Uncertainty Considerations In Spherical Near-field Antenna Measurements

Transcription

1 Uncertainty Considerations In Spherical Near-field Antenna Measurements Phil Miller National Physical Laboratory Industry & Innovation Division Teddington, United Kingdom

2 Outline Introduction and Spherical Configuration Typical NIST 18 Point Uncertainty Budget Consideration of the Terms Identification of the Uncertainties Deriving the Uncertainty Budget Conclusion

3 Introduction The Ability to be able State the Uncertainty to which a Quantity is Measured is as Important as the Measurement itself Performing an Uncertainty Analysis for a Validated Measurement Facility can involve a Lot of Work. Reducing the Confidence in the Uncertainty can Reduce Effort Need to perform Measurement Validation to avoid Large Systematic Errors

4 Spherical Configuration Theta Axis Chi Axis Phi Axis Probe θ Test Antenna φ θ Model Tower Spherical Range Configuration

5 18 Point Error Budget No UNCERTAINTY CONTRIBUTION Gain Calibration Uncertainty Probe Polarisation Uncertainty Probe Relative Pattern Probe Alignment Uncertainty Normalisation Constant Impedance Mismatch Uncertainty Aliasing Uncertainty Truncation Uncertainty θ, φ Position Uncertainty

6 18 Point Error Budget (Cont.) R Position Uncertainty Positioner and AUT Misalignment Uncertainty Probe-AUT Multiple Reflections Receiver Amplitude Non-linearity System Phase Errors due to Receiver Phase Uncertainty Cable Errors/Rotary Joints Temperature Effects Receiver Phase Uncertainty Cable Errors/Rotary Joints Temperature Effects Receiver Dynamic Range

7 SGH and Probe Calibration Uncertainty Determined when SGH and Probe are Calibrated SGH and/or Probe Gain Uncertainty is a Direct Contribution to Gain Uncertainty Budget 0. db Probe Pattern Error at Edge of Reflector produces a 0.03 db Gain Uncertainty 0.3 db Uncertainty on a 6.8 db First Sidelobe (-55 db error level signal)

8 Probe Alignment Uncertainty Horizontal Probe Positioning Uncertainty can produce Large Measurement Uncertainty in Polar Mode, Smaller in Equatorial Mode Chi Axis Misalignments causes Polarisation Uncertainty proportional to the Sine of the Angle of Misalignment The Effect of Range Length Uncertainty can be calculated by varying the Inputted Range Length in the Transform

9 Normalisation Constant and Mismatch Uncertainty Normalisation Constant Uncertainty can be determined by Repeatedly Disconnecting and Reconnecting the Relative/Direct Connection and Noting the Variation Mismatch Uncertainty is Determined by applying the Measurement Uncertainty in the Reflection Coefficient Measurement in turn to the Real and Imaginary Part of each Reflection Coefficient in :- M c = 1 Γ L Γ G ( 1 Γ )( 1 ) L ΓG

10 Aliasing Error Caused by Under-Sampling the Data Use the TICRA result to Estimate Uncertainty Δθ π N + 1 Δφ = π M + 1 N = kr + 0 n1 M N n = kr ( P 1 0 tr ) where P tr is the Power Level of the Neglected Modes

11 Truncation Error and θ and φ Position Errors Truncation Error is caused by Acquiring Too Small an Area of Data Estimate the Error due to Truncation by Acquiring a Larger Area of Data and then Perform Transforms on Progressively Reduced Area Data Sets θ and φ Position Errors can cause Pointing Errors if Systematic. Otherwise of Second Order Importance unless Antenna is Offset in the Minimum Sphere When Antenna is Offset use R Position Uncertainty Techniques

12 R Position Errors Primarily Phase Errors caused by Run-Out Errors and Tilt Errors in the Positioner System If in the Antenna Near-Field can Estimate Uncertainty using Ruze Theory ` G ( θ, φ) ( θ, φ)exp = G δ 0 where λ is the wavelength,, U = sin( θ) Bound using NIST Theory πc + exp δ λ n = c is thecorrelation 1 n δ π exp cu! n n λ distance of the errors n

13 Range and AUT Alignment Uncertainty Uncertainty due to Range Alignment Errors best Estimated using J. E. Hansen (ed). Spherical Near-Field Antenna Measurements AUT Alignment Errors causes Error in the Pointing Measurement Uncertainty due to Antenna Flexure can be Estimated using Data Acquisition in the Alternative Sphere

14 Probe-AUT Interaction Errors Caused by Multiple Reflections between the Probe and the AUT The Measurement Uncertainty caused by the Probe-AUT Interaction can be estimated by Comparing Two Identical Measurements made with the Range Length Changed between then by λ/4

15 Receiver Amplitude Non-linearity and System Phase Errors Receiver Amplitude Errors cause a Gain Error directly equal to the Receiver Compression Error below 0.1 db System Phase Errors can be caused by RF Cable and AUT instabilities, Rotary Joint Errors and Temperature Effects The Uncertainty in the Measurement can be estimated using the same techniques as for the R Uncertainty Effects Rotary Joint Errors can be removed using a Polar Acquisition

16 Receiver Dynamic Range For a Far-Field Range the Receiver Dynamic Range defines the Noise Floor for the Measurements For a Near-Field Measurement the Noise Floor is reduced by the difference between the Near-Field Gain and the Far-Field Gain The Amplitude of the Noise Floor has the Largest Effect on the Transformed Pattern

17 Random Errors Caused by any Uncertainty in the Measurements not Previously Considered Estimate by Performing Repeat Measurements and Comparing Transformed Data. Use: - ε ( θ φ), = 0.*log ( θ φ) ( θ ) E1, E, φ Where the Quantities have been Normalised to Zero

18 The Expression of Uncertainty Use UKAS Standard M3003 and Type A Evaluation Assume Error in Measurement has Already Been Calculated so that the Sensitivity Coefficient is 1 Calculate Divisor from the Probability P(x) of each Uncertainty Term : - D x = x x 1 P( `x) dx

19 Common Divisors Probability Distribution Rectangular U Shaped Normal Normal from Calibration Certificate Divisor 3 1 1/k Comment Phase Noise Uncertainty Single Multipath Uncertainty Gaussian Distribution A Coverage Factor k will have been used to obtain an Expanded Uncertainty

20 Coverage Factor and Coverage Probability Coverage Probability P 90% 95% 95.45% 99% 99.73% Coverage Factor k

21 Uncertainty Probability Coverage Probability P 90% 95% 95.45% 99% 99.73% Coverage Factor k

22 Gain Uncertainty Analysis - Simplified Example Source of Uncertainty Value db Distribution Divisor Standard Uncertainty U i (y) Abs Multipath Error.01 U-Shaped Repeatability Gain Calibration Error Standard Uncertainty Peak Normal Normal k = Expanded Uncertainty k = Giving a Confidence of Approximately 95% db

23 Conclusions Presented a Cook Book Methodology to Performing an Uncertainty Analysis Methods may seem Complicated but they Get Easier with Use Possessing Independent Calibrated Standards is a Good Way of Validating Your Measurements for Yourself and Your Customer and for Checking your Uncertainty Analysis