Reducing Measurement Time and Estimated Uncertainties for the NIST 18 Term Error Technique
Allen Newell
Nearfield Systems Inc.
19730 Magellan Drive
Torrance, CA 90502
Zachary Newbold
L3 Communications, CSW
640 N 2200 W
Salt Lake City,
UT 84116
ABSTRACT
This paper describes some improvements in the measurement process of the NIST 18 term error analysis that reduces the required measurement time and also improves the sensitivity of some of the tests to the individual sources of uncertainty. As a result, the measurement time is reduced by about 40 % and some of the estimated uncertainties are also improved without a reduction in the confidence levels. The reduction in measurements is accomplished by using one measurement for two or more error terms or using centerline rather than full 2D data scans for some of the terms.
Keywords: Antenna Measurements, Error Analysis, NearField Measurements
1.0 Introduction
The NIST 18 Term Error Analysis Technique[1] uses a combination of mathematical analysis, computer simulation and nearfield measurements to estimate the uncertainty for the results of nearfield range measurements on a given antenna/probe combination and frequency range. Nine of the terms can be evaluated using mathematical analysis and do not require any special nearfield measurements. The measurements for the remaining nine terms can be time consuming and require high stability and repeatability of the measurement system. In a typical evaluation, the equivalent of at least 25 complete nearfield measurements must be obtained on the AUT under carefully defined conditions. Improvements in the process have recently been developed and applied to a planar nearfield facility that reduces the number of measurements to 16 and also makes it possible to improve some of the uncertainties to the actual system performance rather than the limits of the measurement process. The improved process will be described and examples shown for a planar nearfield range.
2.0 NIST 18 Term Error Analysis Procedure
The individual terms in the error analysis process are listed in Table 1. The first nine do not require any nearfield RF measurements on the antenna under test (AUT) and are evaluated using derived equations. Note that the terms have been reordered to group the analysis terms together. The input data for the equations comes from the calibration data on the probe and/or gain standard, impedance measurements on the transmission line components, alignment data on the AUT and probe and position error data obtained from optical measurements on the mechanical scanner.
The remaining nine terms are evaluated using a self comparison measurement process. This process depends on the stability and repeatability of the AUT, probe and the total measurement system. It does not depend on a knowledge of the “true” properties of the AUT and none of the terms are derived from a comparison of results with a known or ideal farfield pattern. An estimate of the uncertainty for each term is obtained by comparing two or more nearfield measurements that are identical in all respects except for one carefully controlled difference. The difference can be in the calculation process such as truncating the nearfield data to produce a smaller scan area or in the measurement setup such as changing the zseparation distance between the AUT and probe. If the system is stable and the measurement changes are carefully chosen, the difference between the resulting farfield patterns will be due to a single error term and provide an estimate of the uncertainty due to only that term. This process requires a reference measurement and one or more additional measurements with changes induced in the system and the typical numbers of measurements for each term are shown in Table 1. For the usual approach, the equivalent of at least 25 nearfield measurements must be completed to evaluate all the terms. A complete nearfield measurement is defined as one with approximately half wavelength spacing in both X and Y directions, two polarizations and covering an area large enough to minimize the truncation error. If the testing involves multiple beams or multiple frequencies the scan speed must be adjusted for these conditions.
Table 1 Summary of the NIST 18 Term Error Model.


Number of Tests Required 

Error Source 
Primary 
Original 
New 

Evaluation Method 


Probe relative pattern 
Analysis 


Probe polarization ratio 
Analysis 


Probe gain measurement 
Analysis 


Probe alignment error 
Analysis 


Normalization constant 
Analysis 


Impedance mismatch 
Analysis 


AUT alignment error 
Analysis 


Probe x, yposition errors 
Analysis 


Probe zposition errors 
Analysis 


Data point spacing 
Measurement 
3 
2 
Meas. area truncation 
Measurement 
1 
1 
Multiple reflections (probe/AUT) 
Measurement 
5 
5 
Receiver amplitude nonlinearity 
Measurement 
4 
1 
System phase error due to: 



Flexing cables/rotary joints 
Measurement 


Temperature effects 
Measurement 


Receiver phase errors 
Simulation 


Receiver dynamic range 
Measurement 
3 
3 
Room scattering 
Measurement 
2 
2 
Leakage and crosstalk 
Measurement 
2 
2 
Random errors in amplitude/phase 
Measurement 
5 
0 


25 
16 
The data point spacing tests requires the equivalent of three full measurements since one is taken with quarter wavelength spacing requiring at least double the measurement time and another is taken at the regular spacing for comparison. In the case of multiple reflections and random errors, multiple measurements are required so they can be averaged to provide a reference result that has a reduced level of the error term.
The setup, measurement and analysis of each of the 25 measurements can be time consuming and typically will require on the order of one week to complete using the original approach. If a gain standard is used as the reference for gain measurements, additional comparison measurements must be performed on the gain standard/probe for at least the truncation, multiple reflections and room scattering terms. In the following sections, improved procedures will be described that reduce the number of measurements or the time required for a given measurement while at the same time improving the sensitivity of the results.
3.0 Measurement System and Antenna
The measurement system being evaluated was an NSI combination planar/cylindrical scanner with a maximum scan area of 12 by 12 feet that was installed at L3 Communications, CSW in Salt Lake City, UT . The AUT was a circularly polarized planar array with input feeds for both WR42 and WR22 waveguide bands and tests were carried out in both bands. The antenna was designed and developed by ThinKom Solutions, Inc. and was very well suited for use in the range evaluation since it was very stable, could be aligned accurately to a mechanical reference and had a very narrow beam that is appropriate for the planar measurements. In addition, the array elements produced a multiple reflection characteristic that occurs only with a periodic structure and demonstrates how this can affect the choice of data point spacing.
4.0 Combining Data Point Spacing and Random Error Tests
As shown in Table 1, the data point spacing and random error tests normally require a total of eight nearfield measurements. With the new approach, this is reduced to a single reference measurement at the quarter wavelength spacing which takes the same time as two regular measurements. Instead of taking another measurement at half wavelength spacing to compare with the reference, a script was developed that would produce a new data file by setting the amplitude of every other point in both X and Y to zero. The farfields of the reference and thinned files were then compared to produce estimates of uncertainty between quarter and half wavelength spacing. In addition to reducing the measurement time, this procedure is also less sensitive to drift, slight differences in cable flexing errors and room scattering changes that might occur between two completely different measurements.
A method was also developed to use the quarter wavelength data to estimate the random error signal level without additional measurements. If the angular spectrum of the measured data is computed without applying either the probe correction or the Cos(θ) factor, the resulting spectrum will cover a span in normalized kspace _{} from 2 to +2 as shown in Figure 2. The portion of the spectrum within the unit circle is produced primarily by the AUT with relatively small contributions from all sources of measurement error. The portion of the spectrum outside of the unit circle also has contributions from both the AUT and measurement errors, but the AUT component is exponentially attenuated since the AUT plane waves in this region are evanescent modes. The spectrum in this region is therefore dominated by measurement error sources that have a nearfield period of less than one RF wavelength. Experience has shown that the two primary error sources are modulation of the multiple reflection signals by the periodic structure of the AUT array and random errors from all electrical and mechanical sources. The localized peaks in Figure 2 can be identified with the multiple reflection mechanism and these lobes in the evanescent region must be considered when selecting the data point spacing.
If farfield pattern results are required over the full front hemisphere, and a minimum aliasing error is desired, the data point spacing must be chosen using a band limit that is larger than the kvalue of the last lobe. In Figure 2 the last lobe due to the multiple reflections is at _{}and the required data point spacing is 0.38λ as calculated from,
_{}
The comparison of the farfield from the reference quarter wavelength and thinned data will also show the aliasing error due to the multiple reflection lobes. If the farfield pattern is not required over the full hemisphere, a larger spacing can be determined from the equations
_{}
The random error level is estimated from the “noise” level of the spectrum in the evanescent region. Excluding the localized peaks due to the multiple reflections, the random error level is at least 70 dB below the peak of the main beam. Using this approach, five measurements are eliminated, and the error level is not influenced by drift, or changes in room scattering and cable flexing between repeat measurements.
5.0 Estimating Receiver NonLinearity Errors
In the past, nonlinearity has been estimated by comparing the farfield results of measurements where the input power level to the mixer was changed along with the receiver averaging to maintain a constant signaltonoise ratio. Computer simulation has shown that the primary effect of receiver nonlinearity is a change in the mainbeam width and so a pattern difference similar to Figure 4 was expected and used as a measure of the receiver nonlinearity. However the measured differences rarely show this regular pattern since the nonlinearity of most receivers is very low and usually less than random and repeatability errors.
In principle, the linearity could be checked using a highly repeatable step attenuator and phase shifter. If the receiver is linear, the observed change in amplitude or phase for a given switch should be independent of the power level to the mixer. The receiver averaging can be increased to reduce the effect of random errors and this measurement can be completed fairly quickly. Reliable and repeatable step attenuators and phase shifters are generally not available in all the frequency bands where range evaluation is performed, so this approach is not generally used. A variation of this approach has been developed and used in the current range evaluation with very good success.
The variation uses a portion of the centerline nearfield data to produce repeatable changes in amplitude and phase as shown in Figure 5. The receiver averaging is increased to the maximum to reduce random errors, the probe is stopped at each data point to reduce position errors, and the centerline is scanned in both the plus and minus directions and then averaged to reduce the effect of drift and cable hysteresis. Typically 68 bidirectional scans are made along the same centerline with an amplitude variation of approximately 2030 dB and then averaged using a script. Comparison of the averages from two or more repeat measurement sets demonstrates the level of repeatability. The process is then repeated for different levels of power to the mixer. Figure 6 shows one result where the measurement is repeated without any change in mixer power level and then a six dB pad is inserted before the mixer. Without any change, the amplitude difference is constant to within 0.005 dB which indicates the stability and sensitivity of the test. When the pad is inserted, a small and repeatable nonlinearity is clearly observed with a maximum deviation of less than 0.1 dB over the 30 dB dynamic range.
A similar result is seen in the phase difference plots as shown in Figure 7. Without any mixer power change, the phase differences are less than 0.05 degrees while with the pad added, the nonlinear error is on the order of 0.3 degrees. It is possible that the observed variations are due to something other than nonlinearity. At this level, changes in impedance mismatch or interference signals could produce some or all of the changes in the measured amplitude or phase. But this result does set an upper limit to possible receiver nonlinearity and this limit is much lower than available from previous tests. This is because the new test can isolate the nonlinearity error from other sources that would be embedded in the result from the normal full 2D measurements.
The approximate effect on farfield parameters is obtained by computing the farfield patterns from the centerline scans and calculating the error signal level from the difference in the patterns as shown in Figure 8. The very small linear phase variation shown in Figure 7 will produce a small offset in the peak of the main beam that is not due to nonlinearity but will produce the same difference curve as nonlinearity. Therefore, one beam is shifted to precisely align the beam peaks and remove this effect before calculating the error signal level. The end result in this case demonstrates that the nonlinear error signal is at least 70 dB below the peak of the main beam. Typical levels using previous methods were in the range of 50 to 60 dB and so this is a big improvement.
6.0 Summary
New procedures have been described and illustrated with recent measurements that reduce the time required for performing the NIST 18 Term Error Analysis process. They also generally produce lower estimates of the error signals due to aliasing, random errors and nonlinearity.
8. REFERENCES
[1] A. C. Newell, Error analysis techniques for planar nearfield measurements, IEEE Trans. Antennas & Propagation, AP36, p. 581, 1988.
9. ACKNOWLEDGMENTS
The authors wish to thank ThinKom Solutions, Inc. for the use of the array antenna used in these measurements and the L3 Communications, CSW for the support and cooperation in the use of their nearfield measurement facility.