8. Electromagnetic sources

Amelet HDF defines six kinds of electromagnetic sources :

  • Plane wave

  • Spherical wave

  • Generator

  • Dipole

  • Antenna

  • Source on mesh

They are all associated with an Amelet HDF category :

electromagneticSource/
|-- planeWave/
|-- sphericalWave/
|-- generator/
|-- antenna/
`-- sourceOnMesh/

8.1. The magnitude element

Elements in /electromagneticSource often contain a magnitude child that is a floatingType and represents the magnitude of a source (current generator, voltage generator, plane wave…).

magnitude has two important attributes :

  • delay. If the magnitude is defined in the time domain, delay which is a real HDF5 attribute for a time value in second represents a delay to add to the values of the floatingType.

  • automaticMaximumValue. automaticMaximumValue is a real HDF5 attribute. If it is present, magnitude values must be scaled in order to make the maximum value magnitude equals automaticMaximumValue.

8.2. Plane wave

The category /electromagneticSource/planeWave contains plane wave definitions.

A plane wave is defined by :

  • A null phase point (xo, yo, zo) in meter.

  • A direction of propagation in polar coordinates, in degree:

    • \(\theta\), where \(\theta \in [0, \pi]\)

    • \(\varphi\), where \(\varphi \in [0, 2 \pi[\)

  • A polarization type :

    • linear, it is defined by the angle \(\psi\) in degree

    • elliptical, it is defined by \(E_{\theta}\) and \(E_{\varphi}\) that are complex electric components

  • An electric field magnitude in volt per meter

The null phase point (xo, yo, zo) appears as three HDF5 real attributes xo, yo, zo.

In the global cartesian coordinate system, a spherical coordinate system is defined by the two angles \((\theta, \varphi)\) which induce the three unit vectors \((\vec{u}_r, \vec{u}_{\theta}, \vec{u}_{\varphi})\).

The propagation vector is \(\vec{k}=-\frac{2\pi f}{c}.\vec{u}_r\)

and the coordinates of \((\vec{u}_r, \vec{u}_{\theta}, \vec{u}_{\varphi})\) in the global (x, y, z) coordinate system are :

\(\vec{u}_r = \begin{pmatrix} \sin\theta.\cos\varphi \\ \sin\theta.\sin\varphi \\ \cos\theta \end{pmatrix}\), \(\vec{u}_{\theta} = \begin{pmatrix} +\cos\theta.\cos\varphi \\ +\cos\theta.\sin\varphi \\ -\sin\theta \end{pmatrix}\) and \(\vec{u}_{\varphi} = \begin{pmatrix} -\sin\varphi \\ +\cos\varphi \\ 0 \end{pmatrix}\)

_images/sphericalcoordinatesystem.png

Fig. 8.1 Wave plane definition

The electric field vector is \(\vec{E} = E_o e^{-j\vec{k}.\vec{r}}(E_{\theta}.\vec{u}_{\theta} + E_{\varphi}.\vec{u}_{\varphi})\) where \(E_o\) is the magnitude, \(E_{\theta}\) and \(E_{\varphi}\) are complex numbers (this allows to describe linear polarization and elliptical polarization)

Warning

\(E_{\theta}\) and \(E_{\varphi}\) satisfy the condition \(\|E_{\theta}.\vec{u}_{\theta} + E_{\varphi}\vec{u}_{\varphi}\|\) = 1

The magnetic field is \(\vec{H} = \frac{1}{\eta \|\vec{k}\|}.\vec{k}\wedge\vec{E}\), \(\eta\) is the wave impedance of the medium.

In Amelet HDF a plane wave is described as follows. A plane wave is a named HDF5 group.

The direction of propagation is given by :

  • theta, a real HDF5 attribute, it is an angle in degree and corresponds to \(\theta\)

  • phi, a real HDF5 attribute, it is an angle in degree and corresponds to \(\varphi\)

The polarization can be “linear” or “elliptic” :

  • If the polarization is linear, the HDF5 real attribute linearPolarization gives the value of the polarization in degree, it corresponds to \(\psi\) defined by \(E_{\theta}=\sin\psi\) and \(E_{\varphi}=\cos\psi\).

_images/linearpolarizationangle.png

Fig. 8.2 Linear polarization definition

  • If the polarization is elliptical, the HDF5 complex attributes ellipticalPolarizationETheta (corresponding to \(E_{\theta}\)) and ellipticalPolarizationEPhi (corresponding to \(E_{\varphi}\)) give the definition of the polarization.

The magnitude is an Amelet HDF floatingType in volt per meter.

Example :

data.h5
`-- electromagneticSource
    `-- planeWave
        |-- $plane-wave1[@xo=0.0
        |   |            @yo=0.0
        |   |            @zo=0.0
        |   |            @theta=0.0
        |   |            @phi=0.0
        |   |            @linearPolarization=0.0]
        |    `-- magnitude[@floatingType=arraySet]
        `-- $ellipt-wave1[@xo=0.0
            |             @yo=0.0
            |             @zo=0.0
            |             @theta=0.0
            |             @phi=0.0
            |             @ellipticalPolarizationETheta=(0.0, 0.1)
            |             @ellipticalPolarizationEPhi=(0.0, 0.0)]
            `-- magnitude[@floatingType=arraySet]

8.3. Spherical wave

The category /electromagneticSource/sphericalWave contains spherical wave definitions.

A spherical wave is defined by :

  • A null phase point (xo, yo, zo) in meter.

  • A power magnitude in watt. magnitude is a floatingType

Example :

data.h5
`-- electromagneticSource
    `-- sphericalWave
        `-- $a_spherical_wave[@xo=0.0
            |                 @yo=0.0
            |                 @zo=0.0]
            `-- magnitude[@floatingType=arraySet]

8.4. Generator

Generators are multi-pole electric devices and there are four kinds of generator in Amelet HDF :

  • the voltage generator

  • the current generator

  • the power generator

  • the power density generator

In Amelet HDF, generators are in the /electromagneticSource/generator category.

A generator in a named HDF5 group with two floatingType children :

  • innerImpedance representing its inner impedance in ohm.

  • magnitude which is the magnitude of the signal. It is a real Amelet HDF parameter, its unit is

    • volt if it is a voltage generator

    • ampere if is a current generator

    • watt if it is a power generator

    • wattPerCubicMeter if it is a power density generator

In addition it can have three optional attributes :

  • delay, HDF5 real attribute in second, it is time delay applied to the magnitude

  • initialValue, an HDF5 real attribute, it is initial value expressed in same unit as the magnitude

  • maximumValue, an HDF5 real attribute, the maximum value is fixed by this attribute, a function is applied to magnitude to obtain those values, same unit as magnitude.

Example

data.h5
|-- physicalModel
|   `-- multiport
|       `-- $imp1
`-- electromagneticSource
    `-- generator
        `-- $a-generator[@type=current]
            |-- innerImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(10,0)]
            `-- magnitude[@floatingType=singleReal
                          @value=10.0]

8.5. Dipole

The category /electromagneticSource/dipole contains dipole definitions.

A dipole is a thin wire (the wire radius is wireRadius in meter), its type can be electric (with a length in meter) or magnetic (with a radius in meter). Then, it is localized in the 3d space (x, y, z) and rotated (theta, phi).

A dipole has a floatingType child loadImpedance representing its load impedance in ohm.

Example, this Amelet HDF instance has two dipoles definition data.h5:/electromagneticSource/dipole/elec-dipole and data.h5:/electromagneticSource/dipole/mag-dipole

data.h5
`-- electromagneticSource
    `-- dipole
        |-- $elec-dipole[@type=electric
        |   |            @x=0.0
        |   |            @y=0.0
        |   |            @z=0.0
        |   |            @theta=0.0
        |   |            @phi=0.0
        |   |            @length=0.2
        |   |            @wireRadius=1e-4]
        |   |-- innerImpedance[@floatingType=singleComplex
        |   |                  @physicalNature=impedance
        |   |                  @value=(10,0)]
        |   `-- magnitude[@floatingType=singleReal
        |                 @delay=0.0
        |                 @value=10.0]
        `-- $mag-dipole[@type=magnetic
            |           @x=0.0
            |           @y=0.0
            |           @z=0.0
            |           @theta=0.0
            |           @phi=0.0
            |           @radius=0.2
            |           @wireRadius=1e-4]
            |-- innerImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(10,0)]
            `-- magnitude[@floatingType=singleReal]

8.6. Antenna

Amelet HDF proposes a general description of an antenna, however some predefined antennas are suitable. An antenna is a named group child of /electromagneticSource/antenna category.

An antenna is defined by some electrical characteristics and radiating characteristics.

8.6.1. Electrical properties

The electrical properties are :

  • The efficiency. The efficiency is an optional real HDF5 attribute.

  • The input impedance. The inputImpedance is an optional floatingType element, its physicalNature is impedance vs frequency.

  • The load impedance. The loadImpedance is an optional floatingType element, its physicalNature is impedance vs frequency.

  • The feeder impedance. The feederImpedance is an optional floatingType element, its physicalNature is impedance vs frequency.

  • The magnitude. The magnitude is an optional floatingType element.

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $antenna1[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            `-- magnitude[@floatingType=arraySet]

8.6.2. Radiation properties

The radiation properties of an antenna can be numerical or expressed thanks to a predefined model. The type of an antenna is expressed in a model child HDF5 group which has a type string attribute :

Example for a rectangular horn :

data.h5
`-- electromagneticSource/
    `-- antenna/
        `-- $antenna1[@efficiency=0.5]
            `-- model[@type=rectangularHorn
                      ...]

8.6.2.1. Numerical values

An antenna can be described by one of the following quantities :

  • The gain

    • it depends on theta, phi and the frequency.

    • gain is a floatingType element child of the model group .

    • type equals gain

  • The effective area

    • It depends on theta, phi and the frequency.

    • effectiveArea is a floatingType element child of the model group.

    • type equals effectiveArea

  • The far field

    • It depends on theta, phi and the frequency.

    • farField is a floatingType element child of the model group.

    • type equals farField

All these quantity are expressed in the global spherical coordinate system :

_images/sphericalcoordinatesystem.png

Fig. 8.3 Spherical coordinate system definition

Example of an antenna defined by its gain :

data.h5
`-- electromagneticSource/
    `-- antenna/
        `-- $antenna1[@efficiency=0.5]
            `-- model[@type=gain]
                `-- gain[floatingType=arraySet]

8.6.2.2. Predefined antennas

In addition, an antenna can be one of the following predefined types :

  • A rectangular horn optionally with a reflector. The horn’s aperture is in the xOy plane and radiates toward the positive-z.

    • apertureLargestDimension.

      • It is a real HDF5 attribute.

      • It is the aperture’s size in the largest dimension

      • A length in meter

    • apertureSmallestDimension

      • It is a real HDF5 attribute.

      • It is the aperture’s size in the smallest dimension

      • A length in meter

    • flareAngleLargestDimension

      • It is a real HDF5

      • It is the flare angle in the largest dimension

      • A angle in degree

    • flareAngleSmallestDimension

      • It is a real HDF5

      • It is the flare angle in the smallest dimension

      • A angle in degree

  • A circular horn optionally with a reflector. The horn’s aperture is in the xOy plane and radiates toward the positive-z .

    • apertureDiameter

      • It is a real HDF5 attribute.

      • It is the aperture’s diameter

      • A length in meter

    • flareAngle

      • It is a real HDF5

      • It is the flare angle of the horn

      • A angle in degree

  • A whip antenna. The whip antenna is orthogonal to the xOy plane.

    • length

      • It is a real HDF5 attribute.

      • It is the whip length

      • A length in meter

    • radius

      • It is a real HDF5 attribute.

      • It is the whip radius

      • A length in meter

  • A log periodic antenna. The array of dipole is in yOz plane and radiates toward the positive-z.

    • AngularAperture

      • It is a real HDF5

      • It is the angular aperture of the antenna

      • A angle in degree

    • scaleFactor

      • It is a real HDF5

      • It is the scale factor between two consecutive dipole

      • without dimension

    • firstDipoleLength

      • It is a real HDF5 attribute.

      • It is the length of the first dipole

      • A length in meter

    • lastDipoleLength

      • It is a real HDF5 attribute.

      • It is the length of the last dipole

      • A length in meter

The following sketch summarizes the convention orientation for the predefined antennas :

_images/antenna.png

Fig. 8.4 Predefined antenna

  • A generic antenna is defined by

    • An angularAperture real HDF5 attribute which corresponds to the angular aperture of the antenna.

    • A pattern HDF5 string attribute, its possible values are :

      • omnidirectional

      • gaussian

      • cosecante

_images/genericantenna.png

Fig. 8.5 Generic antenna

Note

A generic antenna has an axis-z revolution symmetry

We have seen that a horn antenna could have a reflector. Only parabolic reflector is defined in Amelet HDF.

A parabolic reflector is a parabolicReflector HDF5 group contained in the model group if type is rectangularHorn or circularHorn.

Parabolic reflector has three mandatory attributes

  • type. type is a string HDF5 attribute and is either circular or rectangular

    • If type is circular, the diameter attribute is used to give the diameter of the reflector. It is a real HDF5 attribute in meter

    • If type is rectangular, the length and width attributes are used to give the length and the width of

      the reflector. It is a real HDF5 attribute in meter

  • focalLength. It is a real HDF5 attribute in meter, it represents the focal length of the reflector.

  • aspectAngle

Example for a rectangular horn with a circular reflector :

data.h5
`-- electromagneticSource/
    `-- antenna/
        `-- $antenna1[@efficiency=0.5]
            `-- model[@type=rectangularHorn
                |      ...]
                `-- parabolicReflector[@focalLength=0.2
                                       @aspectAngle=1.
                                       @type=circular
                                       @diameter=1.0]

8.6.3. Definition by example

A rectangular horn antenna with a circular reflector :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $rectHorn[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            |           ...
            `-- model[@type=rectangularHorn
                |     @apertureLargestDimension=0.2    # measure : length
                |     @apertureSmallestDimension=0.1   # measure : length
                |     @flareAngleLargestDimension=0.2  # measure : angle
                |     @flareAngleSmallestDimension=0.1 # measure : angle
                `-- parabolicReflector[@focalLength=0.2
                                       @aspectAngle=1.
                                       @type=circular
                                       @diameter=1.0]

A rectangular horn antenna with a rectangular reflector :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $rectHorn[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                  # measure : time
            |           ...
            `-- model[@type=rectangularHorn
                |     @apertureLargestDimension=0.2     # measure : length
                |     @apertureSmallestDimension=0.1    # measure : length
                |     @flareAngleLargestDimension=0.2   # measure : angle
                |     @flareAngleSmallestDimension=0.1  # measure : angle
                `-- parabolicReflector[@focalLength=0.2 # measure : length
                                       @aspectAngle=1.
                                       @type=rectangular
                                       @length=1.0      # measure : length
                                       @with=1.0]       # measure : length

A circular horn antenna :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $circHorn[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            |           ...
            `-- model[@type=circularHorn
                      @apertureDiameter=0.2            # measure : length
                      @flareAngle=0.2                  # measure : angle
                     ]

A log periodic antenna :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $logperiodic[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]
            |           ...
            `-- model[@type=logPeriodic
                      @apertureAngle=0.2
                      @scaleFactor=0.1
                      @firstDipoleLength=0.1
                      @lastDipoleLength=0.7]

A whip antenna :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $whip[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            |           ...
            `-- model[@type=whip
                      @length=0.2                      # measure : length
                      @radius=0.1]                     # measure : angle

A generic antenna :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $generic[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]
            `-- model[@type=generic
                      @angularAperture=0.1
                      @pattern=gaussian]               # omnidirectional
                                                       # gaussian
                                                       # cosecante

An antenna defined by a gain :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $by-gain[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6                  # measure : time
            |             @initialValue=0]
            `-- model[@type=gain]
                `-- gain[floatingType=arraySet]

An antenna defined by the effective area :

data.h5
`-- electromagneticSource
    `-- antenna
        `-- $by-area[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            `-- model[@type=effectiveArea]
                `-- effectiveArea[@floatingType=arraySet]

An antenna defined by the far field :

data.h5
`-- electromagneticSource
    `-- antenna
        -- $by-field[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            `-- model[@type=farField]
                `-- farField[@floatingType=arraySet]

An antenna defined by an exchange surface :

data.h5
|-- mesh
|   `-- $gmesh1
|       `-- $mesh1
|-- exchangeSurface
|   `-- $exchange-surface
`-- electromagneticSource
    `-- antenna
        -- $by-field[@efficiency=0.5]
            |-- inputImpedance[@floatingType=singleComplex
            |                  @physicalNature=impedance
            |                  @value=(50,0)]
            |-- loadImpedance[@floatingType=singleComplex
            |                 @physicalNature=impedance
            |                 @value=(10,0)]
            |-- feederImpedance[@floatingType=singleComplex
            |                   @physicalNature=impedance
            |                   @value=(10,0)]
            |-- magnitude[@floatingType=arraySet
            |             @delay=1e-6]                 # measure : time
            `-- model[@type=exchangeSurface
                      @exchangeSurface=/exchangeSurface/$exchange-surface]

8.7. Source on mesh

8.7.1. Data on mesh

An electromagnetic source can be set by using numerical data on mesh (see Numerical data on mesh for details).

data.h5
|-- mesh
|   `-- $gmesh1
|       `-- $mesh1
|           `-- group
|               `-- $group1
`-- electromagneticSource
    `-- sourceOnMesh
        `-- $by-data-on-mesh[@type=arraySet
            |                @label=Electric field]
            |-- data[@label=electric field
            |        @physicalNature=electricField
            |        @unit=voltPerMeter]
            `-- ds/
                |-- dim1[@label=component x y z
                |        @physicalNature=component]
                |-- dim2[@label=mesh elements
                |        @physicalNature=meshEntity]
                `-- dim3[@label=the time
                         @physicalNature=time
                         @unit=second]

with /floatingType/$dataOne/ds/dim2 :

/mesh/$gmesh1/$mesh1/group/$group1

In the preceding example, data on mesh named data.h5:/electromagneticSource/sourceOnMesh/$by-data-on-mesh is used as an electromagneticSource of type sourceOnMesh. It relies on the mesh group data.h5:/mesh/$gmesh1/$mesh1/group/$group1.

8.7.2. Exchange surface

data.h5
|-- exchangeSurface
|   `-- $exchange-surface
`-- electromagneticSource
    `-- sourceOnMesh
        `-- $by-ex-surf[@type=exchangeSurface
                        @exchangeSurface=/exchangeSurface/$exchange-surface]

8.7.3. Dipole cloud

A dipole cloud source is a source characterized by an optional electric dipole cloud and an optional magnetic dipole cloud. This kind of source is often generated by a signal processing step to obtain an equivalent source which radiates as a given antenna.

A dipole cloud is an arraySet where data are scalar values (electric current or magnetic current) and dimensions are:

  • A mesh support: the edge set which gives the position and the orientation of the dipoles. The edge’s length is important for the dipole cloud source model

  • A dimension which gives the interval and the definition domain of the source: in time or frequency domain

The electric dipole cloud and the magnetic dipole cloud are named respectively electricDipoleCloud and magneticDipoleCloud.

An example of dipole cloud source is given hereafter:

data.h5
|-- mesh
|   `-- $gmesh1
|       `-- $mesh1
|           `-- group
|               |-- $electric-dipole-group
|               `-- $magnetic-dipole-group
`-- electromagneticSource
    `-- sourceOnMesh
        `-- $by-dipole-cloud[@type=dipoleCloud
            |                @label=Patch antenna equivalent dipole cloud source]
            |-- electricDipoleCloud[@floatingType=arraySet
            |   |                   @label=Electric dipole cloud]
            |   |-- data[@label=Electric dipole values
            |   |        @physicalNature=electricCurrent
            |   |        @unit=ampere]
            |   `-- ds
            |       |-- dim1[@label=mesh elements
            |       |        @physicalNature=meshEntity]
            |       `-- dim2[@label=the time
            |                @physicalNature=time
            |                @unit=second]
            `-- magneticDipoleCloud[@floatingType=arraySet
                |                   @label=Magnetic dipole cloud]
                |-- data[@label=Magnetic dipole values
                |        @physicalNature=magneticCurrent
                |        @unit=volt]
                `-- ds
                    |-- dim1[@label=mesh elements
                    |        @physicalNature=meshEntity]
                    `-- dim2[@label=the time
                             @physicalNature=time
                             @unit=second]