# Leaky Wave Array in Full Planar Substrate with EBG-Based Wave Guiding Channel

Authors: Linghui Kong; Sen Yan; Vladimir Volskiy; Binke Huang; Guy A. E Vandenbosch
Journal: International Journal of Antennas and Propagation
 (2021)

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## Abstract

A new type of wave guiding structure is proposed is this paper. The guiding channel is developed on the full planar dielectric substrate and aligned with electromagnetic bandgap (EBG) units. Since the bandgap of these mushroom-like units is calculated with a coverage of the channel working band, these units are of great importance on ensuring the transmission efficiency and eliminating the coupling effect between channels. Then, this wave guiding structure is extended to the design of a six-element leaky wave antenna array with a complete size of 25.6 mm × 80.6 mm, which is working at Ku band from 12.0 GHz to 12.8 GHz and achieving a bandwidth of about 0.8 GHz, a gain of 11.36 dBi, and an efficiency of ca. 86.7% at 12.0 GHz. Within the working frequency band, this antenna topology achieves a frequency-dependent beam scanning in the forward directions, and it offers a potential for radar application on road speed detecting with low costs.


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## Body

## 1. Introduction

Nowadays, the development of CMOS technology enables circuits to operate in higher and higher frequency ranges, such as the mm-wave frequency band of 30 GHz to 300 GHz. By making use of carrier frequencies in this frequency domain, wideband communication systems can benefit from the large bandwidth and high data rate. However, one of today’s challenges is to transmit these wave carriers over a limited distance from several centimeters to meters to provide a multi-gigabit communication link [1]. The traditional planar strip lines such as microstrip or coplanar waveguide will be seriously suffered from both dielectric and conductor losses. In contrast, dielectric transmission media always enjoy with the low material loss which makes it an ideal candidate for a low-loss, cost-friendly, and light-weight wave-guiding channel [2].Several decades ago, dielectric transmission lines such as the Goubau line and dielectric strips were known for their very low transmission loss but at the expense of a complicated mechanical mounting structure and a rather large extension of the fields into free space [3, 4]. Later, grounded dielectric rods and rectangular strips (the so-called image guide) were investigated, also showing a quite low attenuation [5, 6]. A nonradiative dielectric (NRD) waveguide is proposed to work at 94 GHz band with the air holes to lower the dielectric permittivity [7]. The substrate integrated waveguide (SIW) has gained a wide popularity in millimeter wave range, but it still faces with the conductive losses as enclosed by metal shielding parts [8]. A new version of the image guide, called the Substrate Integrated Image Guide (SIIG), was first proposed in [9]. With a thinner insulator layer, it offers a new type of dielectric transmission line for multiple layer applications. A comparison of the propagation characteristics of these different transmission lines is presented in Table 1.Table 1
Comparison of different structures.
Trans. linesRDW [4]NRG [7]SIW [8]SIIG [9]Bandwidth (GHz)10-1892∼99.238∼5980∼95S21(dB)<−2−5.4∼−3−1.2∼−1.0<−3S11(dB)<−13<−10<−15<−10Trans. loss (dB/mm)0.019∼0.04//0.025Trans. modeHE11LSE11TE11Ey11Dimension (mm)10 × 25 × 100.635 × 2.84 × 26.30.381 × 2.6 × 40.525 × 11.49 × 40MaterialRO3010AluminaAluminaTMM10i, siliconMode transitionWR-62WR-10CPWWR-10To further extend the range of applications, wave guiding channels can be realized in full planar substrates with the electromagnetic bandgap (EBG) units [10]. EBG structures are categorized as a type of metamaterial with artificial or nonartificial periodic units. With the adequate design parameters, materials, and shapes, they can be used to control and modulate the propagation of electromagnetic waves in the planar substrate. In the design of planar antennas, this can be applied to suppress side leakages and avoid the mutual couplings between channels [11].Leaky wave antennas (LWAs) can achieve a high directivity with a simple structure without the need for a complex and costly feeding network [12], and the capability of beam scanning with frequency changes [13]. Radiations from LWAs are generated by the continuous or periodic power leakage from transmission lines into the exterior region. The first LWA was proposed in the 1940s in the form of a slotted rectangular waveguide [14]. Recent developments are focusing on planar LWAs to improve the scanning range and overcome the ‘stop band’ problem in the broadside direction [15, 16].In this paper, an innovating 1D leaky wave antenna topology is proposed, which combines several aspects:The structure is based on a fully planar and very low-profile substrateA dielectric waveguide is formed based on this grounded substrate in combination with mushroom EBG units along the guiding channelThis waveguide is used as the feeding mechanism for a leaky wave planar array [17]Furthermore, a dedicated CPW to SIW transition structure with a V slot is adopted to achieve a smooth mode conversion to the guiding channelAs far as the authors can see, this is the first structure described in literature combining all these features. This topology offers significant advantages in integration, fabrication, and a broad working band when compared with the conventional transmission lines.The content is organized as follows. First, the EBG-based dielectric waveguide is described and the propagation efficiency is verified. Then, a CPW to SIW feeding topology is employed to excite the working mode inside the waveguide. Finally, a Ku-band periodic leaky wave antenna, which is made of six metal strips on top of the guiding channel, is proposed. The measured return loss, far field pattern, and realized gain are compared with simulations, and a good agreement is observed.


## 2. Wave Guiding Structure

The complete topology of the proposed transmission medium is shown in Figure1. It is composed of three parts: the middle guiding channel, the feeding part, and the EBG units. While the middle channel is designed to work in the required frequency band, the EBG units are optimized to obtain the stopband with a coverage of the frequency band. In this way, the side leakages and channel couplings can be suppressed to achieve a board-level dielectric interconnector design. In this work, all the simulations are performed within CST Microwave Studio.Figure 1
EBG-based dielectric waveguide.


### 2.1. Dielectric Guiding Channel

The initial dielectric image guide (DIG), as shown in Figure2, is designed with a piece of low-loss high permittivity Rogers RT 6010 substrate (permittivity 11.4, loss tangent 0.0023, and thickness 2.54 mm). The high permittivity material is chosen to have a higher field concentration within the waveguide core. The degenerate Ex11 mode with a parallel electric field can be avoided by the metal ground. Hence, only the Ey11 mode (Figure 3(a)) is left as the dominant mode and to propagate inside the channel (Figures 3(b), and Figure 4 gives the insertion losses of the first two modes. It can be seen that a single mode transmission has been achieved below 14.5 GHz.Figure 2
Grounded image guide (a = 8.8 mm, b = 2.54 mm, and L = 30 mm).Figure 3
Ey11 mode of the dielectric image guide: (a) port mode field and (b) propagation mode field.
(a)(b)Figure 4
Transmission efficiency of the first two modes (with (1) and (2) representE11y and E21y, respectively) of the grounded DIG.


### 2.2. Eigenmode Analysis of EBG Unit

In many cases, the eigenmode analysis of EBG structures is based on the Bloch–Floquet theorem, which describes the wave propagation in an infinite medium consisting of periodic unit cells. The relationship between the propagation constant and frequency can be given by the dispersion diagram.For a two-dimensional periodical structure, the dispersion diagram can be given by starting fromΓ (0, 0), going to X (0, π), then to M (π, π) and back to Γ, as indicated in Figure 5(a). In this work, a mushroom-like unit is used (also see in Figure 5(a)), consisting of one central square patch with metal vias connected to the ground.Figure 5
(a) Mushroom-type square EBG unit of sized = 2.8 mm, consisting of a square patch with size a = 2.0 mm, connected in the center to the ground by a via with radius r = 0.3 mm. The points defining the path in the Brillouin zone are also indicated. (b) Boundary conditions in the simulations.
(a)(b)In order to mimic the periodicity of the structure, the boundary conditions at the side walls are defined as periodic boundaries. As the eigenmode solver in CST does not support open boundary conditions, both the top and bottom sides are defined as electric conductors, see Figure5(b). Also, consider that the fields are mainly concentrated inside the substrate, and just above the substrate, air interface, a proper height of the air layer, i.e., more than ten times the substrate thickness, yields the correct field distribution of the eigenmodes.The dispersion diagram is plotted in Figure6. As discussed, it incorporates three intervals (Γ to X,X to M, and M to Γ) to describe all possible propagation directions in the xy plane. In each direction, the phase changes are swept from 0 to π, and the cutoff frequency for each eigenmode is calculated.Figure 6
Dispersion diagram of the EBG unit (with red lines for the light cutoff frequency).It is known that the mushroom-like EBG structure allows the propagation of TM waves at low frequencies and TE waves at high frequencies [18]. The first mode is thus a TM mode, which starts as a forward propagating TEM mode at very low frequency and low wavenumber and changes into a forward TM surface wave. Modes 2, 3, and 4 are hybrid modes that start as TE waves at a very low wavenumber and transform into TM waves at high frequencies.Figure7 presents the electric field distribution in the yz plane of the first four eigenmodes. We can see that mode 2 is orthogonal to the transmission mode inside the waveguide, and mode 2 will not be excited and can be neglected from considerations. Meanwhile, since the transmission mode inside the dielectric image guide is a slow wave with the phase speed slower that the light, the frequency band gap should also below the frequency line of light [19], as seen in Figure 6. Therefore, the band gap for this periodic structure is ranging from about 6.5 GHz to 15.0 GHz.Figure 7
Sectional view of electric field distribution of the four eigenmode inyz plane. (a) Mode 1. (b) Mode 2. (c) Mode 3. (d) Mode 4.
(a)(b)(c)(d)


### 2.3. Feeding Structure

In order to achieve a smooth mode conversion from the feeding structure to the guiding channel, a CPW to SIW (substrate integrated waveguide) transition with a V slot is used to excite the transmission mode inside the guiding channel (Figure8). The complete feeding structure is obtained by a step-by-step design procedure and finally assembles each part together. The listed parameters are optimized to ensure that the different parts can satisfy the working frequency band. Among them, the dimensions of the tapered CPW and V-slot play the key roles on determining the frequency range and transmission efficiency. Besides, this planar structure is important for the interconnections between MMIC chips and coaxial cables. The tapered CPW feed line with ground is employed to match with SIW and results in a wide band transition [20, 21]. The fundamental mode inside the waveguide is similar to TE10 mode, while the cutoff frequency can be calculated by the sectional dimensions and the design parameters of the metal vias as follows [22]:(1)fc=c2εras−d2/0.95p,and the equivalent wavelength of SIW is obtained by(2)λg=2πεr2πf2/π/as2,where εr is the relative permittivity of the substrate material, as refers to the distance between the two rows of metal vias, d is the diameter of the vias, p represents the periodical distance between vias, and c is the speed of light. With the design parameters listed in Figure 8, we can get fcTE10=6.61GHz and fcTE20=13.22GHz. In the upper frequency limit of 12.8 GHz, the equivalent wavelength is calculated with λg=7.92mm>as. Therefore, these computed results show that only the dominant mode can be propagated inside the SIW within the operation frequency range of 12.0 to 12.8 GHz.Figure 8
Feeding structure (w = 11.35, w1 = 1.3, w2 = 3.2, s1 = 0.8, s2 = 1.8, d1 = 2, d2 = 1.4, dv = 5.6, dx = 3.4, dz = 10.4, dr = 3.6, p = 0.8, and r = 0.3. Unit: mm).In Figure9, the electric field distributions in the different parts of the structure are presented. The transmitted TE10 mode within SIW is well matched with the dominant E11y mode in DIG, delivering a smooth mode conversion. The simulated S parameters (Figure 10) show that a reasonable transmission efficiency is achieved in the desired frequency range. In order to illustrate the influence from the EBG units, the reflection and transmission parameters are also given in this figure for the original dielectric waveguide without these units in comparison. It is clearly seen that the presence of these mushroom units can generate a wave guiding channel and, moreover, eliminate a series of resonances in the structure, giving it a much more stable S21 in the operational band than the original dielectric waveguide. Although there are some ripples appeared in the S11 performance, it still keeps below -10 dB at the target frequency range (12.0 – 12.8 GHz) even when compared with the structure without EBG units.Figure 9
Mode conversion from the feeding structure to guiding channel. The length of the structureL = 71.2 mm.Figure 10
Comparison of the simulated reflection and transmission parameters of the waveguide realized with the EBG units and the original dielectric waveguide.


## 2.1. Dielectric Guiding Channel

The initial dielectric image guide (DIG), as shown in Figure2, is designed with a piece of low-loss high permittivity Rogers RT 6010 substrate (permittivity 11.4, loss tangent 0.0023, and thickness 2.54 mm). The high permittivity material is chosen to have a higher field concentration within the waveguide core. The degenerate Ex11 mode with a parallel electric field can be avoided by the metal ground. Hence, only the Ey11 mode (Figure 3(a)) is left as the dominant mode and to propagate inside the channel (Figures 3(b), and Figure 4 gives the insertion losses of the first two modes. It can be seen that a single mode transmission has been achieved below 14.5 GHz.Figure 2
Grounded image guide (a = 8.8 mm, b = 2.54 mm, and L = 30 mm).Figure 3
Ey11 mode of the dielectric image guide: (a) port mode field and (b) propagation mode field.
(a)(b)Figure 4
Transmission efficiency of the first two modes (with (1) and (2) representE11y and E21y, respectively) of the grounded DIG.


## 2.2. Eigenmode Analysis of EBG Unit

In many cases, the eigenmode analysis of EBG structures is based on the Bloch–Floquet theorem, which describes the wave propagation in an infinite medium consisting of periodic unit cells. The relationship between the propagation constant and frequency can be given by the dispersion diagram.For a two-dimensional periodical structure, the dispersion diagram can be given by starting fromΓ (0, 0), going to X (0, π), then to M (π, π) and back to Γ, as indicated in Figure 5(a). In this work, a mushroom-like unit is used (also see in Figure 5(a)), consisting of one central square patch with metal vias connected to the ground.Figure 5
(a) Mushroom-type square EBG unit of sized = 2.8 mm, consisting of a square patch with size a = 2.0 mm, connected in the center to the ground by a via with radius r = 0.3 mm. The points defining the path in the Brillouin zone are also indicated. (b) Boundary conditions in the simulations.
(a)(b)In order to mimic the periodicity of the structure, the boundary conditions at the side walls are defined as periodic boundaries. As the eigenmode solver in CST does not support open boundary conditions, both the top and bottom sides are defined as electric conductors, see Figure5(b). Also, consider that the fields are mainly concentrated inside the substrate, and just above the substrate, air interface, a proper height of the air layer, i.e., more than ten times the substrate thickness, yields the correct field distribution of the eigenmodes.The dispersion diagram is plotted in Figure6. As discussed, it incorporates three intervals (Γ to X,X to M, and M to Γ) to describe all possible propagation directions in the xy plane. In each direction, the phase changes are swept from 0 to π, and the cutoff frequency for each eigenmode is calculated.Figure 6
Dispersion diagram of the EBG unit (with red lines for the light cutoff frequency).It is known that the mushroom-like EBG structure allows the propagation of TM waves at low frequencies and TE waves at high frequencies [18]. The first mode is thus a TM mode, which starts as a forward propagating TEM mode at very low frequency and low wavenumber and changes into a forward TM surface wave. Modes 2, 3, and 4 are hybrid modes that start as TE waves at a very low wavenumber and transform into TM waves at high frequencies.Figure7 presents the electric field distribution in the yz plane of the first four eigenmodes. We can see that mode 2 is orthogonal to the transmission mode inside the waveguide, and mode 2 will not be excited and can be neglected from considerations. Meanwhile, since the transmission mode inside the dielectric image guide is a slow wave with the phase speed slower that the light, the frequency band gap should also below the frequency line of light [19], as seen in Figure 6. Therefore, the band gap for this periodic structure is ranging from about 6.5 GHz to 15.0 GHz.Figure 7
Sectional view of electric field distribution of the four eigenmode inyz plane. (a) Mode 1. (b) Mode 2. (c) Mode 3. (d) Mode 4.
(a)(b)(c)(d)


## 2.3. Feeding Structure

In order to achieve a smooth mode conversion from the feeding structure to the guiding channel, a CPW to SIW (substrate integrated waveguide) transition with a V slot is used to excite the transmission mode inside the guiding channel (Figure8). The complete feeding structure is obtained by a step-by-step design procedure and finally assembles each part together. The listed parameters are optimized to ensure that the different parts can satisfy the working frequency band. Among them, the dimensions of the tapered CPW and V-slot play the key roles on determining the frequency range and transmission efficiency. Besides, this planar structure is important for the interconnections between MMIC chips and coaxial cables. The tapered CPW feed line with ground is employed to match with SIW and results in a wide band transition [20, 21]. The fundamental mode inside the waveguide is similar to TE10 mode, while the cutoff frequency can be calculated by the sectional dimensions and the design parameters of the metal vias as follows [22]:(1)fc=c2εras−d2/0.95p,and the equivalent wavelength of SIW is obtained by(2)λg=2πεr2πf2/π/as2,where εr is the relative permittivity of the substrate material, as refers to the distance between the two rows of metal vias, d is the diameter of the vias, p represents the periodical distance between vias, and c is the speed of light. With the design parameters listed in Figure 8, we can get fcTE10=6.61GHz and fcTE20=13.22GHz. In the upper frequency limit of 12.8 GHz, the equivalent wavelength is calculated with λg=7.92mm>as. Therefore, these computed results show that only the dominant mode can be propagated inside the SIW within the operation frequency range of 12.0 to 12.8 GHz.Figure 8
Feeding structure (w = 11.35, w1 = 1.3, w2 = 3.2, s1 = 0.8, s2 = 1.8, d1 = 2, d2 = 1.4, dv = 5.6, dx = 3.4, dz = 10.4, dr = 3.6, p = 0.8, and r = 0.3. Unit: mm).In Figure9, the electric field distributions in the different parts of the structure are presented. The transmitted TE10 mode within SIW is well matched with the dominant E11y mode in DIG, delivering a smooth mode conversion. The simulated S parameters (Figure 10) show that a reasonable transmission efficiency is achieved in the desired frequency range. In order to illustrate the influence from the EBG units, the reflection and transmission parameters are also given in this figure for the original dielectric waveguide without these units in comparison. It is clearly seen that the presence of these mushroom units can generate a wave guiding channel and, moreover, eliminate a series of resonances in the structure, giving it a much more stable S21 in the operational band than the original dielectric waveguide. Although there are some ripples appeared in the S11 performance, it still keeps below -10 dB at the target frequency range (12.0 – 12.8 GHz) even when compared with the structure without EBG units.Figure 9
Mode conversion from the feeding structure to guiding channel. The length of the structureL = 71.2 mm.Figure 10
Comparison of the simulated reflection and transmission parameters of the waveguide realized with the EBG units and the original dielectric waveguide.


## 3. Leaky Wave Antenna Array

Based on the proposed dielectric waveguide, a Ku-band periodic leaky wave antenna array is designed and shown in Figure11. It contains six metal strips in the top interface.Figure 11
Configuration of the proposed Ku-band periodic leaky wave antenna array (La = 4, Wa = 0.8, Pa = 12, da = 13.4, unit: mm).The fabricated prototype and the measurement setup in the anechoic chamber are shown in Figure12. The return loss is measured with a network analyzer and agrees satisfactory with simulations (Figure 13). The reflection coefficient is below -10 dB in the frequency range of 12.0–12.8 GHz, which proves that this antenna prototype can work efficiently at this band. Also, the simulation yields that, at 12.5 GHz, about 79.9% of the total energy is radiated.Figure 12
Far field measurement setup with the fabricated prototype.Figure 13
Comparisons ofS parameters and the radiation efficiency, with red lines for S parameters and blue ones for the radiation efficiency, solid lines represent the simulated results, and the dashed lines represent the measurements.In Figure14, the polar radiation pattern is plotted at different frequencies, 12.0 GHz, 12.5 GHz, and 12.8 GHz, with main beam directions of 82°, 65°, and 52°, respectively, indicating a scanning in the forward quadrant. The main lobe magnitude at these frequencies is 11.36 dBi, 11.97 dBi, and 11.71 dBi, respectively.Figure 14
Simulated radiation pattern in E-plane (yOz plane); Cpol refers to the co-polarization (Eθ) component.In Figure15, the normalized far field patterns at 12.0 GHz, 12.5 GHz, and 12.8 GHz are plotted in XOY and YOZ planes with both co- and cross-polarization components, respectively. In the XOZ plane, since the main beam is changed from the normal direction to the forward sides, as seen in Figure 14, the co-polarizations also decrease a lot at the frequency of 12.5 GHz and 12.8 GHz. Even though, there is still a good agreement between the measured and simulated results on co-polarized components. As the measurements are easily influenced by the small radiation from the feeding cable at a quite low magnitude, a large discrepancy is observed in Figure 12. However, a similar trend can be seen between the measured and simulated results on the cross-polarization component.Figure 15
Radiation patterns at 12.0 GHz, 12.5 GHz, and 12.8 GHz with both co- and cross-polarization components; red and blue lines represent the measured and simulated results, respectively. Mea.Co and Mea.X refer to the measured co-polarization and cross-polarization components, respectively, while Sim.Co and Sim.X represent the simulated results.In theXOY plane, the radiation beam magnitude in the broadside direction is close to that in the YOZ plane at 12.0 GHz, as the main beam direction is close to broadside at this frequency point. However, with the frequency increase, the main beam starts to tilt away from the normal direction, resulting in the fact that the maximal value in the XOY plane decreases a lot at both 12.5 GHz and 12.8 GHz with respect to the one in the XOZ plane.The maximal realized gain is presented in Table2 in both simulations and measurements; this gain is almost constant over the band considered. The maximum variations are about 0.5 dB. Also, the measured gain is about 1.5 – 2.0 dB lower than the simulated one. This is partially due to the conductor losses in the many solderings, which are difficult to take into account in the simulations.Table 2
Realized gain and radiation efficiency at different frequency points.
Freq./GHz12.012.512.8Simu.Gain/dBi11.3611.9711.71η86.72%91.62%82.34%Meas.Gain/dBi10.09.9310.4η80.04%82.23%89.18%


## 4. Conclusion

In this paper, the EBG units are used to generate a guiding channel on a planar board. These units are essential to ensure the transmission efficiency and eliminate the coupling effect between channels. The planar topology offers a great potential for the PCB-based practical applications and extends to design a six-element periodical leaky wave array. With a low profile (80.6 × 25.6 mm), a high radiation efficiency (86.7%), and a reasonable gain performance (11.36 dB) in combination with the frequency-dependent beam scanning of 30 degrees in the forward direction, this antenna topology can be applied for radar applications involving of target tracking and speed detection on road.



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*Source: 5527445-2021-05-25.xml*