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Analysis

Imaging a Range's Stray Signals with a Planar Scanner
Scott T Mcbride, John Hatzis, November 2018

The fundamental purpose of absorber treatment in an anechoic chamber is to ensure that only the direct-path signal is coupled between the range antenna(s) and the device under test. For many simple and standard geometries, this is readily accomplished with conventional processes and procedures. When the geometry and/or stray-signal requirements deviate from the norm, however, it can be very beneficial to have an easy and reliable way to locate and quantify sources of stray signals. This paper discusses a straightforward algorithm for creating images of those stray signals in a range when a planar scanner and broad-beamed probe are available in the test zone. Measured data from multiple facilities are evaluated, along with absorber-treatment improvements made based on some of the images produced.

Antenna Modeling on Complex Platforms Through Constrained Equivalent Aperture Distributions
Leo Tchorowski, Inder " Jiti, " Gupta, November 2018

Accurate in situ antenna manifolds are desired for performance evaluation of radio frequency systems, including communication, navigation, and radar among others. In situ antenna measurements are the most accurate way to obtain antenna manifolds on the platform of interest, but are often impractical or impossible to obtain. Instead, combinations of simulations and measurements are used to estimate antenna manifolds on platforms. First, the gain and phase of the target antenna are measured on a simple ground plane, over the frequencies and field of view of interest. The measurements are then imported into computational electromagnetics codes to simulate platform scattering from the platform of interest. However, the representation of the measured data is not unique, which leads to inaccuracies and/or a large run time in computational electromagnetics codes. This paper presents a new method to represent measured antenna data in electromagnetics codes through aperture current distributions of simulated cross-slots and monopoles. A weighted sum of far-fields from the simulated equivalent elements approximates the measured antenna far-fields, with weights determined by the minimization of the L2-norm difference between measured far-fields and equivalent element far-fields. However, the least square solution may place large, unrealizable currents on the aperture. A constraint is introduced to limit the amount of current on the aperture, by minimizing the length of the solution vector. In this paper, the details of the suggested method will be presented. We will also illustrate the accuracy of the method through example simulations, where good agreement is achieved between truth data and equivalent antennas on complex platforms.

Effective Polarization Filtering Techniques for Ground Penetrating Radar Applications
Sebastian G Wirth, Ivor L Morrow, November 2018

The effect of different decomposition techniques on the imaging and detection accuracy for polarimet-ric surface penetrating data is studied. We derive the general expressions for coherent polarimetric decomposition using the Stokes parameters and model based polarimetric decomposition using the Yamaguchi technique. These techniques are applied to multi-frequency (0.4-4.8GHz) full polarimetric near-field radar measurements of scattering from surface laid calibration objects and shallow buried landmine types and show in detail how the decomposition results provide effective surface and sub-surface clutter reduction and guide the interpretation of scattering from subsurface objects. Data processing methods assume cross-polar symmetry and a novel bistatic calibration procedure was developed to enforce this condition. The Yamaguchi polarimetric decomposition provides significant clutter reduction and image contrast with some loss in signal power; while Stokes parameters also provide imagery localising targets, complementary information on the scattering mechanism is also obtained. Finally a third novel polarimetric filter was formulated based on differential interferometric polarimetric decomposition. The three combined techniques contribute to a significant improvement of subsurface radar performance and detection image contrast.

A study of the Low-frequency Coaxial Reflectometer measurement procedure for evaluation of RF absorbers' reflectivity -II
Anoop Adhyapak, Zhong Chen, November 2018

The Low frequency Coaxial Reflectometer is the recommended procedure to measure the absorbers' reflectivity as per the IEEE 1128-1998 standard. The standard recommends the operable frequency range up to 500 MHz with a permissible error of 2 dB and higher error beyond 600 MHz. This paper studies and discusses the error on different types of absorber. Each of the absorber type is simulated in the square section of the reflectometer setup to compute the absorber's reflectivity using Ansys HFSS. An effective time gating technique is applied to reduce the effect of edge effects. These results are compared to the unit cell simulation results with a plane wave excitation and periodic boundary conditions. The absorbers are then simulated in the complete reflectometer setup to include the mismatch associated with the transition and compared to the unit cell model results. The errors associated with the comparison of the absorbers' simulation results for these different models are analyzed. The combination of these different absorbers is simulated in unit cell model. The absorbers are placed in different regions and orientations inside the reflectometer. The comparison between the unit cell results of the combination of the absorbers and the results of the absorbers inside the reflectometer in different orientations give the effect of the non-uniform field distribution inside the reflectometer.

Application of Complex Image Theory for Nearfield Antenna Measurements over Seawater
David A Tonn, November 2018

The principles of near-field antenna measurements in Cartesian, cylindrical, and spherical coordinates are well established and documented in the literature and in standards used on antenna ranges throughout government, industry, and academia. However the measurement methods used and the mathematics that are applied to compute the gain and radiation of the pattern of the test antenna from the near-field data assume that the antenna is operating in free space. This leaves several questions open when dealing with antennas operating over a lossy ground plane, such as the ocean. In this paper, we shall discuss a possible avenue for addressing this problem : the use of Complex Image Theory (CIT). The CIT approach allows the lossy earth to be removed and an image of each equivalent source point in the space above it to be constructed in the now empty space below it, but where the depth of that image is in general a complex number. While it might appear confusing to define a complex depth, such a depth is merely a mathematical construct that accounts for a magnitude and phase shift that occurs due to the presence of the lossy ground. The depth is computed so that the boundary condition at the surface of the original lossy ground is maintained; in this way, an equivalent problem is formulated. We propose an approach based on CIT that can be applied to the problem of a spherical nearfield antenna measurement taken over seawater. A limiting case of measurements taken over a metal ground plane shall be presented, along with thoughts about some practical concerns involved in the performance of such measurements.

A Modern, Indoor Far-Field Extrapolation Range
Dale Canterbury, Corey Garner, William Dykeman, November 2018

Prior literature in the subject area of far-field antenna measurements has demonstrated an extrapolation technique to isolate and correct the errors due to near-zone proximity effects as well as multi-path range reflections, thus allowing data to be collected at distances much less than the conventionally defined far-field criteria. This paper describes a modern, indoor, far-field antenna measurement range specifically designed to support this extrapolation technique. A multi-axis positioning system featuring a mobile horn tower capable of motion along the chamber Z-axis is emphasized. High-speed RF instrumentation and advanced software control support the full automation of the extrapolation method. This contemporary approach is demonstrated, and measurement examples are provided for an X-band slotted waveguide array. The resultant far-field gain calculations are also compared to similar data extracted using near-field scanning techniques.

Resurfacing the NASA Langley Experimental Test Range Reflector
Ron Schulze, Matthew Bray, Nathanael Flores-Palomera, Chris Vandelinder, Richard Boucher, George Szatkowski, Larry Ticatach, Angelo Cavone, Matthew Ayers, Michael Draszt, John Rooks, , , ,, November 2018

An ambitious resurfacing campaign was launched in late 2017 to correct for large reflector surface distortions present at the NASA LaRC Experiment Test Range (ETR) in support of performing Europa Clipper flight High Gain Antenna (HGA) measurements at X-and Ka-band frequencies. The effort was successful as the worst case peak-to-peak amplitude ripple was reduced from 4.0-dB to 1.5-dB across the 4.1-meter quiet zone.

Uncertainty Analysis Technique for Planar Field-Probing Measurements and Quiet-Zone Simulations of a Compact Antenna Test Range
T M Gemmer, D Heberling, November 2018

The performance of a compact antenna test range is evaluated by field-probing measurements of the quiet zone. The comparison between the simulated and measured data, however, is misleading due to the finite measurement accuracy and the limited nature of the numerical model. In order to allow a comparison, the uncertainty terms of the field-probing measurements and the numerical model are identified based on the National Institute of Standards and Technology 18-term uncertainty analysis technique. The individual terms are evaluated with simulations or measurements using the equivalent-stray-signal model. Bearing the differences between the model and the actual measurements in mind, the electrical field can be estimated precisely within the overlapping region of both uncertainty budgets.

A Novel GO-PSO Algorithm for Designing 3D- Printed Optimized Pixelized Inhomogenous and Shaped-Profiled Lens Antennas
Jordan Budhu, Yahya Rahmat-Samii, November 2018

In this paper, a novel algorithm for designing 3D-printed shaped inhomogeneous dielectric lens antennas is provided. The synthesis approach is based on a novel combination of Geometrical Optics (GO) and the Particle Swarm Optimization (PSO) method. The GO method can trace rays through inhomogeneous media and calculate the amplitude, phase, and polarization of the electric field. The algorithm is used to design an inhomogeneous lens antenna to produce an electronically scanned revolving conical beam to replace a mechanically scanned parabolic reflector antenna for spaceborne weather radar satellite antenna applications. Two breadboard model on-axis fed lens designs are presented and measured results given to validate the approach. A representative optimum off-axis design is presented which produces the revolving conically scanned beam. Imposition of a Body-of-Revolution restriction allows the optimization to be performed at a single offset feed location. The complex inhomogeneous engineered materials that results from optimization are printed using new 3D printers.

A New Dielectric Analyzer for Rapid Measurement of Microwave Substrates up to 6 GHz
John W Schultz, November 2018

This paper presents a new measurement method based on the parallel plate capacitor concept, which determines complex permittivity of dielectric sheets and films with thicknesses up to about 3.5 mm. Unlike the conventional devices, this new method uses a greatly simplified calibration procedure and is capable of measuring at frequencies from 10 MHz to 2 GHz, and in some cases up to 6 GHz. It solves the parasitic impedance limitations in conventional capacitor methods by explicitly modeling the fixture with a full-wave computational electromagnetic code. Specifically, a finite difference time domain (FDTD) code was used to not only design the fixture, but to create a database-based inversion algorithm. The inversion algorithm converts measured fixture reflection (S11) into dielectric properties of the specimen under test. This paper provides details of the fixture design and inversion method. Finally, example measurements are shown to demonstrate the utility of the method on typical microwave substrates.

Analysis of Time and Direction of Arrival (TADOA) Data using Basis Pursuit in the AFRL One-RY Antenna Measurement Range
Brian Fischer, Ivan LaHaie, Michael Blischke, Brian Kent, Brittany Wells, James Stewart, October 2017

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.

Measurements of Incident Radio Frequency Power levels from the L3 Technologies ProVision Body Scanner for the National Academy of Science
Brian Kent, Tri Van, Ton Van, Kevin Hamblin, Jennifer Westhoven, October 2017

The Transportation Security Administration is tasked with the job of performing safety screening of millions of air travel passengers annually in a safe and efficient manner. One of the most widely deployed detection system is the L3 Technologies “Provision” body scanner, which utilizes millimeter wave radio frequencies (RF). Have you ever wondered what type and levels of RF energy are used to execute this routine security screening test? Recently, the Department of Homeland Security, Transportation Security Administration, tasked the National Academies of Science (NAS) to execute an updated safety analysis of the L3-Comm manufactured TSA ProVision Body Scanner units deployed in airports world-wide. In the process of executing their charter, the NAS realized there was very little peer-reviewed published data on calibrated field incident power within the ProVision scanner itself. While L3-Comm has their own factory acceptance program, the NAS wanted independent measurements executed on L3-Comm machines at four randomly selected airports. The NAS therefore contracted with the team of BerrieHill Research and Applied Research Associates to design a specialized field probe that could measure the RF emanations of the ProVision Units. This very challenging measurement environment required design ingenuity to fulfill the contract needs, since our team was not allowed to physically connect to any part of the ProVision machine. We had to place a field measurement device inside the unit where the passenger stands, and record all data over the air only. This paper will completely describe the BRC/ARA ProVision Scanner field probe measurement system, and present calibrated RF field measurements along with an uncertainty analysis of typical results.

Radiation Center Estimation from Near-Field Data Using a Direct and an Iterative Approach
Cosme Culotta-López, Kui Wu, Dirk Heberling, October 2017

Spherical Near-Field (SNF) measurements are an established technique for the characterization of an Antenna Under Test (AUT). The normal sampling criterion follows the Nyquist theorem, taking equiangular samples. The sampling step size depend on the smallest sphere that, centered in the measurement’s coordinate system, encloses the AUT, i.e. the global minimum sphere. In addition, a local minimum sphere can be defined as the sphere with minimum radius which, centered in the AUT, encloses it alone. The local minimum sphere is always equal or smaller than the global minimum sphere, being equal when the AUT is centered in the measurement’s coordinate system. It is assumed that the local minimum sphere’s center coincides with the radiation center. Furthermore, it is possible to compute a Translated Spherical Wave Expansion (TSWE) centered in the local minimum sphere, thus needing less measurement points, as long as the relative position of its center is known. Due to practical reasons, it is not always possible to easily locate the radiation center. In this paper, the relative position of the radiation center of an AUT with respect to the measurement's coordinate system’s center is estimated from SNF data using two approaches. The first approach takes the phase center as an estimation of the radiation center and is based on the method of moving reference point, strictly valid for the far-field case, analyzing its error at different near-field distances. The second approach is based on a spherical modes' spectrum analysis: the closer the AUT’s radiation center is to the coordinate system's center, the larger the power fraction in the lower modes will be. The proposed algorithm iteratively displaces the SWE and checks the power in a predefined number of modes until the convergence criterion is fulfilled. It is important to note that no near-field to far-field transformation is used, for the less measurement points taken do not allow it. A thorough analysis of the estimation error is done by simulation for different cases and antennas. The estimation error of both methods is compared and discussed, highlighting the convenience of each method depending on the requirements.

Common Microwave Absorbers Evaluations in W-band (75-100 GHz)
Zhong Chen, October 2017

Understanding absorber performance in the W band (75-100 GHz) has become increasingly important, especially with the popular use of W band radars for automotive range detections. Commercial absorber performance data is typically available only to 40 GHz. Measurements performed in the W band in anechoic chambers are often under the assumptions that high frequency absorber data can be extrapolated from the data below 40 GHz. In this paper, we provide a survey of common microwave absorbers in the W band. It shows that the extrapolated data from the lower frequencies are not accurate. Absorber analysis models for low frequencies such using homogenization concept are no longer valid. This is because, for the millimeter wave, microstructures of the foam substrate become important, and the dimensions of the pyramids are much greater than the wavelengths. We examine performance variations due to parameters, such as carbon loading, shape, and thickness of the absorbers. We will also show how paint on the absorber surface might affect the absorber reflectivity, and if the common practice of black-tipping (leaving the tip of the absorbers unpainted) is an effective technique to alleviate paint effects.

Analysis of Near-Field RCS Behavior for mm-Wave Automotive Radar Testing Procedures
Domenic Belgiovane, Chi-Chih Chen, October 2017

Millimeter wave vehicular radar operating in the 77 GHz band for automatic emergency breaking (AEB) applications in detecting vehicles, pedestrians, and bicyclists, test data has shown that the radar cross section (RCS) of a target decreases significantly with distance at short range distances typically measured by automotive radar systems, where the reliable detection is most critical. Some attribute this reduction to a reducing illumination spot size from the antenna beam pattern. Another theory points to the spherical phase front due to measurement in the Fresnel region of the target, when the distance for the far-field zone is not met. The illumination of the target depends on the antenna patterns of the radar, whereas the Fresnel region effects depend on the target geometry and size. Due to fluctuations in measured data for RCS as a function of range in the near-field, upper and lower bounds for the target RCS versus range have been determined empirically as a method for describing the expected RCS of target. So far, the range-dependent RCS bounds used in AEB test protocols have been determined empirically. The study discussed in this paper aims to study the underlying physics that produces range-dependent RCS in near field and provide analytical model of such behavior. The resultant analytical model can then be used to objectively determine the RCS upper and lower bounds according to the radar system parameters such as antenna patterns and height. A comparison of the analytically predicted model and empirical near-field RCS as a function of range data will be presented for pedestrian, bicyclist, and vehicle targets.

Validation of Measured Source Antenna Representation in the Numerical Simulation of a GNSS Antenna on Sentinel Satellite
Maria Saporetti, Lucia Scialacqua, Francesco Saccardi, Lars Foged, Jan Zackrisson, Luca Salghetti Drioli, Damiano Trenta, October 2017

The measured source or Huygens box antenna representation has become an increasing popular solution to create accurate computational models of measured source antennas for the numerical analysis of antenna placement on complex platforms such as satellites. The equivalent representation of the measured antenna is obtained through the equivalent current (EQC) or inverse source technique, which is a measurement post-processing method that represents the measured antenna in equivalent electric and magnetic currents on a surface conformal to the antenna. The highly accurate representation of the measured antenna can be used for both suspended and flush mounted antenna and the format is compatible with most commonly used commercial CEM solvers. This technique enables computation of complex antenna scenarios in which the source antenna is physically available but the computational details are unknown. This is often the case for space antenna testing in which antennas from different suppliers are integrated on a platform representing the complex scenario. In this paper, the validation of this technique in space antenna testing application is presented. The test object is a GNSS antenna mounted on a Sentinel satellite mock-up working at 1227 and 1575 GHz. The GNSS antenna and Sentinel satellite structure have been designed, manufactured and measured by RUAG SPACE. Simulations of the sentinel satellite using the measured source technique are compared to measurement of the satellite mock-up model at the working frequencies of 1227 MHz and 1575 MHz. Preliminary results of this validation activity have been previously presented. This paper reports on the full validation activity including the possibility to use different CEM solvers. The activity has been partly supported by ESA ESTEC contract 4000116755 “Time Efficient satellite antenna testing technique based on NF measurement and simulation with controlled accuracy”.

Intermodulation Analysis and Detection of Radio Broadcasting Services Using Real-Spectrum Monitoring Systems
Andres Navarro, Marcos Pineda, Gilma Angel, October 2017

In this paper, an analysis of the intermodulation effects observed in radio communication signals measurement systems, placed in vicinity of highly congested FM stations sites is presented. This work is required due to intermodulation issues have been a widely-studied topic in frequency analysis for communication stations, nevertheless the perspective of those analysis is mainly focused on avoiding the generation of intermodulation products that represents real spectrum occupancy but there is no an analysis for the intermodulation caused by the susceptibility of monitoring devices that, due to the non-linear behavior of the electronic components, present intermodulation products like real signals. The causes of intermodulation phenomena are discussed, which are mainly due to the non-linear behavior of one or several components of the monitoring system, and due to the proximity between transmission sites or between the measurement system and the site of the transmission. As a complement, a review of technical specifications for different monitoring instrumentation like receptors, active and passive antenna system, amplifiers, and filters and its effects on unwanted Intermodulation generation is done. With the goal of suppressing or minimize the Intermodulation Distortion of the electronic devices used for monitoring, a procedure for identification, according ITU recommendations, based on attenuators for common spectrum analyzers and using passive antennas have been designed and tested in different sites in different countries. The measurements obtained with different active devices and passive devices in the measurement system are presented and compared, identifying with the procedure the spectral characteristics of the intermodulation products and the reduction or filtering of these effects analytically and graphically.

Regarding Network Characteristics of Flared Notch Arrays
James Stamm, Ryan Gough, Austin Bowman, October 2017

Flared notch (“Vivaldi”) arrays have been a subject of great interest since the mid 1990s for use in broadband phased-array systems. These arrays are popular in large part due to their ultra-wide bandwidths, which can span multiple octaves, exceeding the bandwidths of the individual flared notch elements themselves. This effect is achieved via strong inter-element coupling, a departure from the conventional wisdom of minimizing mutual coupling between elements in a phased array. The benefits of this design choice have been widely reported on in the literature - however, this dependence on element coupling also places serious constraints on array performance, especially with regards to scan angle, active impedance, and array efficiency, which often go unreported. In addition, reliance on inter-element coupling necessitates an array that can be safely approximated as “infinitely” planar. If an array does not strictly meet this condition, significant VSWR issues can result, especially for elements near the edges of the array. This paper discusses the common pitfalls inherent in practical flared-notch array design that are often overlooked in the literature. To aid in this analysis, a network-centric approach to array modeling is demonstrated that allows for an examination of both element- and array-level performance metrics in a way that minimizes computation time and resources. Special attention is paid to parameters such as active impedance as a function of scan angle, which, though vital to array performance, are often mischaracterized by “infinite array” approximations commonly used by engineers in the design phase. The effects of mutual coupling on different array performance metrics, both beneficial and detrimental, are examined in detail so that an informed decision can be made on the suitability of the flared-notch topology for a given application.

Serial-Robotic-Arm-Joint Characterization Measurements for Antenna Metrology
Michael Allman, David Novotny, Scott Sandwith, Alexandra Curtin, Josh Gordon, October 2017

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

Filtering Antenna-to-Antenna Reflections in Antenna Extrapolation Measurements
Robert Horansky, Mohit Mujumdar, Dylan Williams, Kate Remley, Joshua Gordon, David Novotny, Michael Francis, October 2017

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







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