In order to evaluate how mechanical or electrical errors may affect in the final results (i.e.  radiation patterns, directivity, side lobe levels (SLL), beam width, maximum and null  position…), an error simulator based on virtual acquisitions of the measurement of the  radiation characteristics in a cylindrical near-field facility has been implemented [1], [2].  In this case, the Antenna Under Test (AUT) is modelled as an array of vertical dipoles  and the probe is assumed to be a corrugated horn antenna. This tool allows simulating an  acquisition containing mechanical errors – deterministic and random errors in the x-, y-  and z-position – and also electrical inaccuracies – such as phase errors or noise –. Then,  after a near-to-far-field transformation [3], by comparing the results obtained in the ideal  case and when including errors, the deviation produced can be estimated. As a result,  through virtual simulations, it is possible to determine if the measurement accuracy  requirements can be satisfied or not and the effect of the errors on the measurement  results can be checked. This paper describes the error simulator implemented and the  results achieved for some of the error sources considered for an L-band RADAR  antennas in a 15 meters cylindrical near field syste

Besada Sanmartin, Jose Luis

Burgos Martínez, Sara

Martín Jiménez, Fernando

Sierra Castañer, Manuel

Besada Sanmartín, José Luis

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Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

 1 
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 
Grupo de Radiación, Dpto. Señales, Sistemas y Radiocomunicaciones, 
Universidad Politécnica Madrid, 28040 Madrid, Spain 
E-mail:  sarab@gr.ssr.upm.es 
 
Introduction 
In order to evaluate how mechanical or electrical errors may affect in the final results (i.e. 
radiation patterns, directivity, side lobe levels (SLL), beam width, maximum and null 
position…), an error simulator based on virtual acquisitions of the measurement of the 
radiation characteristics in a cylindrical near-field facility has been implemented [1], [2]. 
In this case, the Antenna Under Test (AUT) is modelled as an array of vertical dipoles 
and the probe is assumed to be a corrugated horn antenna. This tool allows simulating an 
acquisition containing mechanical errors – deterministic and random errors in the x-, y- 
and z-position – and also electrical inaccuracies – such as phase errors or noise –. Then, 
after a near-to-far-field transformation [3], by comparing the results obtained in the ideal 
case and when including errors, the deviation produced can be estimated. As a result, 
through virtual simulations, it is possible to determine if the measurement accuracy 
requirements can be satisfied or not and the effect of the errors on the measurement 
results can be checked. This paper describes the error simulator implemented and the 
results achieved for some of the error sources considered for an L-band RADAR 
antennas in a 15 meters cylindrical near field system.  
Description of the error simulator for the inaccuracies evaluation 
In this case, since the system where this work is applied is an outdoor system, there are 
some error sources more relevant than the others. Actually, the effects of the wind for the 
probe positioning and the temperature changes that affect the phase response of the 
cables are the ones to be considered. Thus, the strategy adopted to evaluate the sources of 
error is to simulate these deviations and to examine the influence that they have in the 
final results. This procedure starts with the modelling of the transmitting and receiving 
antennas. Then, the near-to-far-field transformation is applied to obtain the far-field 
radiation patterns. So, to evaluate how errors could affect the final results, a model of the 
antennas and a simulation of the acquisition process including errors has been performed. 
Finally, the simulator compares the outcomes achieved from the reference data (i.e. the 
array infinite far-field) with the ones including the deviations.  
The received field in each point of the grid was calculated taking into account the 
field radiated by all the dipoles modified by the probe pattern. The field from a dipole in 
each point of the grid is given by the sum of three spherical waves [4]. The probe is an 
ideal conical corrugated horn characterized by the calculated radiation pattern of the main 
planes. For this investigation, the AUT evaluated is 5.3 meters long and 2.1 meters high. 
In addition, the probe is modelled as an ideal horn (keeping µ=±1). Besides, the AUT 
radiating elements considered are vertical λ/2 dipoles over a ground plane at a distance 
equal to λ/4, and assumed to be infinite, so “Image Theory” can be applied. In addition, a 
uniform column and row excitation in amplitude and phase is considered, the distance 
from AUT to probe is 5 meters, the vertical path of the probe is 15 meters and the 
frequency selected is 1215MHz.  
 2 
Error simulator for computational, mechanical and electrical errors 
Computational errors 
To validate the software and checking the computational errors of the algorithm, the array 
infinite far-field of the antenna (product of factor array by the radiation element pattern) 
is compared with the far-field calculated through the cylindrical near-field acquisition. 
This tool was also useful for testing the elevation validity range of the near-to-far-field 
transformation. The next figures show the results achieved: 
-80 -60 -40 -20 0 20 40 60 80
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Far Field: Horizontal Cut
Angle (degrees)
Fi
el
d 
M
od
ul
e 
(dB
)
Theoretical
Ideal Aquisition
 
Figure 1: Horizontal cut: Theoretical versus 
Ideal Acquisition 
40 60 80 100 120 140
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Far Field: Vertical Cut
Angle (degrees)
Fi
el
d 
M
od
u
le
 
(dB
)
Theoretical
Ideal Aquisition
 
Figure 2: Vertical cut: Theoretical versus 
Ideal Acquisition 
The diagrams obtained showed a very good agreement between the theoretical far field 
and the computed field and the validity of the angular margin of the measurement was 
confirmed. 
Pointing errors 
There are two different sources of deterministic errors that affect the AUT pointing: the 
axis non parallelism and the determination of the zero position of the azimuthal direction 
(in this case, the random errors caused by the wind effect are not considered). Both 
inaccuracies are directly translated to the error pointing, and they could be evaluated and 
corrected to minimize them. While the axis non parallelism can be measured with an 
optical procedure (i.e. laser tracker), the zero position of the azimuthal direction depends 
on the RADAR positioner encoder and the triggering of the vector network analyzer that 
can be either calculated or measured. Therefore, both errors can be compensated with a 
rotation of the electric field [5], and as a result they are omitted for this study.  
Mechanical errors in positioning system 
The positioning errors in x- and y-direction can be very important because of the windy 
outdoor conditions. To evaluate the effects of the mechanical errors on the outcomes, 
some simulations were developed including systematic and random errors in each sample 
in x, y and z directions. While the origin of the errors in x- and y-directions is the wind, in 
the z direction is the mechanical system of the measurement tower. Besides, the 
simulations were carried out with peak to peak error amplitudes in each sample from 
±0.05λ to ± 0.2 λ. From the diagrams acquired, it was clearly seen the noticeable 
influence of the errors on the main planes of the far-field radiation pattern. In addition, 
since the directivity is one of the most characteristic figures-of-merit that can describe the 
behaviour of an antenna, a detailed investigation has been carried out to evaluate how the 
mechanical errors may influence the directivity. In the simulations performed, the 
directivity was calculated when including a sinusoidal systematic error in the x-position 
of the probe, a uniform random error in the x-, y- and z-position of the probe.  
 3 
It is worthwhile noting that for the uniform random error in x-, y- and z-probe the 
mean and standard deviation of the error introduced in the directivity were achievable. 
From the results, it could be noticed that as expected the magnitude of the error in the 
directivity increase while augmenting the error introduced in the acquisition process, as 
shown in Figure 3 and Figure 4.  
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]
Di
re
c
tiv
ity
 
(dB
i)
Dir without error
Dir with error
 
Figure 3: Effect of a random error in the X-
position of the probe on the directivity 
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]
M
ea
n
Mean Error Difference Standard Deviation Error Difference
 
Figure 4: Mean and σ of the difference between the directivity with 
and without random error in the X-position of the probe 
Phase errors  
In near field antenna measurement systems the phase errors can be caused by temperature 
variations during the acquisition process. The study carried out establishes the influence 
that this inaccuracy may induce on the radiation pattern and directivity. As a 
representative example of the results achieved, Figure 5 illustrates the effect of the 
random phase error in the directivity when increasing the error magnitude. The line 
shows the average values, the broken line the directivity without error and the triangles 
show the result for each individual simulation. In this case, 10 iterations were carried out 
for each of the peak to peak error amplitude. Since several simulations were performed 
for each phase error, the mean and the standard deviations (σ) of the error in the 
directivity were calculated, as Figure 6 shows. 
1 2 3 4 5 6 7
26.9
26.91
26.92
26.93
26.94
26.95
26.96
Directivity with and without error (dBi)
Error in Zprobe (random) [1/lambda]
Di
re
c
tiv
ity
 
(dB
i)
Dir without error
Dir with error
 
Figure 5: Effect of a random error in  Phase 
on the directivity 
 
Mean and Standard Deviation of the Difference between the 
Directivity with and without Error (dB)
0,00
0,01
0,02
0,03
0,04
0,05
2 4 6
Error in Phase (random) [degrees]
M
ea
n
&S
ta
n
d-
De
v
 
(dB
)
Mean Error Difference Standard Deviation Error Difference
 
Figure 6: Mean and σ of the difference between the 
directivity with and without random phase error 
Once more, it could be observed, that the error in the directivity, the mean of this 
error and the standard deviation of this error increase linearly while the phase error 
introduced in the acquired field becomes larger. 
 4 
Errors due to the dynamic range 
Regarding the Signal to Noise Ratio (SNR) in the receiver, this magnitude can be 
evaluated for considering its influence on the side lobe levels. This effect was 
accomplished adding a white Gaussian noise to each value of the acquired field with 
respect to the maximum. Figure 7 and Figure 8 represent the results achieved:  
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)
Di
re
ct
iv
ity
 
(dB
i)
Dir without error
Dir with error
 
Figure 7: Effect of the noise on the directivity 
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
M
e
an
&
St
an
d-
D
ev
(d
B
)
Mean Error Difference Standard Deviation Error Difference
 
Figure 8: Mean and σ of the difference between the directivity with 
and without random error due to the noise 
From these outcomes, it is noteworthy that the mean and the standard deviation of the 
error in the directivity increase while augmenting the noise.  
Conclusion 
A simulator has been implemented for calculating the errors in the measurement 
parameters of the AUT in a cylindrical near field antenna measurement system. The 
simulator changes the parameters of the measurement system introducing deterministic 
and random errors and evaluating the acquired field through the near field generated by 
the array of dipoles. Afterwards, it calculates the different radiation parameters and 
extracts the results. In addition, through the comparison between the results achieved and 
the infinite far-field the error and the uncertainty on the final outcomes − radiation 
patterns, directivity, beam width, position of the maximum − could be determined. 
Therefore, this simulation tool allows not only to quantify a priori the value of the 
systematic error and the uncertainty introduced in the measurement system but also to 
evaluate the limits of the accuracy in the antenna measurements according to the kind of 
antenna and the mechanical and electrical performances of the systems. 
References: 
[1] F. Martín Jiménez, S. Burgos Martínez, M. Sierra Castañer, J.L. Besada, “Design of a 
Cylindrical Near Field System for RADAR antennas”, Proceedings of the 1st EuCap 
Conference, Nize, November 2006. 
[2] S. Burgos Martínez, F. Martín Jiménez, M. Sierra Castañer, J.L. Besada, “Error 
Estimator in Cylindrical Near Field System for large RADAR antennas”, Proceedings 
of the 1st EuCap Conference, Nize, November 2006. 
[3] W. M. Leach, Jr., D. T. Paris, “Probe Compensated Near-Field Measurements on a 
Cylinder”, IEEE Transactions on Antennas and Propagation, Vol. AP-21, No.4, pp. 
435-445, July 1973.  
[4] Robert S. Elliot, “Antenna Theory and Design”, Ed. Prentice-Hall, Inc., Englewood 
Cliffs, New Jersey.  
 5 
[5] Y. Rahmat-Samii, “Useful Coordinate Transformations for Antenna Applications”, 
IEEE Transactions on Antennas and Propagation, Vol. AP-27, No. 4, pp. 571-574, 
July 1979.  


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Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems

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