Parametric Study of Angular and Radial Probe Positioning Errors In a Large Spherical Near-field Automotive Antenna Test System

Daniël Janse van Rensburg Nearfield Systems Inc

19730 Magellan Drive, Torrance, CA 90502-1104, USA e-mail: drensburg@nearfield.com

Abstract The testing of modern automotive antennas is often accomplished by using spherical near-field test facilities. This paper presents sensitivity analysis data for errors introduced in the probe position of such a test system. The purpose of this study is to establish mechanical design goals for the gantry structure required in the implementation of the probe positioning system. Far-field error levels are calculated to demonstrate the effect of the probe positioning anomalies.

Keywords : Antenna measurements, Spherical near-field, Automotive antenna testing.

1. Introduction This document describes a parametric study performed to investigate the sensitivity of spherical near-field measurement results on errors in the probe radial distance and angular positioning parameters. The specific type of test system is as depicted in Figure 1 and consists of a large turntable containing the vehicle and an overhead gantry containing the probe antenna.

Figure 1: Scale model of the SNF automotive test system considered.

The turntable offers φ rotation and the gantry θ rotation (both variables used in a conventional spherical coordinate system). The radial distance (r) of the probe is fixed. The combined motion of the gantry and turntable provides for hemi-spherical coverage only. This paper presents sensitivity analysis data for errors introduced in the probe positioning (i.e. the gantry structure) of such a test system. The study is based on a combination of measured and simulated data and various techniques have been used to introduce the required errors. The simulated data presented here is based on work described in [1-3].

2. Radiation Test Cases

Two test cases are considered here. The first case represents the upper end of the frequency range of operation and the second, the lower end. In both cases the sources are considered offset from the turntable axis of rotation, since this increases the near-field sampling density required and is regarded as a more demanding test scenario. The first test case (Source #1) is for a planar current sheet of dimensions 15cm x 15cm (with Taylor distribution) moved off φ-axis by 50cm (done to increase the minimu m radial envelope – MRE) and this source gives rise to an electric field distribution at a distance of 12m as shown in Figure 2. The rapid phase variation is evident and the slight boresight shift of the near-field data is also detected (due to the 50cm offset).

The second simulated data set (Source #2) is for a sheet current distribution of dimensions 2m x 2m (with Taylor distribution) moved off φ-axis by 1m, and this source gives rise to an electric field at a dis tance of 12m as shown in Figure 3. Note the skewing in Figure 3 due to the source offset from the coordinate system origin.

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Figure 2: Near-field amplitude & phase distribution of 15cm x 15cm simulated source (offset by 50cm from coordinate system origin) at a distance of 12m – 6 GHz.

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Figure 3: Near-field amplitude distribution for 2m x 2m simulated source (offset by 2m from coordinate system origin) at a distance of 12m – 400 MHz.

These two simulated source distributions were selected to represent two nominal extremes of near-field operation in the specific facility. Both cases are used to investigate the specific probe positioning errors of interest. The cases compare as follows:

# Freq MRE [λ] Probe distance [λ]

Probe distance/MRE

1 6 GHz 20 240 12 2 0.4 GHz 4.7 16 3.4

Note that the probe distance is at 12m and the ratio of the probe distance to MRE value is shown as a potential gauge of the near-field to far-field transformation sensitivity to the radial distance parameter. In each instance below a reference pattern is calculated with no probe positioning error and a second test pattern is calculated with the error introduced and a difference pattern is calculated as a measure of the far-field induced error.

3. Probe radial distance errors Radial distance variation of the probe due to gantry flexing and temperature expansion/contraction can be modeled through the introduction of a phase perturbation added to the near-field data. As such, simulated or existing measured data sets can be used. Since this error will most likely be systematic, no random component is investigated here.

From the physical structure of the probe gantry it is expected that maximum radial deflection due to sag of the structure radially will take place in the vertical position. This gantry radial sag can then be related to the θ angle through a cosine relationship.

Initial investigations using Source #1 show a very high level of tolerance to radial error introduced in this fashion. Phase perturbations starting from zero to ±500° (corresponding to a total radial distance of ±70mm) can be introduced, with negligible impact on the far-field radiation pattern level (error was added as a cosθ function. Freq = 6 GHz, MRE=1m, R/MRE = 12).

Since the relative insensitivity could be due to a fairly large r/MRE ratio, Source #2 was considered as well. At the lower frequency of 400 MHz a representative phase change is ±33° (corresponding to a total radial distance of ±70mm) and the effect of the phase change can be detected in the pattern nulls, but are at a level < –50dB (error was added as a cosθ function. Freq = 400 MHz, MRE=3.5m, r/MRE = 3.4).

By applying this radial distance error model to a separate actual measured data set also confirms the relative insensitivity of the far-field on the variation of this parameter. The relative insensitivity in this particular case can be attributed to the large probe radial distance due to the size of the gantry.

4. Probe errors in angle θ The angular errors investigated for the probe positioning using the gantry are firstly random and secondly systematic. The first case considered is that of a random error and a maximum value of ±0.5° was selected. When both the reference and test data is transformed to the far-field, the patterns shown in Figure 4 are obtained. This data shows a residual error level of <–20dB and significant deformation of the beam peak of the pattern (top image).

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Figure 4: Far-field error level due to ±0.5° random θ error introduced. Beam peak area is shown above (Source #1 - 6 GHz).

By reducing the angular error to a random value of ±0.25°, the residual error level is reduced to <–30dB.

The third case considered is that of a systematic error with peak value of ±0.25°, applied as a sin θ function to the absolute θ value. This error function models the expected bowing of the structure due to gravity. Figure 5 shows the resultant effect on the far-field data and a residual error level of –47dB is noted.

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Figure 5: Far-field error level due to ±0.25° systematic azimuth error introduced (Source#1 - 6 GHz).

Due to the apparent sensitivity of the far-field on the random θ error, Source #2 is also considered and a maximum value of ±0.25° was selected. Figure 6 shows the resultant effect on the far-field data of Source #2 (400 MHz) and the residual error level detected is <–40dB.

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Figure 6: Far-field error level due to ±0.25° random azimuth error introduced (Source#2 - 400 MHz).

5. Conclusions The data presented here represents a limited study to assess the probe gantry angular and radial specifications for a large automotive antenna test system. Simulated data sets have been used for the analyses presented and an ideal probe has been assumed (no probe correction).

The results show that the derived far-field patterns are fairly insensitive to phase variations that are introduced as a measure for radial variation of the probe location. A phase variation corresponding to a total radial variation of up to ±70mm can be tolerated in all of the cases considered without a noticeable change in far-field pattern levels.

The corresponding sensitivity of the far-field data on the gantry angular location (θ angle) is considerably higher for the errors considered. It is also evident that this sensitivity becomes more pronounced at higher frequencies. Random angular and systematic angular errors of up to ±0.5° were considered. Systematic angular errors (to simulate bowing of the gantry) do not have as significant an impact as random errors. From the results shown a random error of less than ±0.25° is required to achieve far-field error levels of lower than –30dB.

The results presented here are by no means exhaustive and merely serve to give an initial indication of the sensitivity of far-field patterns on some of the probe positioning parameters that will be affected by a large gantry positioning system. The results also give an indication of the feasibility of building such a structure with sufficient mechanical rigidity to allow for reliable spherical near-field antenna testing.

6. References [1] D. J. Janse van Rensburg, "Final report on the estimation of measurement errors in a spherical near-field test range", InfoMagnetics Technologies Corp, 15 December 1995.

[2] D. J. Janse van Rensburg, S R Mishra & Guy Séguin, "Simulation of errors in near-field facilities", AMTA 17th Annual Meeting & Symposium, Williamsburg, Virginia, USA, Nov. 1995.

[3] D. J. Janse van Rensburg, "Phased-array simulation for antenna test range design", AMTA 20th Annual Meeting & Symposium, Montreal, Quebec, Canada, Nov. 1998.