Uncertainty simulator to evaluate the electrical and mechanical - - PowerPoint PPT Presentation

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

2 main ways of evaluating the uncertainty

in the antenna parameters: 1.Through measurements Comparison of measurements with different configurations, i.e. scan in & in , 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…

Measured value

UNCERTAINTY = that part of

the expression of the result of a measurement which states the range of values within which the true value is estimated to lie.

17m 2.1m

Uncertainty analysis through simulations

AUT modelled as array of 28x16

• /2 dipoles

vertically displaced, over a ground plane at a distance=/4.

AUT total size = 5.3 m x 2.1 m. Excitation=separable in vertical & horizontal

planes.

Probe = ideal conical corrugated horn.

CNIFT

(Near-To-Far Field Transformation) Acquisition with ERRORS

Far field Radiation Pattern COMPARARISON IDEAL

Acquisition

CNIFT

(Near-To-Far Field Transformation)

Far field Radiation Pattern

Single or Montecarlo simulations

Xprobe

• Systematic & random,

Yprobe & Zprobe

• random,

Phase

• random,

White Gaussian Noise.

Source of Errors analyzed:

Cylindrical System & Mechanical deviations

Z X Y Z X Y

Random Error in Xprobe Random Error in Yprobe Random Error in Zprobe Systematic Error in Xprobe (sine, 4 periods)

Probe A.U.T.

MECHANICAL ERRORS: Xprobe

• Systematic & random,

Yprobe & Zprobe

• random

Uncertainty analysis through simulations

Error in Zprobe Error in Yprobe Error in Xprobe

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20 40 60 80

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Far Field: Horizontal Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Ideal Aquisition 40 60 80 100 120 140

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Far Field: Vertical Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Ideal Aquisition

Uncertainty analysis through simulations: Systematic error in Xprobe (sine, 4 periods)

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 26.9 26.95 27 27.05 27.1 27.15 27.2 27.25 27.3 27.35 Directivity with and without error (dBi) Error in Xprobe (systematic,sine) [1/lambda] Directivity (dBi) Dir without error Dir with error

Mispointing Error (degrees)

0,5 1 1,5 2 2,5 3 3,5 0,000 0,050 0,100 0,150 0,200 0,250 Error in Xs [1/lambda] Mispointing error (degrees) Mispointing Error Lineal (Mispointing Error)

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20 40 60 80

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Far Field: Horizontal Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 40 60 80 100 120 140

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Far Field: Vertical Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition

Uncertainty analysis through simulations: Random error in Xprobe

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20 40 60 80

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Far Field: Horizontal Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 40 60 80 100 120 140

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Far Field: Vertical Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 22 23 24 25 26 27 Directivity with and without error (dBi) Error in Xprobe (random) [1/lambda] Directivity (dBi) Dir without error Dir with error

Mean and Standard Deviation of the Difference between the Directivity with and without Error

0,00 1,00 2,00 3,00 4,00 5,00 0,05 0,10 0,15 0,20

Error in Xprobe (random) [1/lambda] Mean

Mean Error Difference Standard Deviation Error Difference

Error Uncertainty

Mean and Standard Deviation of the Difference between the Directivity with and without Error (dB)

0,00 0,05 0,10 0,15 0,20 0,25 0,05 0,10 0,15 0,20

Error in Xprobe (random) [1/lambda] Mean&Stand-Dev (dB)

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 26.65 26.7 26.75 26.8 26.85 26.9 26.95 27 Directivity with and without error (dBi) Error in Yprobe (random) [1/lambda] Directivity (dBi) Dir without error Dir with error

Uncertainty analysis through simulations: Random Error in Yprobe

Error Uncertainty

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20 40 60 80

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Far Field: Horizontal Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 40 60 80 100 120 140

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Far Field: Vertical Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition

Uncertainty analysis through simulations: White Gaussian Noise

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20 40 60 80

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Far Field: Horizontal Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 40 60 80 100 120 140

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Far Field: Vertical Cut Angle (degrees) Field Module (dB) Infinite Far-Field Processed Aquisition 40 42 44 46 48 50 52 54 56 58 60 26.7 26.75 26.8 26.85 26.9 26.95 27 Directivity with and without error (dBi) SNR (dB) Directivity (dBi) Dir without error Dir with error

Mean and Standard Deviation of the Difference between the Directivity with and without Error (dB)

0,00 0,05 0,10 0,15 0,20 0,25 60 55 50 45 40

N/S Mean&Stand-Dev(dB)

Mean Error Difference Standard Deviation Error Difference

Error Uncertainty

• 0.015
• 0.01
• 0.005

0.005 0.01 5 10 15 20 25 Error Histogram: Error in the Directivity dBi Cases

Montecarlo simulations

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20 40 60 80

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Far Field: Horizontal Cut Field Module (dB) Angle (degrees)

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20 40 60 80

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Far Field: Horizontal Cut Field Module (dB) Angle (degrees)

• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 5 10 15 20 25 Error Histogram: Error in the Beam Width (Vertical Cut) Angle (degrees) Cases

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1 2 3 x 10

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5 10 15 20 25 30 Error Histogram: Error in the Maximum Position (Horizontal Cut) Angle (degrees) Cases

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

• n 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

I(z) z d 2 = -L 1 z d 1 = L 1 z P R O B E : P (x, y, z) x r R 2 R

1

2 1

• D IP O L E

I(z) z d 2 = -L 1 z d 1 = L 1 z P R O B E : P (x, y, z) x r R 2 R

1

2 1

• D IP O L E
• s

jkr s jkR s jkR mn z

f r e kL f R e f R e I E ) cos( 2

1 2 2 1 1

2 1

• z

1

x 2 D L tan