Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-02T21:17:54.326Z Has data issue: false hasContentIssue false

8 - Numerical Modeling of Phased Array Antennas

Published online by Cambridge University Press:  14 July 2018

Karl F. Warnick
Affiliation:
Brigham Young University, Utah
Rob Maaskant
Affiliation:
Chalmers University of Technology, Gothenberg
Marianna V. Ivashina
Affiliation:
Chalmers University of Technology, Gothenberg
David B. Davidson
Affiliation:
Curtin University, Perth
Brian D. Jeffs
Affiliation:
Brigham Young University, Utah
Get access

Summary

Computational electromagnetics (CEM), the numerical solution of Maxwell's equations, is now a well-established field [1]–[3]. Growing steadily from pioneering work in the 1960s, a range of commercial CEM tools is now available.Well known general purpose software packages in the field are FEKO (Altair), HFSS (Ansys), and Microwave Studio (CST); specifically for reflector analysis, GRASP (TICRA) is a leading code. There are also many public domain codes available, with the venerable NEC-2 code among the most popular. From the perspective of the underlying algorithm, the most widely used methods are the method of moments (MoM), finite element method (FEM) and the finite difference time domain method (FDTD). Many textbooks on computational electromagnetics are available; a basic introduction to FDTD, MoM, and FEM can be found in [4].

Large, broadband aperture and phased array antenna systems can have characteristic dimensions beyond the size that commercial modeling tools can accommodate within a reasonable computation time or memory requirement. Array antenna systems exhibit multiscale features and include both dielectric and metal materials, and elements in the array are strongly coupled. Simulations over a wide range of frequencies and beam scan angles must be considered, and for PAFs the model must include a large reflector. In particular for PAFs, edge effects are important, so analytical infinite array approximations have limited value and full wave techniques are required. Given the computationally intensive nature of the analysis, optimization of astronomical antenna systems by evaluating the entire structure in full detail is challenging.

For radio astronomy applications in particular, designers try to minimize the inclusion of significant volumes of dielectric material in the phased array antennas, to avoid the losses which dielectrics usually bring with them. As a result, the MoM is usually the most efficient technique, as it handles highly (or perfectly) conducting antennas in a very efficient formulation, and using surface or volume equivalence, dielectric materials can be included in the analysis. Since many commercial software packages are built around FEM and FDTD, it is also common for these methods to be used in the design of antenna systems for high sensitivity receiver applications.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] D. B., Davidson, Computational Electromagnetics for RF and Microwave Engineering, 2nd edn. Cambridge, UK: Cambridge University Press, 2011.Google Scholar
[2] K. F., Warnick, Numerical Analysis for Electromagnetic Integral Equations. Boston: Artech House, 2008.Google Scholar
[3] A., Bondeson, T., Rylander, and P., Ingelström, Computational Electromagnetics. New York, NY: Springer Science, 2005.Google Scholar
[4] K. F., Warnick, Numerical Methods for Engineering: An Introduction Using MATLAB and Computational Electromagnetics Examples. Rayleigh, NC: Sci- Tech, 2011.Google Scholar
[5] R. G., Marchand and D. B., Davidson, “Verification of the method-of-moment codes using the method of manufactured solutions,” IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 4, pp. 835–843, 2014.Google Scholar
[6] C. P., Davis and K. F., Warnick, “Error analysis of 2D MoM for MFIE/EFIE/CFIE based on the circular cylinder,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 321–331, Jan. 2005.Google Scholar
[7] C. P., Davis and K. F., Warnick, “High order convergence with a low-order discretization of the 2-D MFIE,” IEEE Ant. Wireless Propag. Lett., vol. 3, no. 16, pp. 355–358, Dec. 2005.Google Scholar
[8] S., Rao, D., Wilton, and A., Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. 30, no. 3, pp. 409–418, Ma. 1982.Google Scholar
[9] D. B., Davidson and J. T., Aberle, “An introduction to spectral domain methodof- moments formulations,” IEEE Antennas Propag. Mag., vol. 46, no. 3, pp. 11–19, Jun. 2004. doi: 10.1109/MAP.2004.1374083.Google Scholar
[10] C., Craeye, “Including spatial correlation of thermal noise in the noise model of high-sensitivity arrays,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3845–3848, Nov. 2005.Google Scholar
[11] C., Craeye, B., Parvais, and X., Dardenne, “MoM simulation of signal-to-noise patterns in infinite and finite receiving antenna arrays,” IEEE Trans. Antennas Propag., vol. 52, no. 12, pp. 3245–3256, Dec. 2004.Google Scholar
[12] S., Ponnapalli, A., Deutsch, and R., Bertin, “A package analysis tool based on a method of moments surface formulation,” IEEE Trans. Components, Hybrids and Manufact. Techn., vol. 16, no. 8, pp. 884–892, 1993.Google Scholar
[13] D., Bekers, Finite Antenna Arrays –An Eigencurrent Approach, PhD thesis, Eindhoven University of Technology, Eindhoven, 2004. [Online]. Available: http://alexandria.tue.nl/extra2/200411410.pdf.
[14] R. F., Harrington, Field Computation by Moment Methods. New York: The Macmillan Company, 1968.Google Scholar
[15] S., Tretyakov, Analytical Modeling in Applied Electromagnetics. Boston and London: Artech House, 2003.Google Scholar
[16] “EM Software & Systems –S.A. (Pty) Ltd, Stellenbosch, South Africa, FEKO, Suite 6.2,” 2012. [Online]. Available: www.feko.info.
[17] U., Jakobus, “Comparison of different techniques for the treatment of lossy dielectric/magnetic bodies within the MoM formulation,” Int. J. Electron. Commun. (AEU), vol. 54, no. 1, pp. 1–10, 2000.Google Scholar
[18] D. J., Bekers, S. J. L. van, Eijndhoven, and A. A. F. van de, Ven, “Modeling and analysis of a long thin conducting stripline,” J. Eng. Math., vol. 49, no. 4, pp. 373–390, 2004.Google Scholar
[19] L., Matekovits, V. A., Laza, and G., Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag., vol. 55, no. 9, pp. 2509–2521, Sep. 2007.Google Scholar
[20] R., Maaskant, R., Mittra, and A. G., Tijhuis, “Application of trapezoidal-shaped characteristic basis functions to arrays of electrically interconnected antenna elements,” in Proc. International Conference on Electromagnetics and Applications (ICEAA), Torino, Sep. 2007, pp. 567–571.Google Scholar
[21] V., Prakash and R., Mittra, “Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations,” Micr. Opt. Technol., vol. 36, pp. 95–100, Jan. 2003.Google Scholar
[22] D. J., Ludick, R., Maaskant, D. B., Davidson, et al., “Efficient analysis of large aperiodic antenna arrays using the domain Green's function method,” IEEE Trans. Antennas Propag., vol. 62, no. 4, pp. 1579–1588, Apr. 2014.Google Scholar
[23] L., Matekovits, G., Vecchi, G., Dassano, and M., Orefice, “Synthetic function analysis of large printed structures: The solution space sampling approach,” in Proc. IEEE Antennas and Propagation Society International Symposium (APS), Boston, Massachusetts, Jul. 2001, pp. 568–571.Google Scholar
[24] E., Suter and J. R., Mosig, “A subdomain multilevel approach for the efficient MoM analysis of large planar antennas,” Micr. Opt. Technol., vol. 26, no. 4, pp. 270–277, Aug. 2000.Google Scholar
[25] R., Maaskant, Analysis of large antenna systems, PhD thesis, Eindhoven University of Technology, Eindhoven, 2010. [Online]. Available: http://alexandria.tue.nl/extra2/201010409.pdf.
[26] C., Craeye, “Finite-array characterization with the help of the ASM-MBF method : Eigenmode analysis,” in Proc. International URSI Commission B Electromagnetic Theory Symposium (EMTS), Berlin, Germany, Aug. 2010, pp. 168–170.Google Scholar
[27] D., Gonzalez-Ovejero, E., Acedo, N., Razavi-Ghods, and C., Craeye, “Fast MBF based method for large random array characterization,” in Proc. IEEE Antennas and Propagation Society International Symposium (AP-S), Charleston, South Carolina, Jun. 2009.Google Scholar
[28] R., Mittra, G., Bianconi, C., Pelletti, et al., “Fast-factorization acceleration of MoM compressive domain-decomposition,” Proc. IEEE, vol. 100, no. 7, pp. 2122–2131, Jul. 2011.Google Scholar
[29] S. G., Hay, J. D., O'Sullivan, and R., Mittra, “Connected patch array analysis using the characteristic basis function method,” IEEE Trans. Antennas Propag., vol. 59, no. 6, pp. 1828–1837, Jun. 2011.Google Scholar
[30] O., Iupikov, R., Maaskant, M., Ivashina, A., Young, and P.-S., Kildal, “Fast and accurate analysis of reflector antennas with phased array feeds including multiple reflections between feed and reflector,” IEEE Trans. Antennas Propag., vol. 62, no. 7, pp. 3450–3462, Jul. 2014.Google Scholar
[31] S., Hay, R., Mittra, and N., Huang, “Analysis of reflector and feed scattering and coupling effects on the sensitivity of phased array feeds,” in International Workshop on Phased Array Antenna Systems for Radio Astronomy, Brigham Young University, Provo, UT USA, Ma. 2010, pp. 1–35. [Online]. Available: http://csas.ee.byu.edu/docs/Workshop/BYU_SGH.pdf.Google Scholar
[32] C., Craeye, “A fast impedance and pattern computation scheme for finite antenna arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 10, pp. 3030–3034, Oct. 2006.Google Scholar
[33] S. N., Jha and C., Craeye, “Fast spectral-domain MBF method for printed antennas,” in Proc. European Conference on Antennas and Propagation (EuCAP), Prague, Czech Republic, Mar. 2012, pp. 292–295.Google Scholar
[34] C., Craeye, J., Laviada, R., Maaskant, and R., Mittra, “Macro basis function framework for solving Maxwell's equations in surface-integral-equation form,” Forum for Electromagnetic Research Methods and Application Technologies (FERMAT), vol. 3, pp. 1–16, 2014. [Online]. Available: www.e-fermat.org/files/articles/1536cfcaaae952.pdf.Google Scholar
[35] G., Tiberi, A., Monorchio, G., Manara, and R., Mittra, “Hybridizing asymptotic and numerically rigorous techniques for solving electromagnetic scattering problems using the characterisitic basis functions (CBFs),” in Proc. IEEE Antennas and Propagation Society International Symposium (AP-S), Columbus, Ohio, Jun. 2003, pp. 22–27.Google Scholar
[36] J., Yeo, V., Prakash, and R., Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Micr. Opt. Technol., vol. 39, pp. 456–464, Dec. 2003.Google Scholar
[37] J., Laviada, M. R., Pino, and F., Las-Heras, “Generation of excitation-independent characteristic basis functions for three-dimensional homogeneous dielectric bodies,” IEEE Trans. Antennas Propag., vol. 59, no. 9, pp. 3318–3327, Sep. 2011.Google Scholar
[38] S. J., Kwon, K., Du, and R., Mittra, “Characteristic basis function method: A numerically efficient technique for analyzing microwave and RF circuits,” Micr. Opt. Technol., vol. 38, no. 6, pp. 444–448, Jul. 2003.Google Scholar
[39] R., Maaskant, P., Takook, and P.-S., Kildal, “Fast analysis of gap waveguides using the characteristic basis function method and the parallel-plate Green's function,” in Proc. International Conference on Electromagnetics and Applications (ICEAA), CapeTown, South Africa, Sep. 2012, pp. 788–791.Google Scholar
[40] C., Delgado, M. F., Catedra, and R., Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large scatters,” IEEE Trans. Antennas Propag., vol. 56, no. 7, pp. 2134–2137, Jul. 2008.Google Scholar
[41] R., Maaskant, M. V., Ivashina, O., Iupikov, et al., “Analysis of large microstripfed tapered slot antenna arrays by combining electrodynamic and quasi-static field models,” IEEE Trans. Antennas Propag., vol. 56, no. 6, pp. 1798–1807, Jun. 2011.Google Scholar
[42] J., Laviada, M. R., Pino, F., Las-Heras, and R., Mittra, “Interpolation scheme for fast calculation of reaction terms in the characteristic basis function method,” Micr. Opt. Technol., vol. 51, no. 8, pp. 1818–1824, Aug. 2009.Google Scholar
[43] E., Garcia, C., Delgado, I., Diego, and M., Catedra, “An iterative solution for electrically large problems combining the characteristic basis function method and the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2363–2371, Aug. 2008.Google Scholar
[44] E., Garcia, C., Delgado, I., Gonzalez, and F., Cátedra, “Efficient parallelization of a CBFM-MLFMA scheme for the computation of complex electromagnetic problems,” in Proc. IEEE Antennas and Propagation Society International Symposium (AP-S), San Diego, California, Jul. 2008.Google Scholar
[45] D. J., Ludick and D. B., Davidson, “Investigating efficient parallelization techniques for the characteristic basis function method (CBFM),” in Proc. International Conference on Electromagnetics and Applications (ICEAA), Torino, Sep. 2009, pp. 400–403.Google Scholar
[46] J., Laviada, F., Las-Heras, M. R., Pino, and R., Mittra, “Solution of electrically large problems with multilevel characteristic basis functions,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3189–3198, Oct. 2009.Google Scholar
[47] R., Maaskant, R., Mittra, and A. G., Tijhuis, “Multi-level characteristic basis function method (CBFM) for the analysis of large antenna arrays,” Special Issue on: CEM for Modeling Large Finite Antenna Arrays, The Radio Science Bulletin, vol. 336, no. 3, pp. 23–34, 2011.Google Scholar
[48] L., Matekovits, G., Vecchi, and V. A., Laza, “Degrees of freedom and synthetic functions in the analysis of large antennas,” in Proc. International URSI Commission B Electromagnetic Theory Symposium (EMTS), Pisa, Italy, Ma. 2004, pp. 138–140.Google Scholar
[49] P. D., Vita, A., Freni, L., Matekovits, P., Pirinoli, and G., Vecchi, “A combined AIM-SFX approach for large complex arrays,” in Proc. IEEE Antennas and Propagation Society International Symposium (AP-S), Honolulu, Hawaii, Jun. 2007, pp. 3452–3455.Google Scholar
[50] L., Matekovits, G., Vecchi, M., Bercigli, and M., Bandinelli, “Synthetic-functions analysis of large aperture-coupled antennas,” IEEE Trans. Antennas Propag., vol. 57, no. 7, pp. 1936–1943, Jul. 2009.Google Scholar
[51] P., Pirinoli, L., Matekovits, F., Vipiana, G., Vecchi, and M., Orefice, “Multigrid SFX-MR approach for the analysis of large arrays,” in Proc. International Conference on Applied Electromagnetics and Communications (ICECom), Dubrovnik, Croatia, Oct. 2005.Google Scholar
[52] C., Craeye, “On the connection between multiple-scattering based macro basis functions and Krylov subspace methods,” in Proc. International Conference on Electromagnetics and Applications (ICEAA), Torino, Sep. 2009, pp. 938–941.Google Scholar
[53] N. A., Ozdemir, D., Gonzalez-Ovejero, and C., Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace iterative methods,” IEEE Trans. Antennas Propag., vol. 61, no. 4, pp. 2088–2098, Apr. 2013.Google Scholar
[54] W. B., Lu, T. J., Cui, Z. G., Qian, X. X., Yin, and W., Hong, “Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 3078–3085, Nov. 2004.Google Scholar
[55] D. J., Bekers, S. J. L. van, Eijndhoven, A. A. F. van de, Ven, P. P., Borsboom, and A. G., Tijhuis, “Eigencurrent analysis of resonant behavior in finite antenna arrays,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2821–2829, Jun. 2006.Google Scholar
[56] A. V., Mrstik and P. G., Smith, “Scanning capabilities of large parabolic cylinder reflector antennas with phased-array feeds,” IEEE Trans. Antennas Propag., vol. 29, no. 3, pp. 455–462, Ma. 1981.Google Scholar
[57] S. M., Rao, “A true domain decomposition procedure based on method of moments to handle electrically large bodies,” IEEE Trans. Antennas Propag., vol. 60, no. 9, pp. 4233–4238, Sep. 2012.Google Scholar
[58] R., Maaskant, R., Mittra, and A. G., Tijhuis, “Fast solution of multi-scale antenna problems for the Square Kilometre Array (SKA) radio telescope using the characteristic basis function method (CBFM),” Applied Computational Electromagnetics Society (ACES) Journal, vol. 24, no. 2, pp. 174–188, Apr. 2009.Google Scholar
[59] R., Maaskant, R., Mittra, and A. G., Tijhuis, “Fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3440–3451, Nov. 2008.Google Scholar
[60] C., Craeye, “Combination of multipole and macro basis function approaches for the analysis of finite arrays with dielectric elements,” in Proc. European Conference on Antennas and Propagation (EuCAP), Nice, France, Apr. 2006.
[61] R., Maaskant, R., Mittra, and A. G., Tijhuis, “Multilevel characteristic basis function method (MLCBFM) for the analysis of large antenna arrays,” Special Section on Computational Electromagnetics for Large Antenna Arrays, The Radio Science Bulletin, no. 336, pp. 23–34, Mar. 2011.Google Scholar
[62] A. K., Skrivervik and J. R., Mosig, “Analysis of finite phased arrays of microstrip patches,” IEEE Trans. Antennas Propag., vol. 41, no. 9, pp. 1105–1114, Aug. 1993.Google Scholar
[63] A. K., Skrivervik and J. R., Mosig, “Analysis of printed array antennas,” IEEE Trans. Antennas Propag., vol. 45, no. 9, pp. 1411–1418, Sep. 1997.Google Scholar
[64] D. J., Ludick, Efficient numerical analysis of finite antenna arrays using domain decomposition methods, PhD thesis, Dept. Electrical & Electronic Engineering, University of Stellenbosch, Dec. 2014.
[65] D. J., Ludick, M. M., Botha, R., Maaskant, and D. B., Davidson, “Comparison of the iterative Jacobi method and the iterative domain green's function method for finite array analysis,” in Proc. European Conference on Antennas and Propagation (EuCAP), Apr. 2016, pp. 1–5. doi: 10.1109/EuCAP.2016.7481687.Google Scholar
[66] D. J., Ludick, R., Maaskant, R., Mittra, U., Jakobus, and D. B., Davidson, “Applying the CBFM-enhanced domain Green's function method to the analysis of large disjoint subarray antennas,” in Proc. International Conference on Elec tromagnetics and Applications (ICEAA), Sep. 2013, pp. 94–97. doi: 10.1109/ ICEAA.2013.6632195.Google Scholar
[67] D., Ludick, R., Maaskant, D., Davidson, et al., “A comparison of domain decomposition techniques for analysing disjoint finite antenna arrays,” in Proc. European Conference on Antennas and Propagation (EuCAP), Den Haag, The Netherlands, Apr. 2014, pp. 2994–2998.Google Scholar
[68] Y., Brand, A. K., Skrivervik, J. R., Mosig, and F. E., Gardiol, “New iterative integral equation technique for multilayered printed array antennas,” in Mathematical Methods in Electromagnetic Theory, Kharkov, Ukraine, Jun. 1998, pp. 615–617.Google Scholar
[69] A. C., Polycarpou, “Evaluation of stationary block iterative techniques for the solution of finite arrays using the FE-BI method and domain decomposition,” in Proc. European Conference on Antennas and Propagation (EuCAP), Nice, France, Nov. 2006.
[70] D. J., Ludick, R., Maaskant, D. B., Davidson, and U., Jakobus, “Accelerating the domain Green's function method through adaptive cross approximation,” in Proc. International Conference on Electromagnetics and Applications (ICEAA), Aug. 2014, pp. 636–639. doi: 10.1109/ICEAA.2014.6903935.Google Scholar
[71] Y., Brand, A. K., Skrivervik, and J. R., Mosig, “An iterative scheme solution for the analysis of printed arrays,” Microwave and Optical Technology Letters, vol. 16, no. 2, pp. 106–115, 1997, issn: 1098-2760.Google Scholar
[72] A. K., Skriverik, “What can integral equations do for array analysis?” In Proc. European Conference on Antennas and Propagation (EuCAP), Den Haag, The Netherlands, Apr. 2014, pp. 758–761.Google Scholar
[73] Y., Saad and M. H., Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 7, no. 3, pp. 856–869, Jul. 1986.Google Scholar
[74] Y.-F., Jing and T.-Z., Huang, “Restarted weighted full orthogonalization method for shifted linear systems,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1583 –1591, 2009, issn: 0898-1221. doi: https://doi.org/10.1016/j.camwa.2008.10.088. [Online]. Available: www.sciencedirect.com/science/article/pii/S0898122108006160.
[75] O. A., Iupikov, C., Craeye, R., Maaskant, and M. V., Ivashina, “Domain-decomposition approach to Krylov subspace iteration,” IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 1414–1417, 2016, issn: 1536-1225. doi: 10. 1109/LAWP.2015.2511195.Google Scholar
[76] V., Rokhlin, “Rapid solution of integral equations of classical potential theory,” Journal of Computational Physics, vol. 60, no. 2, pp. 187–207, 1985.Google Scholar
[77] R., Coifman, V., Rokhlin, and S., Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Antennas Propag. Mag., vol. 35, no. 3, pp. 7–12, 1993.Google Scholar
[78] W. C., Chew, J., Jin, E., Michielssen, and J., Song, Fast and Efficient Algorithms in Computational Electromagentics. Boston: Artech House, 2001.Google Scholar
[79] M., Abramowitz and I. A., Stegun, Eds., Handbook of Mathematical Functions. New York: Dover, 1972.Google Scholar
[80] S., Kurz, O., Rain, and S., Rjasanow, “The adaptive cross-approximation technique for the 3-D boundary-element method,” IEEE Transactions on Magnetics, vol. 38, no. 2, pp. 421–424, 2002.Google Scholar
[81] W., Imbriale, P., Ingerson, and W., Wong, “Large lateral feed displacements in a parabolic reflector,” IEEE Trans. Antennas Propag., vol. 22, no. 6, pp. 742–745, 1974.Google Scholar
[82] A., Boag and C., Letrou, “Multilevel fast physical optics algorithm for radiation from non-planar apertures,” IEEE Trans. Antennas Propag., vol. 53, no. 6, pp. 2064–2072, 2005.Google Scholar
[83] GRASP website, www.ticra.com, Ticra.
[84] “Altair, FEKO, Suite 7.0,” [Online]. Available: www.feko.info.
[85] M., Apeldoorn, Characterizing Reflector–feed Interaction for Parabolic Reflector Antennas, M. Eng. thesis, TU Delft, Delft, Netherlands, Jan. 2011.
[86] D. I. L. de, Villiers, “Prediction of aperture efficiency ripple in clear aperture offset Gregorian antennas,” IEEE Trans. Antennas Propag., vol. 61, no. 5, pp. 2457–2465, Ma. 2013, issn: 0018-926X. doi: 10. 1109 / TAP. 2013. 2239953.Google Scholar
[87] O. A., Iupikov, R., Maaskant, and M. V., Ivashina, “A plane wave approximation in the computation of multiscattering effects in reflector systems,” in Proc. European Conference on Antennas and Propagation (EuCAP), Gothenburg, Sweden, Apr. 2013.Google Scholar
[88] J. P., McKay and Y., Rahmat-Samii, “Compact range reflector analysis using the plane wave spectrum approach with an adjustable sampling rate,” IEEE Trans. Antennas Propag., vol. 39, no. 6, pp. 746–753, Jun. 1991.Google Scholar
[89] J. J. H., Wang, “An examination of the theory and practices of planar near-field measurement,” IEEE Trans. Antennas Propag., vol. 36, no. 6, pp. 746–753, Jun. 1988.Google Scholar
[90] K., Yee, “Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media,” IEEE Trans. Antennas Propag., vol. 14, pp. 302–307, Ma. 1966.Google Scholar
[91] A., Taflove and S., Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd edn. Boston: Artech House, 2005.Google Scholar
[92] P. P., Silvester and R. L., Ferrari, Finite Elements for Electrical Engineers, 3rd edn. Cambridge, UK: Cambridge University Press, 1996.Google Scholar
[93] J.-M., Jin, The Finite Element Method in Electromagnetics, 2nd edn. New York: John Wiley and Sons, 2002.Google Scholar
[94] K., Kurokawa, “Power waves and the scattering matrix,” IEEE Trans. Microw. Theory Tech., vol. 13, no. 2, pp. 194–202, Mar. 1965.Google Scholar
[95] J. A., Dobrowolski, Introduction to Computer Methods for Microwave Circuit Analysis and Design. Warsaw University of Technology: Artech House, 1991.Google Scholar
[96] H., Hillbrand and P., Russer, “An efficient method for computer aided noise analysis of linear amplifier networks,” IEEE Trans. Circuits Syst., vol. 23, no. 4, pp. 235–238, Apr. 1976.Google Scholar
[97] W. van, Etten, “Stochastische signaaltheorie,” Eindhoven University of Technology, Eindhoven, The Netherlands, Course Notes 13e editie, 5H130, 1999.Google Scholar
[98] L. W., Couch II, Digital and Analog Communication Systems, 6th edn. Upper Saddle River, NJ: Prentice Hall, 2001.Google Scholar
[99] A. van der, Ziel, Ed., Noise, Sources, Characterization, Measurement. Englewood Cliffs, NJ: Prentice Hall, Jan. 1970.Google Scholar
[100] J. P., Hamaker, “Instrumental techniques of aperture synthesis,” Netherlands Institute for Radio Astronomy, Dwingeloo, The Netherlands, Course Notes, Second printing, March, 2001.Google Scholar
[101] S. W., Wedge and D. B., Rutledge, “Wave techniques for noise modeling and measurement,” IEEE Trans. Antennas Propag., vol. 40, no. 11, pp. 2004–2012, Nov. 1992.Google Scholar
[102] H., Bosma, “On the theory of linear noisy systems,” Philips Research, Eindhoven, The Netherlands, Philips Research Reports, Supplement 10, 2005.
[103] R., Maaskant, E. E. M., Woestenburg, and M. J., Arts, “A generalized method of modeling the sensitivity of array antennas at system level,” in Proc. European Microwave Conference, Amsterdam, Oct. 2004, pp. 1541–1544.Google Scholar
[104] R., Maaskant and B., Yang, “A combined electromagnetic and microwave antenna system simulator for radio astronomy,” in Proc. European Conference on Antennas and Propagation (EuCAP), Nice, France, Nov. 2006.
[105] R., Maaskant, D. J., Bekers, M. J., Arts, W. A. van, Cappellen, and M. V., Ivashina, “Evaluation of the radiation efficiency and the noise temperature of low-loss antennas,” IEEE Antennas and Wireless Propagation Letters, vol. 8, no. 8, pp. 1536–1225, Jan. 2009.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×