1 Introduction

To realize the requirements of long-term-evolution (LTE) and fifth generation (5G) of wireless networks, an antenna of a mobile unit should provide wideband operation, high data rate and low power consumption. This follows that such antennas should be able to operate in the range of millimeter-wave to support the high data rates required for the future applications. Furthermore, due to size limitations, it may be important that a mobile unit antenna is able to efficiently operate at multiple frequency bands to meet the application requirements of the forthcoming mobile generations [1,2,3,4]. For long-range communications in the mobile networks of the LTE, 5G, and the forthcoming generations, the operation at 28 GHz frequency may be recommended due to its low atmospheric absorption relative to the higher millimeter-wave frequencies like \(60\,\mathrm{ GHz}\) [5].

Circularly polarized antennas may be recommended in many applications of modern wireless communications. The main advantage of a circularly polarized antenna is its ability, as a receiver, to capture the main component of the signal power regardless of its position and orientation and regardless of the polarization of the incoming wave. Hence, in many situations in wireless communication channels, an antenna with circular polarization allows better performance than linearly polarized antennas. The present work proposes a compact-size antenna that can efficiently operate at five millimeter-wave frequencies 28, 51, 55, 59, and 63 GHz with reasonable bandwidth around each frequency. This antenna produces circular polarization at 28 GHz and linear polarization over the remaining four frequency bands.

Over the past few years, a lot of research work has been interested in the design of compact-size antennas capable of producing circular polarization at 28 GHz and the near millimeter-wave frequency bands for 5G and forthcoming mobile communications. For example, the work of Ref. [6] proposes a dielectric resonator antenna for 5G millimeter-wave applications with dual frequency bands. This antenna produces circular polarization at the first band and linear polarization at the second band. The impedance-matching bandwidths are (19.52–26.36 GHz) and (28.26–30.26 GHz) at the first and second bands, respectively. In Ref. [7], a dual-band circularly polarized patch antenna is designed by making a rectangular slot at angle \(45^\circ\) to produce circular polarization. This antenna can operate at 28 and 38 GHz with impedance-matching bandwidths of 0.9 and 1.3 GHz, respectively, and axial-ratio bandwidths of \(210\) and \(300\,\mathrm{ MHz}\), respectively. The research of Ref. [8] introduces a dual-band microstrip patch antenna to operate for 5G millimeter-wave applications with circular polarization at 28 and 38 GHz. In Ref. [9], a dual-band (28 and 38 GHz) circularly polarized patch antenna is proposed for millimeter-wave applications in future mobile communications. To achieve circular polarization, this antenna has circumferential slot near its edges and is fed through a microstrip line with an offset distance from the patch center. In Ref. [10], a dual-beam cavity-backed patch antenna is proposed to produce circular polarization over the frequency band 27.8–30.9 GHz for the 5G wireless communications. This antenna comprises a substrate-integrated cavity and a symmetrical patch. The work of Ref. [11] proposes a wideband ring loaded fractal patch antenna to operate over the frequency range 20–25 GHz with good circular polarization at 24 GHz for 5G applications. In Ref. [12], a modified circular patch antenna is introduced to produce circular polarization at 28 GHz for the 5G of mobile communications. The ground plane is defected by making diagonally aligned circular cuts to realize odd and even symmetries of the entire antenna structure. Instead of the conventional inset feed, the patch is fed through a tapered microstrip line for impedance matching to maintain the diagonal geometric symmetry required for good circular polarization. Reference [13] proposes a millimeter-wave antenna in which the feeding microstrip line is coupled with a nearly square patch through \(45^\circ\) inclined V-shaped slot aperture on the other side to produce circular polarization at 28 GHz.

The antenna proposed in the present work is five-band and is designed to produce circular polarization at 28 GHz and linear polarization at the other four frequency bands. The basic idea to achieve circular polarization is to employ a square patch as the main radiator and to excite two degenerate modes in the cavity beneath the square patch. The two modes should be excited with the same magnitude by making narrow slits at two corners of the square patch. In this way, the two excited modes will have orthogonal orientations of their electric fields, one with even symmetry with respect to the 45°-diagonal of the patch and the other with odd symmetry with respect to the same diagonal. If the dimensions of the patch and the diagonal slits are set properly, the two excited modes will have 90°-phase shift and, thus, producing circular polarization. Five parasitic elements are capacitively coupled to the square patch through a narrow gap to adjust the resonant frequencies of the remaining four radiating modes.

The remaining of the paper is organized as follows. Section 2 provides detailed description of the design idea and geometry of the proposed antenna including the parametric study and the final design. Section 3 gives presentations and discussions of the simulation and experimental results concerned with the evaluation of the antenna performance. Section 4 provides comparisons of the proposed antenna performance with some recently published work. Finally, the most important conclusions are summarized in Sect. 5.

2 Design of the Proposed Antenna

As the proposed antenna is planar and intended to operate in the frequency range of millimeter-waves, a low-loss thin substrate is selected for this purpose. It is proposed to print the antenna on a dielectric substrate of type Rogers RO3003™ of thickness \(h=0.25\,\mathrm{ mm}\), dielectric constant \({\varepsilon }_{r}=3\), loss tangent \(\mathrm{tan}\delta =0.001\). The design principles and the geometry of the antenna are presented in Sect. 2.1. The design process is complicated and requires extensive parametric studies to arrive at the best values of the antenna dimensional parameters to optimize its performance over the intended five frequency bands. Section 2.2 of the present paper is dedicated for this purpose. The final design of the proposed antenna is presented in Sect. 2.3.

2.1 Design Principles and Geometry of the Proposed Antenna

The proposed antenna is constructed as square patch with a small control cut and two diagonal cuts made at two of its corners as shown in Fig. 1. The central cut is cross-shaped and has the functions of assisting for antenna impedance matching over wider band and modifying the distribution of the surface current formed at higher order resonance of the square patch to improve the shape of the radiation patterns produced at these resonances. Also, the square patch is surrounded by five parasitic elements which are capacitively coupled to it. The purpose of these parasitic elements is to facilitate impedance matching at higher-order resonances. The ground structure has two trapezoidal-shaped cuts as shown in Fig. 1. The ground cuts are made just beneath the corner cuts of the square patch. The ground defects and the corner cuts of the patch are made keeping the diagonal symmetry of the overall antenna structure to enable circular polarization at the first-order resonance of the square patch. The square patch length is set to get the first-order resonance at 28 GHz with the aid of the following design equation [14].

$$L_{P} = \frac{c}{{2f_{r} \sqrt {\varepsilon_{r\,eff} } }} - 0.824 h \frac{{\varepsilon_{r\,eff} + 0.3}}{{\varepsilon_{r\,eff} - 0.258}} \frac{{L_{P} + 0.264 h}}{{L_{P} + 0.8 h}}$$
(1)

where \(c=3\times {10}^{8}\,\,\mathrm{ m}/\mathrm{s}\), is the speed of light in free space, \(h\) is the substrate thickness, and \({{\varepsilon }_{r}}_{eff}\) is the effective dielectric constant and can be expressed as follows.

$$\varepsilon_{r\,eff} = \frac{{\varepsilon_{r} + 1}}{2} + \frac{{\varepsilon_{r} - 1}}{2}\sqrt {1 + 12\frac{h}{{L_{P} }}}$$
(2)
Fig. 1
figure 1

Structure of the proposed antenna with the detailed dimensional parameters. a Zoomed view of the patch, b top view to show the printed antenna, c bottom view to show the defected ground structure

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Due to the existence of the unknown \({L}_{P}\) on both sides of Eq. (1), this equation can be solved by iterative techniques.

To achieve circular polarization the proposed antenna is based on a square patch as the main radiator. Two degenerate modes can be excited in the cavity beneath the square patch. To produce circular polarization, the two modes should be excited with the same magnitude. This can be achieved by making diagonally-facing corner slits of the square patch. In this way, the two excited modes will have orthogonal orientations of their electric fields, one with even symmetry with respect to the 45°-diagonal of the patch and the other with odd symmetry with respect to the same diagonal. If the dimensions of the patch and the diagonal slits are set properly, the two excited modes will have 90°-phase shift and, thus, producing circular polarization. Five parasitic elements are capacitively coupled to the square patch through a gap to adjust the resonant frequencies of the remaining four radiating modes of the square patch. It is shown that the first, second, and fourth resonant modes are normal modes of the square patch whereas the third and fifth mode are singular modes that are related to the presence of the upper-left and the lower-right slits of the square patch, respectively.

The antenna impedance matching at the five resonant frequencies is achieved using the suitable dimensions of the patch and ground cuts as well as the appropriate dimensions of the five parasitic elements and the width of the coupling gap between the square patch and these parasitic elements. It should be noted that the inset feed is not used for impedance matching in this design not to disturb the diagonal symmetry of the antenna structure which degrades the circular polarization at 28 GHz. The antenna is designed to operate at other four millimeter-wave frequencies as higher-order resonances of the square patch while being reactively loaded by the parasitic elements. The antenna produces linearly polarized fields at the four higher-frequency bands.

It should be noted that the longer width, \({W}_{G}\), and the shorter width, \({W}_{1}\), of the ground cuts can be expressed in terms of the patch length, \({L}_{P}\), the length, \({L}_{G}\), of each cut and the diagonal distance between the two cuts, \({D}_{G}\), as follows.

$$W_{G} = \sqrt 2 L_{P} - D_{G}$$
(3)
$$W_{1} = \sqrt 2 L_{P} - D_{G} - 2L_{G}$$
(4)

2.2 Parametric Study for the Optimum Design of the Proposed Antenna

In the antenna design process, the dimensional parameters should be determined to get the best performance of the proposed antenna. In this section, the effects of each dimensional parameter on the antenna characteristics are studied individually. The numerical results concerned with the effects of changing these parameters are presented and discussed in the following subsections.

2.2.1 Effects of Changing the Antenna Dimensional Parameters on the Impedance Matching

The effect of changing the patch length,\({L}_{P}\), on the frequency response of the reflection coefficient, \(\left| {S_{11} } \right|\), is presented in Fig. 2. It is shown that the patch length has major effects on the location and value of the \(\left| {S_{11} } \right|\) minimum and, also, on the impedance matching bandwidth at the five resonant frequencies of the proposed antenna. At all the resonant frequencies except for the fifth one, the resonant frequency increases with decreasing\({L}_{P}\). The best choice to get the antenna resonances at the desired frequencies, is to set \({L}_{P}=2.89\). This value of \({L}_{P}\) results in the best value of the average bandwidth over the five resonant frequencies.

Fig. 2
figure 2

Dependence of the magnitude of the reflection coefficient, \(\left|{S}_{11}\right|\) on the frequency around the five resonances for different values of the patch length, \({L}_{P}\) in the frequency bands, a 26-30 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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The dimensions of the corner slits of the square patch, \({L}_{C}\) and \({W}_{C}\), have major effects on the frequency response of \(\left|{S}_{11}\right|\) at the five resonant frequencies as shown in Figs. 3 and 4, respectively. Except for the first resonance of the proposed patch antenna, the resonant frequencies increase with decreasing the slit length, \({L}_{C}\). The width, \({W}_{C}\), of the patch corner slit acts almost in the same way as \({L}_{C}\). The resonant frequencies increase with decreasing \({W}_{C}\) at all the antenna resonances except for the first one. The dimensions \({L}_{C}\) and \({W}_{C}\) affect the minimum value of \(\left|{S}_{11}\right|\) rather than its location at the first resonance 28 GHz. The values of both \({L}_{C}\) and \({W}_{C}\) can be used to improve the impedance matching at this resonance. However, unlike the parameter \({L}_{C}\), the parameter \({W}_{C}\) has a major effect on the antenna impedance matching bandwidth at 28 GHz as shown in Fig. 4a. It will be shown later that both \({L}_{C}\) and \({W}_{C}\) have major effects on the axial ratio of the radiated field at 28 GHz. Also, it is noticed that, among the five resonant frequencies, the proposed antenna performance at the fourth resonance (around 59 GHz) is the most affected by changing the parameters \({L}_{C}\) and \({W}_{C}\).

Fig. 3
figure 3

Dependence of the magnitude of the reflection coefficient,\(\left|{S}_{11}\right|\), on the frequency around the five resonances for different values of the length, \({L}_{C}\), of the patch corner slits in the frequency bands, a 26-30 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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Fig. 4
figure 4

Dependence of the magnitude of the reflection coefficient, \(\left|{S}_{11}\right|\), on the frequency around the five resonances for different values of the width, \({W}_{C}\), of the patch corner slits in the frequency bands, a 26-30 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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The second, third and fourth resonances are more related to the five parasitic elements that are capacitively coupled to the square patch. This can be shown by studying the effect of changing the coupling gap width, \({G}_{1}\), on the frequency response of \(\left|{S}_{11}\right|\). As shown in Fig. 5, the first and fifth resonances of the antenna are slightly affected by changing \({G}_{1}\), whereas, the second, third, and fourth resonances are significantly affected by changing \({G}_{1}\). The resonant frequencies at the first and fifth operational band seem to be independent of \({G}_{1}\). On the other hand, both the resonant frequency and the impedance-matching bandwidth at the other three bands are significantly affected by changing \({G}_{1}\). The best choice to obtain the desired operational frequencies and bandwidths is to set \({G}_{1}=0.24 \mathrm{mm}\).

Fig. 5
figure 5

Dependence of the magnitude of the reflection coefficient, \(\left|{S}_{11}\right|\), on the frequency around the five resonances for different values of the width, \({G}_{1}\), of the coupling gap between the main patch and the parasitic elements in the frequency bands, a 26-30 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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The effect of changing the diagonally separating distance, \({D}_{G}\), between the cuts of the ground plane on the frequency response of \(\left|{S}_{11}\right|\) is presented in Fig. 6. Changing the separating distance, \({D}_{G}\), between the cuts of the ground plane has a major effect on the impedance matching at the fifth resonant frequency as shown in Fig. 6e.

Fig. 6
figure 6

Dependence of the magnitude of the reflection coefficient, \(\left|{S}_{11}\right|\), on the frequency around the five resonances for different values of the diagonally separating distance, \({D}_{G}\), between the two cuts of the ground plane in the frequency bands, a 26-30 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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Generally, it is noticeable that, at the fourth and fifth resonances, the antenna performance regarding the impedance matching is more sensitive to the variations of the ground cuts and also, to the corner slits of the square patch as they are vertically aligned. This can be explained in view of the surface current distributions discussed in Sect. 2.3.

2.2.2 Effects of Changing the Antenna Dimensional Parameters on the Circular Polarization at the First Resonance

The effects of changing some important dimensional parameters on the axial ratio (AR) of the radiated fields at the first resonance of the antenna (around 28 GHz) are presented in Fig. 7. It is shown, in Fig. 7a, that, with increasing the square patch length, \({L}_{P}\), the frequency at which the AR is minimum decreases. To obtain the \(3\,\mathrm{ dB}\)-AR bandwidth centered at \(28\,\mathrm{ GHz}\) it is required to set \({L}_{P}=2.89 \,\mathrm{mm}\). Changing the length of the patch corner cut, \({L}_{C}\), affects the minimum value of AR rather than the frequency at which this minimum value occurs as shown in Fig. 7b. The width of the corner slit, \({W}_{C}\), affects both the value and the location of the AR minimum on the frequency-AR curve as shown in Fig. 7c. To get the minimum of \(|{S}_{11} |\) and the 3 dB-AR bandwidth centered at \(28\,\mathrm{ GHz}\), the best choice is to set \({L}_{C}=0.6 \mathrm{mm}\) and \({W}_{C}=0.3 \mathrm{mm}\). The distance between the ground cuts, \({D}_{G}\), has a slight effect on the value of AR at \(28\,\mathrm{ GHz}\). The lowest value of the minimum AR is obtained when \({D}_{G}=2.8 \mathrm{mm}\) as shown in Fig. 7d.

Fig. 7
figure 7

Dependence of the AR on the frequency around the first resonance (\(28\, \mathrm{GHz}\)) for different values of the dimensional parameters a \({L}_{P}\), b \({L}_{C}\), c \({W}_{C}\), d \({D}_{G}\), and e \({G}_{1}\)

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As mentioned before, the five parasitic elements placed around the main patch affects only higher-order modes. As the circular polarization is obtained only at the first-order mode (around \(28\,\mathrm{ GHz}\)); therefore, changing the width, \({G}_{1}\), of the coupling gap between the main patch and the parasitic elements has almost no effect on the AR as shown in Fig. 7e. The choice is to set \({G}_{1}=0.24 \mathrm{mm}\) to get the best impedance matching (return to Fig. 6).

2.3 Final Design of the Proposed Antenna

Finally, the best values of the dimensional parameters presented in Fig. 1 obtained through the detailed parametric study, are listed in Table 1. These values of the dimensional parameters give the optimum performance of the antenna over the five operational bands regarding the impedance matching and the circular polarization over the first band.

Table 1 Final values of the dimensional parameters of the antenna presented in Fig. 1
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3 Simulation and Experimental Results

In this section, the five-band printed antenna proposed in the present work, with the geometry shown in Fig. 1 and the final values of the dimensional parameters listed in Table 1, is subjected to performance assessment through electromagnetic simulation using the commercially available CST® software package as well as the experimental measurements using the Rhode and Schwartz vector network analyzer (VNA) model ZVA-67.

3.1 Antenna Fabrication and Measurement of the Return Loss

A laboratory prototype of the proposed five-band millimeter-wave antenna is fabricated for the purpose of experimental assessment. As previously mentioned, the substrate material is Rogers RO3003 with \({\epsilon }_{r}=3\), \(\mathrm{tan}\delta =0.001\), and \(h = 0.25 \mathrm{mm}\). The top and bottom views of the fabricated antenna are presented in Fig. 8.

Fig. 8
figure 8

Fabricated prototype of the proposed five-band millimeter-wave antenna on defected ground. a Top view, b Bottom view

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The VNA of Rhode and Schwartz model ZVA-67 is used for measuring the frequency response of the reflection coefficient \({S}_{11}\) using the experimental setup shown in Fig. 9. The \(1.85 \mathrm{mm}\) end-launch connector from Southwest Microwave Inc. is used for connecting the antenna to the VNA as shown in Fig. 9a and b. The measurement is performed over the frequency range 25–67 \(\mathrm{GHz}\) to cover the five operational millimeter-wave bands of the antenna.

Fig. 9
figure 9

The fabricated prototype is mounted to a coaxial end-launch connector and connected to the VNA for measuring the reflection coefficient \(\left|{S}_{11}\right|\) over the frequency range 25–67 GHz. a Front view of the antenna connected to the end launcher. b The antenna connected to the VNA port 2

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The simulation results and the experimental measurements concerned with the dependence of the antenna reflection coefficient \(\left|{S}_{11}\right|\) on the frequency show good agreement with each other as presented in Fig. 10. It is shown that the antenna has five resonances at 28, 51, 55, 59, and 63 GHz with impedance matching (\(\left|{S}_{11}\right|<-10 \mathrm{dB}\)) bandwidths of 2.0, 0.9, 1.2, 1.1, and 1.6 GHz, respectively.

Fig. 10
figure 10

Frequency dependence of the reflection coefficient magnitude, \(\left|{S}_{11}\right|\), of the five-band millimeter-wave antenna obtained by the CST® simulator and the VNA measurement

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3.2 Surface Current Distribution

Studying the surface current distribution gives physical insight of the radiation mechanisms at the five operational frequency bands of the antenna. The mechanisms of radiation and the characteristics of the proposed antenna at the operational frequencies can be understood in view of the surface current distributions on the patch and on the defected ground plane. The current distributions on the patch surface and on the ground plane are presented in Figs. 11 and 12 at the central frequencies of the five operational bands of the proposed antenna. At 28 GHz, the current distributions on the patch surface, Fig. 11a, and on the ground plane, Fig. 12a, presents a first-order mode with even symmetry about the diagonal of symmetry ab. At 51 GHz, the current distribution on the patch surface presents a second-order mode with higher concentration at the edges of the corner cuts and the ground apertures as shown in Figs. 11b and 12b. The current distribution of this mode presents odd symmetry with respect to the diagonal ab. At 55 GHz, the current is concentrated on the upper-left corner of the patch and on the ground and exhibits the edge behavior at the edges of the patch slit and on the edges of the ground aperture as shown in Figs. 11c and 12c, respectively. It seems that this mode is not related to the patch itself and it can be a singular mode related to the upper-left patch slit and the ground aperture lying below it. At 59 GHz, the current distributions on the patch and on the ground plane present a third order mode with even symmetry about the diagonal ab with more concentration of the surface current density on the edges of the patch slits and ground apertures as shown in Figs. 11d and 12d, respectively. At 63 GHz the current is concentrated near the bottom-right slit of the patch and near the bottom-right aperture of the ground plane as shown in Figs. 11e and 12e. Like the radiation mode at 55 GHz, it seems that the mode at 63 GHz is a singular mode that is related to bottom-right patch slit and the ground aperture lying just below it.

Fig. 11
figure 11

Current distribution on the antenna surface at the five resonances a \(28\, \mathrm{GHz}\), b \(51\, \mathrm{GHz}\), c \(55\, \mathrm{GHz}\), d \(59\, \mathrm{GHz}\), and e \(63\, \mathrm{GHz}\)

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Fig. 12
figure 12

Current distribution on the ground surface at the five resonances a \(28\, \mathrm{GHz}\), b \(51\, \mathrm{GHz}\), c \(55\, \mathrm{GHz}\), d \(59\, \mathrm{GHz}\), and e \(63\, \mathrm{GHz}\)

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From the above discussions it can be concluded that the radiating modes at 28, 51, and 59 GHz belong to the set of normal cavity modes of the square patch with their configurations presenting first, second, and third-order spatial distribution patterns. On the other hand, the radiating modes at 55 and 63 GHz are singular modes that are related to the existence of the upper-left patch slit with the ground aperture below it and the lower-right patch slit and the ground aperture below it, respectively. This can be more emphasized by presenting the current distributions around the apertures of the ground plane at the five resonant frequencies of the proposed antenna. As shown in Fig. 12c, the surface current on the ground plane is enhanced near the edges of the upper-left aperture of the ground plane at 55 GHz (third resonance) rather than the four remaining modes. In the same way, Fig. 12e shows that the concentration of the surface current near the edges of the lower-right aperture of the ground plane is more enhanced at 63 GHz (the fifth resonance) than its concentration at the other four resonances.

The surface current distributions on the square patch at 28 GHz at sequential times separated by quarter the periodic time are presented in Fig. 13 ordered from Fig. 13a–d. The circular polarization demonstrated by the uniformly rotating arrows representing the surface current directions. The arrows rotate right wise by the rate of 90° per quarter the periodic time showing good circular polarization. Also, the successive current distributions present left-hand sense of circular polarization.

Fig. 13
figure 13

Directions of the current on the surface of the square patch at the times a \(t={t}_{0}\), b \(t={t}_{0}+T/4\), c \(t={t}_{0}+T/2\), and d \(t={t}_{0}+3T/4\), where \({t}_{0}\) is a reference time and \(T\) is the periodic time of a sinusoidal wave at \(28\, \mathrm{GHz}\)

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3.3 Gain and Radiation Patterns

The patterns of the far fields produced by the proposed antenna at the central frequency of each operational frequency band as well as the maximum gain and radiation efficiency are evaluated using the CST® simulator and the experimental measurements.

3.3.1 Experimental Setup for Measurement of the Gain and Radiation Patterns

For gain and far field pattern measurement, a reference horn antenna is oriented towards the antenna under test (AUT) as shown in Fig. 14. The AUT can be rotated about its axis in its horizontal and elevation planes. The AUT should be in the far field region of the reference horn antenna, where the minimum far-field distance is given as (\(2{L}^{2}/\lambda\)) where \(L\) is largest dimension of the antenna and \(\lambda\) is the shortest wavelength during measurement. The AUT is connected to port 1 of the VNA and the reference horn antenna is connected to port 2 through flexible coaxial cables of high quality. The ratio of the received-to-transmitted power, \({P}_{R}\left(\theta ,\phi \right)/{P}_{T}\) can be obtained from the S-parameter \({S}_{21}\left(\theta ,\phi \right)\) when the AUT is rotated in the direction \(\left(\theta ,\phi \right)\) as follows.

$$\frac{{P_{R} \left( {\theta ,\phi } \right)}}{{P_{T} }} = \left| {S_{21} \left( {\theta ,\phi } \right)} \right|^{2}$$
(5)
Fig. 14
figure 14

Experimental apparatus for measuring the radiation patterns of the proposed five-band antenna

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Thus, the gain pattern \({G}_{T}\left(\theta ,\phi \right)\) of the AUT can be calculated from the readings \({S}_{21}\left(\theta ,\phi \right)\) (obtained by the VNA) as follows.

$$G_{T} \left( {\theta ,\phi } \right) = \left( {\frac{4\pi D}{\lambda }} \right)^{2} G_{R} \left| {S_{21} \left( {\theta ,\phi } \right)} \right|^{2}$$
(6)

where D is the distance between the AUT and the reference horn antenna.

3.3.2 Radiation Patterns of the Five Band Antenna

The radiation patterns of the total far field produced by the proposed antenna at 28 GHz in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) are presented in Fig. 15. The radiation patterns, obtained by measurement as described in Sect. 3.3.1, show excellent agreement with those obtained by simulation. It should be noted that the far field at \(28\,\mathrm{ GHz}\) is dominated by circularly polarized component with left-hand sense. The radiation patterns of the RHCP and LHCP fields are presented later on in the present paper. The maximum gain of the total field obtained at 28 GHz is about 7 dBi.

Fig. 15
figure 15

Radiation patterns of the total field at \(28\, \mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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The far field elevation patterns produced at 51 GHz in the planes \(\phi =0^\circ\) and \(\phi =90^\circ\) are presented in Fig. 16 where the measured patterns show good agreement with those obtained by simulations. The dip of the radiation pattern appearing in the direction \(\theta ={0}^{^\circ }\) is attributed to that the far field at this frequency is actually produced by a second-order mode of the square patch. The maximum gain obtained at 51 GHz is 6.8 dBi.

Fig. 16
figure 16

Radiation patterns of the total field at \(51\, \mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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The radiation patterns of the far field produced at \(55\,\mathrm{ GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) are presented in Fig. 17. Like the field radiated at \(51\,\mathrm{ GHz}\), the radiation pattern at \(55\,\mathrm{ GHz}\) shows a minimum at \(\theta =0^\circ\). The asymmetry of the radiation pattern about the plane \(\theta =0^\circ\); see Fig. 17b, is attributed to that this field is radiated due to a singular resonant patch mode (i.e. related to the presence of the slit of the patch). The maximum gain obtained at \(55\,\mathrm{ GHz}\) is \(6.0\,\mathrm{ dBi}\).

Fig. 17
figure 17

Radiation patterns of the total field at \(55 \,\mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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At the fourth operational band, the far field patterns in the plane \(\phi =0^\circ\) and \(\phi =90^\circ\) at \(59\,\mathrm{ GHz}\) are presented in Fig. 18. As shown in this figure, the radiation pattern is not symmetric about the plane \(\phi\) = 0° or the plane \(\phi\) = 90°. This mode is a third-order mode whose surface current distribution on the patch shows even symmetry with respect to the diagonal \(ab\) (see Figs. 11d and 12d) and is strongly affected by the slits made at the corners of the square patch as previously discussed in Sect. 3.2. This can, also, be noticed while studying the effects of changing the dimensions \({L}_{C}\) and \({W}_{C}\) of the corner slits as previously mentioned in Sect. 2.2.1. The maximum gain obtained at 59 GHz is about 6.0 dBi.

Fig. 18
figure 18

Radiation patterns of the total field at \(59\, \mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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The elevation radiation patterns at \(63\,\mathrm{ GHz}\) are presented in Fig. 19. This pattern is not symmetric about the plane \(\phi =0^\circ\) as shown in Fig. 19b. This can be attributed to that field radiated at this frequency is produced by a singular patch mode that is related to the presence of the lower-left slit as previously discussed in Sect. 2.3 (See Fig. 11e and 12e) and aperture made in the ground plane just below it. This can be ensured by noticing the effects of changing the distance, \({D}_{G}\), between the two cuts of the ground plane on the antenna impedance matching as presented in Fig. 6b as previously mentioned in Sect. 2.2.1.

Fig. 19
figure 19

Radiation patterns of the total field at \(63\, \mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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3.4 Circularly Polarized Radiated Field

The proposed antenna is designed to produce circularly-polarized far-field in the first operational frequency band centered at \(28\,\mathrm{ GHz}\). The radiation patterns of the RHCP and LHCP field in the planes \(\phi =0^\circ\) and \(\phi =90^\circ\) are presented in Fig. 20. It is shown that the antenna is dominated by a LHCP field. It should be noted that the sense of polarization is determined by the two corners of the square patch at which the slits are made. To produce LHCP field in the far zone, the slits are made at the upper-left and lower-right corners of the patch, and to produce RHCP field, the slits are made at the upper-right and lower-left corners of the patch.

Fig. 20
figure 20

Radiation patterns of the circularly polarized field components at \(28\, \mathrm{GHz}\) in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\) in the elevation planes, a phi = 0, b phi = 90

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The AR patterns in the elevation planes \(\phi ={0}^{^\circ }\) and \(\phi ={90}^{^\circ }\) are plotted in the Cartesian coordinates in Fig. 21. It is shown that the 3 dB-AR beam widths are \(180^\circ\) and 135° in the elevation planes \(\phi =0^\circ\) and \(\phi =90^\circ\), respectively.

Fig. 21
figure 21

Variation of the axial ratio of the radiated field with the elevation angle, \(\theta\), in the planes \(\phi =0^\circ\) and \(\phi =90^\circ\) at \(28\, \mathrm{GHz}\)

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3.5 Dependence of the Gain and Radiation Efficiency on the Frequency

The simulation results and the experimental measurements concerned with the dependence of the maximum antenna gain and radiation efficiency on the frequency are presented in Figs. 22 and 23, respectively. It is shown that maximum antenna gain has the values \(7.0\), \(6.8\), \(6\), \(6\), and \(8\,\mathrm{ dBi}\) at the frequencies \(28\), \(51\), \(55\), \(59\), and \(63\,\mathrm{ GHz}\), respectively. The radiation efficiencies has the values \(90\), \(90\), \(91\), \(78\), and \(86\%\) at the frequencies \(28\), \(51\), \(55\), \(59\), and \(63\,\mathrm{ GHz}\), respectively. For both the maximum gain and radiation efficiency, it is shown that the simulation results and experimental measurements come in good agreement with each other, however, the experimental measurements have been considered as the actual values of these parameters.

Fig. 22
figure 22

Frequency dependence of the maximum gain of the proposed antenna around each of the five resonant frequencies in the frequency bands, a 27-29 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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Fig. 23
figure 23

Frequency dependence of the radiation efficiency of the proposed antenna around each of the five resonant frequencies in the frequency bands, a 27-29 GHz, b 50-52 GHz, c 54-56 GHz, d 58-60 GHz, e 62-64 GHz

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4 Comparison with Published Work

The performance parameters of the proposed antenna including the impedance matching bandwidth (BW), the 3 dB-AR bandwidth, the gain and the dimensions of the radiating elements are presented in Table 2 in comparison to the results available in some recently published work.

Table 2 Comparisons among the characteristics of the antenna proposed in the present work and some recently published work
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5 Conclusion

A five-band millimeter-wave antenna operating at 28, 51, 55, 59, and 63 GHz has been proposed in the present work. The proposed antenna produces circular polarization at 28 GHz and linear polarization at the other four frequencies. The five specific frequencies have been selected, with 4 GHz separation between the center frequencies of each band, to provide enough number of multiple bands at such unlicensed frequency range to be used as alternatives for the different applications of the future generations of mobile communication systems and to avoid the operation at 60 GHz, in particular, due to the peak atmospheric absorption of millimeter-wave encountered at this frequency. The antenna design is based on employing a main patch surrounded by five parasitic elements that are capacitively coupled to the main patch so as to realize the location of the resonant frequencies of the higher frequency bands. The simulation and experimental results for the performance assessment of the proposed antenna have come in good agreement and have shown that the proposed antenna operates efficiently over the five frequency bands 28, 51, 55, 59, and 63 GHz providing impedance matching bandwidths of 2.0, 0.9, 1.2, 1.1, and 1.6 GHz, respectively, values of the maximum gain of 7.0, 6.8, 6.0, 6.0, and 8.0 dBi, respectively, and radiation efficiencies of 90, 90, 91, 78, and 86%, respectively. Also, the 3 dB-axial ratio bandwidth at 28 GHz is about 1.2 GHz, which is wide enough for most of the applications in mobile communications.