for smartphones is the increasing of their screen-to-body ratios.Smartphones with big-screen or even full-screen (also called all-screen or bezel-less) become popular [2].In these smartphones, the screen's border width is shortened to only a couple of millimeters [3], [4].Due to the small spacing between the screen and the metal-frame antenna, they are strongly coupled.The antenna's performance is significantly degraded, especially the significantly narrowed bandwidth, The associate editor coordinating the review of this article and approving it for publication was Hassan Tariq Chattha.as analyzed in [5].In Section III of this paper, this conclusion is also validated by the characteristic mode analysis.This result theoretically proves the common experience of antenna designers that the narrower the screen's spacing, the more difficult to achieve wide bandwidth of the metal-frame antennas in big-screen smartphones [6].Thus, this problem needs to be addressed urgently.
Numerous researches have been conducted on metal-frame smartphone antennas [7]- [14].To the authors' best knowledge, the screen panel has not been considered independently in these designs.One possible reason is that previously the screen is far from the metal-frame, e.g. 10 mm.The effect of the screen could, to some extent, be neglected.In this condition, the classical PIFA, monopole, or loop antenna theory [15] could be directly applied in analyzing these antennas.However, for antennas in big-screen smartphones, due to the non-negligible electromagnetic effect of the screen panel, the antenna's ''ground'' of single-layer printed circuit board (PCB) turns to the ''ground'' of the connected parallel screen and PCB.In this situation, it is not suitable to apply the classical analysis methods directly.Based on the above reason, we resort to the theory of characteristic modes (TCM).
In this paper, we proposed the methodology of antenna design for big-screen smartphones by TCM.The antenna has the chassis modes (CMs) and the frame modes (FMs).All the modes of these two kinds are analyzed.Then, we selectively excited the above-mentioned CMs and FMs.By merging the characteristic modes [16], [17], the narrowed bandwidth affected by the screen panel could be expanded again.The simulated and measured results show this antenna can cover the frequency bands of 824-960 MHz (GSM850/900), 1452-1496 MHz (LTE1500), 1710-2690 MHz (DCS, PCS, UMTS2100, LTE2300/2500), and 3400-3600 MHz (3.5 GHz 5G).The gap widths of the screen and the copper clad PCB to the metal frame are compared in Table 1 between the existing literature and the proposed one.The antenna efficiencies are also compared.This method devotes a simple structure to the final deliverable of the multiple-band antenna.It gives the advantage for expanding the narrowed operating bandwidth due to the very close screen for present big-screen smartphone antennas.

II. CHARACTERISTIC MODE ANALYSIS
TCM is firstly developed by Garbacz and then refined by Harrington and Mautz [18], [19].It could provide the radiating modes of an arbitrarily-shaped metallic structure, without considering the feeding arrangement.These radiating modes, known as characteristic modes, bring physical insight into the radiating phenomena of the antenna [16], [20], [21].Characteristic modes are obtained by solving an eigenvalue equation that is derived from the method of moments.
where X and R are the imaginary and real parts of an impedance matrix Z .J n denotes the eigencurrent of n-th mode on the structure, and λ n is the corresponding eigenvalue.The current on a conductive surface can be expressed as a linear superposition of the normalized eigencurrents.The corresponding characteristic angle can be computed from At a given frequency, we can determine whether or not characteristic modes are good radiators by looking at their characteristic angles.When the eigenvalue λ n approaches zero, or the characteristic angle approaches 180 • , the mode is at resonance.
Present smartphones have different sizes and inner structures.In this paper, we generally make iPhone 8, which is released in 2017 [22], as a reference for the basic structures.In this smartphone, the screen assembly and the system PCB are separated with a certain distance.The screen almost takes the whole front side of the smartphone.The system PCB is fixed by metallic screws to the rectangular metallic middle frame for good grounding.The size of the middle frame is almost the same as the smartphone's external length and width.From this structure, we can see that for many smartphones, even though the size of the system PCB is getting smaller and smaller, the ground of the antenna model could still be analyzed as full size.The definition of the antenna's ground has expanded from the system PCB to the smartphone's metallic middle frame.However, in this paper, we still use the name of PCB for the continuity of terminologies in academic studies.
For this structure, the antenna will have both chassis modes and frame modes: The screen of smartphones is usually a rectangularly shaped structure with only two or three millimeters thick, but assembled by multiple layers, including the glass cover, touch panel, liquid crystal display (LCD), backlight, and metal cover plate (from outside to inside), which make the screen a sandwich structure.As analyzed in [5], this multi-layer screen assembly is simplified and modeled as a single layer PCB.
The screen panel is parallel and above to the system PCB and electrically connects the PCB by the flexible printed circuit (FPC).FPCs are widely used for interconnecting components to transmit and receive signals in consumer electronic products.In this paper, the FPC is simplified and modeled as a conductive narrow strip connecting the screen and the PCB [5].The external height and width of this smartphone model are 129 mm by 67 mm.For the initial characteristic mode analysis, the size of the screen is set as 127 mm by 55 mm.The size of the PCB is 124 mm by 57 mm.

1) THE ANTENNA'S GROUND: FROM SINGLE LAYER TO CONNECTED PARALLEL TWO LAYERS
Previously, the researches on smartphone antennas are all based on a single-layer PCB.It serves as the antenna's ground [15].This chassis plays an important role in the smartphone antenna design [23].However, for big-screen smartphones, due to the screen's large size, the single-layer ''ground'' turns to the ''ground'' of two connected parallel plates.This change to the shape of the smartphone chassis will bring different and new resonating characteristic modes.
For general smartphones, the normalized eigencurrent distributions of the lowest three single PCB modes (PMs) are numerically calculated using the CM-solver of CST Microwave Studio [24] and shown in Fig. 1(a).The size of  the PCB is 124 mm by 57 mm.The lowest-order mode is a longitudinal 0.5λ-dipole mode.The second mode is a longitudinal 1λ-dipole mode.The third one is a transverse 0.5λdipole mode.The results are similar to previous researches of single-layer PCB in general smartphones [25], [26].
However, for big-screen smartphones, the chassis modes (CMs) are no longer equivalent to PMs.As shown in Fig. 1(b), The size of the screen is 127 mm by 55 mm.The distance between the FPC and top edge of the PCB is marked as FPC_Y.HereFPC_Y is 26 mm.The spacing between the screen and the PCB h is 8 mm.Then, the lowest-order mode CM 1 resonates at a much lower frequency of 0.5 GHz due to the connecting FPC.The whole chassis produces a 0.5λ mode.The eigencurrents on the PCB go through the FPC and come back on the screen.The second-order mode CM 2 is similar to PM 1. directions of the eigencurrents of CM 2 are the same on the screen and the PCB.For the third-order mode CM 3, the eigencurrents go through the FPC.The currents on the screen and the PCB are in opposite directions.CM 4 is similar to PM 2, but the currents on the screen and on the PCB are in opposite directions.CM 5 is similar to PM 3, but the currents on the screen and on the PCB are in opposite directions.

2) THE INFLUENCE OF THE LOCATION OF THE FPC
The size of the chassis and the location of the FPC are factors that affect the resonant frequencies of the CMs.Generally, the sizes of the smartphone's screen and PCB are usually predefined in the Research and Development process, and their influence are obvious.However, the location of the FPC could be moved in a certain range, and its impact is unclear until now.
Fig. 2 shows the influence of characteristic angles with varying FPC_Y, from 6 mm to 46 mm with an interval of 10 mm.For CMs 2, 4, and 5, the influence is not obvious.But for CM 1 and CM 3, which are two new modes introduced by the FPC, they are significantly affected.For CM 1, as shown in Fig. 1(b), the eigencurrents go along the PCB, through the FPC, go backward on the screen.The FPC is in the middle of this half-wavelength current path.So, the larger the FPC_Y, the lower the FPC's location, the shorter the current paths, the higher the resonant frequency.
For CM 3, also shown in Fig. 1(b), the eigencurrents, on both the screen and the PCB, are distorted by the FPC, and thus the current paths are extended by the FPC.When the FPC_Y is smaller, the location of the FPC is higher, this distortion is weaker, the current paths are shorter, so the resonant frequency is higher.

B. CHARACTERISTIC MODES OF THE INTEGRATION OF CHASSIS AND METAL FRAME
Based on the chassis modes analyzed above, we have acquired some resonating frequencies.But they are far from covering all the desired frequency bands.So, the metal frame is then set to surround the upper half of the smartphone for more resonating frequencies to cover the desired several frequency bands.We arrange two grounding points to the metal frame, separating the metal frame into three parts.The middle part is a half loop.Different lengths are extended at both ends of the half loop in order to produce more resonant modes, as shown in Fig. 4(a).Thus, this configuration makes the metal frame a deformed loop antenna.
Then the characteristic modes of the integration of the chassis and the metal frame are calculated using the CM-solver of CST Microwave Studio [24].The result of characteristic angles versus frequency is shown in Fig. 3.Only modes resonating below 2.8 GHz are shown.Characteristic eigencurrents of each mode are shown in Fig. 4. It is observed by the eigencurrents that previously analyzed chassis modes still exist in this integration of the metal frame and the chassis.Other newly-produced characteristic modes are frame modes judged by the characteristic eigencurrents.For a better look at the current of the frame modes, the screens are shown in transparent for Fig. 4(c).The five frame modes resonating below 2.8 GHz are shown in Fig. 5.The resonating frequencies of frame modes can be changed by varying the length of each segment of the frame.FM 1 is a quarter-wavelength monopole mode resonating at 0.86 GHz.FM 2 is a three-quarter-wavelength monopole mode resonating at 1.02 GHz.FM 3 is a one-and-a-quarterwavelength monopole mode resonating at 1.70 GHz.FM 4 is a one-and-a-half-wavelength mode resonating at 2.03 GHz.FM 5 is a two-wavelength mode resonating at 2.70 GHz.

C. ADDITIONAL MODES
In Fig. 4, we can see for this structure, no characteristic modes are resonating in the frequency band from 1.8 GHz to 2.2 GHz.So, a monopole stub is added on the PCB resonating at around 2 GHz, as shown in Fig. 6(a).Besides, in order to cover 3.4-3.6GHz frequency band, which is a frequency band for 5G communication under 6 GHz [27], One frame mode of FM 6 is found resonating at 3.5 GHz.It is a three-wavelength mode, as shown in Fig. 7(b).

III. INFLUENCE OF THE SPACING BETWEEN SCREEN AND METAL FRAME
A narrower spacing between the screen and the metalframe has always been pursued by smartphone manufacturers, because it is necessary for the implementation of a high screen-to-body ratio smartphone.In [5], the influence of the spacing between the metal frame and the screen is given.The bandwidth of the metal-frame antenna will be significantly narrowed as the spacing decreases, from infinity  (the condition of ignoring the screen) to 5 mm to 1 mm.It is because of the large capacitance introduced by the narrow spacing.In industry, when the bandwidth is narrowed by the very close screen, antenna switches [28] or open/closed-loop tuners [29]- [31] are usually used to expand the achievable antenna bandwidth to cover the required frequency bands.In order to verify this conclusion, we analyzed the influence of s, the spacing between the screen and the metal frame, to the radiation bandwidth of the resonant modes in this antenna model.It can be obtained from the slope at 180 • of the curve of the characteristic angle.The steeper the slope, the narrower the bandwidth of the corresponding mode [26].Fig. 7 shows the characteristic angles versus s.From 10 mm to 2 mm, the slopes of almost all the modes' characteristic angles, are getting steeper, indicating the bandwidth potential is decreasing.The results theoretically prove the conclusion in [5] that the narrower the spacing, the more difficult to achieve wide bandwidth of the metal-frame antennas in large-screen smartphones.

IV. EXCITATION
In the above model, the metal frame has two grounding points.For this reason, the whole antenna is a deformed loop antenna.So, a current source could be added to replace one of the grounding points to excite the antenna.This configuration could avoid an additional coupler or slot for exciting, simplifying the antenna structure.In this section, we will select which grounding point to be chosen.
CM 1 resonates at 500 MHz, which is much lower than the lower frequency band 824-960 MHz.So, we will not consider it.CMs 2, 3, 4, and 5 could be selected to excite.
Figs. 4(b2) -(b5) show the characteristic eigencurrents of these four chassis modes.Each characteristic mode has its maxima and minima of the current distribution at specific locations.A specific mode can be inductively excited at the maxima of the eigencurrent distribution [32], [33].If the left grounding point is replaced by the feeding point, all of them could be excited because they have current maxima at the left grounding points.Otherwise, if the top right grounding point is replaced by the feeding point, CMs 2, 3, and 4 could be excited because they have current maxima at the top right grounding points, But CM 5 will not.
Figs. 4(c1) -(c5) show the characteristic eigencurrents of the five frame modes.For a clear observation of the current distribution on the metal frame, the screen is shown in transparent in the figures.If the left grounding point is replaced by the feeding point, FMs 1, 3, 4, and 5 could be excited because they have current maxima at the left grounding points.Instead, if the top right grounding point is replaced by the feeding point, FM 1 and FM 2 could be excited because they have current maxima at the top right grounding points.
Based on the analysis above, in order to excite more modes, the left grounding point will be replaced by the feeding point.

V. PROTOTYPE AND MEASURED RESULTS
After some fine tuning and adjustment of the dimensions, the detailed structure of the proposed antenna is shown in Fig. 8.The metal frame is noted as ABCDEF.The feeding point locates at Point B. A shorting pin (the grounding point) locates at Point E. AB is the part at the left side of feeding point.BCDE is the part between the feeding point and the grounding point.EF is the part at the right of grounding point.For a better look, the screen is shown in semi-transparent.In smartphones, sometimes there is also a square loop made of different materials supporting in the inner side of the metal frame.Because the supporting material clings to the metal frame, the material's dielectric constant has an influence on the electrical length, hence the resonant frequencies.Here, for general studies, the supporting material is set as foam, with a dielectric constant of nearly 1.
Two PCBs with single-layer Rogers RT/Duroid 5880 substrate with the thickness of 0.508 mm are used for representing the system PCB and the screen.The size of the system PCB is 124 mm by 57 mm.The size of the screen is 127 mm by 55 mm.The spacing between the screen and the PCB is h.The spacing between the screen and the side edge of the metal frame is s 1 .The spacing between the screen and the top edge of the metal frame is s 2 .The spacing between the PCB and the side edge of the metal frame is b 1 .The spacing between the PCB and the top edge of the metal frame is b 2 .The width of the FPC is FPC_w.The detail dimensions are shown in Table 2.A T-shape impedance matching network is designed to tune the antenna.Then a prototype of the proposed antenna was made as shown in Fig. 9.The simulated reflection coefficients of the proposed antenna before and after impedance matching and the measured result are shown in Fig. 10.The corresponding characteristic modes are annotated in the figure.The result exhibits good overall agreement and validates the existence of the modes.The deviations between measured and simulated results may be due to the error of machining accuracy in fabrication.
The radiation performance of the fabricated antenna was measured in SATIMO microwave anechoic chamber.The measured total efficiency and gain are shown in Fig. 11.The measured efficiency is more than 48% in the desired frequency bands.The measured radiation patterns are shown in Fig. 12.In the three mutually orthogonal planes, ϕ = 0 • , ϕ = 90 • , and θ = 90 • , Co-polarization and Crosspolarization have comparable magnitudes.The obtained result showed that this proposed antenna is applicable to the smartphone design.
It is noteworthy that, the proposed antenna could be further extended to the MIMO dual antenna operation for 4G and 5G communication.In this paper, we used the foam as the supporting material for general studies.If we use supporting materials with higher dielectric constant, such as polycarbonate, which is frequently used in real products, the length   of the metal-frame antenna could be shortened.Then the proposed antenna will only take less than half the perimeter of the smartphone body.Thus, the other antenna could be placed in the other half perimeter.Meanwhile, the two MIMO antennas could also be separated at a certain distance which is beneficial for decoupling between them.Furthermore, they could be interposed by grounded metal frame sections to reduce the mutual coupling.Besides, more decoupling methods could be considered to reduce the envelop correlation coefficient (ECC), such as neutralization line [34], parasitic decoupling network [35], defected ground structure (DGS) [36], electromagnetic bandgap (EBG) [37], et al.

VI. CONCLUSION
A metal-frame antenna for big-screen smartphones has been proposed by the method of characteristic mode analysis.In big-screen smartphones, the effect of the very close screen significantly narrows the metal-frame antenna's bandwidth.
By selectively exciting and merging as many as possible the characteristic modes, the narrowed bandwidth could be expanded to fulfill the GSM/UMTS/LTE/5G requirements.This technique could help to improve the performance of the big-screen smartphone antennas.

FIGURE 1 .
FIGURE 1. Characteristic currents and corresponding resonating frequencies of (a) single-PCB modes in general smartphone and (b) chassis modes in big-screen smartphone.(In (b), solid arrows are the eigencurrents on the surface of the screen, while the dashed arrows are the eigencurrents on the surface of the PCB.)

FIGURE 3 .
FIGURE 3. Characteristic angles versus frequency for the integration.

FIGURE 4 .
FIGURE 4. Characteristic eigencurrents of (b) CMs and (c) FMs of (a) the whole antenna.

FIGURE 7 .
FIGURE 7. Characteristic angles versus the spacing s between the screen and the metal frame from 10 mm to 2 mm in (a) 0.85 -1.25 GHz, (b) 1.4 -2.8 GHz.

FIGURE 8 .
FIGURE 8.The structure and dimensions of the proposed antenna.

FIGURE 9 .
FIGURE 9.The fabricated antenna and the matching network.

FIGURE 10 .
FIGURE 10.Simulated reflection coefficients of the proposed antenna with and without impedance matching and the measured result.

FIGURE 11 .
FIGURE 11.Measured total efficiency and gain of the antenna.

TABLE 1 .
Summary of gap width of metal-frame and efficiency of some smartphone antennas.

TABLE 2 .
Dimensions of the proposed antenna.