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This presentation explores the relationship between wavelength-to-DUT size ratio and the number of lobes in the resulting radiation pattern. Understanding this behavior helps determine the required measurement point density for accurate TRP and TIS testing. Examples, dipole evaluation, multi-lobe patterns, and modeled results are discussed.

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## Surface Point Density Requirements for TRP and TIS Testing

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**Surface Point Density Requirements for TRP and TIS Testing**June 21st, 2007 Madrid, Spain Michael Foegelle foegelle@ets-lindgren.com Director of Technology Development ETS-Lindgren**Overview**• Introduction • Examples • Dipole Evaluation • Multi-lobe Patterns • Modeled Results • Data Point Reduction • Summary • References**Introduction**• This presentation demonstrates the relationship between the ratio of wavelength to DUT size and the number of lobes that can be expected in the resulting pattern. • The number and size of lobes, as well as the expected depth of nulls in the pattern, determines the required measurement point density required to accurately determine quantities like TRP and TIS. • Understanding this behavior allows determination of suitable step size requirements and associated measurement uncertainties.**Examples**• Tests of existing products of different sizes with radios operating at different frequencies shows that radiation patterns vary widely from the target dipole antenna pattern.**Examples**• An angular step size that may be suitable for a simple pattern is not suitable for more complicated patterns.**Dipole Evaluation**• A dipole pattern represents the most general possible pattern with the slowest surface variation. • Data point resolution obviously affects ability to represent the actual surface. 30° 5° 15° 1°**Dipole Evaluation**• Orientation of the dipole within the measurement system will change the measured points. • Different subset of points on surface can produce different results.**Dipole Evaluation**• The error in the resulting surface integral can be evaluated as a function of orientation and angular step size.**Multi-lobe Patterns**• For complex patterns with multiple lobes, the surface point resolution needs to be sufficient to resolve the lobes and nulls of the pattern. • In general, lobes are wide in comparison to the width of nulls, so when evaluating integral quantities like TRP and TIS, it’s not necessary to hit deepest nulls. • Individual point quantities like Peak EIRP and Gain are much more dependent on angular resolution.**Multi-lobe Patterns**• In general, the number of lobes in a pattern is related to the ratio between the maximum dimension of the DUT (D) and the wavelength (l). • The error in quantities determined from a measured pattern will be some function of the surface resolution relative to the size of features on the surface. • For integral quantities, it’s also a function of the depth of nulls in the surface. • What we’d like to know is the expected error as a function of the D/l ratio. • From this, we can then determine surface point resolution requirements. • A wide range of configurations have been simulated to try to determine this relationship.**Modeled Results**• A tool was developed to use point dipole sources in various array configurations to represent the potential multi-lobe behavior of electrically large devices. • The relative phase and magnitude of radiation from different points in a test volume (DUT volume) can be varied to represent different levels of secondary radiation from fixed structures. • The goal was to determine the range of possible patterns as a function of D/l ratio and not to represent any particular device. • Results shown here are intended to reflect a worst-case situation. Real devices are expected, on average, to have behaviors that are encapsulated by these results.**Modeled Results**• One simple geometry that was tested is a corner arrangement, with the primary radiator at the corner and three additional dipoles offset the same distance in each of the three principal axes (X, Y, and Z). • In these calculations, D represents the dimension along each of the X, Y, and Z directions, rather than the maximal overall dimension.**Modeled Results**• While by no means identical, the model can produce lobes with similar size to those from a real device having the same D/l ratio. Laptop Corner Model**Modeled Results**• Examples of lobes vs. D/l ratio for corner layout. D = 0.25l D = 1.0l D = 2.0l D = 3.0l**Modeled Results**• Sample results showing TRP errors due to chosen step size. • Note oscillation due to symmetry issues.**Modeled Results**• TRP error data rearranged to show relationship to D/l ratio.**Modeled Results**• Symmetry of this particular model results in non-ideal results. • Some D/l ratios result in lobes that line up with point locations, resulting in small errors in integrated result where a randomly oriented pattern would have a random level of error with a much larger range. • Patterns have many evenly spaced lobes with identical peak power resulting in peak EIRP results that mirror the TRP results. • Realistic multi-lobed patterns typically have one or two main lobes with random orientations that produce the peak EIRP value. In that case, the chance of a measured point hitting the peak is greatly reduced. • Further work is required to produce random patterns and obtain a statistical distribution of error vs. D/l ratios.**Modeled Results**• Some conclusions may be drawn based on this preliminary data. • Even for a dipole, 30 degrees is probably the maximum allowable step size for any randomly oriented antenna. • Assumes limiting TRP/TIS error contribution due to step size integration errors to < 0.2 dB max. • A formulation based on this data is consistent with existing real-world tests but may still be slightly loose. • It is expected that future evaluations including minimization of errors in peak EIRP will necessitate a tighter requirement. • Supports target step sizes used by CTIA for TRP testing and increased uncertainty for TIS step size.**Modeled Results**• Potential formulation based on current modeled results.**Modeled Results**• Another desired quantity is an indication of the expected measurement uncertainty as a function of step size relative to the D/l ratio. • Would potentially allow increasing the step size (for test speed) at the cost of an additional contribution to the uncertainty budget. • Actual error/uncertainty can be expected to be a function of the depth of nulls, in addition to the number of peaks and nulls in a pattern. • Defining a suitable formula for this will take additional research.**Modeled Results**• Examples of varying peak/null ratio. (Pmain= 0 dBm) Pimage= 0 dBm Pimage= -5 dBm Pimage= -20 dBm Pimage= -10 dBm**Data Point Reduction**• For tests like TIS, where the measurement time of individual data points is expected to be extensive, it is desirable to reduce the overall test time by reducing the total number of points measured. • The traditional spherical pattern measurement sequence (even steps in q and f) is based on ease of operation and mechanical positioning. • The result is that points are closer together on the spherical surface near q = 0° and q = 180°, and further apart near q = 90°. • Integration requires a sin(q) term to give proper weight to each data point.**Data Point Reduction**• Illustration of point density on a spherical surface for fixed 15-degree steps. Only 9 points intersect the highlighted surface area at q = 90° (left inset) while 25 points intersect the same area at q = 0° (right inset).**Data Point Reduction**• The ideal solution is to measure points evenly spaced on the surface rather than at even orthogonal angle locations. • TRP/TIS calculations are simple if spacing is exact, since they’re just an average of all points. • Only certain numbers of points will allow an even distribution. • Complex positioning to reach specific points could increase test time. • Integration of complex point arrangements (spirals, pseudo-equivalent spacing) can be complicated. • A good alternate solution is to use sin(q) weighting to determine the required number of points for each conical cut. • Similar positioning and integration algorithms to those used now.**Data Point Reduction**• The sin(q) weighting is easily applied through the following formula: Nq = 1 + int((N90 – 1) sin(q)) where Nq is the number of points required for the cut at the given q angle, N90 is the number of points in the q = 90° cut, (for the non-optimized cut, equal to = 360 ° divided by step size) and int takes the integer part of the number. • The starting point for each cut should be dithered to avoid a line of points along f = 0. • Simple solution is to start 1/2 step from f = 0 on every other conical section cut.**Data Point Reduction**• Using this formulation, the number of data points required can be reduced from 25-35%, improving as more points are required.**Data Point Reduction**• A quick check of the accuracy on use with a dipole gives similar results to that for even q and f spacing.**Summary**• In general, as a DUT gets larger compared to the wavelength, the pattern becomes more complex. • In order to measure a complex pattern adequately, it’s necessary to measure enough data points to represent the major features in the surface. • Given the range of frequencies and devices that we expect to test with the RPT test plan, we need a generic specification for defining the required data point resolution. • This presentation shows research used to determine the approximate relationship, and provides an initial estimate for the requirement. • Additional work is required to validate this formula and determine the expected uncertainty when the target values are exceeded.**Summary**• In order to reduce the total measurement time, a new method has been presented to reduce the required number of points while maintaining the required data point resolution (and thus the required level of uncertainty). • This method can be easily implemented on existing test systems.**References**• 1. M. D. Foegelle, “Introduction to Over-the-Air Performance Testing”, WiMAX TWG RPT, Sophia-Antipolis, France.

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