The sub-array beamforming network block diagram

Theory

In a linear array with interleaved sub-arrays and maximum beam location at ${\theta_\alpha }$, the sub-array factor can be calculated as given in (4).

(4)\begin{equation}A{F_{{\textrm{sub}}}} = \sum\limits_{n = 1}^N {{B_n}} {\textrm{exp}}\left( {j{{2\pi } \over {{\lambda_0}}}\left( {n - 1} \right){d_{\textrm{s}}}\left( {{\textrm{sin}}\theta - {\textrm{sin}}{\theta_{\alpha}}} \right)} \right)\end{equation}

where $n$ is the sub-array element index, and ${B_n}$ is the magnitude of the $n{\textrm{th}}$ sub-array element. The main beam peak location has been calculated as given in (5).

(5)\begin{equation}{\textrm{sin}}{\theta_\alpha } = \alpha \Delta {\textrm{sin}}{\theta_{{\textrm{peak}}}} = \alpha {{{\lambda_0}} \over {P{d_{\textrm{s}}}}}\end{equation}

Considering (4) and (5), $A{F_{{\textrm{sub}}}}$ can be calculated as follows:

(6)\begin{equation}\begin{aligned} A{F_{{\text{sub}}}} &= \sum\limits_{n = 1}^N {{B_n}} {\text{exp}}\left( {j\frac{{2\pi }}{{{\lambda_0}}}\left( {n - 1} \right){d_{\text{s}}}\left( {{\text{sin}}\theta - \alpha \frac{{{\lambda_0}}}{{P{d_{\text{s}}}}}} \right)} \right) \\ & = \;\sum\limits_{n = 1}^N {{B_n}} {\text{exp}}\left( {j\frac{{2\pi }}{{{\lambda_0}}}\left( {n - 1} \right){d_{\text{s}}}{\text{sin}}\theta - j2\pi \left( {n - 1} \right)\frac{\alpha }{P}} \right) \hfill \\ \end{aligned} \end{equation}

where $\alpha $ is a parameter related to the beam index $\left( {{\alpha_i}} \right)$ and can be calculated from (7). The beam index varies from 1 to $P$ as depicted in Fig. 3.

(7)\begin{equation}\alpha = {\alpha_i} - 0.5 - P/2\end{equation}

Therefore, the $n{\textrm{th}}$sub-array element exhibits a phase shift of $j2\pi \left( {n - 1} \right){\alpha \over P}$ for the $\alpha {\textrm{th}}$ beam.

Figure 3. The beams and their polarizations in one of the rows of the coverage area $({\textbf{ P}} = 8)$.

The right lateral elements are fed from the first elements of the first ${N_{\textrm{L}}}$ subarrays, as illustrated in Fig. 2. The left lateral elements are fed from the last elements of the last ${N_{\textrm{L}}}$ subarrays. ${N_L}$ is the number of right- and left-side lateral-elements. For maintaining the beam pointing angles, an extra phase shift, which compensates the distance between the lateral element and the corresponding subarray element, should be added to each lateral element. This phase shift varies for different beams, and can be calculated from (8).

(8)\begin{equation}\Delta {\varphi_\alpha } = {{ - 2\pi } \over {{\lambda_0}}}{N_{\textrm{c}}}d{\textrm{sin}}{\theta_\alpha }\end{equation}

where ${N_{\textrm{c}}}$ is the total number of core elements and is equal to ${N_{\textrm{s}}} \times N$. Using (3), it can be deduced that

(9)\begin{equation}{{\Delta }}{\varphi_\alpha } = {{ - 2\pi N\alpha } \over P}\end{equation}

It can be proved that ${\Delta }{\varphi_\alpha }$ is equal for the beams that are $P/N$ beams apart. As a result, using the aforementioned formulas, the block diagram of an SABFN for an array with interleaved sub-arrays can be derived.

SABFN block diagram design regarding the HTS requirements

For an HTS in GEO, an MBPAA that can generate 8 × 8 sub-beams with 0.5° beam-width and 42 dBi gain at the EOC needs a PAA with 18 interleaved sub-arrays and 8 lateral elements [Reference Sharifi Moghaddam and Ahmadi11]. In Fig. 3, the spot beams in each row of the coverage area have been depicted. The number of elements in each sub-array, and element spacing should be 2 and $0.92{\lambda_0}$, respectively. The previously mentioned values for the array parameters have been achieved considering the beams orthogonality condition in (3) and the assumption of a tiny angular distance between the adjacent sub-beams $\left( {{\theta_{dx}} = {{0.43}^\circ },{\ }{\theta_{dy}} = {{0.37}^\circ }} \right)$. The ${\theta_{{\textrm{d}}x}}$ and ${\theta_{{\textrm{d}}y}}$ are the angular distances between adjacent sub-beams in the x and y directions, respectively. Since the angular distance between adjacent spots is very small, this approximation has been used:

(10)\begin{equation}\Delta {\textrm{sin}}{\theta_{{\textrm{peak}}x}} \cong {\theta_{{\textrm{d}}x}}\;\left( {{\textrm{rad}}} \right);\Delta {\textrm{sin}}{\theta_{{\textrm{peak}}y}} \cong {\theta_{{\textrm{d}}y}}\;\left( {{\textrm{rad}}} \right)\end{equation}

The array radiating elements have been assumed to be the conventional circular microstrip patch antennas.

Accordingly, Type I and Type II SABFNs can feed two core elements and one lateral element. Each array element is fed with two ports which create orthogonal polarizations. So, the SABFN should have eight beam ports and six antenna ports. This SABFN can be used for exciting the rows of the array as well as the columns. According to the contents of this section, a block diagram for the type I SABFN has been designed and illustrated in Fig. 4. Realizing this block diagram with a planar microstrip circuit in the C-band is the main subject of this paper, and it has been discussed in the next sections.

Figure 4. Type I SABFN block diagram.

Design of the SABFN components

As can be inferred from the block diagram in Fig. 4, the main components of this SABFN are the 180° hybrid, crossovers (0-dB couplers), power dividers/combiners, and phase shifters. These components have been designed in the following subsections.

Crossover circuit

In a BFN circuit, for combining the signals related to different beams in each radiating element port, a large number of crossovers are required. A crossover allows two transmission lines to cross each other. A typical crossover consists of two cascaded 90° hybrids. The size of this circuit is more than ${\lambda_{\textrm{g}}}/2 \times {\lambda_{\textrm{g}}}/4$, and is not suitable for applications like the satellite payload where size reduction is critical. So, designing a compact crossover circuit is crucial for the size reduction of the BFN. The crossover in this paper consists of printed microstrip lines on two opposite sides of a suspended substrate, as illustrated in Fig. 5. In this crossover, microstrip lines exhibit slight coupling to each other in the crossing region. This phenomenon decreases the circuit performance and enhances the insertion- and return-loss. The coupling has its lowest amount when the microstrip lines are perpendicular to each other. The insertion loss decrement due to the perpendicular crossing of the two microstrip lines compared to the 60°(120°) crossing is less than 0.1 dB. This is at the expense of more than 20% BFN size increment. So, the crossover with 60°(120°) angle between the crossing lines has been selected in the present design, as depicted in Fig. 5.

Figure 5. The crossover circuit in the full-wave simulation environment: (a) xy plane view, (b) 3-D view, and (c) yz plane view.

Another approach for decreasing the coupling is the line width decrement in the coupling region. On the other hand, the line width reduction causes impedance mismatch, which increases the return- and insertion-loss. Consequently, the line width in the coupling region (w _c) should be determined by a trade-off between these two effects.

The microstrips lose their ground in the vicinity of the crossover region. This causes an abrupt impedance increment. The second cause of impedance-change is the line width reduction in the vicinity of crossover. To provide a matched crossover, the air gap over the microstrips in the vicinity of the crossover region has been reduced. This can be done by embedding perfect-conducting cube-shaped ridges in the circuit box, as shown in Fig. 5. The reduced ground plane spacing over the microstrips compensates the impedance-mismatch due to the loss of the ground plane beneath the micostrips. In addition, inserting a thin polyvinyl chloride (PVC) layer (with a 0.13 mm thickness) on the cube improves the impedance matching and prevents probable contact between microstrips and the cube.

The crossover parameters have been adjusted and presented in Table 1. Full-wave simulation results showed that the isolation between ports and the return-loss in the frequency band of 3–5 GHz are >33 and >21 dB, respectively. The crossover exhibits an insertion loss of 0.1 dB in that frequency band.

Table 1. Geometrical parameters of the crossover

The 180° hybrid

The crossover circuit of the previous section implies that the ∑ and ∆ ports of the hybrid appear on different layers of the suspended substrate. This property can be inferred from the proposed block diagram in Fig. 4.

In this paper, a 180° hybrid consisting of two broadside magnetically coupled strips, which also acts as a 2:1 impedance transforming power divider [Reference Moghaddam and Ahmadi12], is the appropriate choice for the SABFN. The 180° hybrid, which is actually a printed circuit balun, has smaller dimensions compared to a conventional Marchand balun [Reference Marchand13]. The relative bandwidth of this type of hybrids is typically 44%, which is relatively wide due to the intrinsic wideband property of magnetically coupled lines [Reference Moghaddam and Ahmadi12].

As illustrated in the block diagram of Fig. 4, the ∑ and ∆ ports should be located at one side, and the other two ports (ports 2 and 3) should be at the other side of the hybrid. This cannot be realized unless the transmission line connected to port 2 and terminated at the other side crosses over the line leading to the Δ port. This line has been printed on the opposite side of the substrate. Adjusting the crossover parameters of this circuit is similar to the crossover mentioned in the previous section. In this paper, the180° hybrid has been optimized for the frequency range of 3–5 GHz. Figure 6 shows the 180°, which has been realized on a suspended substrate, in the high-frequency simulation software (HFSS) environment. The dimensions of the 180° hybrid have been given in Table 2. The parameters in Table 2 are consistent with the geometrical parameters given in Fig. 6.

Table 2. Geometrical parameters of the 180° hybrid in mm

Figure 6. Model of the 180° hybrid in HFSS: (a) upside view, (b) downside view, and (c) 3D view.

For size reduction of the T-junction divider and the impedance-matching stub, the height of the air gap on the upper side of the circuit has been decreased to ${h_{\textrm{d}}}$. Also, similar to the “Crossover circuit” section, two perfect-conducting cube-shaped ridges in the crossover region have been embedded in the simulation box. To improve the circuit performance, a capacitor has been placed between the two branches of the balun. After some tuning, the appropriate value of this capacitor has been found to be 0.7 pF. This capacitor has been realized by a parallel plate structure of copper–insulator–copper layers [Reference Pozar14]. The dimension of the upper copper-layer is 1.98 × 1.2 mm². The insulator is a PVC layer with a thickness of 0.13 mm. The lower plate of the capacitor is part of the strip conductor. Simulation results of the entire 180° hybrid have been illustrated in Fig. 7. As can be seen from Fig. 7, S21 is between −2.9 and −3.5 dB in the frequency band of 2.9–4.5 GHz. The −10 dB return-loss bandwidth is 3.1–5.1 GHz. The guided wavelength, ${\lambda_{\textrm{g}}}$, in the suspended strip line at 4 GHz is 46.75 mm, and the hybrid occupies a space of $0.39{\lambda_{\textrm{g}}} \times 0.33{\lambda_{\textrm{g}}} \times 0.053{\lambda_{\textrm{g}}}$.

Figure 7. Scattering parameters of the 180° hybrid: (a) magnitude of S12, S13, S24, and S34 in dB, (b) magnitude of S11, S22, S33, and S44 in dB, and (c) phase of S21, S31, S24, and S34.

Power divider

According to the SABFN block diagram in Fig. 4, for feeding the array lateral elements, four 2-way power dividers are needed. For combining the feeding signals of the lateral elements, some crossovers appear in the feed network. The crossover in section the “Crossover circuit” section consists of two strips, which have been printed on the opposite sides of a suspended substrate. So, if using this type of crossover, the output ports of the divider should be located on the two opposite sides of a suspended substrate. In this paper, the divider has been realized by a 3-dB broadside coupler. In the design of the 3-dB broadside coupler, analytical relations presented in papers [Reference Pozar14] and [Reference Mongia, Bahl and Bhartia15] have been used. For equal power division in a broadside coupler, (10) should be satisfied.

(11)\begin{equation}y = {{\sqrt {1 - {C^2}} } \over {C\;{\textrm{sin}}\theta }} = 1\;\end{equation}

where C is the voltage coupling factor between the broadside coupled lines and has been calculated in paper [Reference Pozar14]. In (10), $\theta $ depends on the coupled lines length $\left( l \right)$, and equals $\beta l/\lambda $, where $\beta $ and λ are the propagation constant and wavelength, respectively.

The characteristic impedance of the coupled lines has been determined as presented in papers [Reference Mongia, Bahl and Bhartia15–,Reference Howe17]. By the use of (10) and setting the characteristic impedance of the coupled lines to 50 Ω, the initial values for the width and length of the 3-dB coupler can be calculated. Precise values for these parameters have been obtained after tuning in the HFSS. Figure 8 shows the divider model used in the simulation. Parameters of the final version of the divider have been presented in Table 3. Simulation results shows that the insertion loss in the frequency band of 3–3.9 and 3.9–4.4 GHz is <0.6 and <1 dB, respectively.

Table 3. Parameters of the designed divider in mm and Ω

Figure 8. Simulation model of the power divider: (a) Bottom view and (b) 3D view.

The phase difference between through and coupled ports of a broadside coupler is −90° [Reference Pozar14]. In the proposed power divider, because of adding a bend and a transmission line to the coupled line, the phase difference between S21 and S31 in the 3.4–4.3 GHz band exhibits a value of <−80°, which is <10° higher compared to the theoretical value of −90°.

SABFN simulation

In this section, by incorporating the hybrid, crossover, and power divider of the previous section into the SABFN block diagram of Fig. 4, the entire SABFN has been simulated and analyzed in HFSS. Figure 9 shows the SABFN in the HFSS environment. In this circuit, several Wilkinson power combiners for feeding the array elements have been used. The key point in the design and simulation of the SABFN is that the ground plane of each block must be in contact with the aluminum box of the entire circuit, as demonstrated in Fig. 9(b). Consequently, the ground planes of all blocks are at the same potential. The total size of the circuit is 88 × 90 × 2.5 mm³. The area of SABFN in this paper is half of an SABFN that has been implemented with a one-sided microstrip circuit, and two cascaded branch-line couplers as the crossover.

Figure 9. The simulated model of the SABFN: (a) upper side view and (b) 3D view.

The simulation results of the scattering parameters of the ports adjacent to the hybrid 1 (ports 1, 5, 9, 11, and 13) have been depicted in Fig. 10(a). In the 3.05–4 GHz band, where impedance matching is desirable, the return-loss is >10 dB. The insertion loss in this frequency band is <3 dB.

Figure 10. S-parameters of the ports adjacent to hybrid 1: (a) S11, S55, S99, S11,11, and S13,13, and (b) S19, S5,11, S59, S5,13, and S1,11.

The return-loss of the ports adjacent to hybrid 2 (ports 2, 6, 9, 11, and 13) have been plotted in Fig. 11(a). As is shown in Fig. 11, in the frequency range of 3.5–4.35 GHz, which is the operating frequency of the feed-network, the input matching is acceptable. In this frequency range, as shown in Fig. 12(a), the insertion-losses are <3 dB.

Figure 11. S-parameters of the ports adjacent to hybrid 2: (a) S22, S99, S66, S11,11, and S13,13 and (b) S2,9, S2,11, S2,13, S6,9, S6,11and S6,13.

Figure 12. S-parameters of the ports adjacent to hybrid 3: (a) S33, S77, S10,10, S12,12, and S14,14 and (b) S3,10, S3,12, S7,10, S3,14, and S7,14.

The simulated S-parameters of the ports adjacent to hybrid 3 (ports 3, 7, 10, 12, and 14) have been shown in Fig. 12(a) and (b). The ports return-loss in the frequency band of 3.24–4.25 GHz are >10 dB, and the insertion-losses are <3 dB.

The ports that are connected to the hybrid 4 (ports 4, 8, 10, 12, and 14) exhibit a return-loss of >10 dB in the frequency range of 3.4–4.3 GHz, as depicted in Fig. 13(a). Figure 13(b) shows the insertion-loss of these ports in the frequency band of 3.5–4.5 GHz, which is <2.5 dB.

Figure 13. S-parameters of the ports adjacent to hybrid 4: (a) S44, S88, S12,12, S10,10, and S14,14 and (b) S4,10, S4,12, S4,14, S8,10, and S8,14.

The simulated phases of the S-parameters have been shown in Fig. 14. As can be inferred from the simulation results, in the SABFN, the desired phase differences have been achieved. For proper operation, extra phase-shifting transmission-lines with 180° and 225° phase shifts should be attached to ports 13 and 14, respectively.

Figure 14. Phase of the SABFN S-parameters.

If a criterion of 10 dB return-loss is considered for bandwidth-evaluation, the simulated bandwidth for hybrid 1–4 is 1, 0.85, 1.01, and 0.9 GHz, respectively. In those bandwidths, the insertion-loss of the previously mentioned ports is <3 dB. The required bandwidth of each spot is 40 MHz. As can be inferred from simulation results, in this bandwidth, the insertion-loss of the circuit is <2.5 dB.

Fabrication and measurement of the SABFN

The SABFN has been implemented on a double-sided RO4003 substrate with thickness of 0.5 mm, and is shown in Fig. 15. Two 3-mm thick aluminum plates serve as cover for the entire circuit. As can be seen from Fig. 15, the substrate is sandwiched between the upper and lower cover. Some ridges in the aluminum plates provide connections to the ground of the microstrip board. The aluminum covers have been fabricated with a CNC machine, and with a 0.1 mm accuracy. As illustrated in Fig. 15(a) and (b), on the ridges relevant to crossover regions, thin insulating PVC layers have been attached. These thin insulating layers serve for better impedance matching, and avoid possible short-circuit of the aluminum plate and microstrips due to fabrication tolerances. For adequate connection of the covers to the substrate ground, a lot of screws has been provided in various regions of the covers.

Figure 15. Fabricated SABFN: (a) upper cover and top-view of the substrate, (b) lower cover and bottom-view of the substrate, and (c) substrate with the upper and lower cover.

The 0.7-pF capacitors, which are required for proper operation between the balun stubs, have been fabricated with insulating PVC layers, which have a thickness and area of 0.13 mm and 1.5 × 1.98 mm², respectively. The PVC layer is sandwiched between two copper strips of the same size. Several female SMA connectors have been used for feeding the circuit and for measuring the scattering parameters. In the measurements, the unused ports were terminated into 50-Ω loads.

The measured return-loss of the ports has been illustrated in Fig. 16, and compared with simulation results of Fig. 11(a). Measurements show that in the 4–4.4 GHz band, the ports’ return-losses are >10 dB.

Figure 16. Measured and simulation results of the SABFNs’ return-losses.

The measured insertion-loss between various ports has been compared with simulations in Fig. 17. As is seen from Fig. 17, in the frequency range of 4–4.4 GHz, an acceptable conformance between measurements and simulations exists. The measured values of S1,11, S2,11, S6,11, and S5,11 are between −8.5 and −6.5 dB. The simulated values for these parameters, obtained from simulation, are between −8.5 and −6 dB. The theoretical values for these parameters are −6 dB, as the incident waves pass through two power dividers. As a result, the measured added insertion-loss compared to the theory is 2.5 dB.

Figure 17. Measured and simulation results of the SABFNs’ insertion-losses.

The measured values of S2,9 and S6,9 in the frequency range of 4.3–4.6 GHz are between −12.5 and −11 dB. The simulation results in this frequency band are between −12.5 dB and −9 dB. In the theory, the previously mentioned parameters are −9 dB due to presence of three 2-way power dividers in the transmission path. Therefore, the measured added insertion-loss in the worst case is 3.5 dB.

The measured values of S1,13 and S5,13 in the frequency range of 4–4.5 GHz are between −12 and −9 dB. The simulation values of the previously mentioned parameters are between −12.5 and −11.5 dB.

The measured extra insertion-loss is due to transmission-loss of the cascaded hybrids, power dividers, crossovers, and phase shifters, which are non-ideal components. Some of the added insertion-losses above the theoretical values are due to connectors and fabrication tolerances.

The simulated and measured insertion-phases have been illustrated in Fig. 18(a) and (b), respectively. Figure 18 presents good agreement between simulation and measurement. Measurements show that the required phase shifts in the initial block diagram of the SABFN have been obtained with a phase deviation of maximum 10°, which is acceptable in many applications.

Figure 18. Phase response: (a) simulation and (b) measurement.

MBPAA radiation pattern

Since the cost of manufacturing the entire PAA system is high, in the present work, only the SABFN has been fabricated. To demonstrate the performance of the designed SABFN, and investigate the ability of the SABFN in generating multiple beams, a planar array with interleaved sub-arrays in two dimensions has been simulated in MATLAB. This procedure is conventional for testing the capability of BFNs in producing multiple beams [Reference Lian, Ban, Zhu and Guo18, Reference Ding and Kishk19].

The array can provide 8 × 8 beams simultaneously, and has been designed and optimized for the following requirements: ${G_{{\textrm{EOC}}}}$ = 42 dBi, contour level = 1 dB, beam width = 0.5°, ${\theta_{{\textrm{d}}x}} = 0.43^\circ ,\;{\theta_{{\textrm{d}}y}} = 0.375^\circ $, and SLL = −16 dB [Reference Sharifi Moghaddam and Ahmadi11].

The measured scattering parameters of the fabricated SABFN have been used for feeding the array. As mentioned in the “The sub-array beamforming network block diagram” section, in each row, the numbers of sub-arrays, sub-array elements, and lateral elements are 18, 2, and 8, respectively. In addition, interleaved sub-arraying technique has been used for the array columns. The numbers of sub-arrays, sub-array elements, and lateral elements for each column are 20, 2, and 8, respectively. The radiating elements are circular patches, and the element spacing in the x and y directions are 0.92λ ₀ and 0.95λ ₀, respectively. The array is in the xy plane. The directivity patterns in the $\varphi = 0^\circ $ and $\varphi = 90^\circ $ constant planes have been plotted in Fig. 19(a) and (b), respectively. The distance between array elements and the number of sub-arrays comply with (3), so the excitation vectors of the array ports are mutually orthogonal and their scalar multiplication is zero. Consequently, the designed BFN is orthogonal and the sub-beams do not couple despite very small angular distance between the adjacent sub-beams.

Figure 19. Simulated gain patterns of the planer array fed by the measured S-parameters of the SABFN (a) φ = 0°, (b) φ = 90°.

In Fig. 20, the directivity patterns of the array obtained by measured scattering parameters of the SABFN have been compared with an ideally fed array. It can be deduced that the amount of gain degradation due to an imbalance in the transmission-losses and fabricated tolerances of the SABFN is <0.5 dB.

Figure 20. Comparison of gain patterns of the array fed by the BFN (red lines) with the ideally fed array (blue dashed lines).

In this work, mutual coupling between array elements has not been considered in the MATLAB simulations. Applying electromagnetic bandgap (EBG) structure between array elements is a conventional method for reducing mutual coupling without degrading the antenna performance. This technique has been frequently used and verified in real antenna array models [Reference Yang and Rahmat-Samii20–Reference Assimonis, Yioultsis and Antonopoulos25]. Therefore, it can be considered as a reliable method for mitigating the mutual coupling, and it will be used for future works where an implementation of the whole PAA system is intended. EBG is a periodic structure which prevents wave propagation in a special frequency band [Reference Orlandi, Archambeault, de Paulis and Connor26, Reference Caloz and Itoh27] and suppresses the surface wave propagation on the radiating aperture surface. In paper [Reference Yang and Rahmat-Samii20], a mushroom-type EBG has been utilized between microstrip patches in C-band for reducing the mutual coupling. By using microstrip EBG in an array of patch elements with half wavelength element-spacing, the mutual coupling has been reduced more than 24 dB in the C-band [Reference Mohamadzade and Afsahi21]. In paper [Reference Rajo-Iglesias, Quevedo-Teruel and Inclán-Sánchez22], a planar microstrip EBG structure has been printed between patch elements, and the mutual coupling has been reduced more than 10 dB. The uniplanar compact EBG printed on the superstrate has been successfully used in paper [Reference Sarbandi Farahani, Veysi, Kamyab and Tadjalli23] with more than 10 dB mutual coupling reduction.

Consequently, in the final model of the antenna, EBG structures will be used between array elements. So, the assumption of zero mutual coupling in the simulated model of the array antenna is valid.

It should be mentioned that the design and optimization of the EBG structure for surface wave suppression is not subject of this paper but has been suggested for placement in the final antenna system.

Comparison and discussion

A comprehensive comparison between presented BFN in this paper and other references has been made in this section. The main characteristics of the compared BFNs are provided in Table 4.

Table 4. Comparison between present design and other works

FB: frequency band, IL: insertion loss, RL: return-loss, NG: not given, λ: wavelength in free space

The BM has been implemented by microstrip, stripline, and substrate-integrated waveguide (SIW) technologies in papers [Reference Kwang and Gardner28–Reference Chen, Hong, Kuai and Wang30], respectively. In all of these works, the antenna’s field of view is wide and the distance between adjacent beams is between 30° and 45°. In paper [Reference Chen, Hong, Kuai and Xu31], a 4 × 16 Blass matrix has been implemented using double-layer SIW technology. The distance between adjacent beam ports is 7.5°, but the beams are not orthogonal. So, it is not suggested for C-band applications.

In paper [Reference Fakoukakis and Kyriacou32], a 4 × 4 Nolen matrix by using microstrip technology has been designed in S-band. This BFN is larger than the present design, despite the smaller value of antenna and beam ports.

An eight-port hybrid for realizing a 4 × 4 BFN has been designed in paper [Reference Cheng, Hong and Wu33] using SIW technology. The number of beam and antenna ports of this circuit cannot be extended, and it is suitable for special applications.

The frequency band and dimension of the BFN in paper [Reference Ding, Fang and Wang34] are similar to the BFN of the present paper, but the number of beam and array ports is limited to 3.

In paper [Reference Maximidis, Caratelli, Toso and Smolders35], the overlapped sub-arraying technique has been implemented without any complex BFN, and the free-space coupling method has been applied. Each sub-array consists of 13 open-ended waveguide elements, with the central element directly fed, and the other elements have been reactively loaded. In that work, the overlapped sub-arraying technique has been realized by coupling between adjacent sub-array elements. The whole array has been designed for 0.5° HPBW and consisted of 38 sub-arrays. Due to the overlapped sub-arrays, the grating lobes have been eliminated in this array antenna. The field of view of this antenna is limited, and the angular distance between adjacent beam ports is 4.5°. As can be seen in Table 4, the size of this multibeam antenna is considerably larger than the size of the antenna in this paper despite smaller number of beam and array ports, and is not suitable for C-band applications.

As can be inferred from Table 4, the bandwidths of all BFNs are less than 16% except [Reference Sarbandi Farahani, Veysi, Kamyab and Tadjalli23], which exhibits a wide bandwidth due to a double-layer stripline structure. In that work, a wide bandwidth was achieved but at the cost of a large circuit size.

SIW circuits at Ku and Ka band exhibit lower insertion loss compared to a microstrip and stripline circuit, but the size and circuit complexity make SIW circuits improper for lower frequency applications.

As can be inferred from Table 4, the proposed BFN has the lowest size for a specified number of beam and array ports compared to other works. Also, compared to other works, it has the narrowest angular distance between adjacent beams while keeping the beams orthogonality. In this paper, and to the knowledge of the authors, it is the first time that the printed microstrips on the two opposite sides of a suspended substrate have been used in the BFN realization, and as can be deduced from Table 4, this technique has reduced the circuit size considerably.