An Effective Spherical NF/FF Transformation Suitable for Characterising an Antenna under Test in Presence of an Infinite Perfectly Conducting Ground Plane
<p>Spherical scan of heavy volumetric AUTs over a PEC ground plane.</p> "> Figure 2
<p>View in the meridian plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 0: (<b>a</b>) original formulation of the problem; (<b>b</b>) equivalent formulation of the problem.</p> "> Figure 3
<p><math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>p</mi> </msub> </mrow> </semantics></math> on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 0°. Blue solid line: exact. Red dots: interpolated from the non-redundant samples: (<b>a</b>) Amplitude; (<b>b</b>) Phase.</p> "> Figure 4
<p><math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°. Blue solid line: exact. Red dots: interpolated from the non-redundant samples: (<b>a</b>) Amplitude; (<b>b</b>) Phase.</p> "> Figure 5
<p>Voltage amplitude on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 60°. Blue solid line: exact. Red dots: interpolated from the non-redundant samples: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>p</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p> "> Figure 6
<p>Normalised mean-square errors in the reconstruction of the probe voltage: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>p</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p> "> Figure 7
<p><math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°. Blue solid line: exact. Red dots: recovered from the error affected NF samples: (<b>a</b>) Amplitude; (<b>b</b>) Phase.</p> "> Figure 8
<p>Far-field pattern. Blue solid line: exact. Red dots: obtained from the non-redundant samples: (<b>a</b>) <math display="inline"><semantics> <mi>φ</mi> </semantics></math>—component on the cut plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 0°; (<b>b</b>) <span class="html-italic">ϑ</span>—component on the cut plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 60°; (<b>c</b>) <math display="inline"><semantics> <mi>φ</mi> </semantics></math>—component on the cut plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 60°; (<b>d</b>) <span class="html-italic">ϑ</span>—component on the cut plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°.</p> "> Figure 9
<p><math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math> on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°. Blue solid line: exact. Red dots: interpolated from the non-redundant samples: (<b>a</b>) Amplitude; (<b>b</b>) Phase.</p> "> Figure 10
<p>Relevant to the reconstruction of <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>r</mi> </msub> </mrow> </semantics></math>: (<b>a</b>) Normalised mean-square errors; (<b>b</b>) Amplitude on the meridian at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°. Blue solid line: exact. Red dots: recovered from the error-affected NF samples.</p> "> Figure 11
<p>Far-field pattern. Blue solid line: exact. Red dots: interpolated from the non-redundant samples: (<b>a</b>) <span class="html-italic">ϑ</span>—component on the cut plane at <math display="inline"><semantics> <mi>φ</mi> </semantics></math> = 90°; (<b>b</b>) <span class="html-italic">ϑ</span>—component on the cut plane at <span class="html-italic">ϑ</span> = 90°.</p> ">
Abstract
:1. Introduction
2. Sampling Representation over the Upper Hemisphere
3. Numerical Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Yaghjian, A.D. An overview of near-field antenna measurements. IEEE Trans. Antennas Propag. 1986, 34, 30–45. [Google Scholar] [CrossRef]
- Appel-Hansen, J.; Dyson, J.D.; Gillespie, E.S.; Hickman, T.G. Antenna measurements. In The Handbook of Antenna Design; Rudge, A.W., Milne, K., Olver, A.D., Knight, P., Eds.; Peter Peregrinus: London, UK, 1986; pp. 584–694. [Google Scholar]
- Gillespie, E.S. (Ed.) Special Issue on near-field scanning techniques. IEEE Trans. Antennas Propag. 1988, 36, 727–901. [Google Scholar]
- Francis, M.H.; Wittmann, R.W. Near-field scanning measurements: Theory and practice. In Modern Antenna Handbook; Balanis, C.A., Ed.; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2008; pp. 929–976. [Google Scholar]
- IEEE Standard 1720-2012; IEEE Recommended Practice for Near-Field Antenna Measurements. Francis, M.H. (Ed.) IEEE: Piscataway, NJ, USA, 2012.
- Sierra Castañer, M.; Foged, L.J. Post-Processing Techniques in Antenna Measurement; SciTech Publishing IET: London, UK, 2019. [Google Scholar]
- Parini, C.; Gregson, S.; McCormick, J.; Van Rensburg, D.J. Theory and Practice of Modern Antenna Range Measurements; SciTech Publishing IET: London, UK, 2020. [Google Scholar]
- Gennarelli, C.; Ferrara, F.; Guerriero, G.; D’Agostino, F. Non-Redundant Near-Field to Far-Field Transformation Techniques; SciTech Publishing IET: London, UK, 2022. [Google Scholar]
- Jensen, F. On the probe compensation for near-field measurements on a sphere. Archiv Elektr. Übertr. 1975, 29, 306–308. [Google Scholar]
- NBSIR 75-809; Non-Planar Near-Field Measurements: Spherical Scanning. Wacker, P.F. (Ed.) National Institute of Standards and Technology: Boulder, CO, USA, 1975.
- Larsen, F.H. Probe correction of spherical near-field measurements. Electr. Lett. 1977, 13, 393–395. [Google Scholar] [CrossRef]
- Yaghjian, A.D. Simplified approach to probe-corrected spherical near-field scanning. Electr. Lett. 1984, 20, 195–196. [Google Scholar]
- Yaghjian, A.D.; Wittmann, R.C. The receiving antenna as a linear differential operator: Application to spherical near-field measurements. IEEE Trans. Antennas Propag. 1985, 33, 1175–1185. [Google Scholar] [CrossRef]
- Hansen, J.E.; Jensen, F. Spherical near-field scanning at the technical university of Denmark. IEEE Trans. Antennas Propag. 1988, 36, 734–739. [Google Scholar] [CrossRef]
- Hald, J.; Hansen, J.E.; Jensen, F.; Larsen, F.H. Spherical Near-Field Antenna Measurements; Hansen, J.E., Ed.; Peregrinus: London, UK, 1998. [Google Scholar]
- Bucci, O.M.; Gennarelli, C.; Riccio, G.; Savarese, C. Data reduction in the NF-FF transformation technique with spherical scanning. J. Electromagn. Waves Appl. 2001, 15, 755–775. [Google Scholar] [CrossRef]
- Laitinen, T.; Pivnenko, S.; Breinbjerg, O. Application of the iterative probe correction technique for a high-order probe in spherical near-field antenna measurements. IEEE Antennas Propag. Mag. 2006, 48, 179–185. [Google Scholar] [CrossRef]
- Laitinen, T.; Pivnenko, S. Probe correction technique for symmetric odd-order probes for spherical near-field antenna measurements. IEEE Antennas Wirel. Propag. Lett. 2007, 6, 635–638. [Google Scholar] [CrossRef]
- Laitinen, T.; Breinbjerg, O. A first/third-order probe correction technique for spherical near-field antenna measurements using three probe orientations. IEEE Trans. Antennas Propag. 2008, 56, 1259–1268. [Google Scholar] [CrossRef]
- Laitinen, T. Double φ-step θ-scanning technique for spherical near-field antenna measurements. IEEE Trans. Antennas Propag. 2008, 56, 1633–1639. [Google Scholar] [CrossRef]
- Laitinen, T. Modified θ-scanning technique for first/third-order probes for spherical near-field antenna measurements. IEEE Trans. Antennas Propag. 2008, 57, 1590–1596. [Google Scholar] [CrossRef]
- Laitinen, T.; Pivnenko, S.; Nielsen, J.M.; Breinbjerg, O. Theory and practice of the FFT/matrix inversion technique for probe-corrected spherical near-field antenna measurements with high-order probes. IEEE Trans. Antennas Propag. 2010, 58, 2623–2631. [Google Scholar] [CrossRef]
- Hansen, T.B. Spherical near-field scanning with higher-order probes. IEEE Trans. Antennas Propag. 2011, 59, 4049–4059. [Google Scholar]
- Cornelius, R.; Heberling, D. Spherical wave expansion with arbitrary origin for near-field antenna measurements. IEEE Trans. Antennas Propag. 2017, 65, 4385–4388. [Google Scholar] [CrossRef]
- Cornelius, R.; Heberling, D. Spherical near-field scanning with pointwise probe correction. IEEE Trans. Antennas Propag. 2017, 65, 995–996. [Google Scholar] [CrossRef]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Migliozzi, M. Effective antenna modellings for NF-FF transformations with spherical scanning using the minimum number of data. Int. J. Antennas Propag. 2011, 2011, 936781. [Google Scholar] [CrossRef]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Migliozzi, M. Non-redundant spherical NF—FF transformations using ellipsoidal antenna modeling: Experimental assessments. IEEE Antennas Propag. Mag. 2013, 55, 166–175. [Google Scholar] [CrossRef]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Migliozzi, M. A spherical near-to-far-field transformation using a non-redundant voltage representation optimized for non-centered mounted quasi-planar antennas. Electronics 2020, 9, 944. [Google Scholar] [CrossRef]
- Varela, F.R.; Iragüen, B.G.; Sierra Castañer, M. Fast spherical near-field to far-field transformation for offset-mounted antenna measurements. IEEE Antennas Wirel. Propag. Lett. 2020, 19, 2255–2259. [Google Scholar] [CrossRef]
- Hansen, T.B. Numerical investigation of the system-matrix method for higher-order probe correction in spherical near-field antenna measurements. Int. J. Antennas Propag. 2012, 2012, 493705. [Google Scholar] [CrossRef]
- Qureshi, M.A.; Schmidt, C.H.; Eibert, T.F. Adaptive sampling in spherical and cylindrical near-field antenna measurements’. IEEE Antennas Propag. Mag. 2013, 55, 243–249. [Google Scholar] [CrossRef]
- Saccardi, F.; Rossi, F.; Mioc, F.; Foged, L.J.; Iversen, P.O. Application of the translated-SWE algorithm for the characterization of antennas installed on cars using a minimum number of samples. In Proceedings of the Antenna Measurement Techniques Association Symposium, Atlanta, GE, USA, 15–20 October 2017; pp. 1–6. [Google Scholar]
- Bucci, O.M.; Gennarelli, C.; Savarese, C. Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples. IEEE Trans. Antennas Propag. 1998, 46, 351–359. [Google Scholar]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Riccio, G. Pattern reconstruction of 3-D modular antennas by means of a non-redundant near-field spherical scan. Electronics 2022, 11, 2060. [Google Scholar] [CrossRef]
- Camacho-Perez, J.R.; Moreno, P. Initial considerations towards hemispherical near-field antenna measurements. IEEE Antennas Wirel. Propag. Lett. 2014, 13, 1441–1444. [Google Scholar] [CrossRef]
- Mauermayer, R.A.M.; Eibert, T.F. Spherical field transformation above perfectly electrically conducting ground planes. IEEE Trans. Antennas Prop. 2018, 66, 1465–1478. [Google Scholar]
- Harrington, R.F. Time-Harmonic Electromagnetic Fields; John Wiley & Sons, Inc.: New York, NY, USA, 2001. [Google Scholar]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Migliozzi, M. A non-redundant spherical NF/FF transformation for an AUT measured over an infinite perfectly conducting ground plane. In Proceedings of the Antennas Propagation Conference, Birmingham, UK, 11–12 November 2019; pp. 1–5. [Google Scholar]
- D’Agostino, F.; Ferrara, F.; Gennarelli, C.; Guerriero, R.; Migliozzi, M. AUT far-field pattern reconstruction from a reduced set of spherical near-field data collected in presence of an infinite perfectly conducting ground plane. In Proceedings of the European Conference on Antennas and Propagation, Copenhagen, Denmark, 15–20 March 2020; pp. 1–5. [Google Scholar]
- Bucci, O.M.; D’Elia, G.; Migliore, M.D. Advanced field interpolation from plane-polar samples: Experimental verification. IEEE Trans. Antennas Propag. 1998, 46, 204–210. [Google Scholar] [CrossRef]
AUT Case | Here Proposed | NF/FF Transformation [15] in Presence of PEC Ground Plane |
---|---|---|
Case A | 14,521 | 20,736 |
Case B | 13,297 | 36,864 |
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Ferrara, F.; Gennarelli, C.; Guerriero, R.; Riccio, G. An Effective Spherical NF/FF Transformation Suitable for Characterising an Antenna under Test in Presence of an Infinite Perfectly Conducting Ground Plane. Electronics 2024, 13, 397. https://doi.org/10.3390/electronics13020397
Ferrara F, Gennarelli C, Guerriero R, Riccio G. An Effective Spherical NF/FF Transformation Suitable for Characterising an Antenna under Test in Presence of an Infinite Perfectly Conducting Ground Plane. Electronics. 2024; 13(2):397. https://doi.org/10.3390/electronics13020397
Chicago/Turabian StyleFerrara, Flaminio, Claudio Gennarelli, Rocco Guerriero, and Giovanni Riccio. 2024. "An Effective Spherical NF/FF Transformation Suitable for Characterising an Antenna under Test in Presence of an Infinite Perfectly Conducting Ground Plane" Electronics 13, no. 2: 397. https://doi.org/10.3390/electronics13020397