# A Wideband Differential-Fed Microstrip Patch Antenna Based on Radiation of Three Resonant Modes

Authors: Taohua Chen; Yueyun Chen; Rongling Jian
Journal: International Journal of Antennas and Propagation
 (2019)

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## Abstract

A wideband differential-fed microstrip patch antenna based on radiation of three resonant modes of TM12, TM30, and slot is proposed in this paper. Firstly, two symmetrical rectangular slots are cut on the radiating patch where the zero-current position of the TM30 mode excites another resonant slot mode. In addition, the slot’s length is enlarged to decrease the frequency of the slot mode with little effect on that of the TM30 mode. To further expand the impedance bandwidth, the width of patch is reduced to increase the frequency of the TM12 mode, while having little influence on that of the TM30 and slot modes. Moreover, a pair of small rectangular strips is adopted on the top of the feeding probes to achieve a good impedance matching. Finally, based on the arrangements above, a broadband microstrip patch antenna with three in-band minima is realized. The results show that the impedance bandwidth (Sdd11<−10dB) of the proposed antenna is extended to 35.8% at the profile of 0.067 free-space wavelength. Meanwhile, the proposed antenna maintains a stable radiation pattern in the operating band.


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## Body

## 1. Introduction

Microstrip patch antennas (MPAs) have been extensively investigated and developed over the past decades because of their advantages of low profile, small cost, ease of manufacture, and so on [1]. However, conventional MPAs always suffer from a narrow impedance bandwidth of about 3% because of the high-quality factor Q [2]. In order to expand the impedance bandwidth, a few approaches have been proposed in past decades.The simplest method to expand the bandwidth is to enhance the antenna thickness and decrease the substrate permittivity, which can reduce the quality factor Q [3]. However, thick substrates enlarge the surface wave leakage leading to poor radiation efficiency, and decreasing the permittivity is limited because the lowest substrate dielectric constant is 1. In addition, the feeding scheme was reconfigured in [4] to extend the impedance bandwidth to 115% at the profile of 0.25 λ0 (λ0 is the free-space wavelength); the reason for bandwidth enhancement is that another nonradiative resonant mode is introduced around the fundamental mode. However, it is difficult to implement the feeding scheme in a thin substrate. Moreover, the authors in [5] used a Wang-shaped radiating patch to extend the bandwidth of 49.3% with the profile of 0.2 λ0. In [6], an inverted U-shaped slot was adopted on the radiating patch to extend the impedance bandwidth to 17.8% with the thickness of 0.09 λ0. In [7], a simple E-shaped patch was proposed for bandwidth enhancement, and the impedance bandwidth was expanded to 30.3% at the 0.1 λ0 profile. Nevertheless, all the antennas mentioned above always need a high profile, which will destroy the low-profile property of microstrip antenna.Furthermore, in recent years, coupling two odd modes of MPAs together becomes a new attractive method because of keeping the advantage of low profile of MPAs. In [8], the TM10 and TM30 modes were combined to extend the bandwidth to 18% at the height of 0.08 λ0. In [9], the authors proposed to combine TM10 and TM12 modes together, and the impedance bandwidth was enlarged to 10% with the profile of 0.039 λ0. Additionally, The TM12 and TM30 modes were also adopted to achieve bandwidth enhancement in [10], and a bandwidth of 14.8% was realized at the profile of 0.048 λ0. However, since only two odd modes are combined, the impedance bandwidth of these antennas is only twice as wide as that of traditional microstrip antennas, which may hinder the application of these MPAs in broadband communication systems.In this paper, a novel wideband differential-fed MPA based on radiation of three resonant modes of TM12, TM30, and slot is proposed. Firstly, two symmetrical rectangular slots are cut at the position of zero-current of the TM30 mode of the radiating patch to excite another resonant slot mode with little effect on the TM30 mode. Besides, through increasing the slot’s length, the TM30 and slot modes can be adjusted in proximity to each other. To further expand the impedance bandwidth, the patch width is reduced to increase the frequency of the TM12 mode. With these arrangements, the TM12, TM30, and slot modes can be combined to form a wideband. Moreover, a pair of small rectangular strips is used on the top of the feeding probes to achieve a good impedance matching. The results show that the proposed antenna has realized an impedance bandwidth (Sdd11<−10dB) of 35.8% at the profile of 0.067 λ0. Additionally, the proposed antenna maintains a stable radiation pattern over the operating band.


## 2. Geometry and Design Process

The geometry of the proposed differential-fed wideband MPA is shown in Figure1. It consists of a radiating patch with the size of L × W and a ground plane with the size of LS  ×  WS. And a dielectric substrate RO5880 with permittivity of εr=2.2 and thickness of H1=0.508mm is selected in this paper for antenna design. The radiating patch is printed on the top surface of the substrate RO5880, while the ground plane is placed below the substrate with an air gap of H = 3 mm. Meanwhile, two symmetrical rectangular slots (L1 × W1) with the spacing of D1 are cut on the radiating patch, which can excite another resonant slot mode. In addition, differential-fed with spacing of D2 is used and a pair of small rectangular strips (L2 × W2) is adopted on the top of the feeding probes. All parameters for the proposed antenna in Figure 1 are tabulated in Table 1. In this paper, HFSS 13.0 is used for simulation calculation.Figure 1
Geometry of the proposed wideband antenna.Table 1
Dimensions of the proposed antenna.
Parameters
L
L
S
L
1
L
2
W
W
S
W
1
W
2
D
1
D
2
H
H
1
Values (mm)
63
94.5
38
4
56
84
3
3
25.8
60
3
0.508Firstly, as can be seen from Figure2(a), a square MPA with differential-fed scheme is used for antenna design to suppress the undesired even-order modes which are null in the boresight [11]. Secondly, in Figure 2(b), two symmetrical rectangular slots are cut on the radiating patch to excite another slot mode near the TM30 mode to expand the bandwidth. Thirdly, to further enlarge the bandwidth, in Figure 2(c), the patch width is reduced to increase the frequency of the TM12 mode to proximity to that of the slot and TM30 modes. Finally, in Figure 2(d), the slot’s width and position are modified slightly and a pair of small rectangular strips is adopted on the top of the feeding probes to achieve a good impedance matching.Figure 2
Design process of proposed wideband antenna. (a) Conventional MPA. (b) MPA with two slots. (c) MPA with two slots and shortened patch. (d) MPA with two slots, shortened patch and a pair of strips.
(a)
(b)
(c)
(d)


## 3. Parametric Studies and Design Flow

### 3.1. Exciting Another Resonant Slot Mode

The current distribution of the TM30 mode of the patch is plotted in Figure 3. It can be seen from Figure 3 that there are two zero-current lines on the patch. Therefore, as shown in Figure 2(b), when slots are cut on the patch near these positions, it will have little effect on the TM30 mode while can excite the resonant slot mode. Through modifying the slot’s length properly, TM30 and slot modes can be combined to expand the bandwidth. To better understand the effect of slot length, the frequency of the TM30 mode (f30) and slot mode (fslot) under different slot length L1 is plotted in Figure 4. Note that, in this subsection, the W1 is 1 mm and D1 is 21 mm.Figure 3
Current distribution of TM30 mode.Figure 4
f
30 and fslot at different slots length L1.It can be observed from Figure4 that when slot length increases from 18 to 38 mm, the fslot decreases from 7.2 GHz to 5.1 GHz clearly while f30 keeps constant at 6.24 GHz. Considering the whole performance, in this paper, L1 = 38 mm is selected for the widest bandwidth.


### 3.2. Increasing the Frequency of TM12 Mode

To further extend the bandwidth, the TM12 mode is adjusted in proximity to slot and TM30 modes in this paper. According to the cavity model [12], the resonant frequencies (fmn) of TMmn modes in MPA can be expressed as follows:(1)fmn=c2εr×mL2+nW2,where c is the light speed in the free space, εr is the dielectric constant of substrate, and m=1,2,3,…, and n=1,2,3,…Based on formula (1), the patch width (W) plays an important role in the frequency of TM12 mode (f12), yet has little effect on f30. And the fslot is mainly decided on the slot length, so the patch width also has little effect on fslot. Therefore, when W is reduced, f12 will be increased while f30 and fslot keep constant. To better understand how the patch width influences f12, f30, and fslot, Figure 5 plots f12, f30, and fslot varying with patch width W. W1, D1, and L1 are selected as 1 mm, 21 mm, and 38 mm, respectively.Figure 5
f
12, f30 and fslot varies with patch width W.We can see from Figure5 that when W reduces from 63 to 56 mm, f12 increases from 4.18 GHz to 4.44 GHz while f30 and fslot keep constant, which is consistent with the analysis above. Note that when W = 56 mm, the spacing of TM12 and slot modes is enough to form the wideband. Therefore, in this paper, we choose W = 56 mm for antenna design.


### 3.3. Impedance Matching

With the arrangements above, the TM12, TM30, and slot modes have been in proximity to each other. However, the input impedance is mismatch. To finally obtain a wideband MPA, the slot position (D1) and width (W1) are modified and a pair of small rectangular strips is adopted on the top of the feeding probes to achieve a good impedance matching. In this subsection, we analyze the effects of slots and rectangular strips on impedance matching. When one parameter is studied, the other parameters are fixed as listed in Table 1.Figure6 illustrates Sdd11 as a function of frequency at different slot position D1. As can be seen from Figure 6, the slot position has great effects on impedance matching and bandwidth. Proper design of the slots position can achieve a better impedance matching and wider bandwidth. In this paper, considering the whole Sdd11 performance in Figure 6, the D1=25.8mm is selected for antenna design.Figure 6
S
dd
11 as a function of frequency at different slots position D1.Figure7 shows Sdd11 as a function of frequency at different slot width W1. Like slots position D1, the slots width W1 also has large influences on impedance matching and bandwidth. Compare the whole Sdd11 performance at different slot width W1, the best bandwidth is achieved at W1=3mm.Figure 7
S
dd
11 as a function of frequency at different slots width W1.Besides, in this paper, a pair of small rectangular strips is adopted on the top of the feeding probes to eliminate the inductance introduced by probes for good impedance matching. Note that the value of capacitance introduced by the rectangular strips is mainly decided with the area of these rectangular strips. Therefore, we only modify the strips lengthL2 to achieve impedance matching and keep W2 as listed in Table 1. Figure 8 plots the Smith chart of proposed wideband MPA at different L2.Figure 8
Smith chart of proposed wideband MPA at differentL2.From Figure8, we can find that the input impedance is inductive as the probes connect radiating patch directly. When a pair of rectangular strips is adopted on the top of the probes to capacitive-coupled feed and L2 decreases from 6 mm to 2 mm, the input impedance gradually changes from inductive to capacitive. It can also be observed from Figure 8 that the best L2 is 4 mm.


## 3.1. Exciting Another Resonant Slot Mode

The current distribution of the TM30 mode of the patch is plotted in Figure 3. It can be seen from Figure 3 that there are two zero-current lines on the patch. Therefore, as shown in Figure 2(b), when slots are cut on the patch near these positions, it will have little effect on the TM30 mode while can excite the resonant slot mode. Through modifying the slot’s length properly, TM30 and slot modes can be combined to expand the bandwidth. To better understand the effect of slot length, the frequency of the TM30 mode (f30) and slot mode (fslot) under different slot length L1 is plotted in Figure 4. Note that, in this subsection, the W1 is 1 mm and D1 is 21 mm.Figure 3
Current distribution of TM30 mode.Figure 4
f
30 and fslot at different slots length L1.It can be observed from Figure4 that when slot length increases from 18 to 38 mm, the fslot decreases from 7.2 GHz to 5.1 GHz clearly while f30 keeps constant at 6.24 GHz. Considering the whole performance, in this paper, L1 = 38 mm is selected for the widest bandwidth.


## 3.2. Increasing the Frequency of TM12 Mode

To further extend the bandwidth, the TM12 mode is adjusted in proximity to slot and TM30 modes in this paper. According to the cavity model [12], the resonant frequencies (fmn) of TMmn modes in MPA can be expressed as follows:(1)fmn=c2εr×mL2+nW2,where c is the light speed in the free space, εr is the dielectric constant of substrate, and m=1,2,3,…, and n=1,2,3,…Based on formula (1), the patch width (W) plays an important role in the frequency of TM12 mode (f12), yet has little effect on f30. And the fslot is mainly decided on the slot length, so the patch width also has little effect on fslot. Therefore, when W is reduced, f12 will be increased while f30 and fslot keep constant. To better understand how the patch width influences f12, f30, and fslot, Figure 5 plots f12, f30, and fslot varying with patch width W. W1, D1, and L1 are selected as 1 mm, 21 mm, and 38 mm, respectively.Figure 5
f
12, f30 and fslot varies with patch width W.We can see from Figure5 that when W reduces from 63 to 56 mm, f12 increases from 4.18 GHz to 4.44 GHz while f30 and fslot keep constant, which is consistent with the analysis above. Note that when W = 56 mm, the spacing of TM12 and slot modes is enough to form the wideband. Therefore, in this paper, we choose W = 56 mm for antenna design.


## 3.3. Impedance Matching

With the arrangements above, the TM12, TM30, and slot modes have been in proximity to each other. However, the input impedance is mismatch. To finally obtain a wideband MPA, the slot position (D1) and width (W1) are modified and a pair of small rectangular strips is adopted on the top of the feeding probes to achieve a good impedance matching. In this subsection, we analyze the effects of slots and rectangular strips on impedance matching. When one parameter is studied, the other parameters are fixed as listed in Table 1.Figure6 illustrates Sdd11 as a function of frequency at different slot position D1. As can be seen from Figure 6, the slot position has great effects on impedance matching and bandwidth. Proper design of the slots position can achieve a better impedance matching and wider bandwidth. In this paper, considering the whole Sdd11 performance in Figure 6, the D1=25.8mm is selected for antenna design.Figure 6
S
dd
11 as a function of frequency at different slots position D1.Figure7 shows Sdd11 as a function of frequency at different slot width W1. Like slots position D1, the slots width W1 also has large influences on impedance matching and bandwidth. Compare the whole Sdd11 performance at different slot width W1, the best bandwidth is achieved at W1=3mm.Figure 7
S
dd
11 as a function of frequency at different slots width W1.Besides, in this paper, a pair of small rectangular strips is adopted on the top of the feeding probes to eliminate the inductance introduced by probes for good impedance matching. Note that the value of capacitance introduced by the rectangular strips is mainly decided with the area of these rectangular strips. Therefore, we only modify the strips lengthL2 to achieve impedance matching and keep W2 as listed in Table 1. Figure 8 plots the Smith chart of proposed wideband MPA at different L2.Figure 8
Smith chart of proposed wideband MPA at differentL2.From Figure8, we can find that the input impedance is inductive as the probes connect radiating patch directly. When a pair of rectangular strips is adopted on the top of the probes to capacitive-coupled feed and L2 decreases from 6 mm to 2 mm, the input impedance gradually changes from inductive to capacitive. It can also be observed from Figure 8 that the best L2 is 4 mm.


## 4. Results and Discussion

The reflection coefficient of proposed wideband MPA is plotted in Figure9. It can be observed that the impedance bandwidth for Sdd11<−10dB is 35.8%, covering from 4.72 to 6.79 GHz. Besides, there are three minima over the operating band, which is consistent with the three resonant modes mentioned above. Meanwhile, the reflection coefficient of conventional MPA at the same profile is also plotted in Figure 9. Compared with the traditional MPA, the impedance bandwidth of the proposed antenna has enhanced to more than three times, which indicates that the proposed antenna can extend the bandwidth distinctly.Figure 9
Reflection coefficient of proposed wideband MPA and conventional MPA.Figure10 plots the electric field distributions underneath the radiating patch at three minima of 5.02, 5.75, and 6.53 GHz. For the first minimum at 5.02 GHz, it can be found from Figure 10(a) that there are two vertical zero electric field lines and one horizontal zero electric field line, which is same as the electric field distributions of the TM12 mode of a conventional patch antenna. Thus, it is TM12 mode that works at 5.02 GHz. As for the second minimum at 5.75 GHz, the electric field is mainly distributed around two slots and is rarely around the radiative and nonradiative edges of the traditional microstrip antenna, which can be observed from Figure 10(b). This shows that the slot mode works at 5.75 GHz. While for the third minimum at 6.53 GHz, it can be clearly seen from the Figure 10(c) that there are three horizontal zero electric field lines, which indicates the proposed MPA resonates at the TM30 mode.Figure 10
Electric field distributions underneath the radiating patch of proposed wideband MPA. (a) 5.02 GHz. (b) 5.75 GHz. (c) 6.53 GHz.
(a)
(b)
(c)Figure11 gives the normalized radiation patterns of the proposed wideband MPA at three minima of 5.02, 5.75, and 6.53 GHz. The copolarization radiation patterns are symmetric in both E-plane and H-plane and have the peaks in the broadside direction, which shows that the proposed wideband MPA maintains a stable radiation pattern over the operating band. Meanwhile, a good cross-polarization characteristic of lower than −25 dB is achieved.Figure 11
Normalized radiation patterns of proposed wideband MPA.In addition, the gain, directivity, and efficiency as functions of frequency at broadside direction of the proposed antenna are illustrated in Figure12. Over the operating band, the gain ranges from 8.8 to 13.24 dBi and the efficiency is above 90%. It can also be observed from Figure 12 that the gain is dropped at about 5.7-5.8 GHz. The reason is that for the proposed wideband antenna, the slot mode between TM12 and TM30 modes resonates in this band, and the gain of slot mode is lowest among three resonant modes.Figure 12
Gain, directivity, and efficiency as functions of frequency at broadside direction of proposed wideband MPA.


## 5. Conclusion

In this paper, a wideband differential-fed microstrip patch antenna based on radiation of three resonant modes of the TM12, TM30, and slot is proposed and analyzed. First, two symmetrical rectangular slots are cut on the radiating patch, which will excite another resonant slot mode near the TM30 mode to extend the impedance bandwidth. Second, to further expand the bandwidth, the width of the patch is reduced to increase the frequency of the TM12 mode with little effect on that of TM30 and slot modes. Moreover, a good impedance matching is achieved through adopting a pair of small rectangular strips on the top of the feeding probes. Finally, a wideband microstrip patch antenna with an impedance bandwidth of 35.8% is realized under a low profile of 0.067 λ0. Besides, the proposed antenna maintains a stable radiation pattern and a good efficiency above 90% over the operating band. The proposed antenna is compact and has a wideband, it can be used for modern wireless communication systems.



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*Source: 4656141-2019-08-28.xml*