Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems S. Burgos, F. Martín, M. Sierra-Castañer, J. L. Besada Technical University of Madrid (Universidad Politécnica de Madrid, UPM)
Uncertainty analysis Measured � UNCERTAINTY = that part of value the expression of the result of a measurement which states the range of values within which the true value is estimated to lie . � 2 main ways of evaluating the uncertainty in the antenna parameters: 1.Through measurements 17m � Comparison of measurements with different configurations, i.e. scan in � & in � , 2.1m measurements with or without attenuator… � Useful for uncertainty analysis a posteriori. 2.Through simulations � Useful for uncertainty analysis a priori. � i.e. Antenna measurement system design. � The uncertainty could be specially important in outdoor ranges…
Uncertainty analysis through simulations � AUT modelled as array of 28x16 � � � � /2 dipoles IDEAL Acquisition vertically displaced , over a ground plane at a with ERRORS distance= � /4. Acquisition � AUT total size = 5.3 m x 2.1 m. CNIFT CNIFT � Excitation=separable in vertical & horizontal (Near-To-Far Field (Near-To-Far Field planes. Transformation) Transformation) � Probe = ideal conical corrugated horn . Far field Radiation Far field Radiation Pattern Pattern COMPARARISON Single or Montecarlo simulations Source of Errors analyzed: � Xprobe � � � Systematic & random, � � Yprobe & Zprobe � � random, � � � Phase � � � random, � � White Gaussian Noise.
Cylindrical System & Mechanical deviations Z Systematic Error in Xprobe (sine, 4 periods) Random Error � MECHANICAL ERRORS: in Zprobe � Xprobe � � Systematic & random, � � � Yprobe & Zprobe � � random � � A.U.T. X Z Probe Y X Random Error in Xprobe Y Random Error in Yprobe
Uncertainty analysis through simulations Far Field: Horizontal Cut 0 Infinite Far-Field -5 Processed Ideal Aquisition Error in Zprobe -10 -15 Error in Xprobe Field Module (dB) -20 -25 Error in -30 Yprobe Far Field: Vertical Cut -35 0 Infinite Far-Field -40 -5 Processed Ideal Aquisition -45 -10 -50 -15 -80 -60 -40 -20 0 20 40 60 80 Angle (degrees) Field Module (dB) -20 -25 -30 -35 -40 -45 -50 40 60 80 100 120 140 Angle (degrees)
Uncertainty analysis through simulations: Systematic error in Xprobe (sine, 4 periods) Far Field: Vertical Cut Far Field: Horizontal Cut 0 0 Infinite Far-Field Infinite Far-Field -5 -5 Processed Aquisition Processed Aquisition -10 -10 -15 -15 Field Module (dB) Field Module (dB) -20 -20 -25 -25 -30 -30 -35 -35 -40 -40 -45 -45 -50 -50 40 60 80 100 120 140 -80 -60 -40 -20 0 20 40 60 80 Angle (degrees) Angle (degrees) Directivity with and without error (dBi) 27.35 Dir without error Mispointing Error (degrees) Dir with error 27.3 27.25 3,5 Mispointing error 3 27.2 2,5 (degrees) Directivity (dBi) 2 27.15 1,5 1 27.1 0,5 0 27.05 0,000 0,050 0,100 0,150 0,200 0,250 27 Error in Xs [1/lambda] 26.95 Mispointing Error Lineal (Mispointing Error) 26.9 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 Error in Xprobe (systematic,sine) [1/lambda]
Uncertainty analysis through simulations: Random error in Xprobe Far Field: Horizontal Cut Far Field: Vertical Cut 0 0 Infinite Far-Field Infinite Far-Field -5 -5 Processed Aquisition Processed Aquisition -10 -10 -15 -15 Field Module (dB) Field Module (dB) -20 -20 -25 -25 -30 -30 -35 -35 -40 -40 -45 -45 -50 -50 40 60 80 100 120 140 -80 -60 -40 -20 0 20 40 60 80 Angle (degrees) Angle (degrees) Error Uncertainty Directivity with and without error (dBi) Dir without error Mean and Standard Deviation of the Difference between the Directivity with and Dir with error without Error 27 5,00 26 4,00 Directivity (dBi) 3,00 25 Mean 2,00 24 1,00 0,00 23 0,05 0,10 0,15 0,20 Error in Xprobe (random) [1/lambda] 22 Mean Error Difference Standard Deviation Error Difference 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 Error in Xprobe (random) [1/lambda]
Uncertainty analysis through simulations: Random Error in Yprobe Far Field: Horizontal Cut Far Field: Vertical Cut 0 0 Infinite Far-Field Infinite Far-Field -5 Processed Aquisition -5 Processed Aquisition -10 -10 -15 -15 Field Module (dB) Field Module (dB) -20 -20 -25 -25 -30 -30 -35 -35 -40 -40 -45 -45 -50 -50 40 60 80 100 120 140 -80 -60 -40 -20 0 20 40 60 80 Angle (degrees) Angle (degrees) Error Uncertainty Directivity with and without error (dBi) Mean and Standard Deviation of the Difference between the 27 Dir without error Directivity with and without Error (dB) Dir with error 26.95 0,25 Mean&Stand-Dev (dB) 26.9 0,20 Directivity (dBi) 0,15 26.85 0,10 26.8 0,05 26.75 0,00 0,05 0,10 0,15 0,20 26.7 Error in Xprobe (random) [1/lambda] 26.65 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Mean Error Difference Standard Deviation Error Difference Error in Yprobe (random) [1/lambda]
Uncertainty analysis through simulations: White Gaussian Noise Far Field: Horizontal Cut Far Field: Vertical Cut 0 0 Infinite Far-Field Infinite Far-Field -5 Processed Aquisition -5 Processed Aquisition -10 -10 -15 -15 Field Module (dB) -20 Field Module (dB) -20 -25 -25 -30 -30 -35 -35 -40 -40 -45 -45 -50 -50 -80 -60 -40 -20 0 20 40 60 80 40 60 80 100 120 140 Angle (degrees) Angle (degrees) Error Uncertainty Directivity with and without error (dBi) Dir without error Mean and Standard Deviation of the Difference between the Directivity Dir with error with and without Error (dB) 27 0,25 26.95 Mean&Stand-Dev(dB) 0,20 Directivity (dBi) 0,15 26.9 0,10 26.85 0,05 0,00 26.8 60 55 50 45 40 N/S 26.75 Mean Error Difference Standard Deviation Error Difference 26.7 40 42 44 46 48 50 52 54 56 58 60 SNR (dB)
Montecarlo simulations Far Field: Horizontal Cut Far Field: Horizontal Cut 0 0 -10 -10 -20 -20 Field Module (dB) Field Module (dB) -30 -30 -40 -40 -50 -50 -60 -60 -80 -60 -40 -20 0 20 40 60 80 -80 -60 -40 -20 0 20 40 60 80 Angle (degrees) Angle (degrees) Error Histogram: Error in the Beam Width (Vertical Cut) Error Histogram: Error in the Directivity Error Histogram: Error in the Maximum Position (Horizontal Cut) 25 25 30 25 20 20 20 15 15 Cases Cases Cases 15 10 10 10 5 5 5 0 -0.015 -0.01 -0.005 0 0.005 0.01 0 0 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 -4 -3 -2 -1 0 1 2 3 dBi Angle (degrees) Angle (degrees) -3 x 10
Conclusions � The objective of my work is to perform tools to characterize the uncertainties and the limits of the accuracy in the antenna measurements according to the kind of antenna and the mechanical and electrical performances of the systems. � The tool presented allows simulating errors in the acquisition and analyzing its effects on the antenna parameters : radiation patterns, directivity, beam width, position of the maximum… � While considering random errors , if several iterations are carried out, an statistical analysis allows obtaining the mean and the standard deviation of the errors that gives an estimation of the error and the uncertainty produced. � As seen from the results, the mechanical & electrical deviations may produce not only an uncertainty in the directivity but also an error . � Besides, certain types of errors – i.e. with the shape of a sine or simulating an slope in the X- axis – may also produce a mispointing error in the maximum . � In addition, since the AUT and the probe are aligned along the X-axis of the probe, the errors in the X-direction are the ones that have a larger influence in the antenna parameters. � Furthermore, a Montecarlo simulation study allows establishing the probability distribution of the errors.
Questions
AUT Model + Validity Margin � L D � � � 1 � � z � jkR jkR � jkr � e e e tan 1 � � 2 � � � � � � � 0 � � � � � � E I f f kL f 2 cos( ) 2 x z mn � s s s 1 2 1 R R r o � � 1 2 z z z d 1 = L 1 z d 1 = L 1 P R O B E : P R O B E : P (x, y, z) P (x, y, z) R R 1 1 � 1 � 1 � � � 2 � 2 r r x x R 2 R 2 I(z) I(z) z d 2 = -L 1 z d 2 = -L 1 D IP O L E D IP O L E
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