Eindhoven University of Technology MASTER Uncertainties of radiated emission measurements in the near-field region Bargboer, G.

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Eindhoven University of Technology

MASTER

Uncertainties of radiated emission measurements in the near-field region

Bargboer, G.

Award date:

2006

Link to publication

Disclaimer

This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration.

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TU Ie

technischf' universiteit eindhoven

Faculty of Electrical Engineering

Division Telecommunication Technology and Electromagnetics Chair of Electromagnetics

Uncertainties of radiated emission measurements in the near-field region

by G. Bargboer EM-r-06

February, ²⁰⁰⁶

Report of Master Thesis performed at TUIe, Electromagnetics Section and Philips Applied Technologies, Eindhoven Supervisor:

II. N. van Dijk (Philips)

DI.ir. M.e. van Beurden (TUIe) Prof. dr. A.G. Tijhuis (TUIe)

Copyright © 2002

Nopart ofthis report may be reproduced by any means, or transmitted, or translated into a machine language without the written pennission ofthe Electromagnetics Section, ITE Division, Faculty of Electrical Engineering, Eindhoven University of Technology.

The Faculty of Electrical Engineering of the Eindhoven University of Technology disclaims all responsibility for the contents of traineeship and graduation reports.

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Abstract

Nowadays, wireless and multimedia systems are rapidly becoming more popular in and around the house. These systems need to be tested for electro-magnetic compatibility (EMC). In this report, we focus on the radiated emission measurements.

Currently, the radiated emission standards are defined from 30 MHz to 1 GHz. Because the new systems typically operate in the GHz range, a new measurement method is required. Such a method defined from 1GHz to 18 GHz, CISPR/NI6-2-3-AMDl, was published in the spring of 2005. In this radiated emission measurement method, it is specified that the maximum ofthe radiated E-field of the Equipment Under Test (EUT) is measured. This maximum should be below the limit in order to qualify the EUT as electromagnetically compatible.

Due to expected dynamic range problems, it is permitted in this new method to decrease the measurement distance to 1m. However, the limits ofthe method are defined at a measurement distance of 3 m. For this reason, a transformation is required from the measured E-field at 1m to an E-field at 3 m. When the measurement is performed in the far field, the simplefar-field

approximation can be used to perform the transformation. However, the measurement distance of 1m is so small that it could be possible that we measure in the near field of the EUT, where the relation between the field and the distance is more complicated.

Whether the measurement distance at 1m is actually in the near-field area is dependent on the measurement frequency and the size of the EUT. The E-field obtained by simulation is subtracted from the E-field obtained by the far-field approximation to quantitatively obtain the uncertainty by using a far-field approximation. The goal ofthis work is to investigate for which conditions the EUT is in the near-field region and to qualify the uncertainty.

The conclusion drawn in this report is that for an large size ofthe EUT or a very high frequency the measurement distance of1 m will be situated in the near field of the EUT and causes large uncertainties of up to 6 dB. Furthermore, an EUT with holes and slots shows an uncertainty up to 2 dB.

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List of abbreviations

B CISPR D E EMC EMI EUT

f

H IEC SVSWR k

&

A Jl

OJ

magnetic field [T]

International Special Committee on Radio Interference electric field density [C/m²]

electric field strength [V1m]

Electromagnetic Compatibility Electromagnetic Interference Equipment Under Test frequency [Hz]

magnetic field strength [Nm]

International Electrotechnical Commission Site Voltage Standing Wave Ratio

wave number [rad/m]

electric permitivity [F/m]

wavelength [m]

magnetic permeability[Him]

angular frequency [rad/s]

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1 Introduction and background

1.1 EMC

Almost all electronic equipment generates electromagnetic fields. These fields can disturb other systems through various coupling mechanisms. An electromagnetic interference (EMI) problem arises when three parts are present: a disturbance source, a victim and a coupling mechanism. When the problem is stated like this, three possible solutions are available. The problem can be solved, by modifying the disturbance source or the victim to decrease the EM!.

Most commonly the coupling mechanism is modified, like putting a box around the source or victim. An example of EMI is the disturbance noticeable on the speaker set of a computer caused by a mobile telephone (GSM). In this case the mobile telephone is the disturbance source and the speaker set the victim as shown in Figure 1.

Disturbance ~ Coupling ... ^Victim

source

...

mechanism ...

Wireless LAN Bluetooth ZigBee GSM DCS DECT

PCs Displays Audio & Video Etc.

Figure1: Triptych ofan interference problem in the basic form with some examples.

The configuration shown in Figure 1 is the EMI triptych. This is the basic diagram of an EMI problem. The speaker set in the example should be protected from this EMI in order to become electromagnetic compatible (EMC).

EMC means that a system fulfils these following three requirements:

1 it does not cause inconvenient interference to other systems (emission issues) ; 2 it is not annoyingly susceptible to emissions from other systems (immunity issues);

3 it does not cause self-pollution.

The International Special Committee on Radio Interference (CISPR) was formed in 1933 to develop uniform standards for the protection of e.g., broadcasting radio [15]. More about CISPR can be found in Section 1.2.

Radiated emission standards are currently defined from 30 MHz to 1 GHz and radiated immunity standards form 80 MHz to 1 GHz.

The examples given in Figure 1 are mostly wireless and multimedia systems. Nowadays, there is a rapid trend to use more and more wireless and multimedia systems in and around the house

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the GHz range. The new wireless multimedia systems are new potential sources or victims of interference to the environment and themselves. The development of new wireless equipment implies a new approach towards the already existing immunity and emission standards.

These new wireless and multimedia systems require new measurement methods to measure radiated emission above 1 GHz. For that purpose, a new measurement method will be introduced in Section 1.3 and will be explained in more detail in Chapter 2.

Broadband Internet

Kids'Room

I~l

~

Living Room

1l1li

...

liiJ., _~~ _~ ^"'14. _Ciiiiii'll

^I ^Wireless_Base

H~~~_ US~"""""""'·:.:!:~:-f~.

^Station

...··dCfapter...···· ...,.:

SL~Oi

^···..

·"1116:

^Bedroom

~...

^.

;;.·/~C-i250 ~

,& i .~~~

4!JfJ...

^Study

i f..' .c;l.

~'~1-1fr

^room.

lW""!is.t

_Q®- ^iPronto _DesXcape

~':

^..

MX6000i (built-in module)

Figure 2: The digital house from the CISPRJI multimedia standardization - RF wireless and immunity report.

1.2 The organisation of CISPR

CISPR is part of the International Electrotechnical Commission (lEC), as shown in

Figure 3. The development and maintenance ofEMC standards (emission and immunity) for radio protection are under auspices of CISPR. CISPR consists of different subcommittees.

CISPR subcommittee A (CISPRJA) is responsible for the development of the basic standards.

One of these basic standards, CISPR-16, describes the general aspects of measurement methods. The development of a new multimedia EMC product standard is under auspices of subcommittee CISPRJI. This new multimedia product standard includes a new measurement method for radiated emission above 1 GHz.

The product standard includes the specific demands of the measurement method and the required limits. CISPRJH develops relevant limits. These limits are recommended to other subcommittees.

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lEC

I

EMC

I

CISPR

CISPRIA IB ID IF IH II IS

*

Basic standards

*

ISM (Medical)

*

Vehicles

*

Domestic and household lighting

*

Spectrum management and protection

*

Multimedia

*

Steering committee

Figure3: Chart ofIEC and related committees.

1.3 Measurement method

A step towards the new multimedia EMC product standard is the development of a new radiated emission measurement method above 1 GHz. The classic radiated emission

measurement method, described in CISPR 16, is defined from 30 MHz to 1 GHz. The limits, usedinthis method, are defined at a measurement distance of 10m (CISPR 22). In the spring of 2005, a new radiated emission measurement above 1 GHz has been developed and

publishedinCISPR/A/16-2-3-AMD1 (Amendment 1). Due to expected dynamic range problems, i.e. when the measurement distance is large, the energy of the field gets very small which could cause measurement difficulties for e.g. the spectrum analyser. For that reason, itis pennitted to decrease the measurement distance to 1 m. The consequence of these small

measurement distances is that measurements could be perfonned in the near field of the Equipment Under Test (EUT). Therefore, it is important to investigate and quantify the deviations, expected if far-field approximations are used while near-field contributions are present. The measurement method is explained in more detail in Chapter 2.

1.4 Goal of the graduation study

The goal of this study is to develop insight in the new radiated emission measurement method

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radiated-emission-measurements due to near-field contributions of the EUT. These uncertainties need to be quantified.

1.5 Approach of the graduation study

To achieve this goal the following steps are taken:

1. analyse the existing near-field to far-field transformations, 2. analyse the new measurement method above 1 GHz, 3. apply the transformation in the new measurement method,

4. perform (numerical) simulations to investigate the transformation,

To analyse near-field to far-field transformations a literature study has been performed. The results of the literature study are described in Annex AI. The near-field to far-field

transformations available from the antenna theory seem to be useful for the goal of this graduation study. The analytical transformation derived in the theory will be applied in the measurement method and analysed to give insight in the physical background of near-field to far-field transformations. There is no intention of actually applying a near-field measurement method in the measurement method, but it is intended to investigate the influence of measuring in the near field. To confirm the analytical analysis, numerical simulations are performed.

Also, these simulations are performed in order to investigate the transformation for more complicated EUT configurations. The results and conclusions are reported and presented in this report.

1.6 Outline of the graduation report

The report starts with the analysis of the measurement method in Chapter 2. Then the near-field to far-field transformations are investigated. An analytical expression is chosen to understand the physical background. In Chapter 3, the analytical transformation equation obtained from the literature study, is applied to the measurement method and some simple examples are given. The analytical cases, EUTs consisting of simple apertures, are further analysed in Chapter 4 by performing Matlab simulations.InChapter 5, numerical simulations are performed for different and more complex EUTs. Finally, conclusions and recommendations are reported in Chapter 6.

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2 Definition of the measurement method above 1 GHz

2.1 Introduction

Since the spring of 2005, a new radiated-emission-measurement method above 1 GHz has been published in CISPR/A/16-2-3-AMD1 (Amendment 1) [16]. In Figure 4, the measurement configuration is shown. The main issues of the method will be discussed step by step.

Receive h antenna Receive antenna reference point

...^, . ..." .

, ,.

B3dB ... ' "

...".

Floor d

...^"...

w EUT

...---^...

,,--t"-- -,,

I I I I I I I I

_,f---I

" , I

" I

" I ... _ - - - -

~' ~'...-.. Absorber

I \ , ~ ,'--_"--+...l'...l'--..lo'...~ - - - - J

\ "'---~ ⁾

"'" " " Turntable

---

---^----,"

~~---" Validated test volume

""" _,,~ """\~

, I

.

⁽

'...-

,,':

- " I

" " - ...- - " , :

- - - - ,I I I I

...I

, _,

I I I

Figure4: Radiation measurement configuration in accordance with [16].

The EUT, Equipment Under Test, is put on a turntable at the measurement distance, d,ofthe receive antenna. The EUT is turned and the receive antenna measures the electric field strength, if needed as a function of height. The goal of the measurement method is to obtain the maximum emission in order to certify or condemn the EUT according to EMC guidelines.

Definitions used in Figure 4:

1 Validated test volume: The volume validated during the site validation procedure (CISPR 16-1-4). Typically, this volume is defined by the largest EUT diameter that can be used in the test facility.

2 EUT: The smallest cylindrical diameter that will fully encompass all portions of the actual EUT, including cable racks and a minimum length of 30 cm of cables. The EUT that is located within this cylinder must be capable of rotating about its centre (typically by a remotely controlled turntable). The EUT must be located within the validated test volume. A maximum of30 cm ofw (see definition ofw below) may be below the height ofthe absorbers on the floor, but only when the EUT is floor standing and cannot be raised above the height of the absorbers.

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3

fh

^dB: The minimum 3 dB beamwidth of the receive antenna at each frequency of interest. 83^dBis the minimum of both the E-plane, commonly vertically polarised, and H-plane, commonly horizontally polarised, values at each frequency and may be obtained from manufacturer data of the receive antenna.

4

4:

The measurement distance. This is measured as the horizontal distance between the periphery of the EUT and the reference point of the receive antenna.

5 w: The dimension of the line tangent to the EUT fonned by 8₃^dBat the measurement distanced. Eq. (1) shall be used to calculate w for each actual antenna and measurement distance used. The values ofw shall be included in the test report.

This calculation may be based on the manufacturer-provided receive antenna beamwidth specifications in Eq. (1).

w= 2d tan (0.58_3dB⁾ (1)

w shall be of the minimum dimension at a measurement distance of 1 m as specified in Table 1.

Table1: Minimum dimensionofwmin.

f e-^3dB ^Wmin

[GHz] [0] [m]

1 60 1.15

2 35 0.63

4 35 0.63

6 27 0.48

8 25 0.44

10 25 0.44

12 25 0.44

14 25 0.44

16 5 0.09

18 5 0.09

When the EUT height exceeds w, a height scan is also required.

6

!J.:

The height of the receive antenna, measured from its reference point to the floor. The height range of the height scan is from 1 to 4 m.

2.2 Quantified uncertainty sources

Most uncertainty sources of this new method have already been investigated, such as turntable step-size, height scan, height-scan step-size, and measurement distance. The measurement distance was examined for far-field conditions only.

The turntable step size is not explicitly given in the method. The step-size should increment with 15° or less. The conclusion drawn in [14] is that the uncertainties caused by the step size are independently of the choice of the value for the fixed step size. The uncertainty of a turntable step-size smaller than20°is smaller than 0.8 dB. The behaviour of the field is the main factor for measurement uncertainty. Itis expected that uncertainty in one measurement for a turntable step will be larger than in another EUT measurement because of the different field patterns.

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The conclusion drawn in [14] is that the height step and height range both influence the uncertainty of measurements. A height step larger than 10 cm will cause an uncertainty larger than 1 dB when the height limit is small, for example 1m.A larger height limit, e.g. 4 m, with height steps up to 50 cm, shows an uncertainty with a maximum of 0.8 dB. Moreover, the interaction between the height step and height range uncertainty factors can be seen as significant. The same conclusion is drawn in [17].

In typical EMC measurements, the interaction between turntable steps, height steps and height range does not need to be considered. If small uncertainty is desired, small turntable steps and small height steps should be used. Increasing the height range of the measurement is helpful to decrease the uncertainty.

In [14], a half-sphere scan step is recommended, in order to decrease the uncertainty developed during the height scan ofthe measurements. In [17], this recommendation is confirmed by a decreased measurement uncertainty of 2 dB.

Finally, the uncertainty ofthe measurement distance, from 3 to 10m, has been investigated in [14]

and [17]. The conclusion drawn in these reports is: when the EDT size is similar to or smaller than the wavelength, the influence of the measurement distance can considered as negligible with respect to the uncertainty of the turntable step size, provided the measurements are performed conform the standard.

When the EDT size is larger than the wavelength, even the measurement distance of 3 m could be in the near field, which gives an additional uncertainty, i.e. an uncertainty caused by near-field contributions.

2.3 Formulation of the problem

The different measurement distances of the EDT or antenna in the measurement area can be divided in different zones conform the antenna theory. These zones are shown in Figure 5.

reactive radiating radiating

near near far

field field field

distance [m]

Figure5: radiation zones at different distances of the antenna under measurement.

The three zones of antenna measurement are reactive near field, radiating near field and radiating far field. The reactive near field is influenced by the material and geometrical properties of the antenna and is the field at the shortest distance of, or even inside, the antenna. The radiating near field is the field at a short distance of the antenna at which the antenna actually radiates and the far field starts from a sufficiently large distance ofthe antenna. In Figure 5, the reactive near field and radiating near field are separated by a distance derived by the wavelength divided by2n. The radiating near field and radiating far field are separated by the expression in which the largest size ofthe radiating source,D,is squared and divided by the wavelength. This distance depends on the

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size of the EDT or the frequency used in the measurements. When the radiating far field starts before the radiating near field, the radiating near-field transition is seen as the distance at which the far field starts. This occurs only when the wavelength is large and the size of the EDT is very small.

The frequency range of the measurement method is defined from 1 GHz to 18 GHz.

The relation between wavelength and frequency is given in the following equation:

A=~.

f

Cois the velocity of light. So, the corresponding wavelengthAat a frequency of 1 GHz is 0.3 m.

With increasing frequency the wavelength decreases according to the equation.

The equation to determine the distance znjwhere the radiating near field starts is given by:

A Co Co 1

Z = - = - - = - = -

nf 2rc 27if w k_o

(2)

In this equationw is the angular frequency. According to Eq. (2) the radiating near field starts at 0.05 m. This distance decreases with the increasing frequency.

In the new method, itis permitted to decrease the measurement distance to 1 m, due to expected dynamic range problems i.e. when the measurement distance is large, the energy of the field gets very small which causes measurement difficulties for e.g. the spectrum analyser.

The consequence of these small measurement distances is the chance to measure partly in the near field of both the EDT and the receive antenna.Itcan be concluded that at 1 m, the measurement is not performed in the reactive near field, because of the calculations above. For this reason, in this report near field means the radiating near field. The measurand of the radiated-emission

measurement is the maximum of the electric field. This means, that the uncertainty of finding the maximum of the field of the EDT is considered.

90 1.5

12 60

\

270 1

^I

o

Figure6: Far field with multiple maxima.

In Figure 6 a field with more than one maximum is shown. In this report the highest maximum will be referred to as the maximum. In Figure 6 this maximum can be obtained at 35°. The maximum will be considered in the evaluation of the EDT.

The effects of measuring in the near field of the antenna are not considered in this report.

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The limits of the radiated emission measurement are defined at a distance of 3 m. This requires a translation of the measurements perfonned at a distance of 1m to a distance of 3 m. When the measurements are perfonned in the far field the translation of theE-fieldmeasurements from 1 to 3 m is in accordance with the far-field approximation:

E(

x,y,z

) =

^jkocosOe-Jkorj-(k k)-^x' ^y ^- C ^•

21ll' r

This equation will be explained in more detail in the next chapter. In this equation theE-field is calculated at a distancer far away of the EDT. This calculatedE-fieldis approximately a constant divided by the measurement distancer.

For that reason, the uncertainty can be quantified, by calculating the difference, !!E,between the use of the near-to-far-field transfonnation and this far-field approximation as shown in Eq. (3).

M

₌

E_dB,_max E 201 ( maxElinear,calculated

J

calculated - dB,maxfar- field approximation

=

oglo E •

max linear, far- field approximation

By investigating the measurements in the near field, the measurement method and its behaviour can be understood well and uncertainty budgets can be derived.

2.4 Simulated EUTs

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The measurement distance at which the far field starts is a function of the frequency that is used during the measurements and is a function of the size of the EDT or antenna. The Rayleigh distanceZRat which the far field starts in Figure 5 can be detennined with the following equation:

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This equation is based on the assumption that when the measurement distance tends to infinity the parabolic phase tenn tends to zero. For more details see Appendix A2.

The transition distance^ZR increases with increasing frequency. The uncertainties due to applying the far-field approximation when measuring in the near field are expected to depend on the sizes of the EDT according to Eq. (4).

Another near-field to far-field transition especially used in the field ofEMC is the Fresnel distance:

This is a more rough approximation for the distance, because in the EMC only the maximum value of theE-fieldis important and not the radiation pattern. The Fresnel distance equation shows for the same EDT sizes a far field starting at a smaller measurement distance,z. The different measurement distances and EDT sizes are shown in Table 2 for a frequency of 1 GHz. This frequency is the operating frequency of the measurement method and the frequency used in most

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simulations. When at 1 GHz the uncertainties become very large, they will be very large at higher frequencies according to Eq. (4).

Table 2: Different measurement distances and EUT sizes.

ZR D^l ZF

[m] [m²1 ^[m]

0.93 0.14 0.12 1.00 0.15 0.13 1.67 0.25 0.21 2.40 0.36 0.30 3.00 0.45 0.38 4.27 0.64 0.53 6.67 1.00 0.83 13.33 2.00 1.67 26.67 4.00 3.33 60.00 9.00 7.50 166.67 25.00 20.83

In Table 2 the different EUT sizes are shown. These sizes can be used to define different EUT categories:

1. EUTs with a near-field to far-field Rayleigh transition:::; 3 m orD²:::;0.45 m²^,

2. EUTs with a near-field to far-field Fresnel transition< 1 and a Rayleigh transition> 3 m or D²between 0.45 m²and 1.2 m²^,

3. EUTs with a near-field to far-field Fresnel transition> 1 m orD²> 1.2 m²^•

Based on these categories the simplest EUT to start with, is the uniform aperture illumination. Flat TV's and instrumentation racks are real-life examples, which can be roughly approximated with these apertures. Analytical and numerical simulations have been performed for these uniform apertures. First, analytically to get insight into the physical background and finally, numerically using a method-of-moments-based computer code. With the numerical approach more complex EUTs can be simulated, like a dipole in a box.

This dipole in a box configuration is chosen, because this configuration has already been used in a former investigation [14]. So, this report contains simulations with a half-wave-Iength dipole in boxes of different sizes. Inth~sebox,es holes of different sizes have been created. A box with a hole is a simple representation of a DVD-player. Ventilation slits can be presented in this

simplification as a box with many small holes. The numerical simulation configuration is shown in Figure 7. The sizes of the different boxes are shown in Table 3.

dipole

Figure 7: Configuration of the dipole in a box.

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Table 3: Boxes used for simulation.

I

^Box

II

^{height [m]}

I

width [m] \ length [m]

I

B 0.92 1 0.2

BI 0.92 1 0.5

C 0.4 0.6 0.1

CI 0.4 0.6 0.2

D 0.2 0.15 0.1

E 1.5 2 0.2

Another aspect, which could influence the far-field distance, is the directivity ofthe EUT.

The estimated directivity relation is given by:

{

1.55,

(Gmax)~ ~[0.577+ln(4(kaY+8ka)+ ^(yl ^],

2 8 ka +I6ka

ka~I

ka >1.

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Here k=21rl'Aand ^a, is the minimal sphere radius enclosing the EUT.

This equation is explained further in reference [13]. This estimated directivity is commonly used for realistic complicated EUTs and not for the simple aperture. The directivity is also dependent on the size of the EUT. Because ofthe frequency of 1 GHz chosen, k will be equal to 20,9 rad/m.

When an aperture with a high directivity is used, the transition distance of the near field to far field will be large as well, because of the focussing of the E-field. Hence, this value will be derived as well for the different EUTs used.

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3 Basic analytical formulations

3.1 Introduction

In this chapter the near-field to far-field transfonnation will be applied to the measurement method as mentioned in Section 1.4. Analytical fonnulations will be derived to perfonn the simulations in the following chapter.

The Fourier transfonnation is used to get a plane-wave spectral representation of the E-field located in(x,y, 0).

00 00

j(kx,kJ=

J

JE(x,y,O)ejkrX+JkyY dxdy

-co-oo

j

is the spectral distribution of the E-field located in(x,y, 0);

k_x is the complex wave number in the x-direction;

Icyis the complex wave number in the y-direction;

E(x,y,O) is a Cartesian component of the E-field located in(x,y,O).

The Helmholtz equation obtained from the Maxwell equation is in this case equal to:

(V

² ⁺kg)E(x,y,z)

= o.

k_ois the elementary wave number in vacuum.

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To calculate the E-field at a measurement distance of 3 m the Helmholtz equation is substituted in the Fourier transfonn:

00

_f I

- 2 + - 2 + - 2û^~2 Û^~2 Û^~2 +ko²

J

(x,y,O)e^jkrx+jkyY_dxdy-O.

-0:>-00

ax

^By

oz

This results in:

From this equation the following equation can be obtained:

00 00

where i(kx' ky 'z)

= JJ

E(x, y, z) ejkrx

+jkyY dxdy.

-00-00

Further,k= is introduced as:

e=e-e-e

z 0 x Y

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This equation substituted has as result, shown below:

As a solution for this equation, see Appendix A2 and [12]:

This results in the inverse Fourier transform as shown below:

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The inverse Fourier transformation is used to derive the E-field at a distancezby integrating a spatial frequency spectrum oyer all frequency components. Hence, to derive the field at another distance a Fourier transformation and its inverse is to be performed. To simplify the equations used for the near-field to far-field transfonnation and to understand the problems that may occur due to the application of this transformation, the transfonnation function is presented in the Cartesian coordinate system.

Because this equation is in Cartesian coordinates, a simple example of a unifonn aperture will be analysed. This is followed by analyses of a slot in an infinitely large perfectly conducting plate and finally, by analyses of an electric dipole.

3.2 Uniform aperture

A unifonn aperture is a simple example of a radiating source. Itis defined by a surface at which the field is linearly polarized and has fixed amplitude,Eo, over the whole aperture.

In Figure 8, the simulation set-up for the unifonn aperture is shown.

t

, x

" , ' . /"1 ,

/1

: ,'/ '" i

1 , ' / . / .

, , ' , , , ' '" I

: /. ,',,'- /0 i

f: ,/' :" .

a . :,', , I I

-- £,~'J~--~---~:)-~---~:)---- ~

EUT ,', I."-b . . ! / z

,/ ;.{ /NF ^I ^/ FF

, bioi, . . ,

" -a" '" I . ' "

" I / • • /

, ' v V

~'

:

y :_,

,

Figure 8: The unifonn antenna simulation set-up.

In Figure 8, the unifonn aperture is shown with the origin in the centre of the aperture surface. The measurement area has thex,y origin also in the centre but at a different z-coordinate. This

measurement area is larger than the aperture in order to get a good view of what is happening with

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the E-fields and can be located in the reactive near field, in the radiating near field or in the radiating far field of the unifonn aperture.

TheE-fieldof a unifonn aperture antenna is given by:

(8) The Fourier transfonn is obtained by using the Fourier transfonnation and Eq. (8) for the unifonn aperture, i.e.,

b a

Ix =

JJE)x,y)ej(krx+kYY)dxdy

= J

JEoej(krx+kYY)dxdy

~ ~~

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This result is expected since the unifonn aperture can be seen as a pulse function.

The distance at which the radiating far field starts depends on the length, a,and width, b,of the aperture according to the Rayleigh criterion. In this report the fixed amplitude,Eois 1 V1m.

When the field at another measurement distance is needed, this Fourier transfonn, Eq. (9), should be inverted at that distance with the inverse Fourier transfonnation given in Eq. (7).

E( ) 1 coJcoJf-(k k) -jkrX-jk Y- jkzdk dk x,y, z

=-()2

x' Y e y ' x Y

27r -oe>-co

The E-field is propagating in the positive z-direction and should decrease while propagating. For that reason k_zshould be positive real or negative imaginary as well. Hence, the following radiation conditions apply.

k_z

= ~

^{kg - k; -}

k~

k_z

=-j~k; +k~

^-kg

o

^5.k; +k~ 5.kg e+e>e_x _Y ₀

Anaditional problem of these conditions is that the solution of the complex,kz,as kxandkymay also be complex.

e=e+e_r _x _Y

k_z

= ~kg

^-ki

There are four possible solutions for k_T:

k_r

=

k~ +jk;

k_r

=

-k~ +jk;

k_{r =k~} - jk;

k_{r =-k~} +jk; where,k~ andk; _~

o.

The real maximum ofkTis ko.Forkl this results in:

(21)

As stated before, k_zshould have a real non-negative and a negative imaginary value. Which values for krcan be chosen, to satisfy this condition is reflected in Figure 9.

kz,k/-plane 1m

o

^k.

Figure9: integration range.

Re

• k.

ko k'r

o

•

k"r

o

-ko

•

The negative imaginairy k_z is required and that is the reason, why only the black points in Figure 9 are important. This results in:

For that reason, kxand kyare given by:

k_x = k~ +_jk~

ky

=

k~+jk;

k_x

=

-k~ - jk~, ky

=

-k~ - jk;.

The equation that should be solved was Eq. (7):

In this equation, the integration range may be complex and extends to infinity and therefore, this integral is hard to evaluate.

This gives a need to try to approximate this integral. The two approximations chosen in this report are the paraxial approximation and the far-field approximation.

3.2.1 Narrow angle or paraxial approximation

The inverse Fourier transformation must be approximated, because the integration range of the inverse Fourier integral is complex and extends to infinity and therefore this integral is difficult to evaluate. This approximation should result in a simple transformation.

The inverse Fourier transform is shown in Eq. (7).

(22)

k_zcan be written in spherical coordinates as is shown:

The Taylor series is given:

k_z

=

^kocosO

=kO(I-~+~-!..-+ J.

2! 4! 6!

De higher order terms can be neglected when 0 « 1 rad (⁼ 56°) as shown in Figure 10.

--cos(9)

--- Taylorseries

,...,

...

I

0.9 0.8 0.7 0.6

1

_ _ _ _ .J ¹ ^_

1 I

I I I

1 1 I I

- - - -

1 I I

I 1 I

I 1 I I ' , ^I

- - - - "1 - - - - -1- - - - - I - - - - -1- - ~

,

- - "I - - - -

I I 1 I ' ,

,

I

I I 1 1 '

- - - - --t - - - - - 1- - - - - -+ - - - - ^{-I -} ^- ^- ^- ^- t-'r

,

I I 1 1 I "

I I 1 1 I ' ...

, ,

60 50

40

10

20

30

9 [0]

Figure 10: Difference of Taylor series of the cosine with the exact cosine.

With increasing

o

the error increases. As a rule of thumb, for 0 =1t/4 (= 45°), the approximation represents the cosine acceptably.

For this reasonk_zcan be approximated as follows, see [7]:

e+e (

e+eJ

^e+e

k=~e-e-e=k

_z ₀ _x _Y ₀ ^1- ^x

e

^Y=k⁰ ^1_1² ^x^k² ^{Y =k- x}⁰ ^2k ^Y.

0 0 0

Hence, Eq. (7) can be written as

The inverse Fourier transform of the frequency spectrum is:

1 '" '"

f ) f ff(k k) -

^jk^{x- jk Y}

(x,y

=-()2

^x' ^y e ^r ^Y dkxdky •

2;r -00--'"

(23)

A standard Fourier transfonn pair is used:

With the actual variables substituted this equation becomes:

The convolution of Fourier transfonns is used:

As a result the equation for the paraxial or narrow angle approximation can be obtained:

E ( )

=

^jko -jkoz"'f "'fE (, ,) -~k:^[(x-x')2^+(y-^y')2]dx '^{d '}

x x,y,z e ax x,y e y.

2:rz -00-'"

(10)

E_axis the amplitude of the aperture andzis chosen to be the propagation direction. The area of integration distances in this equation will be the aperture. In Figure 11, the simulation overview for the paraxial approximation is shown.

"x _:

¹

/

I , , / '

:

~' ^",

I " /

I " "

---

_EDT

~-~iJ::~::~:~:C:o.-

,f I ib

e· --- ,/ ^-J.--- _--~

z

'b: }, ,-

;a, /. ,-

, , ' : .",0

, , ' : /0/

.y :

I I I

Figure 11: Simulation overview for the paraxial approximation.

The aperture is situated in the origin as shown. This aperture radiates a plane wave in the z- direction. In this case the spatial angle is equal to the Cartesian angle. The measurement surface is at a distance of the aperture and the angle,

e,

is defined as the angle between the aperture height and the origin of the measurement surface.

The purpose of the paraxial approximation is measuring in a narrow angle around the z-axis. As stated,

e

cannot be larger than 45 ⁰ because of the limited validity of the used Taylor expansion.

(24)

The equation used for the narrow-angle approximation is obtained with the uniform aperture Eq. (8) substituted in Eq. (10).

'k b a jko [( ,)2 ( ')2]

E(

_x _x,y,z

) ⁼

^~_e^-jkoz

IIE

_oe^-2:; ^x-x ⁺^Y-Y ^dx'd_Y^I

2JlZ _-b-a

(11)

This equation can be used to derive the propagating E-field by means of a plane-wave spectrum in the positive z-direction. Unless stated otherwise,Eo

=

1 V1m, A

=

0.3 m and a large measurement area of x

=

4 m and y

=

4 m will be used in this report.

As an example, for the parameters and uniform aperture sizes ofa

=

1 m and b

=

2 m with at a measurement distance of z = 0.044 m are substituted in Eq. (11). This results in a calculatedE- field as shown in Figure 12.

1.5 ,---,---, 1.5 ,---,---,

...

1

^...

a

^- ^- ^{- - -} - - -

a ¹

^- ^{- -} ^{- -} ^{- -} ^- ^{- -}

- ^> ^...

^I₁

> ^...

^I^I

"0 "0 ^I

- ^t.=

_~^~_I

0.5

^- ^{- -} ^{- -} ^I

,---

^I

- t.=

^~^I

_0.5

^{- -} ^- ^{- -} ^-1-^I¹ ^- ^- ^{- - -}

I ~ 1

I I

0 0 0

-5 5 -5 0 5

x [m]

_y

[m]

Figure 12: E-field of a uniform aperture of 1 m . 2 mat z= 0.044 m atf= 1 GHz.

At z= 0.044 m, the measurement takes place in the reactive near field of the measurement area.

Figure 12 shows the plane wave spectrum of the E-field. This spectrum has the general shape of the aperture field, but cannot produce the rapid variation in the field near the comers,

Ixl

= a and

lYl

⁼ b,of the aperture. This causes the peaks in the E-field.

Because of the paraxial restriction this approximation should not be applied for this aperture at this short measurement distance.

At z= 1.1 m, the E-field calculated with Eq. (11) results in Figure 13. At a larger distance of the aperture antenna, the shape of the illumination becomes less visible in the radiated E-field. On the other hand, the spectral function becomes more visible. Figure 13 perfectly shows the problem of measuring in the near field, i.e. the maximum in this case is aty = 0.5 m. The far field, however, has its maximum aty= 0, this introduces a difference when using the far-field approximation while measuring in the near field. Whether this will result in a large deviation will be determined in the next chapters of this report.

At z= 15 m the E-field calculated with Eq. (11) results in Figure 14. Far away from the aperture plane, the field behaves like an expected sine-function. The amplitude of the field becomes a monotonously decreasing function, by a factor 1/r,of the measurement distance. The field distribution is equal to the calculated frequency spectrum, Eq. (9).

(25)

2 ,---,---, 2.---,---.,

5

I I - I -

I I I - I -

I I

o

u"!!!!!.~_L...-~~~I

-5 0 5

y

[m]

1.5

0.5 o

~rm:.~--L~~~~

-5 0

x [m]

1.5

^- ^- ^- ^- ^{- -} ^- ^{- -} ^{- - -}

,...., ,....,

e e

~ ~

... ...

"0

1

- - - - - - - -

---J

"0

-

^~ ^I

-

^~

I;: ^I I;:

I I ^I

~ I- ~

0.5

^{- -} ^- ^{- -}

Figure 13: E-field ofa unifonn aperture 1m' 2 matz= 1.1 m forf=1 GHz.

o

O~---'---'

-5 0 5 -5 0 5

x[m] y[m]

Figure 14:E-field of a unifonn aperture 1m' 2 m atz= 15 m forf= 1 GHz.

0.5 0.5

0.4 0.4

,...., ,....,

e e

~

... 0.3

_~

... 0.3

"0 "0

-

^~

0.2 -

^~

0.2

I;: I;:

I I

~ ~

0.1 0.1

In Figure 15, the field distribution in the measurement plane is shown for increasing measurement distancez. Figure 15 clearly shows what happens if the measurement distance is increased. First, the shape of the aperture is clearly visible with peaks all over the surface, then fewer peaks are left but the shape of the aperture is still visible. At the measurement distance of 3 m one dominant peak becomes visible and at a larger distance such as 15 m only this peak remains. Also, the changing shape of the field is shown, i.e., the aperture has larger length than width and in the far field this is shown as an interchanged field pattern. The small side creates a narrow large bundle, which needs space to spread. This explains the large influence of this side at a large distance.

(26)

a b c

4 4 1.5 4

1.2 1.5

2 1 2 2

g

₀ ^0.8"§' ₀

g

₀

~ 0.6 ';: _~

0.4 0.5

-2 -2 -2

0.2

-4 -4 -4

-4 -2 0 2 4 -4 -2 0 2 4 -4 -2 ⁰ 2 4

x[m] x[m] x [m]

d e f

4 ^1.2 4 4

2 2 0.8 2

g

₀ 0.8_0.6

g

0 ^0.6"§'

...

0

~ 0.4 ~ 0.4 ~

-2 -2 -2

0.2 0.2

-2 ⁰ 2 4 -4-4 -2 0 2 4 -2 ⁰ 2 4

x[m] x[m] x[m]

Figure15: The field distribution in the measurement plane of 1 m . 2 m at a)z= 0.044 m, b)z

=

0.5 m, c)z⁼ 1.1 m d)z⁼ 3 m, e)z⁼ 5 m andf)z

=

15 m.

3.2.2 Far-field approximation

The other approximation to simplify the inverse Fourier transformation is the far-field

approximation. Inthis section this approximation is analysed. The far-field region of the uniform aperture dimensionsa= 1 m andb

=

2 m starts atZR

=

13 m.

In Figure 8 on page 22, the centre of the measurement area is chosen at(O,O,z). In this direction, the uniform-aperture far field has its maximum as demonstrated in Figure 14.

The far-field approximation equation is (see Annex A2):

(12)

Assume uniform aperture sizes ofa= 1 m and b= 2 m with at a measurement distance ofz= 15 m.

The value for the E-field atx= 0 andy= 0 can be derived as follows:

1 0.5 ( )

Ix

=

I Ie}

^kxx+kyY ^dxdy

⁼

2sinc(0.5kJsinc(k

y)'

-1-0.5

As before

k_z

=

^k_o^cosB ^for^k; <kg k;

=

^kg^sin²^B

k_x

=

sinBcoscp k_y

=

sinB sin cp

(27)

The maximum is expected on the z-axis or at

e

⁼ ^0:

Then the maximum of the E-field will be:

E

=

¹ ^e-/20.9·15

f = 2.~.

^e-/20.9·15

=

^0.44V/m.

0.3.15 x 9

E

=

0.44Vimis the maximum value positioned atx= 0 andy= 0 and is shown in Figure 14.

This far-field approximation is only valid in the far field and the subject of investigation is the near-field to far-field transformation. This is the reason why this far-field approximation will not be used for the analytical analyses and the paraxial approximation will be used in the analyses performed on the uniform aperture in the next chapter. In the next section a physically more realistic behaviour of an antenna will be introduced.

3.3 Slot in perfectly conducting infinitely large plate

The uniform aperture is a theoretical model and to get a physically more realistic model, a slot in a perfectly conducting infinitely large plate, will be analysed in this section. Figure 16 shows the slot in a infinitely large perfectly conducting plate.

y

Figure 16: Slot in perfectly conducting infinitely large plate.

In Figure 16, the length of the slot at they-axis is equal to 2b and the width at the x-axis is equal to 2a. The origin is again at the centre ofthe aperture. Itis expected that the E-field propagates in the direction of the z-axis. This axis is perpendicular in relation to the shownx,y-plane. The E-field equation of the slot is given by:

(13) This equation satisfies the boundary condition. Wheny

=

0 andy

=

b the cosine is equal to zero.

This can be observed in Figure 17.

(28)

width

length

Figure 17: Cosine aperture representation.

The Fourier transform can be derived, by substituting Eq. (13) in the Fourier transformation Eq. (6), i.e.,

~(

⁾ ^b

_f ^of ^{ ^{70/ )}

^{(k x+k} ⁾ ^E ⁽ ⁾^2;r ^cos(k ^b)

f

^{k k}

=

E co - e^J ^r ^yYdxdy=-_o sin k a - ^{Y .}

x' ^Y -b-o

°

^2b ^kx ^x ^b

e _ ()2 !!-

Y 2b

(14)

To find the paraxial approximation for this representation, Eq. (13) is substituted in the general paraxial approximation Eq. (10):

E ( )-

^j2;r ^-Jkoz

bfOfE . ^(70/')

-~k;[(x-x,y+(y-y'Yldx'd ^'

x x,y,z - e

°

cos e y.

koz ^-b-o 2b

(15)

This equation can be used to derive the propagating E-field of a slot.

With aperture distances ofa

=

1m, b

=

2m at a distance ofz= 1.11 m in the near field of the aperture substituted in Eq. (15), yields an E-field as is shown in Figure 18.

1.5

,..---~---,

1.5

, . . - - - . - - - " 1 I

I I I I I I I

- - - - - - - I -

I I I I

"5 ¹

~ ...

"C

-

l.;::^~

~

0.5

- - - - I I I I I

I

,---

I I I

o

'~I..!....!..lU=_ _L--_.:....!...L~~I

0

^{L -_ _}~_---l...-_~_ _----l

-5 0 5 -5 0 5

X

[m] y [m]

Figure18:E-field atz⁼ 1.11 m and forf= 1 GHz.

"5 ¹

~ ...

"C

-

^l.;::^~

~

0.5

In Figure 18 theE-field still resembles some of the general shape of the slot, because of the propagating part of the frequency spectrum and the sine-like function becomes more visible. This

(29)

is similar to the uniform aperture antenna mentioned in Section 3.2. The approximation for the far field for the slot can be calculated by using the following expressions derived by substituting Eq. (14) in Eq. (12):

e-jkor sin(k a) cos(k b)

Eo

=-

jkoEoab--cosBcosrp x y 2'

r kxa _{k b -}² ²

(tr)

_-

y 2

e - jkor sin(k a) cos(k b)

E

=

J'k E ab--cosBsinm x y

f/J

0 0

_r ^'t' ^k_xa _{k b -}₂ ₂

(2'

_-

tr)

y 2

The paraxial approximation is found to be also useful to analyse a slot in a perfectly conducting infinitely large plate. These analyses will be performed in the following chapter. In the next section an electric dipole will be analysed to create a background for the numerical analysis.

3.4 Electric dipole

Finally, the electric dipole is analysed in this section to create a background for the numerical analysis. The set-up for the electric dipole is shown in Figure 19.

z Ee

Figure19: Electric dipole set-up.

The dipole is situated in the origin of the coordinate system. The z-axis is again chosen to be the propagation direction. For that reason, the dipole is situated in the x-direction. The angle\jI is the angle between the z-axis and the measurement point. The equations for deriving the E-field of an electric small dipole, like a Hertzian dipole, are:

E_r

=

-J'_2-1.Idx Z cos",(jk₀ _.,. ₂^o

+~)e-jkOr

₃ _'

11,1<.0 r r

E = J - -. Idx

z'

osmlf/ - - - eO.^(k; ^jko 1

J

^-)k^r

'I' 4nk_o r r² r³

In this equationI is the current and r is in this case equal to the measurement distance.

The reactive near field and radiating near field, are presented in this equation by the 1fr³en l/r² terms, respectively.

(30)

The far-field approximation for a dipole can be calculated from the equation

E - . IdxkoZ ' . -jkor 'If - J - - 0smVI e .

4nr

The far field begins at a large distance from the dipole so the IIr³en l/r²terms are very small compared to the llrterm.

The directivity of a Hertzian dipole can be calculated and is equal to 1.5.

3.5 Conclusions

In the analysis of the uniform aperture it is found that uncertainties can be expected when measuring in the radiating near field of an EDT. The phenomena consist of expecting the maximum of the E-field at another position. One of the problems is using the far-field

approximation, when it should not be used, to calculate the E-field.Aninteresting example of the stated problem is shown in Figure 13 on page 28. In this figure the maxima are found in other directions than expected based on the far-field approximation.

Eindhoven University of Technology MASTER Uncertainties of radiated emission measurements in the near-field region Bargboer, G.

TU Ie

Abstract

Contents

List of abbreviations

f

1 Introduction and background

1.1 EMC

...

I~l

1l1li

...

liiJ., ~~ ~ "'14. Ciiiiii'll

H~~~_ US~"""""""'·:.:!:~:-f~.

SL~Oi

·"1116:

~...

;;.·/~C-i250 ~

4!JfJ...

~'~1-1fr

lW""!is.t

~':

1.2 The organisation of CISPR

I

I

*

*

*

*

*

*

*

1.3 Measurement method

1.4 Goal of the graduation study

1.5 Approach of the graduation study

1.6 Outline of the graduation report

2 Definition of the measurement method above 1 GHz

2.1 Introduction

---

""" ,,~ """\~

.

,,':

, ,

fh

4:

!J.:

2.2 Quantified uncertainty sources

2.3 Formulation of the problem

f

90 1.5

12 60

270 1

o

E(

) =

=

J

=

2.4 Simulated EUTs

I

II

I

I

(Gmax)~ ~[0.577+ln(4(kaY+8ka)+ (yl ],

3 Basic analytical formulations

3.1 Introduction

J

j

(V

= o.

f I

J

ax

oz

= JJ

e=e-e-e

3.2 Uniform aperture

t

/1

-- £,~'J~--~---~:)-~---~:)---- ~

liiJ., _~~ _~ ^"'14. _Ciiiiii'll

""" _,,~ """\~

, _,

₌

(Gmax)~ ~[0.577+ln(4(kaY+8ka)+ ^(yl ^],

_f I

"x _:

e· --- ,/ ^-J.--- _--~

) ⁼

a ¹

- ^> ^...

> ^...

- ^t.=

_0.5