EUTs with D 2 larger than 1.2 m 2

For EUTs with an aperture larger than 0.60 m²a Fresnel transition starts beyond 1 m. With EUT sizes of a square of 0.80 m at a distance ofz

=

1 m andz

=

3 m and all other parameters as in the previous section, results in an E-field as shown in Figure 25. In Figure 25 the effects of measuring in the near field and using the far-field approximation are demonstrated clearly. At^z= 1 m the maximumE= 1.66Vim. The far-field approximation results inE= 0.55Vimatz= 3 m. The maximum of the E-field calculated atz =3 m is 0.69Vim. This results in a M of2.0 dB.

For an EUT aperture equal to 1 m²at a distance ofz= 1 m the E-field is calculated and can be observed in Figure 26. Two sinc-like functions are demonstrated again in Figure 26. The shape of the aperture illumination is visible. Atz

=

1 m the maximum isE=1.76Vim. The far-field approximation results in a maximum ofE= 0.59Vim atz= 3 m. The maximum calculated at z⁼ 3 m isE= 1.04 V1m. This results in a M of 4.9 dB.

In the measurement method it is stated that for an EUT of the size 1.15 m the measurement can be performed without a required height scan. In Figure 27 is the 3-dimensional E-field of this square aperture atf= 1 GHz shown. Figure 27 shows the near-field effects are becoming more visible.

This will increase thet1E.

1 I 2:-1m

1.5

- - - -1 - - - -I

1.5

₁

...

(z~lm)13

1 1 1 - - - - - z-3m

1 I ₁

,...., _{I I} ,...., _{1 1}

e

1 ^{I I}

e

^I _ _ _ 1 _ _

->

- - - -

->

¹

I I _{I 1}

...

I I ...

"'0 "'0 ^{I I}

-

_~^{~ I1 I1}

-

_f;:^~

^....

^II ^II

I _ _ _1 _ - _-.J ___ I _.1~

__

r-::l

0.5

_{I I} r-::l

0.5

_I

1 I _I

1 I 1

. -4 -2 0

2

4 -4 -2 0

2

4

x [ro]

y

[ro]

Figure 25: E-Field of square EUT aperture of 0.64 m² atz= 1 m andz

=

3 m andf= 1 GHz.

4

Figure 27: 3-dimensional E-field of a square aperture of 1.32 m2 at/=: 1 GHz.

For the far field derived with a Fresnel transition starting beyond 3 m the aperture should be larger than 2 m^2•The uniform aperture has an unrealistic size ofa=: b =: 5 m. Atz=: 1 m this results in an E-field as is shown in Figure 28. Figure 28 shows the E-field of a very large EUT at a very short distance, which shows the near-field effects very well. The shape of the aperture illumination is visible. The maximum forz=: 1 m is E=: 1.3 V1matx=:2m and forz =: 3 m the maximum of E=: 1.3 V1mis found atx=: 1.6 m. When theE-field atz=: 3 m is calculated atx=:2m it is expected to beE=: 1.0 V1m. The relative!!J.Ein this case is 1.9 dB. The far-field approximation results in anEof 0.42 V1m. This results in a!!J.Eof 8.0 dB. The maximum atz=: 3 m in comparison with the expected value ofE=: 0.42Vim would result in a difference!!J.E of9.9 dB. This large deviation is partly due to the fact that Eq. (11) is not valid atz=: 1 m for an aperture of this size and partly due to measuring in the near field ofthe EUT.

1.2

...-.

1

;> e 0.8 ...

"0

~

0.6

f.;::

~I

0.4 0.2

-4 -2 0

x [m]

2

4 -4 -2 o

y

[m]

2

- - - z = l m

••••••••••• (z=1m)13

4

Figure 28:E-field ofa square EDT aperture of25 m²atz= 1 m and z= 3 m atf= 1 GHz.

4

3 2

1

'E'

₀

"'-'"

>,

-1

-2

-3

-4-4 -2 0 2 ⁴

x [m]

Figure 29: 2-dimensional distribution of theE-field of an aperture of 25 m²at z⁼ 1m and f= 1 GHz

The distribution of the E-field of the aperture of25 m²in the measurement area at z= 1 m is shown in Figure 29. The peaks in the E-field are shown perfectly in Figure 29. The positions at which the E-field is added or subtracted are shown in the peaks and valleys in the figure.

4.2.4 Evaluation of the analytical results of the square uniform aperture

In the case that the uniform EUT aperture is smaller than 0.15 m²and the far field starts at z = 1 m the near-field effects are negligible. When the aperture gets larger than 0.64 m²the far field starts after 3 m and near-field effects could influence theE-fieldcalculations. These near-field effects consist ofE-fieldmaxima at off-axis locations as is shown in Figure 28. When the aperture gets larger than 9 m²these near-field effects occur throughout the whole measurement range from z= 1 to 10m. Also the paraxial approximation applies at z = 1 m only to an aperture with a maximum of 1 m², due to the demand that

e:s

^45°. In Figure 30 theE-field of different square EUT sizes is given at different distances,z, ofthe EUT.

--0.38

m

* 0.38

m

Figure 30:The E-fieldfor different square EUT sizes at differentz atf= 1 GHz.

--0.38

m

* 0.38

m

Figure 31:The peak values of the E-fieldfor differentz andf=1 GHz.

In Figure 30 the E-field calculated for the square apertures, with the paraxial approximation is shown in dBV1magainst the measurement distancezin m. The marks are the distances from which

the far-field approximation is valid. The E-field representation in Figure 30 starts at different z-values for the different apertures, because ofthe demand of

e:s

45°.

The conclusion drawn here is when the EUT aperture is small, the distance at which the l/r approximation can be used, starts at the measurement distancez⁼ 1 m. With increasing aperture the near-field effects start to enter the specified measurement region and cause problems in the use of the far-field approximation for deriving the E-field. The comers of the aperture will be

responsible for peak values in the measurement. In Figure 31 these peak values indicated by marks are shown. Only, the largest aperture shows the peak values. In the E-field at this measurement distance the shape ofthe aperture illumination form is visible, which causes these peak values.

These peaks occur at the comers ofthe aperture. This effect is neglected in the far-field approximation and therefore causes the deviations.

Figure 30 can be translated into a table, which contains the deviation between the results obtained by the far-field approximation and the results obtained by using the paraxial approximation. This deviation is obtained by taking the whole measurement distance range form 1 to 10m into account.

The estimated directivity is derived with Eq. (5). This is also given in Table 4.

Table 4 :Difference between the use of the far-field approximation in the near field for square apertures in dB and the directivityatf= 1 GHz.

Length Width Surface t!E <Gmax>

[m] [m] [m²] [dB] [dB]

0.38 0.38 0.14 0.11 2.86

0.4 0.4 0.16 0.14 2.91

When the aperture becomes larger the deviation increases. Because of the angle restriction, the paraxial approximation equation as used up to now, is not valid for larger apertures at these

measurement distances. This is probably the reason for the very large deviation for large apertures.

For that reason numerical simulations are performed.

In document Eindhoven University of Technology MASTER Uncertainties of radiated emission measurements in the near-field region Bargboer, G. (pagina 34-38)