Design and cold test of an S-band waveguide dual circular polarizer

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1 Radiation Detection Technology and Methods (017) 1:6 ORIGINAL PAPER Design and cold test of an S-band waveguide dual circular polarizer Jie Lei 1, Xiang He 1 Guo-Xi Pei 1 Mi Hou 1 Hui Wang 1 Jian-Bing Zhao 1 Received: 19 September 017 / Revised: November 017 / Accepted: 1 November 017 / Published online: 1 November 017 Institute of High Energy Physics, Chinese Academy of Sciences; China Nuclear Electronics and Nuclear Detection Society and Springer Nature Singapore Pte Ltd. 017 Abstract Purpose An S-band dual circular polarizer has been designed and tested with low power in the paper, which will be applied in a spherical cavity pulse compressor. It converts the TE 10 mode in rectangular waveguide into two polarization degenerated TE 11 modes in cylindrical waveguide. Methods The general scattering matrix of the dual circular polarizer has been deduced based on the properties of the passive microwave network, which is suitable for the usual db coupler, as well as the left/right hand circular polarizer. Based on the D code software CST, the dual circular polarizer was numerically simulated. Then, two prototypes have been manufactured and tested with the vector network analyzer (VNA). Results The simulation results show that the magnitudes and phase difference of the two TE 11 modes are.010/.0104 db and degrees, respectively. The cold test results show good agreement with CST simulation. Conclusion The method of analyzing the relationship between the voltage standing wave ratio (VSWR) and the errors of the magnitudes and phase difference of the two TE 11 modes was given, which can be used to qualitatively analyze the properties of the circular polarizer. The S-band waveguide dual circular polarizer can be applied in the pulse compressor, phase shifter or other frequency bands. Keywords S-band Dual circular polarizer Scattering matrix Pulse compressor Phase shifter PACS c q 41.0.Jb Introduction Circular polarizer is one of the important passive microwave devices. They are widely used in satellite communication systems [1,] for the polarization characteristics conversion of the received signals and the CMB polarization experiments [,4] to understand the very early Universe. There are many kinds of circular polarizers such as the metal septum polarizers [5 7] and the dielectric septum ones [8,9]. The metal septum polarizer typically consists of two standard Supported by the Youth Found of National Natural Science Foundation of China ( ). B Jie Lei leijie@ihep.ac.cn 1 Laboratory of Particle Acceleration Physics and Technology, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing , China University of Chinese Academy of Sciences, Beijing , China rectangular waveguide ports and one output port in square or circular waveguide. By optimizing the widths, lengths and thickness of the stepped septum, one can achieve 90 phase difference and equal magnitude in square or circular waveguide. The dielectric septum polarizer uses the dielectric septum to have different impacts on the orthogonal electric field to achieve the desired phase difference, thus the circular polarized wave forms. Such structure of inserting septum (metal septum or dielectric) makes the circular polarizer complicated and increases fabrication difficulties. And for the dielectric septum polarizer, the relative high loss is another disadvantage. The dual circular polarizer which has the groove [10,11], circular step and pins is complicated [1]. Another dual circular polarizer which has one stub between two rectangular waveguides and two pins at the bottom of the cylindrical waveguide has very compact structure [1]. But the remaining pins may reduce the power capacity and cause thermal instability. Therefore, the circular polarizer without metal septum, dielectric septum, large grooves or pins may be a good choice for future use. Both of the X-band waveg- 1

2 6 Page of 7 J. Lei et al. Fig. 1 The schematic view of the S-band waveguide dual circular polarizer uide dual circular polarizers in [14,15] meet the requirement. However, the shape of the structures may increase the difficulty of fabrication. We intend to design an S-band waveguide dual circular polarizer for a spherical cavity pulse compressor. Based on the special application, we take the circular polarizer model [16,17] in the X-band super-compact SLED system at SLAC as a reference. The difference between the two circular polarizers is that there is no cylindrical waveguide under the overmoded rectangular waveguide in our structure (see Fig. 1), which makes us have the advantage of easier fabrication and that the working different frequency band is also different. Besides, we deduced a more general scattering matrix based on the properties of the passive microwave network and the method is new. The general scattering matrix is suitable for the usual -db coupler (with four rectangular waveguide ports) as well as the left-/right-hand circular polarizer. In addition to the pulse compressor application, if a movable metal shorted plug is inserted into the cylindrical waveguide (Port ), the dual circular polarizer will become a phase shifter [18], which means the wave coming from Port 1 will propagate to Port with a variable phase shifting corresponding to the different positions of the shorted plug. It is worth emphasizing that the S-band dual circular polarizer can be scaled to other frequency bands and will have more application prospects. In the paper, the principle of the S-band dual circular polarizer is introduced and a more general scattering matrix is deduced and presented in detail. The design procedure is also given with the CST [19] simulation results. Then, two prototypes are manufactured and the cold test is accomplished. Finally, the errors of the two prototypes are analyzed. Principle and general scattering matrix The schematic diagram of the dual circular polarizer is shown in Fig. 1. The dual circular polarizer has three physical ports: Port 1 and Port transmit the fundamental rectangular waveguide mode TE 10, while Port transmits two cylindrical waveguide mode TE 11 modes. Thus, it should be treated as a four-port microwave network. The overmoded rectangular waveguide is the essential portion which transmits the TE 10 and TE 0 modes at the same time (without any other modes). The two modes then generate two degenerated and orthogonal TE 11 modes which should have equal amplitude but 90 phase difference after optimizing the parameters of the structure; thus, the function of the S-band waveguide dual circular polarizer can be realized. That is to say, when wave comes from Port 1 (Port ), Port outputs the left-hand circular polarized wave-lhcp wave (right-hand circular polarized wave-rhcp wave), with Port (Port 1) isolated. Conversely, when the LHCP (RHCP) wave comes from Port, Port 1 (Port ) outputs the linear polarized wave. The derivation process of the scattering matrix for the four-port microwave network is as follows. The scattering matrix of the four-port microwave network can be described as the following form, S(1:1, 1:1) S(1:1, :1) S(1:1, :1) S(1:1, :) S(:1, 1:1) S(:1, :1) S(:1, :1) S(:1, :) S(:1, 1:1) S(:1, :1) S(:1, :1) S(:1, :) (1) S(:, 1:1) S(:, :1) S(:, :1) S(:, :) where S(N:M, P:Q) means the M-th (Q-th) mode on Port N (P). The following derivation process is based on the reciprocal, lossless and passive microwave network with all ports matched. Furthermore, because the two TE 11 modes meet the parity forbidden principle, we can get the following equation. S(:1, :) = S(:, :1) = 0 () Thus, the scattering matrix can be written as the following form. 0 S(1:1, :1) S(1:1, :1) S(1:1, :) S(1:1, :1) 0 S(:1, :1) S(:1, :) S(1:1, :1) S(:1, :1) () S(1:1, :) S(:1, :) The product of the scattering matrix and its conjugate matrix is an identity matrix for the reciprocal, lossless and passive microwave network. So we can obtain the following equation. S(1:1, :1) + S(1:1, :1) + S(1:1, :) = 1 (4) S(1:1, :1)S(:1, :1) = 0 S(1:1, :1)S(:1, :) = 0 S(1:1, :1)S(1:1, :1) (5) = 0 S(1:1, :1)S(1:1, :) = 0 S(1:1, :1) + S(:1, :1) + S(:1, :) = 1 (6) S(1:1, :1) + S(:1, :1) = 1 (7) S(1:1, :)S(1:1, :1) + S(:1, :)S(:1, :1) = 0 (8) From Eq. (5), we can get: S(1:1, :1) = 0 (9) Suppose 1

3 Design and cold test of an S-band waveguide dual circular polarizer Page of 7 6 S(1:1, :1) = α 1 e jθ 1 S(1:1, :) = α e jθ S(:1, :1) = α e jθ, (10) S(:1, :) = where j is the imaginary unit; θ i (i = 1,,, 4) and α i (i = 1,,, 4) (suppose α i > 0) can be any real number. When wave comes from Port 1, the output is, α 1 e jθ 1 α e jθ 1 0 α e jθ α 1 e jθ 1 α e jθ 0 0 = 0 α e jθ 0 α 1 e jθ 1 α e jθ (11) When Port is shorted, the two TE 11 modes in Port can be regarded as a new input; the phase shift will be θ. (θ can be any real number.) The wave will be transmitted to Port, with Port 1 no reflection. α 1 e jθ 1 α e jθ 0 α e jθ α 1 e jθ 1 α e jθ 0 α 1 e jθ 1e jθ α e jθ α e jθ e jθ α1 e jθ 1e jθ + α e jθ e jθ (1) = α 1 α e j(θ 1+θ ) e jθ + α α 4 e j(θ +θ 4 ) e jθ 0 0 Then, we can achieve the following equation (Port 1 no reflection). α 1 e jθ 1 e jθ + α e jθ e jθ = 0 (1) BasedonEqs.(4), (9), (10) and (1), we can get, { α 1 = α = θ 1 = θ + n 1+1 π where n 1 is an integer. And from Eqs. (6), (7), (9) and (14), we have, (14) When n 1 is an odd integer, the scattering matrix can be written as, e jθ 1 e j(θ 1+ 1 π) e j(θ 4+ 1 π) e jθ 4 e jθ 1 e j(θ 4+ 1 π) e j(θ 1+ 1 π) e jθ 4 And when n 1 is an even integer, the scattering matrix is, e j(θ + 1 π) e jθ e jθ e j(θ + 1 π) e j(θ + 1 π) e jθ e jθ e j(θ + 1 π) (17) (18) The scattering matrix is suitable for the left-/right-hand circular polarizer in the paper, as well as the usual -db coupler (with four standard rectangular waveguide ports). Design procedure of the S-band waveguide dual circular polarizer The design procedure of the S-band waveguide dual circular polarizer can be divided into two steps. In the first step, a twoport microwave device without the cylindrical waveguide is designed, the D model of which is shown in Fig.. Port 1 and Port are the standard S-band rectangular waveguides (7.14 mm 4.04 mm). The overmoded waveguide transmits TE 10 and TE 0 modes, and the width a of it should meet the condition of λ<a < ( / ) λ, which is 105 mm < a < mm for the frequency of 856 MHz. (λ is the working wavelength in free space.) The triangular portion in the middle of the waveguide is designed to isolate Port. We tried to make the wave reflect to Port 1 as much as possible during simulation. (The magnitude of S11/S1 is 0.09/ db at 856 MHz.) The transient electric field based on CST simulation is shown in Fig. which meets our design requirement. α = α 4 = (15) Then, based on Eqs. (8), (14) and (15), there is, ( θ 4 = θ + n n ) π (16) where n 1 and n are integers. Fig. The D model of the S-band two-port microwave device 1

4 6 Page 4 of 7 J. Lei et al. of the cylindrical waveguide and the rectangular overmoded waveguide). When the input power is 50 MW from Port 1, the maximum electric field will be 8.59 MV/m which is much smaller than the Kilpatrick Limit for S-band (45.8 MV/m). So the dual circular polarizer can stand high power according to the simulation. Fig. The electric field distribution of the S-band two-port microwave device Fig. 4 The S parameters and the phase difference based on CST simulation In the second step, a cylindrical waveguide (Port ) was added. The goal is to make all the power from Port 1 transmit to Port (with Port isolated), and the two TE 11 modes in cylindrical waveguide should have equal amplitude but 90 phase difference. The radius r of the cylindrical waveguide should meet the condition of ( λ/.41 ) < r < ( λ/.61 ), which is 0.79 mm < r < 40. mm for the frequency of 856 MHz. The width and length of the overmoded waveguide are denoted as W and L, and the position of the center of the cylindrical waveguide is denoted as D. The magnitude (phase difference) of the two TE 11 modes is affected by L and D (W and D), which is the simulation guide principle of the second step. The values of W, L and the parameter values of the triangular portion are obtained in the first step and are taken as the initial values for the second step. Finally, all the mentioned parameters are optimized to achieve the required properties of the two TE 11 modes, and the results are shown in Fig. 4 based on CST simulation. From the simulated S parameters, we can see that the two TE 11 modes have equal magnitude and almost 90 phase difference, which agree with the general scattering matrix. The simulated maximum electric field is 115 V/m (the input power is 1 W from Port 1 in CST simulation), which appears at the bottom of the cylindrical waveguide (the joint Cold test of the dual circular polarizer Two prototypes (named M1 and M) are fabricated, and the cold test is done to verify the performance. First, the two prototypes are tested separately with Port shorted (Port 1 is input and Port is output), as shown in Fig. 5. Thetest results are shown in Table 1. From Table 1, we can see that when Port is shorted, nearly all the power from Port 1 transmits to Port with little reflection. Then, the two prototypes are connected for being tested, as shown in Fig. 6. The two rectangular waveguide ports are defined as Port 1 and Port (Port 4 and Port 5) for the prototype M1 (M). The test results are shown in Tables and. From Tables and, we can see that both of the two prototypes have good test results about return loss, insertion loss as well as the isolation. And all the test results (Tables 1,, ) show that the two prototypes have good consistency. According to the test results, the prototype M1 can be proved as a dual circular polarizer: from Table (for M1), S11 = 48.7 db,s1 = 9 db, S1 = 9.1 db and S = 45.8 db (at 856 MHz). We can see that when Port 1 is the input port, the power which reflects back to Port 1 as well as transmits to Port is both about 1/10,000 of the input power, so nearly all the power transmits to Port. It is the same when Port is the input port. Then Eq. (19)istrue based on the cold test results. Fig. 5 The photograph of one prototype 1

5 Design and cold test of an S-band waveguide dual circular polarizer Page 5 of 7 6 Table 1 The test results of M1 and M when Port is shorted Frequency (MHz) (with Port shorted) VSWR (M1) VSWR (M) S1 (db) (M1) S1 (db) (M) and passive microwave network, we can get the following equation, S(:1, :1) = 0, S(:, :) = 0 (0) When Port of M1 is shorted, based on the test results in Table 1, Port 1 can be seen as nearly no reflection (S11 = db when the VSWR is at 856 MHz). Thus Eq. (1) is established, and we can get the scattering matrix of M1 the same as Eqs. (17) or(18). So the first prototype M1 is a dual circular polarizer. And the second prototype M can also be proved as a dual circular polarizer similarly. Fig. 6 The photograph of the two connected prototypes S(1:1, 1:1) = S(1:1, :1) = S(:1, 1:1) = S(:1, :1) = 0 (19) In the prototype, two TE 11 modes which transmit in the cylindrical waveguide will meet the parity forbidden principle; thus, Eq. () is still established. Based on Eqs. (), (19) and the properties of the reciprocal, lossless Error analysis of the magnitude and phase difference of the two TE 11 modes If the prototype is a dual circular polarizer, the errors of the magnitude and phase difference of the two TE 11 modes can be qualitatively analyzed by the tested VSWR (see in Table 1). We assume the errors of magnitude and phase difference are δ and θ, respectively; the scattering matrix of the dual circular polarizer can be written as follows [0]. Table The test results of M1 when the two prototypes are connected Input port (M1) Frequency (MHz) S11 (db) S1 (db) S1 (db) S (db) S41 (db) S51 (db) S4 (db) S5 (db) Port Port Table The test results of M when the two prototypes are connected Input port (M) Frequency (MHz) S44 (db) S54 (db) S45 (db) S55 (db) S14 (db) S4 (db) S15 (db) S5 (db) Port Port

6 6 Page 6 of 7 J. Lei et al. ( 1/ δ)e iθ 1 ( 1/ + δ)e i(θ 1+ 1 π+θ ) ( 1/ + δ)e i(θ 4+ 1 π θ ) ( 1/ δ)e iθ 4 ( 1/ δ)e iθ 1 ( 1/ + δ)e i(θ 4+ 1 π θ ) ( 1/ + δ)e i(θ 1+ 1 π+θ ) ( 1/ δ)e iθ 4 or ( 1/ δ)e i(θ + 1 π) ( 1/ + δ)e i(θ +θ ) ( 1/ + δ)e i(θ θ ) ( 1/ δ)e i(θ + 1 π) ( 1/ δ)e i(θ + 1 π) ( 1/ + δ)e i(θ θ ) ( 1/ + δ)e i(θ +θ ) ( 1/ δ)e i(θ + 1 π) (1) () where 1/ δ 1/, θ i (i = 1,,, 4) and θ can be arbitrary real number. When Port is shorted, for two scattering matrixes (1) and () mentioned above, we can get the S11 and VSWR as follows. { S11 = [(1/4 + δ ) (1/4 δ ) cos (θ )] VSWR = 1+ S11 () 1 S11 When the value of θ is 0, ± 1, ± 1.4, ± 1.8,therelationship between the VSWR and δ is shown in Fig. 7. When Port is shorted, the tested values of VSWR of the two prototypes are both below 1.05 within the frequency bandwidth of MHz (see in Table 1). So from Fig. 7 we can see that the errors of the magnitude and phase difference of the two TE 11 modes of both prototypes are within 0.01 and 1.4. Thus, it can be seen that the two prototypes have good performance as the dual circular polarizer, and the design procedure is also reasonable. Conclusions An S-band waveguide dual circular polarizer has been designed and tested. A theoretical general scattering matrix has been deduced in detail; it is appropriate for the dual circular polarizer and the usual -db coupler. The simulated S parameters from CST have been given, which agree with the general scattering matrix. Two oxygen-free copper prototypes have been fabricated and tested. Cold test results show that the errors of the magnitude and phase difference of the two TE 11 modes are within 0.01 and 1.4 from 846 to 866 MHz, which proves the rationality of design procedure. Error analysis method in the paper is appropriate for estimating the performance of a dual circular polarizer qualitatively. The dual circular polarizer will be applied in a spherical cavity pulse compressor, and it can also serve as an important part for other RF components such as the phase shifter. References Fig. 7 The relationship between VSWR and δ with different values of θ δ and θ is the errors of the magnitude and phase difference of the two TE11 modes in the S-band waveguide dual circular polarizer 1. Y.B. Jung, Ka-band polariser structure and its antenna application. Electron. Lett. 45(18), 91 9 (009). S.Y. Eom, Y.B. Korchemkin, A new comb circular polarizer suitable for millimeter-band application. ETRI J. 8(5), (006). J.M. Kovac, E.M. Leitch, C. Pryke, J.E. Carlstrom, N.W. Halverson, W.L. Holzapfel, Detection of polarization in the cosmic microwave background using DASI. Nature 40(6917), (00) 4. QUIET Collaboration, Fist season quiet observations: measurements of CMB polarization power spectra at 4 GHz in the multipole range 5 l 475. Astrophys. J. 741(), 111 (011) 5. W. Zhong, B. Li, Q. Fan, Z. Shen, X-band compact septum polarizer design, in 011 IEEE International Conference on Microwave Technology & Computational Electromagnetics, pp (011) 6. J. Bornemann, V.A. Labay, Ridge waveguide polarizer with finite and stepped-thickness septum. IEEE Trans. Microw. Tech. 4(8), (1995) 7. B. Piovano, G. Bertin, L. Accatino, M. Mongiardo, CAD and optimization of compact wide-band septum polarizers, in 9th European Microwave Conference, vol., pp. 5 8 (1999) 1

7 Design and cold test of an S-band waveguide dual circular polarizer Page 7 of T.-l. Zhang, Z.-h. Yan, A. Ka, Dual-band circular waveguide polarizer, in 7th International Symposium on Antennas. Propagation & EM Theory, pp. 1 4 (006) 9. S.-W. Wang, C.-H. Chien, C.-L. Wang, W. Ruey-Beei, A circular polarizer designed with a dielectric septum loading. IEEE Trans. Microw. Theory Tech. 5(7), (004) 10. N. Yoneda, M. Miyazaki, T. Horie, H. Satou, Mono-grooved circular waveguide polarizers, in 00 IEEE MTT-S International Microwave Symposium Digest, vol., pp (00) 11. N. Yoneda, M. Miyazaki, H. Matsumura, M. Yamato, A design of novel grooved circular waveguide polarizers. IEEE Trans. Microw. Theory Tech. 48(1), (000) 1. C. Chang, S. Church, S. Tantawi, P. Voll, M. Sieth, K. Devaraj, Theory and experiment of a compact waveguide dual circular polarizer. Prog. Electromagn. Res. 11, 11 5 (01) 1. C. Chang, S. Tantawi, S. Church, J. Neilson, P.V. Larkoski, Novel compact waveguide dual circular polarizer. Prog. Electromagn. Res. 16, 1 16 (01) 14. X. Chen, S. Tantawi, J. Wang, Novel X-band waveguide dual circular polarizer. Prog. Electromagn. Res. 64, (016) 15. X. Chen, S. Tantawi, J. Wang, Conceptual design of X band waveguide dual circular polarizer. Phys. Rev. Accel. Beams 19(6), 0600 (016) 16. J.W. Wang, S.G. Tantawi, X. Chen, Super-compact SLED system used in the LCLS diagnostic system, in Proceedings of LINAC014, Geneva, Switzerland, pp (014) 17. M. Franzi, J. Wang, V. Dolgasher, S. Tantawi, Compact RF polarizer and its application to pulse compression systems. Phys. Rev. Accel. Beams 19(6), 0600 (016) 18. C. Chang, L. Guo, S.G. Tantawi, Y. Liu, J. Li, C. Chen, W. Huang, A new compact high-power microwave phase shifter. IEEE Trans. Microw. Theory Tech. 6(6), (015) 19. CST Microwave Studio, Computer Simulation Technology, www. cst.com 0. S.L. Pei, G.X. Pei, F.L. Zhao, O.Z. Xiao, Error effect of db coupler on energy doubler performance. High Power Laser Part. Beams 4(0), (01) 1