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This contribution details a procedure to collect and process necessary data to describe the antenna patterns of PAAs using a planar near-field (NF) range. It is proposed that a complete characterization methodology involves not only capturing beam-steered antenna patterns, but also measuring embedded element patterns, exhaustive testing of the excitation hardware of the antenna under test (AUT), and performing a phased array calibration technique. Moreover, to demonstrate the feasibility of the proposed approach, the methodology is applied onto a 2x8 microstrip patch PAA, proving its utility and effectiveness. Finally, by means of the collected data, any array pattern could be predicted by post-processing, as proven by the great agreement found between a measured pattern and its computed predicted version.
An efficient technique, which allows the correction of known positioning errors in a near-field to far-field (NF-FF) transformation with planar wide-mesh scanning (PWMS), is here developed and experimentally assessed. The corresponding NF-FF transformation from correctly positioned samples allows a remarkable reduction of the acquisition time with respect to the classical plane-rectangular one, since the NF data needed by this last are accurately recovered from a reduced number of PWMS samples through a 2-D optimal sampling interpolation expansion, attained by modeling the antenna under test with a double bowl and applying the nonredun-dant sampling representations to the voltage detected by the scanning probe. When the PWMS samples are affected by known probe positioning error, the voltage values at the sampling points, set by the representation, are unknown and can be efficiently retrieved from the inaccurately positioned ones by means of a singular value decomposition based technique.
Traditional near-field to far-field transformation algorithms based on modal expansion are unable to deal with arbitrary measurement surfaces. To approach these problems, a matrix inversion method can be used to retrieve the spherical wave expansion (SWE) of the antenna under test (AUT) fields. Modeling the antenna with a set of multiple SWEs centered at arbitrary points over its surface offers a flexible approach for the solution of field transformation problems over arbitrary surfaces. The coefficients of each SWE are obtained using an iterative inversion approach where the matrix-vector products can be replaced by multilevel operators based on recursive aggregations and interpolations of the partial SWE fields, reducing the computational complexity from í µí± ¶(í µí² í µí¿) to í µí± ¶í µí² í µí¿ í µí°¥í µí°¨í µí° í µí². The proposed algorithm is tested using synthetic data and measurements showing good scalability and reduced transformation error.
Time and Direction of Arrival (TADOA) analysis of field probe data has been an accepted method for characterizing stray signals in an antenna measurement range for many years ([1], [2]). Recent uncertainty investigations at the OneRY range have shown a need for increased resolution to isolate and characterize energy in TADOA images so that resources can be carefully applied to reduce the uncertainty from these stray signals. This is accomplished by modeling the TADAO image as the solution to a Basis Pursuit (BP) l1 minimization problem. This paper outlines the model development and shows concrete examples from OneRY field probe data where BP allows for the identification of stray energy which was previously difficult to find. We also show how the BP optimization context can be using to remove contamination from the data through the inclusion of additional basis functions ([3]). I.J. Gupta, E.K. Walton, W.D. Burnside, “Time and Direction of Arrival Estimation of Stray Signals in a RCS/Antenna Range,” Proc. of 18th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '96), Seattle WA, September 30-October 3, 1996, pp. 411-416. I.J. Gupta, T.D. Moore, “Time Domain Processing of Range Probe Data for Stray Signal Analysis,” Proc. of 21st Annual Meeting of the Antenna Measurement Techniques Association (AMTA '99), Monterey Bay CA, October 4-8, 1999, pp. 213-218. B.E. Fischer, I.J. LaHaie, M.H. Hawks, T. Conn, “On the use of Basis Pursuit and a Forward Operator Dictionary to Separate Specific Background Types from Target RCS Data,” Proc. of 36th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '14), Tucson AZ, October 12-17, 2014, pp. 85-90.
Spherical wave coefficients are chosen to minimize a cost function that is a norm of the residual of the fit. For example, in standard orthogonality-based processing algorithms [1], the cost function is an integral (over 4 p steradians) of the squared amplitude of the difference between actual measurements and predicted values. Some recent work [2,3] at NIST has led to the use of discrete norms where the integral is replaced by a weighted sum. We explore issues regarding the choice of these weights, the relative performance of different weighting schemes, and the relation between the continuous and discrete cases. These norms are mathematically equivalent if there is a solution with zero residual. In practice, we have observed noticeable variation due to the presence of measurement errors, including multiple reflections, room reflections… Also, different weighting schemes are associated with widely varying condition numbers. When the condition number is large, small measurement errors can lead to large errors in the result. Additionally, we show that the integral cost function mentioned above can be reduced to a discrete quadrature. M.H. Francis and R.C. Wittmann, Chp. 19, “Near-Field Scanning Measurements: Theory and Practice” in Modern Antenna Handbook, ed. C.A. Balanis, John Wiley & Sons, 2008. R.C. Wittmann, B.K. Alpert, M.H. Francis, “Near-field, spherical-scanning antenna measurements with nonideal probe locations,”IEEE Antennas and Propagat., vol. 52, pp. 2184 – 2186, August 2004. R.C. Wittmann, B.K. Alpert, M.H. Francis, “Near-field antenna measurements with nonideal measurement locations,”IEEE Antennas and Propagat., vol. 46, pp. 716 – 722, May 1998.
One of the sources of the measurement errors in outdoor antenna test ranges, when testing from VHF through C-Band, is the ground reflected signal between probe antenna and the antenna under test (AUT). Those errors are due to antenna(s) relatively large beam width(s) at these frequencies, especially when AUT is placed on the large platform such as an aircraft. If reflected wave is not eliminated by the use of absorbers at the reflection point or redirection by the use of diffraction fences, then the range operates as a ground reflection range (GRR), where the reflected signal creates a lobbing pattern when the direct and reflected signals are overlaying in- and out-of-phase as a function of position and frequency, causing undesirable amplitude variations at the test point. Ground reflections may be a major cause of error for GRR measurements when testing large antennas or antennas mounted on large structures which require a large displacement of the AUT during the antenna pattern collection process. A concept of using vertically positioned two-element array probe antenna (source antenna) to suppress ground-reflected signals in GRR-s is presented in this article. Suppression is achieved by pointing first null of the probes gain pattern towards the reflection point on the ground. All analytical evaluations are based on geometrical optics approach. Comparison of the proposed approach to a traditional single-element probe (source) antenna approach, demonstrates a significant improvement in measurement accuracy. Estimates and verifications of analytical evaluations are based on Computational Electromagnetics (CEM) modeling tool such as WIPL-D code. Simulations are performed in the VHF frequency band (200 MHz).
Among the near-field – far-field (NF-FF) transformation techniques, the one employing the bi-polar scanning is particularly interesting, since it retains all the advantages of that using the plane-polar one, while requiring a mechanically simple, compact, and cheaper measurement facility [1]. In fact, in this scan, the antenna under test (AUT) rotates axially, while the probe is mounted at the end of an arm that rotates around an axis parallel to the AUT one. An effective probe voltage representation on the scanning plane requiring a minimum number of bi-polar NF data has been developed in [2], by properly exploiting the nonredundant sampling representations of electromagnetic (EM) fields [3] and considering the AUT as enclosed in an oblate ellipsoid. A 2-D optimal sampling interpolation (OSI) formula is then employed to efficiently recover the NF data required by the traditional plane-rectangular NF-FF transformation [4] from the acquired nonredundant bi-polar samples. It is so possible to considerably reduce the number of the needed NF data and corresponding measurement time with respect to the previous approach [1], which did not exploit the nonredundant sampling representations. However, due to an imprecise control of the positioning systems and their finite resolution, it may be impossible to exactly locate the probe at the points fixed by the sampling representation, even though their position can be accurately read by optical devices. Therefore, it is very important to develop an effective algorithm for an accurate and stable reconstruction of the NF data needed by the NF-FF transformation from the acquired irregularly spaced ones. A viable and convenient strategy [5] is to retrieve the uniform samples from the nonuniform ones and then reconstruct the required NF data via an accurate and stable OSI expansion. In this framework, two different approaches have been proposed. The former is based on an iterative technique, which converges only if there is a biunique correspondence associating at each uniform sampling point the nearest nonuniform one, and has been applied in [5] to the uniform samples retrieval in the case of cylindrical and spherical surfaces. The latter, based on the singular value decomposition (SVD) method, does not exhibit this constraint and has been applied to the nonredundant bi-polar [6] scanning technique based on the oblate ellipsoidal modeling. However, it can be conveniently used only when the uniform samples recovery can be split in two independent one-dimensional problems. The goal of this work is not only to provide the experimental validation of the SVD based technique [6], but also to develop the approach using the iterative technique and experimentally assess its effectiveness. [1] L.I. Williams, Y. Rahmat-Samii, R.G. Yaccarino, “The bi-polar planar near-field measurement technique, Part I: implementation and measurement comparisons,” IEEE Trans. Antennas Prop., vol. 42, pp. 184-195, Feb. 1994. [2] F. D’Agostino, C. Gennarelli, G. Riccio, C. Savarese, “Data reduction in the NF-FF transformation with bi-polar scanning,” Microw. Optic. Technol. Lett., vol. 36, pp. 32-36, 2003. [3] O.M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Prop., vol. 46, pp. 351-359, March 1998. [4] E.B. Joy, W.M. Leach, Jr., G.P. Rodrigue, D.T. Paris, “Application of probe-compensated near-field measurements,” IEEE Trans. Antennas Prop., vol. AP-26, pp. 379-389, May 1978. [5] O.M. Bucci, C. Gennarelli, G. Riccio, C. Savarese, “Electromagnetic fields interpolation from nonuniform samples over spherical and cylindrical surfaces,” IEE Proc. Microw. Antennas Prop., vol. 141, pp. 77-84, April 1994. [6]F. Ferrara, C. Gennarelli, M. Iacone, G. Riccio, C. Savarese, “NF–FF transformation with bi-polar scanning from nonuniformly spaced data,” Appl. Comp. Electr. Soc. Jour., vol. 20, pp. 35-42, March 2005.
Modern cars are equipped with a large number of antennas which are strongly integrated with the car. A full characterization of the radiating properties of the entire vehicle is thus typically required. In order to characterize the radiating properties of the installed antennas, large measurement systems accommodating the full vehicle are required. As in standard antenna measurements, a full spherical near field (NF) scanning around the car is desirable in order to perform an accurate NF/FF transformation. However, due to size and weight of the Device Under Test (DUT) and/or economic factors a full spherical scan is often unfeasible. For this reason, truncated spherical scanners (such as hemispherical) are typically involved. A classic solution is to combine hemispherical scanning with a metallic ground plane which is assumed to be a Perfect Electric Conductor (PEC) in the NF/FF transformation. However, the PEC ground-plane is less representative of realistic automotive environments such as asphalt that is strongly dielectric. A further drawback is the strong scattering from the large metallic ground-plane which highly compromises the NF measurements at low frequencies. In many situations, it is thus desirable to perform the NF measurements in a condition similar to free-space by using absorber materials on the floor. It is well-known that standard NF/FF transformations applied to partial spherical acquisitions generates the so called truncation errors. Such errors are stronger at lower frequencies due to the lower number of spherical modes for fixed DUT size. Moreover, typical antennas for automotive applications are generally low directive thus, the impact of the truncation on the measured pattern is often non-negligible. In such cases advanced post-processing techniques must be involved to mitigate the effect of the truncation errors. In this paper two truncation error mitigation techniques will be compared when applied to automotive measurements performed in free-space conditions. The first technique is an iterative process which at each iteration applies a modal filtering based on the size of the DUT. The second technique is based on the computation of the equivalent currents of the DUT over an equivalent surface which acts as spatial filter. Both techniques give excellent mitigation performance with different computational effort. The good agreement between two different techniques effectively defining the lower bound for what can be successfully mitigated by post processing techniques.
This paper presents the results of a recent study concerning the computational electromagnetic simulation of a spherical near-field (SNF) antenna test system. The new plane-wave scattering matrix approach [1, 2] allows many of the commonly encountered components within the range uncertainty budget, including range reflections, to be included within the model [3]. This paper presents the results of simulations that verify the utility of the spherical mathematical absorber reflection suppression (S-MARS) technique [3, 4] for the identification and subsequent extraction of artifacts resulting from range reflections. Although past verifications have been obtained using experimental techniques this paper, for the first time, corroborates these findings using purely computational methods. The use of MARS is particularly relevant in applications that inherently include scatterers within the test environment. Such cases include instances where a SNF test system is installed within an existing compact antenna test range (CATR) as is the configuration at the recently upgraded Queen Mary University of London (QMUL) Antenna Laboratory [5, 6]. Thus, this study focuses on this installation with results of CEM simulations and actual range measurements being presented. The method enables a quantitative measure of the levels of suppression offered by the MARS system. References A.C. Newell, S.F. Gregson, “Estimating the Effect of Higher Order Modes in Spherical Near-Field Probe Correction”, Antenna Measurement Techniques Association (AMTA) 34th Annual Meeting & Symposium, Bellevue, Washington October, 2012. A.C. Newell, S.F. Gregson, “Computational Electromagnetic Modelling Of Spherical Near-Field Antenna Test Systems Using Plane Wave Spectrum Scatting Matrix Approach”, Antenna Measurement Techniques Association (AMTA) 36th Annual Meeting & Symposium, Tucson, Arizona, October, 2014. C.G. Parini, S.F. Gregson, J. McCormick, D. Janse van Rensburg “Theory and Practice of Modern Antenna Range Measurements”, IET Press, 2014, ISBN 978-1-84919-560-7. G.E. Hindman, A.C. Newell, “Reflection Suppression in a large spherical near-field range”, Antenna Measurement Techniques Association (AMTA) 27th Annual Meeting & Symposium, Newport, RI, October. 2005. A.D. Olver, C.G. Parini, “Millimetre-wave Compact Antenna Test Range”, JINA Nice, November 1992. C.G. Parini, R. Dubrovka, S.F. Gregson, "CATR Quiet Zone Modelling and the Prediction of 'Measured' Radiation Pattern Errors: Comparison using a Variety of Electromagnetic Simulation Methods" Antenna Measurement Techniques Association (AMTA) 37th Annual Meeting & Symposium, Long Beach California, October 2015.
The accurate alignment of antennas and field probes is a critical aspect of modern antenna metrology systems, particularly in the millimeter-wave region of the spectrum.Commercial off-the-shelf robotic arms provide a sufficient level of positional accuracy for many industrial applications.The Antenna Metrology Project in the Communications Technology Laboratory at the National Institute of Standards and Technology has shown that path-corrected commercial robotic arms, both in hardware and software analysis, can be used to achieve sufficient positioning and alignment accuracies (positioning error ~ /50) for antenna characterization measurements such as gain extrapolation and near-field pattern out to 183 GHz [1]. Position correction is achieved using a laser tracker with a 6 degree of freedom sensor attached to the robot end effector.The end effector’s actual position, measured using the laser tracker, is compared to its commanded position and a path correction is iteratively applied to the robot until the desired level of accuracy is achieved in the frequency range of interest.At lower frequency ranges (< 40 GHz), sufficient positional accuracy can be achieved, without path correction, using a using a calibrated kinematic model of the robot alone [2].This kinematic model is based on knowledge of the link frame transformations between adjacent links and captures deviations due to gravitational loading on the joints and small mechanical offsets between the joints.Additionally, the calibration procedure locates the robot’s base frame in the coordinate system of the robot’s end effector.Each link frame is described by four physical quantities, known as Denavit-Hartenberg (DH) parameters [3]. We performed calibration measurements of our CROMMA system’s DH parameters over a working volume of ~1 m3.We then use the laser tracker to compare the robot’s positional accuracy over this working volume with and without the calibrated kinematic model applied.The path errors for the calibrated case set an upper frequency limit for uncorrected antenna characterization measurements. [1]D. R. Novotny, J.A. Gordon, J.R. Guerrieri, “Antenna Alignment and Positional Validation of a mm Wave Antenna System Using 6D Coordinate Metrology, ” Proceedings of the Antenna Measurements Techniques Association, pp 247-252, 2014 [2]R.Swanson, G. Balandran, S. Sandwith, “50-micron Hole Position Drilling Using Laser Tracker Controlled Robots, ” Journal of the CMSC, Vol 9, No 1, Spring 2014 [3].J.J. Craig, “Introduction to Robotics: Mechanics and Control, 3rd ed.,” New Jersey, Prentice Hall, 2004, pp. 62-69
At NIST, we have developed a precision, wide-band, mmWave modulated-signal source with traceability to primary standards. We are now extending the traceability path for this modulated-signal source into free space to be used for verifying over-the-air measurements in 5G, wireless receivers. However, to obtain a traceable modulated signal in free space, the full scattering matrix of the radiating antenna must be measured. We have extended the extrapolation methods used at NIST, based on the work of Newell, et al. [1]. The extrapolation measurement provides a very accurate, far-field, on-axis, scattering matrix between two antennas. When combined with scattering-matrix measurements made with permutations of pairs of three antennas, far-field scattering, and, thus, gain, is obtained for each antenna. This allows an accurate extrapolation of the antenna’s near-field pattern. We have incorporated the extrapolation fitting algorithms into a Monte Carlo uncertainty engine called the NIST Microwave Uncertainty Framework (MUF) [2]. The MUF provides a framework to cascade scattering matrices from various elements, while propagating uncertainties and maintaining any associated correlations. By incorporating the extrapolation measurements, and the three-antenna method into the MUF, we may provide traceability of all measurement associated with the gain, including the scattering parameters. In this process, we studied several aspects of the gain determination. In this work, we show simulations determining the efficacy of filtering to reduce the effect of multiple reflection on the extrapolation fits. We also show comparisons of using only amplitude (as is traditionally done) to using the full complex data to determine gain. Finally, we compare uncertainties associated with choices in the number of expansion terms, systematic alignment errors, uncertainties in vector network analyzer calibrations and measurements, and phase error introduced by cable movement. With these error mechanisms and their respective correlations, we illustrate the NIST MUF analysis of the antenna scattering-matrix with data at 118 GHz. [1] A. C. Newell, R. C. Baird, and P. Wacker “Accurate Measurement of Antenna Gain and Polarization at reduced distances by an extrapolation technique” IEEE Transactions on Antennas and Propagation. Vol. 21, No 4, July 1973 pp. 418-431. [2] D. F. Williams, NIST Microwave Uncertainty Framework, Beta Version. NIST, Boulder, CO, USA, Jun. 2014. [Online]. Available: http://www.nist.gov/pml/electromagnetics/related-software.cfm
Microstrip patch antennas are well known in the field of communications and other areas where antennas are used. They consist of a metallic conducting surface deposited onto a grounded dielectric substrate and are widely used in situations where a conformal antenna is desired. They are also popular antennas for array applications. But most patch antennas are typically resonant structures owing to the standing wave of current that forms on them. This resonant behavior limits the impedance bandwidth of the antenna to a few percent. In this paper we shall present an approach for improving the bandwidth of a resonant patch antenna which employs an engineered anisotropic superstrate. By proper design of this superstrate and its tensor, and proper alignment of it with the axis of the patch, an antenna with improved impedance bandwidth results. Some of the challenges associated with the measurement of the anisotropic superstrate will be discussed, ranging from 3D simulations to physical models tested in the laboratory. A final working model of the antenna will be discussed; this model consists of a stacked patch arrangement and was designed to operate at the GPS L1 and L2 frequencies. Data collected from 3D simulations using CST Microwave Studio along with laboratory and anechoic chamber measurements will be presented, showing how the bandwidth at both of these frequencies can be increased while maintaining circular polarization in both passbands. Tolerance to errors in alignment and fabrication will also be presented. Additionally, some lessons learned on anechoic chamber measurements of the antenna’s gain and axial ratio will be discussed.
Measurement of the radiation properties of low gain antenna operating at VHF frequencies is well known to be a challenging task. Such antennas are sometimes tested in outdoor Far Field (FF) ranges which are unfortunately subject to errors caused by the electromagnetic pollution and scattering from the environment. Near Field (NF) measurements performed in shielded anechoic chambers are thus preferable to outdoor ranges. However, also in such cases, the accuracy of the results may be compromised by the poor reflectivity of the absorbing material which might be not large enough wrt the VHF wavelength. Other source of errors may be caused by the truncation of the scanning area which generates ripple on the FF pattern after NF/FF transformation. Spherical multi-probe systems developed by MVG are optimal measurement solution for low directive Device Under Test (DUT). Such systems allow to perform a quasi-full spherical acquisition combining a rotation of the DUT along azimuth, with a fast electronically scanned multi-probe vertical arch. The DUT can be accommodated on masts made of polyester material which allows to minimize the interaction with the DUT. Measurements of low directive device above 400 MHz performed with such type of systems have been demonstrated to be accurate and extremely fast in previous publications. In this paper, measurements of a low directivity antenna, performed at VHF frequencies in a MVG spherical multi-probe system, will be presented. The antenna in this study is an array element, part of a larger array, which has been developed for space-born AIS applications. Gain and pattern accuracy of the measurement will be demonstrated by comparison with full wave simulation of the tested antenna.
This paper presents the results of a new measurement technique to determine antenna system noise temperature using data acquired from a planar near-field measurement. The ratio of antenna gain to system noise temperature (G/T) is usually determined in a single measurement when the antenna is alternately pointed towards the “cold sky” and a hot radio source such as the sun or a star with a known flux density. The antenna gain is routinely determined from near-field measurements and with the development of this new technique, the system noise temperature can also be determined. The ratio of G/T can therefore be determined from planar near-field data without moving the antenna to an outdoor range. The noise temperature is obtained by using the plane-wave spectrum of the planar near-field data and focusing on the portion of the spectrum in the evanescent or “imaginary space” portion of the spectrum. Near-field data is obtained using a data point spacing of l/4 or smaller and the plane-wave spectrum is calculated without applying any probe correction or Cos(q) factor. The spectrum is calculated over real space corresponding to propagating modes of the far-field pattern and also the evanescent or imaginary space region where . Actual evanescent modes are highly attenuated in the latter region and therefore the spectrum in this region must be produced by “errors” in the measured data. Some error sources such as multiple reflections will produce distinct localized lobes in the evanescent region and these are recognized and correctly identified by using a data point spacing of less than l/2 to avoid aliasing errors in the far-field pattern. It has been observed that the plane wave spectrum beyond these localized lobes becomes random with a uniform average power. This region of the spectrum must be produced by random noise in the near-field data that is produced by all sources of thermal noise in the electronics and radiated noise sources received by the antenna. By analysing and calibrating this portion of the spectrum in the evanescent region the near-field noise power can be deduced and the corresponding noise temperature determined. Simulated and measured data will be presented to illustrate and validate the measurement and analysis techniques. Keywords — Planar Near-Field, G/T, Figure-of-Merit Measurements, Simulation, Plane Wave Spectrum.
In high-gain array applications such as satellite communications and radars, low sidelobe level is a key performance requirement. Applying a magnitude tapering profile across the aperture is a common way to suppress the sidelobes. Other realizes sidelobe level control method via phase variation across the aperture. Common ways for implementing aperture magnitude taper include applying lumped resistors or introducing proper series feeding, etc. This paper discusses about 33-35 GHz fixed-beam, low-sidelobe array antenna design. In order to minimize the number of the feed network, the 11x32 Ka-band array is composed of 32 sequentially-fed 11-element subarrays. Also, to maximize the antenna efficiency, the Chebyshev tapering selected for achieving -35 dB sidelobe levels was accomplished using a combination of un-even power divider, mismatched feed lines, and different feedline lengths. This approach allows it to achieve magnitude taper control from -0.5 dB to -26 dB from 33 to 35 GHz without using resistors. The unequal power divider arrangement reduces mismatch loss my 1.3dB compared to conventional 2-way even dividers in the corporate feeding network. The paper also studies the impact of the amplitude and phase uncertainty among array elements on the degradation of the sidelobe performance. An 11x32 planar patch array prototype is designed, fabricated and measured. The array obtains a realized gain of 19 dBi with Azimuth 3dB beamwidth of 1.0 degree and -23 dB sidelobe.
Rotating the coordinate system of an antenna pattern can be problematic due to the need to interpolate complex data in spherical coordinates. Common approaches to 2D interpolation often introduce errors because of polarization discontinuities at the spherical coordinate system poles. To overcome these difficulties, it is possible to transform an antenna pattern from field-space into spherical mode-space, perform the desired coordinate system rotation in mode-space, and then transform the modes in the rotated coordinate system back into field-space. This method, while more computationally intensive, is exact and alleviates all of the interpolation-related issues associated with rotations in field-space. Although rotations in mode-space have been implemented in commercially available software (e.g., the ROSCOE algorithm provided by TICRA), these algorithms may not be well understood by the general antenna measurement community. Therefore, the first goal of this paper is to present an easy-to-understand algorithm for performing rotations in mode-space. Next, the paper will address the challenge of computing the rotation coefficients, which are required by the mode-space coordinate system rotation algorithm. Although J. E. Hansen presented a method for recursively computing the rotation coefficients, this method is numerically unstable for large values of N (where N is the upper limit of the polar index). Therefore, this paper will present a numerically stable method for the recursive computation of the rotation coefficients. Finally, this paper will show the relationships between Euler angles and both Az-over-El angles and El-over-Az angles. These relationships are quite useful because it is often desired to rotate an antenna pattern based on Elevation and Azimuth angles, whereas the inputs for the mode-space rotation algorithm are Euler angles. Knowing these relationships, the Euler angles may be computed from the Azimuth and Elevation angles, which can then be used as the inputs to the mode-space rotation algorithm.
GTRI has been developing a method for insertion phase calibration, as discussed in the paper “Insertion Phase Calibration of Space-Fed Arrays,” which was presented at AMTA in 2015 [1]. This method has been implemented to characterize the phase response of phase shifters in a system currently under fabrication at GTRI. One of the primary requirements for the phased-array antenna of this system is a maximum RMS phase error. The RMS phase error for this array is influenced by a variety of error sources, including phase shifter quantization, beam steering computer (BSC) algorithmic error, phase shifter unpredictability error, test fixture induced error, phase shifter thermal drift, and phase shifter frequency dependency. Each of these error sources has been categorized as either a non-deterministic error, whose behavior can be statistically characterized but not calibrated out, or as a deterministic error, whose behavior can be characterized and potentially calibrated out. The non-deterministic errors include element unpredictability, which is induced by the inability of an individual phase shifter to precisely repeat a given phase command, and errors induced by the calibration test fixture itself. The deterministic errors include phase shifter quantization error, which is a function of the phase state bit precision, BSC algorithmic error, which is driven by the numerical preciseness of calculation of the commanded phase states for each element, thermal driven phase drift, and phase shifter frequency dependency across the band of operation. To calibrate the insertion phase and phase-state response curves for all phase shifters used in the system, a custom-built calibration fixture was constructed into a septum wall that separates two semi-anechoic chambers. The realized phase-error budget of the system under fabrication was affected directly by the accuracy of both the calibration method and this fixture. We will present our analysis of all phase-error sources as they contribute to the overall phase-error design goal of the system. We have shown how the design and implementation of both the calibration fixture and methodology meet that goal.
The uncertainty of the far field, obtained from antenna planar near field measurements, against the dynamic range is investigated by means of statistical analysis. The dynamic range is usually limited by the noise floor for low level signals and by the receiver saturation for high level signals. The noise level could be important for high measurement rate, which requires the usage of a high signal level to ensure a sufficient signal to noise ratio. As a result the nonlinearities are increasing, thus a compromise must be accomplished. To evaluate the effects of the limited near field dynamic range on the far field, numerical simulations are performed for dipoles array. Initially, the synthetic near field data corresponding to a given antenna under test were generated and directly processed to yield the corresponding far field patterns. Many far field parameters such as gain, beam width, maximum sidelobe level, etc. are determined and recorded as the error-free values of these parameters. Afterwards, the synthetic near field data are deliberately corrupted by noise and receiver nonlinearities while varying the amplitude through small, medium and large values. The error-corrupted near field data are processed to yield the far field patterns, and the error-corrupted values of the far field parameters are calculated. Finally, a statistical analysis was conducted by means of comparison between the error-corrupted parameters and the error-free parameters to provide a quantitative evaluation of the effects of near field errors on the different far field parameters.
Measuring the RF, microwave or millimeter wave reflectivity of materials and components often requires a substantial length of transmission line or cables to connect the microwave source/receiver to the test apparatus. Such cables may be subject to environmental variations (e.g. temperature or pressure) that change the overall phase delay and amplitude of signals that travel through said cables. Furthermore, some testing requires physical motion of the cable, which is another source of phase and amplitude error. When possible, great care is often taken to design a test apparatus or methodology to minimize movement of the test cables so that these position-induced phase errors are small. However, in some measurements, such as those that require scanning sensors or antennas, position-induced phase and amplitude errors cannot be avoided. In some situations, temperature variations that change the cable phase response are also unavoidable. The problem of cable-induced errors has been a concern for many different applications and there have been previous attempts to address it. These previous methods have used specialized microwave circuitry or a separate phase-stable reference device to measure and compensate for phase errors. In this paper, a new correction method is described, which determines and corrects for phase and amplitude errors in transmission line cables. Unlike previous published methods, the present technique does not require any specialized circuitry at the device under test (DUT). Instead it utilizes in-situ reflections that already exist in the measurement apparatus to obtain a reference phase and amplitude signal. The described algorithm combines these reflections with frequency and time-domain signal processing to compensate for erroneous phase and amplitude shifts that occur during a measurement. This paper demonstrates the correction methodology with materials measurements examples. Additionally, this phase and amplitude correction may be applicable for scatter and antenna measurements. It can be applied to either reflection or transmission measurement data.
This paper presents a study on the low-frequency coaxial reflectometer measurement procedure. A time domain gating algorithm is developed by ETS-Lindgren and the results are validated after comparing to the Keysight 8753-time domain algorithm. The in-house time gating algorithm is then applied to the simulated reflectivity results of absorbers in reflectometer to the simulation results of the same absorbers with plane wave excitation using finite element method numerical computation. Based on the simulation results, the operable upper frequency limit and the minimum length of the straight coaxial section for the reflectometer are suggested. The errors introduced during measurement due to higher order modes are studied and the permissible limit for the errors is analyzed. The different higher order modes and their effects on field distribution are studied. The impact of the non-uniform field distribution on the absorber reflectivity measurement is also discussed.