Improved Measurement Method of Circularly-Polarized Antennas Based on Linear-Component Amplitudes

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1 Open Journal of Antennas and Propagation, 07, 5, ISSN Online: ISSN Print: Improved Measurement Method of Circularl-Polarized Antennas Based on inear-component Amplitudes Daou Wang, Min Wang *, Nuo Xu, Wen Wu JGMT Ministerial Ke aborator, Nanjing Universit of Science and Technolog, Nanjing, China mail: How to cite this paper: Wang, D.Y., Wang, M., Xu, N. and Wu, W. (07) Improved Measurement Method of Circularl- Polarized Antennas Based on inear-component Amplitudes. Open Journal of Antennas and Propagation, 5, eceived: Januar 6, 07 Accepted: March 4, 07 Published: March 7, 07 Copright 07 b authors and Scientific esearch Publishing Inc. This work is licensed under the Creative Commons Attribution International icense (CC BY 4.0). Open Access Abstract An improved measurement method of circularl-polarized (CP) antennas based on linear-component amplitudes is proposed in this paper. B utilizing two sets of orthogonal linear polarization (P) amplitudes, measurement on axial ratio (A) of CP antennas can be realized without phase information. However, the rotation sense of the co-polarization cannot be determined due to the absence of the phase information. Above problem is discussed here for the first time, and a solution is presented to determine the rotation sense of the co-polarization b using common auxiliar CP antennas. In addition, there will be some particular cases with large errors in actual measurement. Here a corresponding solution method is given. Finall, co-polarization and cross-polarization patterns can be further obtained from A results. To verif this improved method, a self-developed CP microstrip arra was measured. The measured results are in agreement with the simulated results, which prove this method is correct, effective and practical. Kewords Circularl-Polarized Antenna, Measurement Method, inear-component Amplitudes, Measurement Improvement. Introduction Circularl-polarized (CP) antennas have man advantages such as insensitivit to polarization locations, elimination of the signal Farada rotation effect caused b the ionosphere, and strong anti-interference abilit. Therefore, the are widel used in satellite communication, radar, GPS and other sstems. It is ver important to measure their characteristics of axial ratio (A), rotation sense, pattern and so on. B means of the measurement based on circular components, it is DOI: 0.436/ojapr March 7, 07

2 eas to measure CP antennas []. However, the auxiliar CP antennas with high polarization purit are rare in realit, so the uncertaint of this method is relativel large. While linearl-polarized antennas can achieve high polarization isolation easil, so it s more effective to stud the method of measuring the CP antenna based on linear components. Two methods about measuring As of CP antennas based on linear components are discussed in []. The first method is to measure one set of orthogonal P amplitudes and phases b utilizing linearl-polarized auxiliar antennas. Another method is to measure onl two sets of orthogonal P amplitudes without phase measurement. As and patterns are separatel obtained in [3] [4] [5] b using the first method. However, the phase measurement is limited b measuring equipment and the error is relativel large in fact. The characteristics of As are got b utilizing the second method in [6] and [7]. It is not necessar to measure phase information, while amplitudes can be measured accuratel. As a result, the measuring accurac of A is improved. But this method also has a problem that the rotation sense of the co-polarization cannot be determined due to the absence of the phase information. There is no analsis about this problem in the related records. An improved measurement method of CP antennas based on linear-component amplitudes is proposed in this paper. It is the first time to point out the problem that the rotation sense of the co-polarization cannot be determined. And a solution is presented to determine the rotation sense b using common CP auxiliar antennas. In addition, some particular cases with large errors occur in practical measurement, here revises and improvements are given. Finall, copolarization and cross-polarization patterns are further obtained from A results. To verif this improved method, a self-developed CP microstrip arra was measured repeatedl. The measured results are in agreement with the simulated results, which prove the correction method is correct, effective and practical.. Measurement Based on inear-component Amplitudes and Phases The polarization state of the electromagnetic wave is distinguished b the orientation of its electric field vector. In the propagation direction of electromagnetic wave, the electric field vector moves around a circle. According to the orbit of the vector, the electromagnetic waves can be divided into linearl-polarized waves, circularl-polarized waves and ellipticall-polarized waves. The transverse electromagnetic wave of antenna radiation in the far field is called plane polarized wave, and its arbitrar polarization state is elliptical polarization, as shown in Figure. The A is defined as the ratio of the major axis A and the minor axis B of the polarization ellipse, denoted as A = A B. While A = B, A = and it is expressed as circular polarization. While A 0 and B = 0, A = and it is expressed as linear polarization. It can be seen that linear polarization and circular polarization are two particular cases of elliptical polarization [8]. The ellipticall-polarized wave can be decomposed into two orthogonal linearl- 37

3 polarized waves [9]. As shown in Figure, for arbitrar electric field vector, it can be decomposed into two orthogonal components x along x-axis and along -axis. For the plane with z = 0, x and can be expressed as: = ωt () sin ( ) x = sin ( ) ω + () t δ where in and are the horizontall-polarized amplitude and the verticall- polarized wave amplitude respectivel. δ is the phase difference between and. In Figure, u-axis and v-axis coincide with major axis and minor axis of polarization ellipse. So the semi-major axis A and semi-minor B can be expressed as [0]: 4 4 ( ( ) ) A= cos δ. (3) 4 4 ( ( ) ) B = cos δ. (4) τ is the inclination of the polarization ellipse with respect to ϕ = 0 and its expression is: cosδ τ = arctan. Comprehensive above, b measuring one set of orthogonal amplitudes, and phase difference δ with a linearl-polarized antenna, the A can be obtained as follows: (5) cos + sin cos + sin + A τ τ δ τ A = =. B sin τ sin τ cosδ cos τ (6) Figure. llipticall polarized wave. 38

4 The rotation sense of the ellipticall-polarized wave can be determined b δ. It is left-handed circular polarization when 0 < δ < 80, while it is right-handed circular polarization when 80 < δ < 0. In general antenna test environment, usuall it is difficult to obtain accurate phase information. However, accurate measurement on amplitude is much easier to implement, so it has unique significance to stud the measurement on A onl based on linear-component amplitudes. 3. Measurement Onl Based on inear-component Amplitudes 3.. Derivation of Phase Information A cannot be obtained b quations (5) and (6) when onl using two linearcomponent amplitudes without phase information. Here a derivation of phase is given from four linear-component amplitudes. In the x plane, as shown in Figure, the projection of electric field vector in arbitrar polarization direction of ϕ can be expressed as: ( ) cos sin. ϕ t = ϕ+ ϕ (7) x quations () and () are substituted into the above equation and the following equation can be derived: ϕ ( t) = ϕ sin ( ωt+ γ) (8) where in ( ) ϕ = + + cos ϕ+ sin ϕ cos δ. quation (9) gives the relationship between ϕ and ϕ, and its corresponding graph is called polarization graph, as shown in Figure. The graph gives the maximum projection of in the direction of ϕ. Actuall, ϕ is the field response of the linearl-polarized antenna rotating to the direction of ϕ in the x plane. The maximum and minimum values of the polarization graph coincide with the maximum and minimum values of the polarization ellipse, respectivel. Given two sets of arbitrar orthogonal linear-component amplitudes, phase information can be obtained when the are substituted into quation (9). For example, through rotating linearl-polarized antenna, two sets of orthogonal P amplitudes,, 3, 4 at φ = 0, 90, 45, 35 can be obtained, phase can be derived b quation (9), as follows: 3.. Derivation of A 3 4 (9) cos δ =. (0) B substituting quation (0) into quations (5) and (6), τ and A can be obtained: 3 arctan 4 τ =. () 39

5 ( ) cos τ sin τ + sin τ A =. sin τ ( 3 4 ) sin τ + cos τ () quation () is the formula about measuring A b utilizing onl four amplitudes. Also because of the principle that total power of arbitrar two orthogo- nal components is the same: = + (3) it can be seen that 4 is redundant. So sometimes, onl three amplitudes,, 3 have to be measured. However, the measurement accurac can be controlled b utilizing four amplitudes. Therefore, it is better to use the method b utilizing four amplitudes Determination of the otation Sense of Co-Polarization Phase information represented b quation (0) can be obtained from above derivation. However, the range of arcos δ is ( 0, π ), so the range of δ cannot be determined whether it is (0, 80 ) or ( 80, 0 ). This means that the method loses part of phase information, so the rotation sense of co-polarization cannot be determined. This problem has not been mentioned in the related records. Here a determination method is given b adopting two CP auxiliar antennas with identical structure but reversed rotation senses. Two auxiliar antennas are separatel used to measure the amplitude of the antenna to be measured. Then the rotation sense of the co-polarization is the rotation sense of the auxiliar antenna which can measure larger amplitude. It is unnecessar to adopt the CP auxiliar antenna with high polarization purit used in the measurement based on circular components. Here CP auxiliar antennas with general performance are used and the are eas to be implemented in the actual situation Treatment of Particular Cases in Measurement When the electric field wave approaches linear polarization in particular directions, there will be particular cases with large errors in the measurement. Four kinds of P cases in particular directions are shown in Figure. And their values of normalized amplitudes, δ and τ are recorded in Table. For the two cases in Figure (a) and Figure (b), the numerator and denominator of quation (0) are all close to 0. It causes relativel large errors since cosδ ma be greater than. Although τ can be stabl solved from quation (), errors are still large. However, for the two cases in Figure (c) and Figure (d), cosδ can be solved accuratel. Thus for the two cases in Figure (a) and Figure (b), cosδ can be accuratel obtained from Figure (c) and Figure (d). et = 3, =, =, =, then cos δ = =. 3 4 (4) 40

6 3 4 x x τ x τ x (a) (b) (c) (d) Figure. P cases in particular directions. Table. Normalized amplitudes, δ and τ values of P cases. Figure 3 4 δ τ (a) 0 / 0 (b) 0 / π (c) 0 0 π 4 (d) 0 π π τ = arctan. ( ) ( ) 3 cos τ + sin τ + 4 sin τ A =. 3 sin τ sin τ + 4 cos τ In practice, the particular case of 3 4 appears occasionall. In this case, performance of circular polarization is prett good. However, the numerator and denominator of quation () are all close to 0, τ has a large error as a result. While δ approximatel equals to ±90 b utilizing quation (0), then A can be accuratel obtained through dividing quation (3) b quation (4) Derivation of Patterns Co-polarization and cross-polarization can be obtained from A results as follows. The ellipticall-polarized wave can also be decomposed into two orthogonal CP waves with reversed rotation senses. For arbitrar electric field vector, it can be decomposed into right-handed CP component and left-handed CP component. If >, the right-hand CP component is co-polarization component and the left-hand CP component is cross-polarization component, otherwise the opposite. and satisf the following relations: + = +. (7) A can also be expressed b et Γ=, then, (suppose that + A =. A Γ=. A + > ): (5) (6) (8) (9) 4

7 Substitute Γ into quation (7), then = = ( + ) +Γ. ( ) Γ + +Γ. (0) () Therefore, patterns of the antenna to be measured can be represented b (0) and (), corresponding to the co-polarization component and the cross-polarization component, respectivel. 4. Measurement Verification A self-developed CP microstrip arra shown in Figure 3 was measured repeatedl b using the improved method. The CP antenna to be measured in Figure 3 is used as a receiving antenna and rotates with the turntable. And the linearlpolarized double-ridged horn shown in Figure 4 is kept still as a transmitting antenna. Figure 3. Self-developed CP antenna. Figure 4. inearl-polarized double-ridged horn. 4

8 The polarization direction of the linearl-polarized transmitting antenna is separatel rotated at 0, 90, 45 and 35, and four linearl-polarized amplitudes can be measured quickl and accuratel. Then As and patterns can be solved from above derivations based on the amplitudes convenientl. The measured results are compared with the simulation results, as shown in Figures 5-7. The simulation results are derived from Ansoft HFSS. 5 Measured Simulated Axialatio/dB f/ghz Figure 5. Curves of As versus frequenc ( ϕ = 0, θ = 0 ) Measured Simulated Axialatio/dB θ/ Figure 6. Curves of As versus θ at center frequenc of 8.6 GHz ( ϕ = 0 ). 43

9 Normalized Pattern/dB θ/ Figure 7. Normalized patterns at center frequenc of 8.6 GHz ( ϕ = 0 ). Measured Co-polarization Simulated Co-polarization Measured Cross-polarization Simulated Cross-polarization Measured results in Figure 5 show that the A curves versus frequenc agree ver well with the simulated one from 8.47 GHz to 8.68 GHz. The minima are both about.5 db at the center frequenc of 8.6 GHz. There are onl some certain differences at lower or upper frequencies, which can be attributed to the machining tolerance. At the center frequenc of 8.6 GHz, measured and simulated curves of As versus θ at ϕ = 0 also maintain good consistenc in Figure 6. B utilizing common auxiliar antennas with determined rotation senses, the antenna to be measured is identified as a left-hand CP antenna. The measured and simulated normalized patterns shown in Figure 7 also match well. In patterns, when the P case occurs, the co-polarization component is approximatel equal to the cross-polarization component, which causes that two components cannot be distinguished. This is the limitation of the proposed work. However, in this case the amplitudes of two components both are small and slight effect occurs on the overall performance of the patterns. It can be solved with nearest distribution according to the smoothness of the curves. Two components of other parts in patterns are clear and can be distinguished easil. To sum up, it can be seen that the improved method is correct, practical and effective. 5. Conclusion A method for measuring characteristic parameters of CP antennas is discussed based on linear-component amplitudes in this paper. B measuring two arbitrar sets of orthogonal P amplitudes, the As can be obtained quickl and convenientl. However, the rotation sense of co-polarization cannot be determined in original measurement method, so here a corresponding solution is presented to determine it b using common CP auxiliar antennas. Also the particular cases 44

10 in the measurement are considered and perfect processing method has been established. The revised and improved method has the advantages of accurac, convenience and efficienc. It can meet the basic demand of scientific research and engineering for CP antenna measurement. Grant Information This work was supported b National Natural Science Foundation of China under Grant eferences [] Zhang, X.P. (006) The Stud on Compensated Compact ange (CC) Antenna Measurement Technolog. Spacecraft nvironment ngineering, 3, [] in, C.. (987) Antenna Measurement Technique. Chengdu Telecommunication ngineering College Press, Chengdu. [3] Toh, B.Y., Cahill,. and Fusco, V.F. (003) Understanding and Measuring Circular Polarization. I Transaction on ducation, 46, [4] Shang, J.P., Fu, D.M., Jiang, S. and Deng, Y.B. (009) Method for Measuring the Characteristic Parameter of the Circular Polarization Antenna. Journal of Xidian Universit (Natural Science), 36, [5] Guo, J. and Wan, S.S. (009) Measuring Method for Circular Polarization Antennas in Far Field. Journal of Nanjing Universit of Aeronautics & Astronautics, 4, [6] i, N.J., Feng, Y.., Wang, J.F. and Dang, J.J. (03) Fast Measuring Axial atio of Circular Polarization Antennas Based on inear Polarization Antenna. Infrared and aser ngineering, 4, 6-0. [7] Zhang, X.P. and Zhou, H.A. (009) An Accurate Test Method for Circular Polarized Antenna. Spacecraft nvironment ngineering, 6, [8] Qin, S.Y., Yang, K.Z. and Chen, H. (003) Measuring Technique of Gain for Different Polarization Antenna. Journal of lectronic Measurement and Instrumentation, 7, [9] Yu, J. and Zhao, J. (04) Analze the Gain esults of Polarized Antenna with Different Method in Anechoic Chamber. Foreign lectronic Measurement Technolog, 33, [0] Fang, D.G. (00) Antenna Theor and Microstrip Antennas. CC Press, Boca aton. 45

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