Frequency [GHz]

Transcription

1 2.3. PRACTICAL CASE Amplitude Unbalance per Phase Shift [db] º Port º Port º Port º Port º Port º Port º Port º Port 2 2.5º Port 1 2.5º Port º Port º Port º Port º Port º Port º Port Frequency [GHz] Figure 2.15: 1 to 2 Power Splitter/Combiner 3 bits Amplitude Unbalance Between Array Ports per Phase Shift Measurement Beam Port 1 1 to 3 0º Power Splitter!!!!!!!!!! 1 DPDT 2 DPDT 3 DPDT!!! -4dB!!! Array Port 1 Array Port 2 Array Port 3 Figure 2.16: 1 to 3 Power Splitter/Combiner 3 bits Phase Shifter 28+ from Mini-Circuits. The device has been measured, testing its behavior at 2.25 GHz. Measurements show a correct performance compared to the data provided by its datasheet: 15 db isolation, 1.2 VSWR, 6 o phase unbalanced, and 1 db insertion losses. 35

2 CHAPTER 2. STUDY OF RF STEERING TECHNIQUES IN ACTIVE RECONFIGURABLE ANTENNAS Table 2.3 shows an estimation of the losses of the whole 1 to 3 combiner/divider 4 bits phase shifter, using maximum and minimum losses provided by the manufacturers. A minimum of 8.4 db and a maximum of 10.7 db losses are expected if losses of both, devices and transmission lines, are taken into account. These losses include split and insertion losses. Table 2.3: 1 to 3 Power Splitter/Combiner 3 bits Phase Shifter Insertion Losses 1 to 3 Power Splitter π Phase Shifter 1 DPDT π 2 Phase Shifter 2 DPDT π 4 Phase Shifter 3 DPDT π 4 Phase Shifter TOTAL L min [db] L max [db] An amplitude mismatched could be observed between array ports 1 or 3, L 10 db, and array port 2, L 6 db, because of DPDT insertion losses. To solve this problem, a 4 db T-attenuator before array port 2 was used, obtaining a quasi-uniform amplitude in every single array port. Figure 2.17 presents the implementation of the 1 to 3 power splitter/combiner 3 bits phase shifter. The device has been measured with a vector analyzer, obtaining the measurements shown in Fig (relative phase shift between array ports) and Fig (unbalance amplitude between array ports). Its performance is within the expected limits, providing a ±5 phase error and a ±0.8 db unbalanced amplitude. If the 1 to 3 power splitter 4.8 db split losses are excluded from Fig. 2.19, the insertion losses of the implemented network would be over 3.8±0.8 db per port. These insertion losses are similar to the insertion losses provided by the commercial phase shifter devices. Worth noting that the beam port to array port 3 path always presents 8.6 db losses for every phase shift step. It is important to remark that every beam/array port presents a good match better than -10 db at the whole band. 36

3 2.3. PRACTICAL CASE Figure 2.17: 1 to 3 Power Splitter/Combiner 3 bits Phase Shifter Implementation º º +67.5º +22.5º 2.5º 67.5º 12.5º 57.5º 150 Phase Step [deg] Frequency [GHz] Figure 2.18: 1 to 3 Power Splitter/Combiner 3 bits Phase Step Between Array Ports per Phase Shift Measurement 37

4 CHAPTER 2. STUDY OF RF STEERING TECHNIQUES IN ACTIVE RECONFIGURABLE ANTENNAS Amplitude Unbalance per Phase Shift [db] º Port º Port º Port º Port º Port º Port º Port º Port 2 2.5º Port 1 2.5º Port º Port º Port º Port º Port º Port º Port Frequency [GHz] Figure 2.19: 1 to 3 Power Splitter/Combiner 3 bits Amplitude Unbalance Between Array Ports per Phase Shift Measurement 38

5 2.4. CONCLUSIONS 2.4 Conclusions Due to the strategic/economic key role played by commercial phase shifters in the implementation of reconfigurable antennas, three different low-cost RF steering alternatives have been presented in this Chapter. Switched line phase shifters have been the first proposal. This technique propose to implement one discrete phase shifter per radiating element by using a combination of SPDT and DPDT switches as shown in Fig Switched-beam networks were the second RF steering approach studied. This technique is based on the combination of different beamforming networks such as Butler matrices, which would provide a fixed number of beams. The scheme of the whole network was shown in Fig Finally, a new phase shifter power splitter/combiner network was presented. These novel technique split/combine the signal providing the required relative phase shifts between array port signals. The whole structure integrated by two basic structures composed of power splitters/combiners, SPDT switches, and DPDT switches: the 1 to 2 phase shifter power splitter/combiner (Fig. 2.3.a), and the 1 to 3 phase shifter power splitter/combiner (Fig. 2.3.b). In order to show a practical use of the three different techniques, the 5-element GEODA-SARAS subarray cell working as a receptor antenna from 2.2 GHz to 2.3 GHz is taken as a conceptual base case. The aim of the study was to propose a low-cost beamsteering system that covers ±30 o in both planes, horizontal and vertical, with a gain losses lower than 0.5 db. After applying the three techniques to the case under study, a performance/complexity/cost balance between the different approaches shows that the best cost-effectiveness is given by the novel phase shifter power splitter/combiner network. To demonstrate the feasibility of this newly phase shifter power splitter/combiner networks, the two main blocks that integrate the proposed network have been built: the 1 to 2 phase shifter power splitter/combiner, and the 1 to 3 phase shifter power splitter/combiner. The implementation of the two blocks has been produced using microstrip technology in RO4350B with mm thickness. Measurement of both networks shows a good agreement with the expected behavior, providing phase and magnitude errors lower than ±5 and ±0.8 db, respectively. Insertion losses of both simple phase shifter power splitters/combiners are over 4 db, which are similar to the insertion losses introduced by commercial phase shifters. Thus, this research remarks some low-cost alternatives to the use of commercial 39

6 CHAPTER 2. STUDY OF RF STEERING TECHNIQUES IN ACTIVE RECONFIGURABLE ANTENNAS phase shifters and show the good performance of the proposed novel phase shifter power splitter/combiner network. 40

7 Chapter 3 Quasi-Orthogonal Switching Beam-Former for Triangular Arrays of 3 Radiating Elements 3.1 Introduction and Motivation From the beginning of telemetry, tracking and command (TT&C) systems, mechanical scanning antennas have been employed at ground stations. As it is well known, this technique is not only sensitive to gravity and mechanical failure, but also slow, increasing the total cost of the system and making simultaneous satellite communications infeasible. The use of electronically scanned antenna arrays overcomes these limitations, allowing much faster multi-beam scans without physical antenna rotation [34, 35]. These types of systems that use information from the link environment to set the proper beam shape are called intelligent architectures [36, 37]. In order to improve the ground station performance, many studies have been carried out in the field of electronic scanning systems, in which large arrays composed of thousands of radiating elements have been considered [32]. Electronic steering technique is based on the control of the relative amplitude and phase of the signal associated with each antenna that composes the whole array. The relative signal can be adjusted by using digital signal processing algorithms, e.g. MUSIC [5] or ESPRIT [6], or placing beam-forming circuits inside the hardware antenna, e.g. phase shifters [28] or switched networks [38]. Nowadays, software/hardware hybrid architectures are gaining special interest because of their versatility. Generally, these huge array structures are divided into sub- 41

8 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS arrays based on unitary cells of at least three radiating elements to reduce not only post-processing data time but also its cost [23, 39, 40]. The unitary cell radiation pattern, the combiner/divider cell circuit and the post-processing data algorithm will define the whole system capabilities. This segmentation may reduce the total number of required active circuits, such as amplifiers or phase shifters [41], decreasing total cost and improving post-processing data efficiency. Usually, this type of antenna performs: a hardware beam steering that selects the willing communication direction area, and a signal data processing algorithm that improves the desired signal to interfering signal/noise rates. Therefore, the study of structures that provide multiple beams in different spatial ranges related to each sub-array cell is needed. The number of radiating elements composing the unitary cell and its distribution state the basic beam scanning shape. A triangular cell of three radiating elements is the simplest way to obtain a planar scanner. In this Chapter, a new multibeam network configuration that provides three orthogonal beams in a desired θ 0 elevation angle and an extra one in the broadside steering direction for a triangular array of three radiating elements will be introduced. Section 3.2 will present a short introduction to the state of art of classical multi-beam networks [42, 43]. Lossless network analysis, including original lossless network designs [38], will be also commented. Section 3.3 will show general dissipative matrices theory as well as applications for array antennas of three radiating elements. In Section 3.4, the proposed final basic multi-beam network will be simulated, built and measured to the GEODA practical case. Section 3.5 will present a combined network that provides six orthogonal beams in a desired θ 0 elevation angle and a double seventh one in the broadside direction by using two complementary proposed basic networks. Measurements of the whole system will be also depicted. Finally, Section 3.6 will collect the conclusion drawn during this Chapter. 3.2 Orthogonal Multi-Beam Forming Networks for Triangular Arrays One of the most important tasks in a phased array antenna is to design the beamforming network (BFN). A BFN essentially combines/divides properly the signal of/to each radiating element compounding the array in order to produce the desired beam. Most common types of BFNs are presented in [41], where Butler matrix [33], Blass network [44], Rotman lens [45], and many more are explained. The Butler matrix is a very common type of beam-former used in practice due to its 42

9 3.2. ORTHOGONAL MULTI-BEAM FORMING NETWORKS FOR TRIANGULAR ARRAYS simple and functional design. Many studies have been developed in order to overcome the limitations of this useful network. As an example, a switching network that generates four beams for three linear radiating elements is presented in [46]. Some network designs presented in this Chapter are based on Butler matrix modifications as shown later. The behavior of a BFN is characterized by its scattering matrix, where each s ij matrix element represents the mutual coupling between each i output port and j input port. Considering beam ports and array ports adapted and isolated from each other, an M by N network responds to the scattering matrix defined in Eq Note [S T ] equals [S R ] H if the network is reciprocal. [ ] S = 0 0 S 1,M+1 S 1,M+N [ ] ] 0 0 S N,M+1 S N,M+N 0 [S R = ] [ ] (3.1) S N+1,1 S N+1,M 0 0 [S T S M+N,1 S M+N,M 0 0 When a network is reciprocal and lossless, the product of the scattering matrix and its conjugated transpose is the identity matrix. This implies that vectors related to the columns of each matrix S T and S R have to be orthonormal to each other in a reciprocal and lossless network. Hence, the number of beam and array ports must be the same; the output power must be equal to the input power; and its scattering matrix vectors must be orthogonal, ensuring isolation between different beams. [ ] ] [ ] ] H [ ] [ ] H 0 [S R S S = ] [ ] 0 [S T ] H [ ] [S T 0 [S R 0 = ] ] H [ ] [S R [S R 0 [ ] H ] ] H = 0 [S T [S T [ ] I (3.2) Steering Analysis: Basic Equations In this Subsection, the lossless scattering matrix of a network associated with a triangular cell of three radiating elements that provides three orthogonal beams in a desired θ 0 elevation angle is presented. Assuming three radiating elements located over vertices of an equilateral triangle in the xy-plane with d side length as in Fig. 3.1, the relation 43

10 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS between the location of the radiating elements and the array signal is shown in Eq. 3.3 and Eq Where r is the spherical unit vector equals to (sin θ cos ϕ) x+(sin θ sin ϕ)ŷ + (cos θ)ẑ. Note Eq. 3.3 is the array factor, and Eq. 3.4 contemplates the fact that feeding phases must satisfy the condition of adding contributions of each array element in the desired steering direction. 3 AF (θ, ϕ) = A i e jα i e jk rr i (3.3) i=1 k 0 rr P atch1 α P atch1 = k 0 rr P atch2 α P atch2 = k 0 rr P atch3 α P atch3 (3.4) Y Beam º 3 Z d Beam 1 X Beam 2 2 Figure 3.1: (Left) Triangular Cell of Three Radiating Elements and Its Orthogonal Beams [Azimuth xy-plane]. (Right) Coordinate System. The lossless scattering parameters of a network associated with a triangular cell of three radiating elements that provides three orthogonal beams in a desired θ 0 elevation angle must satisfy the condition of adding contributions, Eq Hence, it is shown that desired beam is obtained when relations between array port signals are, s P atch1,beam 1 = s P atch2,beam 1 = ae jα (3.5) 44

11 3.2. ORTHOGONAL MULTI-BEAM FORMING NETWORKS FOR TRIANGULAR ARRAYS ports, where, s P atch3,beam 1 = be j(α+β) (3.6) β = 3 πd λ sin (θ 0) (3.7) Two additional orthogonal beams are obtained by rotating signal relations between s P atch1,beam 1 = s P atch2,beam 2 = s P atch3,beam 3 (3.8) s P atch2,beam 1 = s P atch3,beam 2 = s P atch1,beam 3 (3.9) s P atch3,beam 1 = s P atch1,beam 2 = s P atch2,beam 3 (3.10) Every reciprocal and lossless network must fulfill Eq. 3.2, ensuring beam orthogonality. For the first beam, this condition set the relation shown below, s P1,B 1 s P 2,B 1 + s P2,B 1 s P 3,B 1 + s P3,B 1 s P 1,B 1 = 0 (3.11) s P1,B 1 s P 3,B 1 + s P2,B 1 s P 1,B 1 + s P3,B 1 s P 2,B 1 = 0 (3.12) s P1,B 1 s P 1,B 1 + s P2,B 1 s P 2,B 1 + s P3,B 1 s P 3,B 1 = 1 (3.13) Equations 3.11 and 3.12 are equivalent, and Eq represents a signal amplitude normalization. Solving the resulting system of equations Eq Eq. 3.13, it is obtained, a 2 + 2ab cos (β) = 0 (3.14) 2a 2 + b 2 = 1 (3.15) Beam steering direction θ 0 depends on both, array element distance d and feeding signal relation between elements in amplitude a b and phase β, Eq sin (θ 0 ) = λ ( cos a ) 3πd 2b (3.16) It should be noticed that when the feeding amplitude is the same for the three elements, according to Eq.3.7 and Eq.3.16, a β equals 120 o is needed. 45

12 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Figure 3.2 shows the steering elevation direction θ 0 of the array factor for different d, a b and β. As distance between elements d or relation a b increase, beam steering direction θ 0 raise closer to broadside (θ 0 = 0 o ). Beam steering direction θ 0º [deg] a/b = 0.5; β = 104.5º a/b = 0.7; β = 110.5º a/b = 1.0; β = 120º a/b = 1.3; β = 130.5º a/b = 1.5; β = 138.6º Array distance d [λ ] Figure 3.2: Array Factor Steering Direction θ 0 Respect to Array Distances for Different Feeding Signal Relations Lossless Network Designs Once the analysis has been performed, the hard task is to find structures that fulfill the desired behavior. Different lossless schemes of three beam ports by three array ports based on hybrid couplers and fixed phase shifters have been studied, [38]. In this Subsection, two network designs are presented: a three-port symmetric network, and a 3x3 modified Butler matrix. This second network has been designed, built and measured in cooperation with the Universidad de Vigo. The network shows a proper behavior as it is expected. Three-Port Symmetric Network Taking into account the 3x3 network structure under study, a rotational symmetry can be defined in order to get a perfect symmetric behavior between beams and array ports. Figure 3.3 shows a scheme of the network with unbalanced 90 o couplers. Accepting that a feedback between ports arises when the three elements are connected in a closed loop, and considering the scattering matrix of the unbalanced 90 o couplers 46

13 3.2. ORTHOGONAL MULTI-BEAM FORMING NETWORKS FOR TRIANGULAR ARRAYS B2 Fixed Phase Shifter -ϕ!!!! 90º c-coupler B1 P2 -ϕ!!!! P1 P3 -ϕ!!!! B3 Figure 3.3: Three-Port Symmetric Network Scheme. as Eq. 3.17; the scattering parameters associated with the symmetric network are Eq Eq [ ] S = 0 1 c j c 0 1 c 0 0 j c j c c 0 j c 1 c 0 (3.17) s P1,B 1 = j c ce φ 1 j c 3 e φ (3.18) s P2,B 1 = j ce φ 1 c 1 j (3.19) c 3 e φ s P3,B 1 = e φ 1 c 1 j (3.20) c 3 e φ Fixed phase shifters and 90 o c-couplers can be selected to define a required main beam steering direction. Equation 3.5 sets that the amplitude and the phase of at least two of the radiating elements must be the same, thus 90 o c-coupling and φ fixed phase shifter are related as, 47

14 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Case A: c = 4 sin 2 (φ) or Case B: c = 1 4 sin 2 (φ) (3.21) In particular, if -3dB hybrid couplers, where c = 0.5, are implemented, φ equals 20.7 o (or o in case B) and 45 o (or 135 o in case B) fixed phase shifters could be used to obtain three orthogonal beams. Phase and amplitude relation between array ports for this situation are presented in Table 3.1. Table 3.1: Phase and Amplitude Relation Between Array Ports When -3dB 90 o Hybrid Couplers Are Used in the Symmetrical Network. s P1,B 1 s P2,B 1 s P3,B 1 Case A e j0.615π Case B e j0.75π Applying the network to the GEODA-GRUA cell, which is a sub-array module working at 1.7 GHz composed of three radiating elements with 60 o beamwidth and a distance between elements d equal 0.56λ (Fig. 3.1), the array factor and the radiation pattern of the whole architecture are shown in Fig As the beamwidth of the radiating element is narrower than the θ 0 steering direction of the array factor, the θ 0 tilted beam is set closer to broadside in the radiation pattern. Thus, Fig. 3.4 shows that: in the case A, the array factor and radiation pattern main steering directions are θ 0AF =0.68 [rad]=39 o [deg] and θ 0RP =0.35 [rad]=20 o [deg], respectively; in the case B, the array factor and radiation pattern main steering directions are θ 0F A =0.87 [rad]=50 o [deg] and θ 0RP =0.38 [rad]=22 o [deg], respectively. 3x3 Modified Butler Matrix As Shelton studied in [47], the combination of three hybrid couplers and two fixed phase shifters provides a modified Butler matrix with three beam ports and three array ports. Figure 3.5 depicts a scheme that supplies the proper relative amplitude a b and relative phase shift β. The network is composed of two equilibrated hybrid coupler, one nonequilibrated hybrid coupler, and four fixed phase shifters. The scattering parameters associated with the matrix are presented in Eq

15 3.2. ORTHOGONAL MULTI-BEAM FORMING NETWORKS FOR TRIANGULAR ARRAYS Theta [rad] Theta [rad] Phi [rad] (a) Normalized Array Factor Case A Phi [rad] (b) Normalized Radiation Pattern Case A Theta [rad] 0.5 Theta [rad] Phi [rad] (c) Normalized Array Factor Case B Phi [rad] (d) Normalized Radiation Pattern Case B Figure 3.4: (a, b, c, d) [-1 db, -2 db, -3 db Contour Lines] Simulations of the Normalized Array Factor and the Normalized Radiation Pattern of the Whole System, GEODA- GRUA Cell with a Three-Port Symmetric Network, with Theoretical S-Parameters for cases A and B. [ ] S = e j ( π 2 +φ 3) 3 1 ( e j(φ 1 +φ 3 ) e j ( π 2 +φ 1) ( e j ( π 2 +φ 1 +φ 3) e j(π+φ 1 ) e j ( π 2 +φ 4) 3 ) ( ) + e j(π+φ 2 ) e j(π+φ 1 +φ 4 ) ( π e j 2 +φ 2 +φ 4) ( π e j 2 +φ2) ) ( ) e j ( 3π 2 +φ 1 +φ 4) e j(φ 2 +φ 4 ) (3.22)

16 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS P1 P2 P3 -ϕ Fixed 3-4 Phase Shifter 3 db & 90º 4.8 db & 90º Hybrid Coupler -ϕ 2 -ϕ 1 3 db & 90º B1 B2 B3 Figure 3.5: 3x3 Modified Butler Matrix Scheme. For the particular case where uniform amplitudes are desired, the absolute value of every S-parameter must be equal to 1 3, e j(φ 1) e j( π 2 +φ 2) 2 = 1 (3.23) 3 e j( π 2 +φ 1) 2 3 e j( 3π 2 +φ 1) e j(φ 2) 2 + e j(φ 2) 2 = 1 (3.24) 3 = 1 (3.25) 3 Equations set φ 1 = φ 2, thus both paths must have same length. If the orthogonal condition (Eq. 3.2) is considered, φ 3 = φ 4 = π 6 [rad] = 30o [deg]. The final design offers a uniform amplitude distribution with a relative phase shift β = 120 o. If this network fed the sub-array GEODA-GRUA, the simulated array factor and the simulated radiation pattern of the whole structure would be as shown in Fig. 3.6(a) 50

17 3.2. ORTHOGONAL MULTI-BEAM FORMING NETWORKS FOR TRIANGULAR ARRAYS and Fig. 3.6(b) respectively. Once again, the tilted beam steering direction θ 0 is moved closer to the broadside in the radiation pattern due to radiating element beam-width. Tilted angle θ 0 goes from 0.73 [rad]=42 o [deg] in the simulated array factor to 0.38 [rad]=22 o [deg] in the simulated radiation pattern Theta [rad] 0.5 Theta [rad] Phi [rad] (a) Normalized Array Factor Phi [rad] (b) Normalized Radiation Pattern Figure 3.6: (a, b) [-1 db, -2 db, -3 db Contour Lines] Simulations of the Normalized Array Factor and the Normalized Radiation Pattern of the Whole System, GEODA- GRUA Cell with a 3x3 Modified Butler Matrix, with Theoretical S-Parameters. In collaboration with the Universidad de Vigo, a prototype of a 3x3 modified Butler matrix has been built in microstrip technology. Both, fixed phase shifters and hybrid couplers, have been designed in microstrip transmission lines. Figure 3.7 shows the beam-forming network board. Matching and coupling parameters of the whole network have been measured. Figure 3.8 shows the array port scattering parameters when each beam port is used. As expected, amplitude power at 1.7 GHz is the same for all the three output ports, -6 db ±0.5dB. It presents a good isolation and matching ports, better than -20dB. Besides, as desired, a β = 120 o ± 2 o is found. The whole system, subarray and network, has been measured in a spherical compact range. Azimuth radiation pattern obtained for the three beam ports are shown in Fig Elevation radiation pattern in plane ϕ = 0 o of one of the beams is presented in Fig Those figures depict that the steering direction for the three beams are 0 [rad]=0 o [deg], 2.09 [rad]=120 o [deg], and 4.19 [rad]=240 o [deg]±0.03 [rad]=2 o [deg] in 51

18 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Figure 3.7: 3x3 Modified Butler Matrix Prototype. azimuth for each of them and 0.40 [rad]=23 o [deg]±0.02 [rad]=1 o [deg] in elevation for the three of them. Thus, because simulation shown an elevation of 0.38 [rad]=22 o for 0 [rad]=0 o [deg], 2.09 [rad]=120 o [deg], and 4.19 [rad]=240 o [deg] azimuth, radiation patterns obtained are as expected and therefore the implemented network is working properly. Intrinsic features of orthogonal lossless networks limit the number of provided beams to the number of radiating elements and impose the relation between those beams. Therefore, this research leads to consider the possibility of using dissipative networks, which are capable of providing a higher number of beams than the number of radiating elements compounding the cell. 3.3 Dissipative Network for Triangular Arrays Dissipative networks are those that have intrinsic losses associated with each generated beam. This type of network has no need to accomplish beam orthogonal condition, giving a greater degree of freedom to control beam steering directions. When orthogonal condition is fulfilled in all the beams of a network, the maximum array gain is ensured due to lossless implicitness. However, when radiating elements are related to radiofrequency circuits in which amplifiers are found, the relevant parameter that shows the quality of the antenna is the G/T factor. As a result, the use of a dissipative network is not very critical whenever there is an amplifier stage. 52

19 3.3. DISSIPATIVE NETWORK FOR TRIANGULAR ARRAYS (a) B1 (b) B2 (c) B3 Figure 3.8: Scattering Parameters for the Three Beam Ports. 53

20 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS 9 0 º 90º 90º 5dB 15dB 0 º180º º 0º180º 0º 25dB 35dB 45dB º 270º (a) B1: ϕ = 240o, θ = 23o 270º (b) B2: ϕ = 120o, θ = 23o 55dB (c) B3: ϕ = 0o, θ = 23o Figure 3.9: Azimuth Normalized Radiation Patterns per Beam. Figure 3.10: Elevation Normalized Radiation Pattern Beam 3 with ϕ = 0o. In this Subsection, a four beam ports by three array ports quasi-orthogonal dissipative network that generates three orthogonal beams in a desired elevation direction θ0 angle and an additional beam in the broadside direction is studied. To this end, a four beam ports by four array ports network with a matched array port is analyzed. The scattering matrix [ST ] associated to the dissipative network under study is shown in Eq Broadside beam is obtained by maintaining same signal relation between elements at array ports (column one). Three orthogonal beams are generated as analyzed in Subsection thanks to columns two to four. f be jβ a ST = f a be jβ f a a g1 ejα1 g2 ejα2 g3 ejα3 h i 54 a jβ be a g4 ejα4 (3.26)

21 3.3. DISSIPATIVE NETWORK FOR TRIANGULAR ARRAYS The matched array port gives a degree of freedom, as depicted in row four of matrix Eq. 3.26, with which is possible to satisfy the reciprocity lossless condition Eq. 3.2 if the whole 4x4 network is considered. This condition does not remove losses associated to the 4x3 dissipative network but reduces them to the power absorbed by the matched array port. Applying condition Eq. 3.2 to the scattering matrix Eq is obtained, g 2 1 = 1 3f 2 (3.27) g 2 i = 1 2a 2 b 2 with i = [2, 4] (3.28) f ( 2a + be jβ) = g 1 g i e j(α 1 α i ) with i = [2, 4] (3.29) ( a a + be jβ + be jβ) = g i g j e j(α i α j ) with i, j = [2, 4] (3.30) Squaring Eq and substituting in the resulting equation d 2 i it is obtained, values by Eq. 3.28, ( ) ( f 2 4a 2 + b 2 + 4ab cos (β) = 1 3f 2) ( 1 2a 2 b 2) (3.31) Taking into account the fact that the first term of the Eq is a real number, the second term must be a real number too, thus α i α j must be 0 o or 180 o. Considering α i α j = 0 o, Eq can be expressed as, Clearing cos (β) from Eq and Eq. 3.32, a 2 + 2ab cos (β) = + 2a 2 + b 2 (3.32) Combining Eq and Eq. 3.34, cos (β) = 1 3f 2 2a 2 b 2 + 2f 2 c 2 + 2f 2 b 2 4f 2 ab cos (β) = + a2 + b 2 2ab (3.33) (3.34) 2a 2 + b 2 = 1 f 2 (3.35) Taking a and the ratio r = b a as parameters, Eq is expressed as, 55

22 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS a = 1 f r 2 (3.36) 1 f b = ar = r r 2 (3.37) Losses associated with the network are related to the broadside beam as, g 2 1 = 1 3f 2 (3.38) g i = 1 2a 2 b 2 = f 2 with i = [2, 4] (3.39) Total mean losses of the 4x3 dissipative network is, 4 d 2 i = i=1 ( 1 3f 2 + 3f 2) = 1 (3.40) Showing that total mean network losses are independent of its configuration, being a fourth of the total power. The homogeneous losses case is obtained when f = 1 2, in which each beam has 1.25 db losses. The steering direction of the three orthogonal beams with the desired θ 0 elevation angle depends on signal factors, (a, b), and on the distance between elements of the array, (d), as shown below, sin (θ 0 ) = λ ( a cos 2 + b 2 ) 1 3πd 2ab (3.41) This study shows that not all options are viable alternatives because many of them use unfeasible phase shifts. Note that the condition of equal losses for the four beams is reached when a = 0.5. This situation generates main beams quite far from the broadside direction if distance between elements is not big enough, which in turn causes diffraction lobes. A greater disparity between attenuation parameters can involve excessive attenuation to the main lobe, but a better directivity. If the gain of every beam is compared, a good compromise between the different parameters can be achieved. Angles α i can be calculated by equating the arguments of Eq Eq. 3.30, being, ( ) r sin (β) α 1 α i = tan 2 + r cos (β) with i = [2, 4] (3.42) 56

23 3.3. DISSIPATIVE NETWORK FOR TRIANGULAR ARRAYS α i = α j with i, j = [2, 4] (3.43) To find a network configuration where all these conditions are fulfilled is not easy to achieve. Several dissipative networks for triangular arrays have been studied. As an example, the truncated 4x3 Butler matrix for three radiating elements shown in Fig was analyzed. This network provides three orthogonal beams in a tilted θ 0 angle and an additional one in the broadside steering direction. The truncated 4x3 Butler matrix is an example of the particular case where a = 0.5 and r = 1, thus it generates the same amplitude for the three array ports with a β = 180 o. Fig shows the array factor and the radiation pattern curves for a distance between element d = 0.56λ and a radiating element beamwidth of 60 o, as the particular case of GEODA-GRUA cell. Array Ports -90º Fixed Phase Shifter Matched Port 3dB - 90º Hybrid Coupler Beam Ports Figure 3.11: 4x3 Modified Butler Matrix. It is important to bear in mind the fact that the appearance of intrinsic side lobes and diffraction must be considered and avoided in most of the practical implementations. As it is depicted in Fig. 3.12, each beam radiation pattern has two beams, the main beam and its associated diffraction lobes. Those diffraction lobes are inside the visible margin and in a symmetric steering direction respect to the main beam. Diffraction lobes appear when the steering direction angle is closer to end-fire. In this particular case θ 0 =1.46 [rad]=83.8 o [deg] for the array factor, and θ 0 =0.52 [rad]=30 o [deg] for the 57

24 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Theta [rad] 0.5 Theta [rad] Phi [rad] (a) Normalized Array Factor Phi [rad] (b) Normalized Radiation Pattern Figure 3.12: (a, b) [-1 db, -2 db, -3 db Contour Lines] Simulations of the Normalized Array Factor and the Normalized Radiation Pattern of the Whole System, GEODA- GRUA Cell with a 4x3 Modified Butler Matrix, with Theoretical S-Parameters. radiation pattern. To set closer to broadside θ 0, two options can be considered: to increase the distance between elements d; and to decrease the relative phase shift β between elements. Another option is to use unbalanced feeding signals. 3.4 Design and Implementation of a 4x3 Quasi-Orthogonal Beam-Former In previous Sections, results obtained by different solutions to the problem under study have been shown. However, these networks have not fulfilled the required technical specification to completely meet the needs of the problem. First, simple, orthogonal networks have been considered, presenting two main drawbacks: a gain losses between beams bigger than 2 db, which increases the dynamic range in the digital signal processing; and, the lack of coverage in the broadside direction, making unfeasible the communications with targets in this direction. On the other hand, the dissipative network shown in Fig provides a beam in the broadside steering direction. This network present diffraction lobes in the visible range, making it unusable for applications where those effects are not desirable, such as satellite tracking where interferences from other 58

25 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER satellites can blind the communication. In this Section, a quasi-orthogonal beam-former that supplies three orthogonal beams in a desired θ 0 elevation angle and a fourth one in the broadside steering direction is presented. The analysis provides the relation between θ 0 elevation angle and the network component, showing which components must be used in a network to reach a specific θ 0 elevation angle with a defined array Analysis of a 4x3 Quasi-Orthogonal Beam-Former Based on a classical 4x4 Butler matrix, the scheme of a 4x3 quasi-orthogonal beamformer is depicted in Fig As it is shown, this network keeps the main body of a typical 4x4 Butler matrix that is formed by four 4-port 3-dB 90 o hybrid power couplers. This main body is connected by using two α fixed phase shifter; and a 20 log ( c) db 90 o power coupler, which replace the typical crossover in Butler matrices. Additionally, fixed phase shifters φ 3 and φ 4 set the proper relative phase shifts between array ports in order to obtain the desired behavior. Next analysis shows the relation between each beam vector and c, α, φ 3, and φ 4 ; values that ultimately determine the steering direction of the four beams provided by the network. Matched Port ϕ 3 ϕ 4 Array Ports Fixed Phase Shifter α α 90º c-hybrid Coupler 3dB - 90º Hybrid Coupler Beam Ports Figure 3.13: 4x3 Quasi-Orthogonal Beam-Former. To analytically calculate the behavior of this network, the scattering parameter [S T ] associated to the scheme is presented in Eq Note that the scattering associated 59

26 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS with a c-coupler 90 o was presented in Eq [S T ] = 1 2 A B j (A + B) c j c j (A + B) (A B) j c c ce jφ 3 j ce jφ 3 (A B) e jφ 3 j (A + B) e jφ 3 j ce jφ 4 ce jφ 4 j (A + B) e jφ 4 (A B) e jφ 4 A = e jα B = 1 c (3.44) In the previous Subsection, Eq shows the scattering parameter matrix associated to the quasi-orthogonal network that provides the desired beams. Particularizing to the case under study, the network must provide a scattering matrix similar to, 1 2a b 1 3a 1 2a b 1 2a b S T 2 b a a a = a a a b a a b a [ ] arg [S T ] = β β 0 0 β 0 (3.45) (3.46) Thus, to determine the beam steering directions in terms of the parameters c, α, φ 3, and φ 4, phase and module of the scattering parameters Eq is calculated and compared to Eq and Eq c 2D 2 c + 2D c c S T 2 = 1 2 c + 2D 2 c 2D c c 4 c c 2 c 2D 2 c + 2D c c 2 c + 2D 2 c 2D D = 1 c cos α (3.47) 60

27 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER [ ] arg [S T ] = T 1 = T 2 = tan (T 1 ) tan (T 2 ) π 3π 2 tan (T 2 ) tan ( T 1 ) π 2 π π φ 3 π 2 φ 3 tan ( T 1 ) φ 3 tan (T 2 ) φ 3 3π 2 φ 4 π φ 4 tan (T 2 ) φ 4 tan (T 1 ) φ ( ) 4 sin α ( cos α 1 c ) cos α 1 c sin α (3.48) Comparing matrices Eq with Eq. 3.47, it is obtained, 2 c 2 1 c cos α = c (3.49) Thus, cos α = 1 c where sin α = ± c (3.50) The ± sign determines the steering direction ±θ 0, complementary directions. In this analysis, sin α = + c is considered. The sin α = c will be considered to design the complementary network in the Section 3.5. Therefore, the module matrix [S T ] is, c 4 3c c c S T 2 = 1 4 3c c c c 4 c c c 4 3c c c 4 3c c (3.51) By comparing argument matrices Eq and Eq. 3.48, it is obtained, π φ 3 = 3π 2 φ 4 φ 3 = φ 4 + π 2 = φ (3.52) Setting the argument scattering matrix as, 61

28 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS [ ] arg [S T ] = T = π 2 tan (T ) π 3π 2 tan π (T ) 2 π 2 π π φ π 2 φ π 2 φ tan (T ) φ π φ π 2 φ tan (T ) φ + π 2 φ ( ) 1 c c (3.53) Moreover, Eq imposes on Eq that, Setting the value of φ 3 and φ 4 as, π 2 = π 2 φ (3.54) φ 3 = π = π (3.55) φ 4 = 3π 2 = π 2 (3.56) Fixing the argument scattering matrix as, π 2 tan (T ) π 3π 2 [ ] tan π (T ) arg [S T ] = 2 π 2 π π 0 2 π 2 tan (T ) π π 0 2 tan (T ) π 2 π (3.57) Thus, the behavior of the network is governed by the value of the central coupler c, as shown in Eq and Eq Moreover, note that φ 3 and φ 4 are fixed phase shifters not related to the desired steering direction θ 0 of the three orthogonal beams but to the relative phases between array ports needed to generate the different desired beams. As it was presented in Eq. 3.7, the relation between θ 0 steering angle and the relative phase shift β is given by, β = 3 πd λ sin (θ 0) (3.7) Comparing Eq. 3.7 and Eq. 3.57, the relation between θ 0 steering angle and the 62

29 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER c-coupling parameter is set as, ( ) 1 c 1 sin (θ 0 ) = tan λ c 3π d (3.58) Every single dissipative network has associated power losses due to absorbed power by the matched array ports. In this case, these losses are given by the power in the port array matched, given by S AP Matched,Bi 2 where B i is the beam port under study: Broadside beam: ( ) 3 L 0 o = 0 log 4 c (3.59) Tilted beam θ 0 : ( L θ0 = 0 log 1 c ) 4 (3.60) Figure 3.14 shows beam steering directions θ 0 depending on the parameters c, α, and d. Both type of losses, L 0 o and L θ0, associated with broadside and tilted beams respectively, are also depicted in Fig Beam steering direction θ 0º [deg] c = 0.0; α = 0.0º c = 0.4; α = 39.2º c = 0.1; α = 18.4º c = 0.5; α = 45.0º c = 0.8; α = 63.4º 80 c = 0.2; α = 26.6º c = 0.6; α = 50.8º c = 0.9; α = 71.6º c = 0.3; α = 33.2º c = 0.7; α = 56.8º c = 1.0; α = 90.0º Array distance d [λ ] Figure 3.14: Array Factor Steering Direction θ 0 Respect to Array Distances d, Coupling Factor c, and Fixed Phase Shifter α. Figure 3.14 presents the beam steering capabilities of the network, showing that for larger arrays the possible coverage area in the system is reduced. For a beam-switching application, the continuous coverage of the system field-of-view is a critical design requirement, which means that relative amplitudes between every beam compounding the network must be carefully analyzed. The total losses of the system that must be taken 63

30 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS 35 Losses [db] L 0º L θº c Coupler Figure 3.15: 4x3 Beam Losses. (Blue) Broadside Beam. (Red) θ 0 Steering Direction Beam. into account are: intrinsic losses of the proposed network (Fig. 3.15) and losses introduced into the tilted beams because of the beam width of the single element composing the antenna array. The important condition in the design is that both losses should be balanced to provide a quasi-homogeneous radiation pattern in the system field of regard considered. Losses in software/hardware hybrid architectures are compensated by using amplifiers. Figure 3.15 depicts that the intrinsic network losses for the broadside beam decrease as c increases, showing that for c-coupler smaller than 0.4 the losses for the broadside beam will be higher than 5 db. Therefore, it is important to notice that to implement a proposed network with such a small c-coupler might be impractical since it would be very difficult to balance such a high intrinsic losses of the network Implementation of a 4x3 Quasi-Orthogonal Beam-Former In this Section, a microstrip implementation of the proposed dissipative network is presented. The aim of this Section will be to validate that the signal distribution provided by the network is as defined by Eq and Eq The generation of three orthogonal beams with a θ 0 elevation angle and an additional one in the broadside direction when the designed network is applied to a triangular cell of three radiating elements will be verified as well. For this purpose, the simple practical case in which all hybrid power couplers composing the network are 4-port 3-dB quadrature couplers is assumed. This case is obtained when main network parameters are Eq The final network 64

31 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER to implement is shown in Fig Note that the practical case will be appliedx to the GEODA-GRUA cell working at 1.7 GHz with a distance between element of d = 0.56λ and a beam width of 60 o. c = 0.5 with α = 45 o (3.61) Matched Port 180º 90º Array Ports Fixed Phase Shifter 45º 45º 3dB - 90º Hybrid Coupler Beam Ports Figure 3.16: 4x3 Quasi-Orthogonal Beam-Former Based on 3dB-90 o Hybrid Couplers. Taking Eq. 3.61, into Eq and Eq. 3.57, the scattering matrix associated to this network is, S T = o 16.6 o 80 o 70 o 16.6 o +90 o 90 o 80 o arg[s T ] = 0 o +90 o 90 o +63 o 0 o +90 o 06.6 o 80 o (3.62) (3.63) 65

32 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS The ideal network has been simulated with the tool Advanced Design System (ADS) 2009 from Agilent, showing the expected behavior. Though 90 o 3dB hybrid coupler can be designed at 1.7 GHz with transmission lines as depicted in [48], to simplify the implementation and minimize the size of the whole network, commercial four-port 3-dB quadrature hybrid power couplers (Mini Circuits QCN-25) are used. This device is an affordable component, costing less than 3 USD, that optimizes and minimizes the size of the whole network. The QCN-25 is a 50 Ω matched device, working from 1350 to 2450 MHz. Its main technical skills are: 25dB port isolation, 0.4dB insertion losses, 1 o phase unbalance, 0.5dB amplitude unbalance, and 1.2 VSWR. Therefore, the final network is a combination of fixed phase shifter microstrip transmission lines, and commercial hybrid couplers. To check a correct performance, the network with ideal components has been simulated by CST Design Studio Its scattering matrix shows a perfect behavior. Simulated scattering parameters with real measurements of the 4x3 dissipative network components, fixed phase shifters, and QCN o 3dB hybrid couplers are shown in Eq and Eq These parameters show a good agreement with expectations, with a phase error of ±4 o and an amplitude error of ±0.1 db S T = o 14 o 82 o 70 o 18 o +94 o 90 o 81 o arg[s T ] = o +87 o 92 o +66 o 0 o +86 o 08 o 77 o (3.64) (3.65) The network has been implemented in a microstrip RO4350B substrate of mm thickness. All the components compounding the network has been measured and optimized in this technology. These measurements show a proper performance of the QCN-25 device, which behavior is similar as established in its datasheet. Fixed phase shifters also behave as expected. Before presenting the implementation of the final network, it is worth noting the way α = 45 o fixed phase shifter has been implemented. As it is depicted in Fig. 3.17, it is 66

33 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER important to know the fixed phase shift provided by QCN-25 when a signal is introduced through I1. This phase shift has been measured, being α = 12 o ± 2 o, depending on the selected input port. Thus, the fixed phase shifter implemented must be α + α = 57 o. Measurements of the whole system shown in Fig verify its proper behavior. As in all the other fixed phase shifter, the obtained phase shift has ±2 o error, as expected. α Matched Port O1 O2 3dB-90º QCN-25 α' α α' Fixed Phase Shifter I1 I2 Figure 3.17: Relative Fixed Phase Shifter α. Finally, the implemented quasi-orthogonal beam-former is presented in Fig. 3.18; where 3dB-90 o QCN-25 hybrid couplers, and transmission line fixed phase shifters can be observed. It is important to remark that the whole size of the implemented network could have been reduced but, due to SMA measurement connector size, it was not minimized. Scattering parameters of the network have been measured with a network analyzer. The network presents ±0.3 db module error (Eq. 3.66) and ±5 o phase error (Eq. 3.67). Table 3.2 summarizes the important measured data of the network. Signal errors introduced are reasonable, as it is depicted in Fig. 3.19, where a comparative simulation between radiation patterns of the cell GEODA with theoretical and measured S network parameters shows low beam steering deviations. It is worth noting the use in the simulation of the previous measured radiation pattern of the radiating element composing the GEODA-GRUA cell, which consists of two stacked circular patches with 60 o beamwidth. This beamwidth explains not only the mismatch between factor array and radiation pattern elevation steering direction θ 0, shifting from [rad] =-41.9 o [deg] to [rad] =-23.1 o [deg], but also the increase of side lobes shown in following 67

34 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Figure 3.18: Implementation of a 4x3 Quasi-Orthogonal Beam-Former in RO4350B with mm Thickness Composed of 3dB-90 o QCN-25 Hybrid Couplers and Transmission Line Fixed Phase Shifters. radiation pattern measurements of the GEODA-GRUA cell with the implemented network. Figure 3.19 shows an almost continuous coverage by using a patch element with a 60 o beamwidth S T = o +6 o 71 o +97 o arg[s T ] = 80 o +9 o 74 o 9 o 74 o +12 o +75 o +103 o (3.66) (3.67) Moreover, the whole system, dissipative 4x3 network with GEODA cell array, has been measured in the anechoic chamber of the Radiation Group at Technical University of Madrid as shown in Fig Measurements confirm the generation of one beam in the broadside steering direction with an error of ±3 o and three orthogonal beams equidistant in azimuth 120 o ±5 o with an elevation of -23 o ±2 o, as expected, depicted in Fig The radiation patterns associated with the three tilted beams present an increased 68

35 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER Table 3.2: Scattering Matrix and Losses of the 4x3 Quasi-Orthogonal Beam-Former. AP1 AP2 AP3 β Losses BP e +j0.915π 0.305e j0.446π 0.302e j0.412π o ± 3 o 32% BP e +j0.032π 0.312e +j0.049π 0.300e +j0.068π 0.0 o ± 3 o 70% BP e j0.951π 0.327e j0.969π 0.683e +j0.417π o ± 2 o 33% BP e +j0.537π 0.691e j0.108π 0.324e +j0.572π o ± 3 o 32% 1.5 Theory Measurement 1 Theta [rad] Phi [rad] Figure 3.19: [-1 db, -2 db, -3 db Contour Lines] Normalized Radiation Pattern Simulation of the Whole System, GEODA-GRUA Cell with Proposed Network, Using Theoretical (Dashed Line) and Measured (Solid Line) S-Parameters. secondary lobe with a peak of -5 db with respect to the main beam. Comparisons between measured and simulated radiation patterns associated with each beam have shown a good agreement, Fig Main lobe shapes and steering directions fit properly. The three tilted beams present acceptable smooth variations in amplitude, ±2 db, and azimuth, ±7.5 o. These deviations might be related to a mismatch between the prototype and the simulated patch array structure. 69

36 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS Figure 3.20: Whole System, 4x3 Quasi-Orthogonal Beam-Former and GEODA-GRUA cell, in the Anechoic Chamber of the Radiation Group at UPM. 9 0 º -5 db -15 db º -25 db 0 º -35 db -45 db -55 db º (a) BP1 (b) BP2 9 0 º -5 db -15 db º -25 db 0 º -35 db -45 db -55 db º (c) BP3 (d) BP4 Figure 3.21: (a), (b), (c), and (d) Normalized Radiation Pattern Measurements of the Beam-Former and the Subarray GEODA-GRUA Cell by Exciting BP1, BP2, BP3 and BP4, Respectively. 70

37 3.4. DESIGN AND IMPLEMENTATION OF A 4X3 QUASI-ORTHOGONAL BEAM-FORMER 0 0 Normalized RP Module [db] Measurement Simulation Normalized RP Module [db] Measurement Simulation Theta [deg] (a) BP Theta [deg] (b) BP2 0 0 Normalized RP Module [db] Measurement Simulation Normalized RP Module [db] Measurement Simulation Theta [deg] (c) BP Theta [deg] (d) BP4 Figure 3.22: (a), (b), (c), and (d) Normalized Comparison Between Measured (Red) and Simulated (Blue) Radiation Patterns by Exciting BP1, BP2, BP3 and BP4 Respectively. 71

38 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS 3.5 A 7x3 Beam-Forming Network by Using Complementary Networks To find a beam pattern as homogeneous as possible leads to consider the use of switching beam-formers with higher number of beams. While the number of beams provided by the network is increased, the steering losses associated with the switching between contiguous beams are reduced. In this Section, a new 7x3 network is proposed by combining two complementary 4x3 networks as described in Fig The practical implementation is composed of the designed network in the previous section (BFN A) and its complementary network that generates same beams but rotated 180 o in azimuth (BFN B). Both networks are combined/divided thanks to the combiner/divider circuit, which is formed by the commercial 3dB-90 o QCN-25 hybrid coupler. The dissipative nature of the network implies unavoidable losses. These losses have two main sources: insertion losses due to QCN-25 device, and absorbed power in 50Ω matched ports. BPA4 Matched Port Array Port Radiating Element BPB4 BPA3 BPB3 BFN A BFN B BPA2 BPA1 3dB-90º Hybrid Coupler BPB2 BPB1 Figure 3.23: 7x3 Quasi-Orthogonal Beam-Former Scheme. The structure of the complementary BFN B is similar to the network presented in Fig Hence, its scattering matrix is represented by Eq. 3.47, and Eq As shown in previous Section, the relation between c coupler and α in complementary networks is giving by considering in Eq the relation sin α = c. Applying this relation and considering the relation between φ 3 and φ 4 as Eq. 3.52, the argument of 72

39 3.5. A 7X3 BEAM-FORMING NETWORK BY USING COMPLEMENTARY NETWORKS the scattering parameter of the complementary beam-former B is, [ ] arg [S T ] = T = π 2 tan (T ) π 3π 2 tan (T ) π 2 π 2 π π φ π 2 φ π 2 φ tan (T ) φ π φ π 2 φ tan (T ) φ + π 2 π φ ( ) 1 c c (3.68) If the argument matrix of the BFN B from Eq is compared to the expected argument matrix from Eq. 3.46, it is obtained, Setting the value of φ 3 and φ 4 as, π 2 = π 2 φ φ = 0 (3.69) φ 3 = 0 (3.70) φ 4 = π 2 (3.71) Imposing the argument scattering matrix as, π 2 tan (T ) π 3π 2 [ ] tan (T ) π arg [S T ] = 2 π 2 π π π 2 π 2 tan (T ) π π 2 tan (T ) + π 2 π (3.72) Once again, comparing the argument matrix (Eq. 3.72) with the desired argument matrix (Eq. 3.46), it is derived, β = tan ( 1 c c ) + π (3.73) And since relative phase shift β is giving by Eq. 3.7, the relation between the design parameter c coupler and the steering direction θ 0 is, 73

40 CHAPTER 3. QUASI-ORTHOGONAL SWITCHING BEAM-FORMER FOR TRIANGULAR ARRAYS OF 3 RADIATING ELEMENTS sin (θ 0 ) = 1 ( ( ) ) λ 1 c tan + π 3π d c (3.74) In complementary networks, the associated losses are the same as in simple network from previous Section: Eq for broadside beam, and Eq for θ 0 tilted beam. Considering the case under study, where hybrid couplers are implemented with 3dB- 90 o QCN-25 commercial devices from Mini-Circuits, c = 0.5 with α = 45 o. The BFN B scheme is depicted in Fig This network has being simulated and implemented as BFN A, obtaining a similar behavior as its complementary. Matched Port 90º Array Ports Fixed Phase Shifter -45º -45º 3dB - 90º Hybrid Coupler Beam Ports Figure 3.24: 4x3 Complementary Quasi-Orthogonal Beam-Former B Scheme. After validations, the whole 7x3 network has being built as shown in Fig Scattering parameters of the network have being measured. Scattering parameters of the 7x3 network related to A-beam ports are similar to those shown in Table 3.2 but 3 db lower due to coupler combiner/divider between complementary networks. Table 3.3 summarizes measurements of scattering parameters of the whole network, where is shown ±0.3 db error module and a ±5 o error phase. Figure 3.26 shows a simulation of the radiation pattern of the whole system, GEODA-GRUA cell and 7x3 quasi-orthogonal beam-former, when theoretical and measured S-parameters are considered, showing that introduced signal error do not significantly affect the shape of the generated beams. 74

41 3.5. A 7X3 BEAM-FORMING NETWORK BY USING COMPLEMENTARY NETWORKS Figure 3.25: Implementation of a 7x3 Quasi-Orthogonal Beam-Former in RO4350B Composed of 3dB-90 o QCN-25 Hybrid Couplers and Transmission Line Fixed Phase Shifters. Table 3.3: Scattering Matrix and Losses of the 7x3 Quasi-Orthogonal Beam-Former. AP1 AP2 AP3 β Losses BPA1 0.48e +j0.70π 0.21e j0.65π 0.20e j0.66π o ± 1 o 68% BPA2 0.21e j0.19π 0.22e j0.16π 0.20e j0.17π 0.0 o ± 4 o 86% BPA3 0.22e +j0.82π 0.22e +j0.81π 0.46e +j0.20π o ± 1 o 69% BPA4 0.21e +j0.34π 0.48e j0.28π 0.21e +j0.37π o ± 2 o 68% BPB1 0.52e +j0.95π 0.21e +j0.33π 0.22e +j0.31π 14.3 o ± 2 o 64% BPB2 0.20e +j0.85π 0.23e +j0.85π 0.24e +j0.83π 0.0 o ± 2 o 85% BPB3 0.24e +j0.85π 0.19e +j0.83π 0.53e j0.53π 13.5 o ± 2 o 63% BPB4 0.20e +j0.34π 0.49e +j0.96π 0.22e +j0.28π 16.5 o ± 5 o 67% Figure 3.27 depicts the measurement of the general radiation pattern of a tilted beam (a), and shows the measurement of the radiation pattern of the broadside beam (b). Besides, main plane sections of measured and simulated radiation patterns are also presented, showing similar characteristics as previous network A (Fig.3.28). Hence, these measurements show a successful system behavior that provides the desired beams. 75