9. Physical models

The material models category contains models used in electromagnetic simulation like :

  • Dielectric material

    • Debye material

    • Lorentz material

  • Multi layer material for composite elements

  • Electrical models

  • sub-cellular models

    • Slot model

  • Special interfaces

Sub-categories are documented in the next sections.

9.1. Frequency range of validity

For large spectrum simulation, one material model could not be valid for the entire frequency range, so several models have to be used.

Material model have two optional real parameters (two HDF5 real attributes) :

  • frequency_validity_min is the minimum frequency of validity in Hertz

  • frequency_validity_max is the maximum frequency of validity in Hertz

For example

data.h5
`-- physicalModel/
    `-- volume
        `-- $water[@frequency_validity_min=1e3
                   @frequency_validity_max=1e9]

9.2. Predefined model

Amelet HDF predefines some remarkable materials :

  • /physicalModel/perfectElectricConductor, it is the perfect electric condutor material.

  • /physicalModel/perfectMagneticConductor, it is the perfect magnetic conductor material.

  • /physicalModel/vacuum, it represents the EM vacuum.

Note

Predefined material nodes must exist in the Amelet-HDF instance

data.h5
`-- physicalModel/
    |-- perfectElectricConductor
    |-- perfectMagneticConductor
    |-- vacuum
    `-- volume
        `-- $water[@frequency_validity_min=1e3
                   @frequency_validity_max=1e9]

9.3. Volume

A volume material is a material defined by

  • a relative permittivity (dimensionless)

  • a relative permeability (dimensionless)

  • a electric conductivity (in siemens / meter)

  • a magnetic conductivity (in farad / meter), (this conductivity is used in perfectly matched layers (PML) models for instance).

  • a volumetric mass density (in kilogram / cubic meter)

Such a material is a named HDF5 group child of /physicalModel/volume. The name of the group is the name of the material.

For a material called $diel1 the tree schema looks like

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel1[@volumetricMassDensity=1000.]
            |-- relativePermittivity
            |-- relativePermeability
            |-- electricConductivity
            `-- magneticConductivity

The next sections explain how the four components are defined.

9.3.1. Relative permittivity

The relative permittivity is a named HDF5 group, its name is relativePermittivity and can be expressed in different manners :

  • By a complex value

  • By an array of complex values

  • By a rational function

  • By a general rational function

  • By a Debye model

  • By a Lorentz model

9.3.1.1. Complex value

If the relative permittivity is defined by a complex number, relativePermittivity group is a floatingType singleComplex.

relativePermittivity has no children.

Example :

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- relativePermittivity[@floatingType=singleComplex
                                     @value=(80,0)]

9.3.1.2. Complex Array Set

If the relative permittivity is defined by an array (frequency, values), relativePermittivity group is a floatingType arraySet.

relativePermittivity is then an arraySet structure with :

  • relativePermittivity/data is the relative permittivity values, it’s a one dimension HDF5 dataset

  • relativePermittivity/ds/dim1 is the frequency spectrum, it’s a one dimensensional HDF5 real dataset

Example

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- relativePermittivity[@floatingType=arraySet]
                |-- data
                `-- ds
                    `-- dim1[@physicalNature=frequency
                             @unit=hertz]

9.3.1.3. Rational function

The relative permittivity can also be defined by a general rational function, that is to say a floatingType equals rationalFunction :

Example

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel_rat_func
            `-- relativePermittivity[@floatingType=rationalFunction]

where data.h5:/physical/volume/$diel_rat_func/relativePermittivity :

type

A

B

F

1

1

2

2

3

3

4

5

4

6

7

8

5

9

10

11

9.3.1.4. General rational function

The relative permittivity can also be defined by a general rational function, that is to say a floatingType equals generalRationalFunction :

Example

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel_gen_rat_func
            `-- relativePermittivity[@floatingType=generalRationalFunction]

where data.h5:/physical/volume/$diel_gen_rat_func/relativePermittivity :

$a0

$b0

$a1

$b1

$a2

$b2

.

.

.

.

.

.

$an

$bn

9.3.1.5. Debye model

If the permittivity follows a Debye rule, then the relative permittivity can be a multipole Debye model defined by a list of Debye functions :

\[\hat{\varepsilon}(\omega) = \varepsilon_\infty + (\varepsilon_s - \varepsilon_\infty) \displaystyle\sum_{p=1}^{P} {\dfrac{G_p} {1+j\omega\tau_p}}\]

with the condition that \(\displaystyle\sum_{p=1}^{P} G_p = 1\) .

where :

  • \(\varepsilon_\infty\) is the infinite frequency permittivity

  • \(\varepsilon_s\) is the static permittivity at zero frequency

  • \(\tau_p\) is the characteristic relaxation time of the medium

In Amelet HDF a debye permittivity is an HDF5 group with three attributes and a dataset child :

  • type attribute equals debye, it gives the type of the permittivity definition

  • epsilonStatic is an HDF5 real attribute and gives the static value of the permittivity

  • epsilonLimit is an HDF5 real attribute and gives the limit value of the permittivity

Then, the list of debye functions is an HDF5 dataset named listOfFunctions

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel_debye
            `-- relativePermittivity[@type=debye
                |                    @epsilonStatic=3
                |                    @epsilonLimit=80]
                `-- listOfFunctions

listOfFunctions is a two columns HDF5 dataset of reals :

  • \(G_p\) is written in the first column

  • \(\tau_p\) is written in the second column

$g1

$tau1

$g2

$tau2

$g3

$tau3

9.3.1.6. Lorentz model

If the permittivity follows a Lorentz rule, then the relative permittivity can be a multipole Lorentz model defined by a list of Lorentz functions :

\[\hat{\varepsilon}(\omega) = \varepsilon_\infty + (\varepsilon_s - \varepsilon_\infty) \displaystyle\sum_{p=1}^{P} \dfrac{G_p \omega_p^2} {\omega_p^2+2j \omega \delta_p - \omega^2}\]

with the condition that \(\displaystyle\sum_{p=1}^{P} G_p = 1\) .

where :

  • \(\varepsilon_\infty\) is the infinite frequency permittivity

  • \(\varepsilon_s\) is the static permittivity at zero frequency

  • \(\omega_p\) is the resonant frequency

  • \(\delta_p\) is the dumping coefficient

In Amelet HDF a lorentz permittivity is an HDF5 group with three attributes and a dataset child :

  • type attribute equals debye, it gives the type of the permittivity definition

  • epsilonStatic is an HDF5 real attribute and gives the static value of the permittivity

  • epsilonLimit is an HDF5 real attribute and gives the limit value of the permittivity

Then, the list of Lorentz function is an HDF5 real dataset named listOfFunctions

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel_lorentz
            `-- relativePermittivity[@type=lorentz
                |                    @epsilonStatic=3
                |                    @epsilonLimit=80]
                `-- listOfFunctions

listOfFunction has three columns of HDF5 reals:

  • \(G_p\) is written in the first column

  • \(\omega_p\) is written in the second column

  • \(\delta_p\) is written in the third column

$g1

$omega1

$delta1

$g2

$omega2

$delta2

$g3

$omega3

$delta3

9.3.1.7. Cole-Cole model

If the permittivity follows the Cole-Cole model, then the relative permittivity is defined by the following equation :

\[\hat{\varepsilon}(\omega) = \varepsilon_\infty + \displaystyle\sum_{p=1}^{P} \dfrac{ \Delta \varepsilon_p } {1 + (j \omega \tau_p)^{1-\alpha_p}}\]

where \(\hat{\varepsilon}\) is the complex dielectric constant and:

  • \(\omega\) is the angular frequency

  • \(\varepsilon_\infty\) is the infinite frequency permittivity constant

  • \(\Delta \varepsilon_p\) is the change in permittivity due to the pth dispersion

  • \(\alpha_p\) takes a value between 0 and 1, it allow the description of different spectral shapes (when \(\alpha=0\) the Cole-Cole model reduces to the Debye model).

  • \(\tau_p\) is a time constant

For more complete details see https://en.wikipedia.org/wiki/Cole%E2%80%93Cole_equation

In Amelet HDF a Cole-Cole permittivity is an HDF5 group with four attributes and a dataset child :

  • type attribute equals colecole, it gives the type of the permittivity definition

  • epsilonLimit is an HDF5 real attribute and gives the limit value of the permittivity

Example:

data.h5
`-- physicalModel/
    `-- volume
        `-- $diel_colecole
            `-- relativePermittivity[@type=colecole
                |                    @epsilonStatic=3
                |                    @epsilonLimit=80]
                `-- listOfFunctions

listOfFunction has three columns of HDF5 reals:

  • \(\Delta \varepsilon_p\) is written in the first column

  • \(\alpha_p\) is written in the second column

  • \(\tau_p\) is written in the third column

$deltaEps1

$alpha1

$tau1

$deltaEps2

$alpha2

$tau2

$deltaEps3

$alpha3

$tau3

9.3.2. Relative permeability

The relative permeability is a named HDF5 group, its name is relativePermeability and can be expressed in different manners as the relativePermittivity is expressed :

  • By a complex value

  • By an array of complex values

  • By a rational function

  • By a general rational function

  • By a Debye model

  • By a Lorentz model

  • By a Cole-Cole model

Example of a singleComplex relativePermeability

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- relativePermeability[@floatingType=singleComplex]
                                     @value=(1,0)]

9.3.3. Electric conductivity

The electric conductivity is a named HDF5 group, its name is electricConductivity and can be expressed in different manners :

  • By a real value

  • By an array of complex values that vary with the frequency

The electric conductivity is expressed in siemens.

9.3.3.1. Real value

If the electric conductivity is defined by a real number, electricConductivity group is a floatingType singleReal.

electricConductivity has no children.

Example :

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- electricConductivity[@floatingType=singleReal]
                                     @value=10e-6]

9.3.3.2. Complex ArraySet

If the electric conductivity is defined by an array (frequency, values), electricConductivity group is a floatingType arraySet.

electricConductivity is then an arraySet structure with :

  • electricConductivity/data is the electric conductivity values, it’s a one dimension HDF5 complex dataset

  • electricConductivity/ds/dim1 is the frequency spectrum, it’s a one dimensensional HDF5 real dataset

Example

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- electricConductivity[@floatingType=arraySet]
                |-- data
                `-- ds
                    `-- dim1[@physicalNature=frequency
                             @unit=hertz]

9.3.4. Magnetic conductivity

The magnetic conductivity is a named HDF5 group, its name is magneticConductivity and can be expressed in different manners :

  • By a real value

  • By an array of complex values that vary with the frequency

9.3.4.1. Real value

If the magnetic conductivity is defined by a real number, magneticConductivity group is a floatingType singleReal.

magneticConductivity has no children.

Example :

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- magneticConductivity[@floatingType=singleReal]
                                     @value=0]

9.3.4.2. Complex Array Set

If the magnetic conductivity is defined by an array (frequency, values), magneticConductivity group is a floatingType arraySet.

magneticConductivity is then an arraySet structure with :

  • magneticConductivity/data is the magnetic conductivity values, it’s a one dimension HDF5 complex dataset

  • magneticConductivity/ds/dim1 is the frequency spectrum, it’s a one dimensional HDF5 dataset of reals

Example

data.h5
`-- physicalModel/
    `-- volume
        `-- $water
            `-- magneticPermeability[@floatingType=arraySet]
                |-- data
                `-- ds
                    `-- dim1[@physicalNature=frequency
                             @unit=hertz]

9.3.5. Volumetric mass density

The volumetric mass density is a HDF5 attribute, its name is volumetricMassDensity and is expressed by a real scalar value.

Example :

data.h5
`-- physicalModel/
    `-- volume
        `-- $water[@volumetricMassDensity=1000.]

9.4. Multi-layer

A multi-layer material is a material made up of several physicalModel/volume material layers. Multi-layer materials are stored in the /physicalModel/multilayer/ category.

A multi-layer material is a named HDF5 table of two columns, each row is a new layer (a physicalModel/volume material) and the index is implicit.

Columns definition :

  • physicalModel : A column of 100 characters strings. It’s the absolute name of model defined in /physicalModel/volume.

  • thickness : A column of reals. It’s the thickness of the layer in meter.

Example

data.h5
`-- physicalModel/
    |-- volume
    |   |-- $vol1
    |   `-- $vol2
    `-- multilayer
        `-- $multilayer1

and /physicalModel/multilayer/$multilayer1 is :

physicalModel

thickness

/physicalModel/volume/$vol1

0.1

/physicalModel/volume/$vol2

0.2

/physicalModel/volume/$vol1

0.1

9.5. Anisotropic material

Anisotropy is the property of being directionally dependent, as opposed to isotropy, which means homogeneity in all directions (http://en.wikipedia.org/wiki/Anisotropy).

Each characteristic (permittivity, permeability …) of an anisotropic material can be expressed by a 3x3 tensor, see the example for the permittivity :

\[\begin{split}\begin{pmatrix} \varepsilon_{xx}&\varepsilon_{xy}&\varepsilon_{xz} \\ \varepsilon_{yx}&\varepsilon_{yy}&\varepsilon_{yz} \\ \varepsilon_{zx}&\varepsilon_{zy}&\varepsilon_{zz} \end{pmatrix}\end{split}\]

where elements are the material behaviour in one direction.

In Amelet HDF, instead of defining a tensor for all characteristics, each tensor’s element is a physicalModel and expresses all properties in a given direction. An anisotropic material is then an HDF5 3x3 string dataset, each element of the dataset is a physicalModel absolute name.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   |-- $v1
    |   |-- $v2
    |   `-- $v3
    `-- anisotropic/
        `-- $an1

with /physicalModel/anisotropic/$an1 :

#

0

1

2

0

/physicalModel/volume/$v1

/physicalModel/volume/$v2

/physicalModel/volume/$v3

1

/physicalModel/volume/$v2

/physicalModel/volume/$v1

/physicalModel/volume/$v2

2

/physicalModel/volume/$v3

/physicalModel/volume/$v2

/physicalModel/volume/$v1

=

\[\begin{split}\begin{pmatrix} \text{/physicalModel/volume/\$v1}& \text{/physicalModel/volume/\$v2}& \text{/physicalModel/volume/\$v3} \\ \text{/physicalModel/volume/\$v2}& \text{/physicalModel/volume/\$v1}& \text{/physicalModel/volume/\$v2} \\ \text{/physicalModel/volume/\$v3}& \text{/physicalModel/volume/\$v2}& \text{/physicalModel/volume/\$v1} \end{pmatrix}\end{split}\]

9.5.1. Volumetric mass density

An anisotropic material definition can be completed by an optional attribute named volumetricMassDensity as for volume material.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   |-- $v1
    |   |-- $v2
    |   `-- $v3
    `-- anisotropic/
        `-- $an1[@volumetricMassDensity=1026.]

9.6. Multiport

The category /physicalModel/multiport contains electrical models like localized element (resistance …), multiport models and more complex models like scattering parameters.

There are many sub-types in this category : impedance, admittance, resistance, inductance, capacitance, conductance, s-parameter.

Besides, a multiport can be a scalar, a vector (depending on the frequency) or a matrix, even a matrix depending on the frequency, so the floatingType paradigm is used. By a consequence, a multiport can be defined wherever in a Amelet HDF instance (where Amelet HDF specifies its usage).

As usual, the unit is set by Amelet HDF so the attribute unit are optional.

The number of ports of a multiport is given by the dimension of the floatingType :

  • singleReal : the number of ports is 1

  • singleComplex : the number of ports is 1

  • dataSet : the number of ports is the dimension of the dataSet

  • arraySet : the number of ports is the dimension of the children data element.

9.6.1. Electric potential point

An electric potential point is a point where an electric potential can measured. A voltage can be computed between two electric potential points. In Amelet HDF, an electric potential point can be a multiport port, that is why a new physicalNature is introduced : electricPotentialPoint physical nature.

For instance, when a multiport impedance is written in Amelet HDF by an arraySet, port dimension hold the electricPotentialPoint physical nature :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $resistance[@floatinType=arraySet]
            |-- data[@physicalNature=resistance]
            `-- ds
                |-- dim1[@physicalNature=electricPotentialPoint]
                `-- dim2[@physicalNature=electricPotentialPoint]

9.6.2. Predefined multiports

Amelet HDF predefines three multiports :

  • /physicalModel/multiport/shortCircuit, it is the short circuit model short-cut

  • /physicalModel/multiport/openCircuit, it is the open circuit model short-cut

  • /physicalModel/multiport/matched, it is the the matched model short-cut

Note

Predefined multiport nodes must exist in Amelet-HDF instances

data.h5
`-- physicalModel/
    `-- multiport
        |-- shortCircuit
        |-- openCircuit
        `-- matched

9.6.3. Resistance

A resistance is a floatingType element, with a physicalNature attribute equals resistance.

A resistance can be a singleReal, a dataSet or an arraySet, the unit is ohm.

9.6.3.1. Single real

Example of resistance (a dipole) expressed by a singleReal :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $resistance1[@physicalNature=resistance
                         @floatingType=singleReal
                         @unit=ohm
                         @value=80]

9.6.3.2. Real dataset (matrix)

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $resistance2[@floatingType=dataSet
                         @physicalNature=resistance]

9.6.3.3. Real ArraySet (depends on the frequency)

Example of resistance expressed by an arraySet depending on the frequency :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $resistance2[@floatingType=arraySet]
            |-- data[@physicalNature=resistance
            |        @unit=ohm]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

9.6.4. Conductance

A conductance is a floatingType element, with a physicalNature attribute equals conductance.

A conductance can be a singleReal, a dataSet or an arraySet, the unit is siemens.

9.6.4.1. Single real

Example of conductance expressed by a singleReal :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $conductance1[@physicalNature=conductance
                          @floatingType=singleReal
                          @value=1e9]

9.6.4.2. Real Array Set

Example of conductance expressed by an arraySet :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $conductance2[@floatingType=arraySet]
            |-- data[@physicalNature=conductance
            |        @unit=siemens]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

9.6.5. Inductance

An inductance is a floatingType element, with a physicalNature attribute equals inductance.

A inductance can be a singleReal or an arraySet, the unit is henry.

9.6.5.1. Single real

Example of inductance expressed by a singleReal :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $inductance1[@physicalNature=inductance
                         @floatingType=singleReal
                         @value=1e-3]

9.6.5.2. Real Array Set

Example of inductance expressed by an arraySet :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $inductance2[@floatingType=arraySet]
            |-- data[@physicalNature=inductance
            |        @unit=henry]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

9.6.6. Capacitance

An capacitance is a floatingType element, with a physicalNature attribute equals capacitance.

A capacitance can be a singleReal, a dataSet or an arraySet, the unit in farad.

9.6.6.1. Single real

Example of capacitance expressed by a singleReal :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $capacitance1[@physicalNature=capacitance
                          @floatingType=singleReal
                          @value=1e-9]

9.6.6.2. Real Array Set

Example of a capacitance expressed by an arraySet :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $capacitance[@floatingType=arraySet]
            |-- data[@physicalNature=capacitance
            |        @unit=farad]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

9.6.7. Impedance

“Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative amplitudes of the voltage and current, but also the relative phases”. (http://en.wikipedia.org/wiki/Electrical_impedance)

Impedance is measured in ohm and can be expressed with :

  • a complex number

  • an array of complex number

  • some rational functions

9.6.7.1. Single complex

Example of impedance expressed by a singleComplex :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $impedance1[@physicalNature=impedance
                        @floatingType=singleComplex
                        @value=(80,0)]

9.6.7.2. Complex dataSet

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $impedance2[@physicalNature=impedance
                        @floatingType=dataSet]

9.6.7.3. Complex Array Set

Example of impedance expressed by an arraySet :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $impedance3[@floatingType=arraySet]
            |-- data[@physicalNature=impedance]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

9.6.7.4. Rational functions

Example of impedance expressed by a rational :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $impedance1[@floatingType=rational
            |           @physicalNature=impedance]
            |-- function
            |   |-- $rational1[@floatingType=rationalFunction]
            |   `-- $rational2[@floatingType=rationalFunction]
            `-- data

with /physicalModel/multiport/$impedance1/function/$rational1 :

type

A

B

F

1

1

2

2

3

3

4

5

4

6

7

8

5

9

10

11

/physicalModel/multiport/$impedance1/data is a HDF5 dataset, its characteristics are :

  • its rank is 2

  • its dimensions are number_of_ports * number_of_ports

For example for a two port elements, data is :

ports

1

2

1

$rational1

$rational2

2

$rational2

$rational1

9.6.8. Admittance

The admittance (Y) is the inverse of the impedance (Z), Y is measured in siemens.

Admittances are expressed in the same manner as impedances with a physicalNature equals admittance.

Example of admittance expressed by an arraySet :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- $admittance1[@floatingType=arraySet]
            |-- data[@physicalNature=admittance]
            `-- ds
                `-- dim1[@physicalNature=frequency
                         @unit=hertz]

Like impedances, admittances can be defined by :

  • A complex number

  • A complex dataSet

  • An array of complex numbers

  • Some rational functions

9.6.9. RLC model

RLC model represents an RLC circuit consisting of a resistance, an inductance and a capacitance connected in series or in parallel.

The elements can be connected in different ways :

  • type 1:

    R, L and C are in series

o---- R ---- L ---- C ----o

  • type 2:

    C is in parallel with L and R in series

     |---- L --- R ----|
o----|                 |----o
     |------- C -------|

  • type 3:

    L is in parallel with R and C in series

     |---- C --- R ----|
o----|                 |----o
     |------- L -------|

  • type 4:

    R is in series with L and C in parallel

            |---- L ----|
o---- R ----|           |----o
            |---- C ----|

  • type 5:

    R is in parallel with L and C in series

     |---- L --- C ----|
o----|                 |----o
     |------- R -------|

  • type 6:

    L is in series with R and C in parallel

            |---- R ----|
o---- L ----|           |----o
            |---- C ----|

  • type 7:

    C is in series with L and R in parallel

            |---- L ----|
o---- C ----|           |----o
            |---- R ----|

  • type 8:

    R, L et C are in parallel

     |---- R ----|
     |           |
o----|---- L ----|----o
     |           |
     |---- C ----|

In Amelet HDF, RLC circuits are contained in the /physicalModel/multiport/RLC subcategory.

An RLC circuit is a group which contains the name of the multiports defining R, L and C elements.

An RLC circuit has four attributes :

  • type. type is an HDF5 integer and can take values in [1..8], it represents the type detailed above.

  • R. R is the name of the resistance, it is an HDF5 string attribute

  • L. L is the name of the inductance, it is an HDF5 string attribute

  • C. C is the name of the conductance, it is an HDF5 string attribute

Example of an RLC circuit :

data.h5
`-- physicalModel/
    `-- multiport/
        |-- RLC/
        |   `-- $RLC[@type=1
        |            @R=/physicalModel/multiport/$resistance
        |            @L=/physicalModel/multiport/$inductance
        |            @C=/physicalModel/multiport/$conductance]/
        |-- $resistance[@physicalNature=resistance]
        |-- $inductance[@physicalNature=inductance]
        `-- $conductance[@physicalNature=conductance]

9.6.10. Scattering parameters

“Scattering parameters or S-parameters are properties used in electrical engineering, electronics engineering, and communication systems engineering describing the electrical behavior of linear electrical networks when undergoing various steady state stimuli by small signals.” (http://en.wikipedia.org/wiki/Scattering_parameters)

Scattering parameters are expressed in the same manner as impedances and are stored in the /physicalModel/multiport/sParameter category.

However scattering parameters have an optional attribute :

  • referenceImpedance. referenceImpedance is a real attribute. It represents the reference impedance in ohm used to compute the S-parameters.

    If referenceImpedance is missing, the reference impedance is the characteristics impedance of the line.

Examples :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- sParameter
            |-- $sparam-single[@floatingType=singleComplex,
            |                  @value=(10,2)]
            |-- $sparam[@floatingType=arraySet
            |   |       @referenceImpedance=50]
            |   |-- data
            |   `-- ds
            |       |-- dim1[@label=nbPort
            |       |        @physicalNature=electricPotentialPoint]
            |       |-- dim2[@label=nbPort
            |       |        @physicalNature=electricPotentialPoint]
            |       `-- dim3[@label=frequency
            |                @physicalNature=frequency
            |                @unit=hertz]
            `-- $sparam-rational[@floatingType=rational]/
                |-- function
                |   |-- rational1[@floatingType=rationalFunction]
                |   |-- rational2[@floatingType=rationalFunction]
                |   `-- rational3[@floatingType=rationalFunction]
                `-- data

Like impedances, sParameter can be defined by :

  • A complex number, the number of ports is 1

  • An array of complex numbers, the number of ports is the length of dim1

  • Some rational functions, the number of ports is given by the dimensions of /physicalModel/multiport/sParameter/$sparam-rational/data

9.6.11. The connection category

The connection category contains line connection definitions like ideal junction.

9.6.11.1. Ideal junction

The idealJunction connexion is a way to define ideal connectivity between wire strands.

Suppose height wires are connected to an ideal junction like in the following figure.

_images/ideal_junction.png

Fig. 9.1 A height ports ideal junction

Each wire can be in one of three states :

  • Connected to another wire (black circle)

  • Connected to the ground (short-circuit)

  • Not connected at all (open-circuit - OC)

The state set can be sum up in a (n x n) integer matrix C looking like :

X

1

2

3

4

5

6

7

8

1

0

0

0

0

1

0

0

0

2

0

0

0

0

0

1

1

0

3

0

0

1

0

0

0

0

0

4

0

0

0

-1

0

0

0

0

5

1

0

0

0

0

0

0

0

6

0

1

0

0

0

0

1

0

7

0

1

0

0

0

1

0

0

8

0

0

0

0

0

0

0

-1

The matrix’ elements are set up with the following rules :

Diagonal elements

  • If C(i,i) = 1, the port i is connected to the ground

  • If C(i,i) = -1, the port i is an open-circuit

  • If C(i,i) = 0, the port is in the default state : not connected to the ground and not an open-circuit. It is connected to some ports

Non diagonal elements

  • If C(i,j) = 1, the port i is connected to the port j

  • If C(i,j) = 0, the port i is not connected to the port j

In Amelet-HDF, an ideal junction is a number port dimension floatingType=dataSet defined by :

  • A type attribute equals to idealJunction

  • Integer values, values are defined by the rules above.

Examples :

data.h5
`-- physicalModel/
    `-- multiport/
        `-- connection
            `-- $ideal_junction[@type=idealJunction
                                @floatingType=dataSet]

9.7. Distributed Multiport

/physicalModel/multiport/distributed contains transmission line distributed parameters, i.e the RLCG matrices components. Those parameters are :

  • distributed impedance

  • distributed admittance

  • distributed resistance

  • distributed inductance

  • distributed capacitance

  • distributed conductance

A distributed multiport is a floatingType child of /physicalModel/multiport/distributed with a mandatory attribute :

/physicalModel/multiport/distributed are expressed in the same way as /physicalModel/multiport, except that the unit is :

  • ohmPerMeter for impedance

  • siemensPerMeter for admittance

  • ohmPerMeter for resistance

  • henryPerMeter for inductance

  • faradPerMeter for capacitance

  • siemensPerMeter for conductance

All children of these categories can be expressed by :

  • A complex number

  • A complex dataSet

  • An array of complex numbers

  • Some rational functions

Example

data.h5
`-- physicalModel/
    `-- multiport/
        `-- distributed
            |-- $disImp1[@floatingType=singleComplex
            |            @physicalNature=impedance
            |            @unit=ohmPerMeter
            |            @value=(10,2)]
            |-- $disImp2[@floatingType=dataSet
            |            @physicalNature=impedance
            |            @unit=ohmPerMeter]
            `-- $disImp3[@floatingType=arraySet]
                |-- data[@physicalNature=impedance
                |        @unit=ohmPerMeter]
                `-- ds
                    `-- dim1[@physicalNature=frequency]

9.8. Surface

This section describes surface material models, we can see two main types detailed in the next sections :

  • the thin dielectric layer model

  • the surface impedance boundary condition model

Model or genuine surface, instances can have a physicalModel attribute which gives the volume characteristics of the material.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    `-- surface/
        `-- $layer[@type=XXX
                   @physicalModel=/physicalModel/volume/$mat1]

9.8.1. Thin dielectric layer

The thin dielectric layer represents a dielectric layer thinner than the cell dimension. Surface impedance boundary models are not used to make wave propagate through the panel but the equivalent medium is computed from the weighting of the layer characteristics and the surrounding medium properties.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    `-- surface/
        `-- $layer[@type=thinDielectricLayer
                   @physicalModel=/physicalModel/volume/$mat1
                   @thickness=1e-3]

9.8.2. SIBC

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through the panel, the surface impedance is computed by the solver.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    `-- surface/
        `-- $layer[@type=SIBC
                   @physicalModel=/physicalModel/volume/$mat1
                   @thickness=1e-3]

9.8.3. Zs

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through a panel and the surface impedance is given by the model.

The relation between \(\overrightarrow{E}\) and \(\overrightarrow{H}\) is :

\[\overrightarrow{E_{tan}}(\vec{r}) = Z_s(\vec{r}, w)\overrightarrow{J}(\vec{r}) = Z_s(\vec{r}, w)[\vec{n}(\vec{r}) \times \overrightarrow{H}(\vec{r})]\]

\(\overrightarrow{J}\) is the surface current vector.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    |-- multiport/
    |   `-- $Zs[@floatingType=rational
    |       |   @physicalNature=impedance]
    |       |-- function
    |       |   |-- $Z11[@floatingType=generalRationalFunction
                         @type=polynomial]
    |       |   `-- $Z12[@floatingType=generalRationalFunction
                         @type=partialFraction]
    |       `-- data
    `-- surface/
        `-- $layer[@type=Zs
                   @Zs=/physicalModel/multiport/$Zs
                   @physicalModel=/physicalModel/volume/$mat1]

with data.h5:/physicalModel/multiport/Zs/function/Z11 :

(5.9545e69, 0)

(2.9773e69, 0)

(9.0191e59, 0)

(1.3921e59, 0)

(1.9344e49, 0)

(1.6254e48, 0)

(1.3458e38, 0)

(7.0897e36, 0)

(3.7609e26, 0)

(1.2717e26, 0)

(4.2033e14, 0)

(8.3344e05, 0)

(138.73, 0)

(1., 0)

with data.h5:/physicalModel/multiport/Zs/function/Z12 :

degree

A

B

1

(50, 0)

(0.5e-9, 4)

2

(125, 12.5)

(-15.25, 4)

1

(1.e9, 0)

(31, 0)

with data.h5:/physicalModel/multiport/Zs/data :

$Z11

$Z12

$Z21

$Z11

9.8.4. ZsZt

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through the panel, Zs and Zt are given by the model. The material is isotropic and symmetric.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    |-- multiport/
    |   |-- $Zs[@physicalNature=impedance]
    |   `-- $Zt[@physicalNature=impedance]
    `-- surface/
        `-- $layer[@type=ZsZt
                   @Zs=/physicalModel/multiport/$Zs
                   @Zt=/physicalModel/multiport/$Zt
                   @physicalModel=/physicalModel/volume/$mat1]

9.8.5. ZsZt2

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through the panel, Zs and Zt are given by the model. Front face (1) and back face (2) have different behavior. The material is isotropic but asymmetric.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    |-- multiport/
    |   |-- $Zs1[@physicalNature=impedance]
    |   |-- $Zs2[@physicalNature=impedance]
    |   |-- $Zt1[@physicalNature=impedance]
    |   `-- $Zt2[@physicalNature=impedance]
    `-- surface/
        `-- $layer[@type=ZsZt2
                   @Zs1=/physicalModel/multiport/$Zs1
                   @Zt1=/physicalModel/multiport/$Zt1
                   @Zs2=/physicalModel/multiport/$Zs2
                   @Zt2=/physicalModel/multiport/$Zt2
                   @physicalModel=/physicalModel/volume/$mat1]

9.8.6. ZsZtxy

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through the panel, Zs and Zt are given by the model. Front face (1) and back face (2) have same behavior. The material is symmetric but anisotropic.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    |-- multiport/
    |   |-- $Zsx[@physicalNature=impedance]
    |   |-- $Zsy[@physicalNature=impedance]
    |   |-- $Ztx[@physicalNature=impedance]
    |   `-- $Zty[@physicalNature=impedance]
    `-- surface/
        `-- $layer[@type=ZsZtxy
                   @Zsx=/physicalModel/multiport/$Zsx
                   @Zty=/physicalModel/multiport/$Zty
                   @Zsx=/physicalModel/multiport/$Zsx
                   @Zty=/physicalModel/multiport/$Zty
                   @physicalModel=/physicalModel/volume/$mat1]

9.8.7. ZsZt4

The thin dielectric layer represents a dielectric layer thiner than the cell dimension. Surface impedance boundary models are used to make wave propagate through the panel, Zs and Zt are given by the model. The material is asymmetric and anisotropic.

Example

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $mat1
    |-- multiport/
    |   |-- $Z11xx[@physicalNature=impedance]
    |   |-- $Z12xx[@physicalNature=impedance]
    |   |-- $Z21xx[@physicalNature=impedance]
    |   |-- $Z22xx[@physicalNature=impedance]
    |   |-- $Z11xy[@physicalNature=impedance]
    |   |-- $Z12xy[@physicalNature=impedance]
    |   |-- $Z21xy[@physicalNature=impedance]
    |   |-- $Z22xy[@physicalNature=impedance]
    |   |-- $Z11yx[@physicalNature=impedance]
    |   |-- $Z12yx[@physicalNature=impedance]
    |   |-- $Z21yx[@physicalNature=impedance]
    |   |-- $Z22yx[@physicalNature=impedance]
    |   |-- $Z11yy[@physicalNature=impedance]
    |   |-- $Z12yy[@physicalNature=impedance]
    |   |-- $Z21yy[@physicalNature=impedance]
    |   |-- $Z22yy[@physicalNature=impedance]
    `-- surface/
        `-- $layer[@type=ZsZt4
                   @Z11xx=/physicalModel/multiport/$Z11xx
                   @Z12xx=/physicalModel/multiport/$Z12xx
                   @Z21xx=/physicalModel/multiport/$Z21xx
                   @Z22xx=/physicalModel/multiport/$Z22xx
                   @Z11xy=/physicalModel/multiport/$Z11xy
                   @Z12xy=/physicalModel/multiport/$Z12xy
                   @Z21xy=/physicalModel/multiport/$Z21xy
                   @Z22xy=/physicalModel/multiport/$Z22xy
                   @Z11yx=/physicalModel/multiport/$Z11yx
                   @Z12yx=/physicalModel/multiport/$Z12yx
                   @Z21yx=/physicalModel/multiport/$Z21yx
                   @Z22yx=/physicalModel/multiport/$Z22yx
                   @Z11yy=/physicalModel/multiport/$Z11yy
                   @Z12yy=/physicalModel/multiport/$Z12yy
                   @Z21yy=/physicalModel/multiport/$Z21yy
                   @Z22yy=/physicalModel/multiport/$Z22yy
                   @physicalModel=/physicalModel/volume/$mat1]

9.9. Interface

Objects contained in the category /physicalModel/interface define the connection between two media. An interface is a named HDF5 group with two mandatory attributes and one optional attribute :

Mandatory attributes :

  • medium1 is an HDF5 string attribute, it is a pointer to a /physicalModel, first medium of the interface

  • medium2 is an HDF5 string attribute, it is a pointer to a /physicalModel, second medium of the interface

Optional attribute :

  • interface is an HDF5 string attribute, it is a pointer to a /physicalModel, it represents the properties of the interface (infinitely thin, or not meshed).

Below is an example of an interface separating two areas made up of /physicalModel/volume/$diel1 and /physicalModel/volume/$diel2. The interface itself (virtual space between the two media) is an infinitely thin perfectly conducting plane.

data.h5
`-- physicalModel/
    |-- volume
    |   |-- $diel1
    |   `-- $diel2
    `-- interface/
        `-- $interface1[@medium1=/physicalModel/volume/$diel1
                        @medium2=/physicalModel/volume/$diel2
                        @interface=/physicalModel/perfectElectricConductor]

9.10. Aperture

In the electromagnetic simulation domain, little aperture are often described thanks to sub cellular models associated to linear elements, they don’t appear in the mesh as slot but as linear elements. In addition, apertures can be filled (loaded) by a materialModel.

An aperture is a named HDF5 group child of /physicalModel/aperture that have a type attribute. The type is a string HDF5 attribute.

Amelet HDF defines three apertures that are described in the next sections :

  • Slot

  • Rectangular aperture

  • Circular aperture

  • Elliptic aperture

  • Large aperture

  • Measured aperture

9.10.1. Slot

A slot is a named HDF5 group with type equals slot, it has three attributes :

  • witdh : the width of the slot, a length in meter, it is a float HDF5 attribute and is mandatory.

  • thickness : the thickness of the slot, a length in meter, it is a float HDF5 attribute and is mandatory.

  • materialModel : the load material name of the slot, it is a character strings, it is optional.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $diel1
    `-- aperture/
        `-- $slot1[@type=slot
                   @width=10e-3
                   @thickness=2e-3
                   @materialModel=/physicalModel/volume/$diel1]

9.10.2. Rectangular aperture

A rectangular aperture is a named HDF5 group with type equals rectangular, it has two attributes :

  • length : the length of the rectangle, a length in meter, it is a float HDF5 attribute and is mandatory.

  • width : the width of the rectangle, a length in meter, it is a float HDF5 attribute and is mandatory.

  • thickness : the thickness of the aperture, a length in meter, it is a float HDF5 attribute and is mandatory.

  • materialModel : the load material name of the aperture, it is a character strings, it is optional.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $diel1
    `-- aperture/
        `-- $rectangularAperture1[@type=rectangular
                                  @length=10e-3
                                  @width=6e-3
                                  @thickness=2e-3
                                  @materialModel=/physicalModel/volume/$diel1]

9.10.3. Circular aperture

A circular aperture is a named HDF5 group with type equals circular, it has two attributes :

  • diameter : the diameter of the circle, a length in meter, it is a float HDF5 attribute and is mandatory.

  • thickness : the thickness of the aperture, a length in meter, it is a float HDF5 attribute and is mandatory.

  • materialModel : the load material name of the aperture, it is a character strings, it is optional.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $diel1
    `-- aperture/
        `-- $circularAperture1[@type=circular
                               @diameter=10e-3
                               @thickness=2e-3
                               @materialModel=/physicalModel/volume/$diel1]

9.10.4. Elliptic aperture

A elliptic aperture is a named HDF5 group with type equals Elliptic, it has two attributes :

  • semimajorAxis : the semimajor axis of the ellipse, a length in meter, it is a float HDF5 attribute and is mandatory.

  • semiminorAxis : the semiminor axis of the ellipse, a length in meter, it is a float HDF5 attribute and is mandatory.

  • thickness : the thickness of the aperture, a length in meter, it is a float HDF5 attribute and is mandatory.

  • materialModel : the load material name of the aperture, it is a character strings, it is optional.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $diel1
    `-- aperture/
        `-- $ellipticAperture1[@type=elliptic
                               @semimajorAxis=10e-3
                               @semiminorAxis=6e-3
                               @thickness=2e-3
                               @materialModel=/physicalModel/volume/$diel1]

9.10.5. Large aperture

A large aperture relative to the wave length is a named HDF5 group with type equals large, it has three attribute :

  • surface : the surface of the aperture, a surface in square meter, it is a float HDF5 attribute and is mandatory.

  • thickness : the thickness of the aperture, a length in meter, it is a float HDF5 attribute and is mandatory.

  • materialModel : the load material name of the aperture, it is a character strings, it is optional.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $diel1
    `-- aperture/
        `-- $largeAperture1[@type=large
                            @surface=10e-3
                            @thickness=2e-3
                            @materialModel=/physicalModel/volume/$diel1]

9.10.6. Measured aperture

A measured aperture is a named HDF5 group with type equals measured, it has one floatingType child called sigma. sigma is the measured transmission cross section as function of incident field and frequency.

Example :

data.h5
`-- physicalModel/
    `-- aperture/
        `-- $measuredAperture1[@type=measured]
            `-- sigma[@floatingType=arraySet]
                |-- data[@physicalNature=surface
                |        @unit=squareMeter]
                `-- ds/
                    `-- dim1[@physicalNature=frequency
                             @unit=hertz]

9.11. Shield

The shield category contains shields definitions.

9.11.1. Metal braid shield

A metal braid is a shield for a cable or for a bundle of cables :

_images/metal_braid_diameter.png

Fig. 9.2 Metal braid representation

A metal braid is completely described by six parameters :

  • Diameter D (real number, dimension meters)

  • Number of carriers C (i.e. belts of wires) in the braid (integer number)

  • Number of wires N in a carrier (integer number)

  • Diameter d of a single wire (real number, dimension meters)

  • Conductivity \(\sigma\) of the wires (real number, dimension Simens per meters)

  • Weave angle \(\alpha\) (real number, degrees)

_images/metal_braid_characteristics.png

Fig. 9.3 Metal braid chracteristics

In Amelet HDF a metal braid is an HDF5 named group with seven attributes :

  • type : type is an HDF5 string attribute, its value is metalBraid

  • braidDiameter : braidDiameter is an HDF5 real attribute and represents D in meters

  • numberOfCarriers : numberOfCarriers is an HDF5 integer attribute and is the number of carriers C.

  • numberOfWiresPerCarrier : numberOfWiresPerCarrier is an HDF5 integer attribute and represents the number of wires N in a carrier

  • wireDiameter : wireDiameter is an HDF5 real attribute and represents d in meters

  • material : material is an HDF5 string attribute, it contains the name of a /physicalModel/volume material

  • weaveAngle : weaveAngle is an HDF5 real number which represents the angle \(\alpha\) in degrees

and a floatingType child named Zt. Zt contains the transfer impedance of the shield.

Example :

data.h5
`-- physicalModel/
    |-- volume/
    |   `-- $copper
    |       `-- electricConductivity[@floatingType=singleReal
    |                                @value=59.6e6]
    `-- shield/
        `-- $a-metal-braid[@type=metalBraid
            |              @braidDiameter=5e-3
            |              @numberOfCarriers=10
            |              @numberOfWiresPerCarrier=20
            |              @wireDiameter=5e-4
            |              @material=/physicalModel/volume/$copper
            |              @weaveAngle=45]
            `-- Zt[@floatingType=arraySet]
                |-- data
                `-- ds
                    `-- dim1

9.12. Grid

The grid category contains grids definition. Many kinds of grid exist.

_images/grid.png

Fig. 9.4 Grids characteristics

A grid is composed of two materials:

  • The grid itself

  • A material around the grid

A grid is defined by many parameters:

  • Physical characteristics of the surrounding material

  • Physical characteristics of the grid

  • Dimension of the grid’s wires for woven and comb grids (real number in meters):

    • Diameter if wires have a circular section

    • Thickness and width if wires have a rectangular section

  • Texture type (woven, unidirectional, comb, random)

There are specific parameters to describe each kind of grid.

  • A woven/unidirectional grid is defined by:

    • Number of fiber per pitch (integer number)

    • Length of a pitch (real number in meters)

    • Angle between the fiber and the Z-axis (real number in degrees)

    • Model type homgeneous or heterogeneous composite

  • A comb grid is defined by:

    • Angles relative to the X-axis (real number in degrees)

    • Pitches, distances between two wire centers (real number in meters)

    • Height of the grid from the bottom (z=0) in the context of layer

    • Model type homgeneous or heterogeneous composite

  • A random grid:

    • Scale filler : micro or nano (string)

    • Type filler : sphere, rod or disk (string)

    • Volume fraction of filler (real number)

    • Diameter of filler (real number in meter)

    • Length of filler (real number in meter)

In Amelet HDF a grid is an HDF5 named group with the following attributes :

  • surroundingMaterial : surroundingMaterial is an HDF5 string attribute, it contains the name of a /physicalModel/volume material.

  • gridMaterial : gridMaterial is an HDF5 string attribute, it contains the name of a /physicalModel/volume material.

  • textureType : textureType is an HDF5 string attribute and defines the type of grid texture. The accepted values are woven, unilateral, comb and random.

  • pitchFiber : pitchFiber is an optional HDF5 real attribute, it represents the length of a pitch. This attribute is present if textureType is equal to woven.

  • fiberPerPitch : fiberPerPitch is an optional HDF5 integer attribute, it represents the number of fiber per pitch. This attribute is present if textureType is equal to woven.

  • wireSectionType : wireSectionType is an HDF5 string attribute and defines the type of the wire. The accepted values are circular or rectangular.

  • diameterWire : diameterWire is an optional HDF5 real attribute and represents the grid’s wire diameter in meters. This attribute is present if wireSectionType is equal to circular or if textureType is equal to random.

  • thicknessWire : thicknessWire is an optional HDF5 real attribute and represents the grid’s wire thickness in meters. This attribute is present if wireSectionType is equal to rectangular.

  • widthWire : widthWire is an optional HDF5 real attribute and represents the grid’s wire width in meters. This attribute is present if wireSectionType is equal to rectangular.

  • lengthWire : lengthWire is an optional HDF5 real attribute and represents the length of wire in meter which fills the material. This attribute is present if textureType is equal to random.

  • scaleFiller : scaleFiller is an optional HDF5 string attribute and represents the scale filled of the material. This attribute can have only two possible values micro or nano.

  • typeFiller : typeFiller is an optional HDF5 string attribute and represents the filled type of the material. This attribute can have only three possible values sphere, rod or nano.

  • volFractioFiller : volFractioFiller is an optional HDF5 real attribute and represents the ratio of filling volume.

  • shift : shift is the optional distance in meters between the two combs measured on the X-axis (see the sketch).

  • modelType : modelType is the optional HDF5 string attribute and represents the kind of material. Value can be homogeneous or heterogeneous.

and one or two HDF5 group named comb1 (and optionally comb2 if there are two combs) with attributes as follows :

  • Height of the grid from the bottom (z=0) of a layer :

    • relativeHeight represents a relative height relative to the total height of a material layer. It is a dimensionless float between 0 and 1

    • absoluteHeight represents an absolute height from the bottom of a material layer. It is a float number in meters.

  • pitch : pitch is an HDF5 real attribute and represents the distance between two wire centers in meters

  • angle : angle is an HDF5 real attribute and represents the angle in degrees between wires and the X-axis.

Example of a woven Grid with a thickness of 5 mm :

data.h5
`-- physicalModel/
    |-- multilayer/
    |   `-- $multilayerMaterial
    |-- volume/
    |   |-- $resin
    |   |   |-- electricConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- magneticConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- relativePermittivity[@floatingType=singleReal
    |   |   |                        @value=2.0]
    |   |   `-- relativePermeability[@floatingType=singleReal
    |   |                            @value=1.0]
    |   `-- $fiber
    |       |-- electricConductivity[@floatingType=singleReal
    |       |                        @value=1.0e5]
    |       |-- magneticConductivity[@floatingType=singleReal
    |       |                        @value=0.0]
    |       |-- relativePermittivity[@floatingType=singleReal
    |       |                        @value=2.0]
    |       `-- relativePermeability[@floatingType=singleReal
    |                                @value=1.0]
    `-- grid/
        `-- $a-wovengrid[@surroundingMaterial=/physicalModel/volume/$resin
             |           @gridMaterial=/physicalModel/volume/$fiber
             |           @textureType=woven
             |           @pitchFiber=0.1e-3
             |           @fiberPerPitch=10
             |           @modelType=homogeneous]
             `-- comb1[@relativeHeight=0.5
                       @angle=90.0
                       @diameterWire=2.5e-5
                       @wireSectionType=circular]

$multilayerMaterial is a table which contains:

physicalModel

thickness

/physicalModel/grid/$a-wovengrid

5.0e-3

Example of a two single comb Grid with a thickness of 3 mm :

data.h5
`-- physicalModel/
    |-- multilayer/
    |   `-- $multilayerMaterial
    |-- volume/
    |   |-- $resin
    |   |   |-- electricConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- magneticConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- relativePermittivity[@floatingType=singleReal
    |   |   |                        @value=2.0]
    |   |   `-- relativePermeability[@floatingType=singleReal
    |   |                            @value=1.0]
    |   `-- $fiber
    |       |-- electricConductivity[@floatingType=singleReal
    |       |                        @value=1.0e5]
    |       |-- magneticConductivity[@floatingType=singleReal
    |       |                        @value=0.0]
    |       |-- relativePermittivity[@floatingType=singleReal
    |       |                        @value=2.0]
    |       `-- relativePermeability[@floatingType=singleReal
    |                                @value=1.0]
    `-- grid/
        `-- $a-combgrid[@surroundingMaterial=/physicalModel/volume/$resin
             |          @gridMaterial=/physicalModel/volume/$fiber
             |          @textureType=comb
             |          @shift=0.3e-4
             |          @modelType=heterogeneous]
             |-- comb1[@relativeHeight=0.5
             |         @angle=45.0
             |         @pitch=1.0e-4
             |         @thicknessWire=2.5e-5
             |         @widthWire=5.0e-5
             |         @wireSectionType=rectangular]
             `-- comb2[@relativeHeight=0.4
                       @angle=135.0
                       @pitch=1.0e-4
                       @thicknessWire=2.5e-5
                       @widthWire=5.0e-5
                       @wireSectionType=rectangular]

$multilayerMaterial is a table which contains:

physicalModel

thickness

/physicalModel/grid/$a-combgrid

3.0e-3

Example of a random Grid with a thickness of 4 mm and three kind of wire:

data.h5
`-- physicalModel/
    |-- multilayer/
    |   `-- $multilayerMaterial
    |-- volume/
    |   |-- $resin
    |   |   |-- electricConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- magneticConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- relativePermittivity[@floatingType=singleReal
    |   |   |                        @value=2.0]
    |   |   `-- relativePermeability[@floatingType=singleReal
    |   |                            @value=1.0]
    |   |-- $fiber1
    |   |   |-- electricConductivity[@floatingType=singleReal
    |   |   |                        @value=1.5e5]
    |   |   |-- magneticConductivity[@floatingType=singleReal
    |   |   |                        @value=0.0]
    |   |   |-- relativePermittivity[@floatingType=singleReal
    |   |   |                        @value=1.0]
    |   |   `-- relativePermeability[@floatingType=singleReal
    |   |
    |   `-- $fiber2
    |       |-- electricConductivity[@floatingType=singleReal
    |       |                        @value=1.0e5]
    |       |-- magneticConductivity[@floatingType=singleReal
    |       |                        @value=0.0]
    |       |-- relativePermittivity[@floatingType=singleReal
    |       |                        @value=1.0]
    |       `-- relativePermeability[@floatingType=singleReal
    |                                @value=1.0]
    `-- grid/
        `-- $a-randomgrid[@surroundingMaterial=/physicalModel/volume/$resin
            |             @textureType=random]
            |-- a-nano-filler[@gridMaterial=/physicalModel/volume/$fiber1
            |                 @scaleFiller=nano
            |                 @typeFiller=rod
            |                 @volFractioFiller=0.1
            |                 @diameterWire=1.e-9
            |                 @lengthWire=5.0e-8]
            |-- a-micro-filler[@gridMaterial=/physicalModel/volume/$fiber2
            |                  @scaleFiller=micro
            |                  @typeFiller=rod
            |                  @volFractioFiller=0.2
            |                  @diameterWire=1.e-5
            |                  @lengthWire=5.0e-5]
            `-- another-micro-filler[@gridMaterial=/physicalModel/volume/$fiber2
                                     @scaleFiller=micro
                                     @typeFiller=rod
                                     @volFractioFiller=0.05
                                     @diameterWire=0.5e-6
                                     @lengthWire=1.0e-5]

$multilayerMaterial is a table which contains:

physicalModel

thickness

/physicalModel/grid/$a-randomgrid

4.0e-3