# buildingMaterialPermittivity

## Description

`[`

calculates the real relative permittivity, conductivity, and complex relative permittivity
of the specified material at the specified frequency.`epsilon`

,`sigma`

,`complexepsilon`

] = buildingMaterialPermittivity(`material`

,`fc`

)

The methods and equations modeled by the `buildingMaterialPermittivity`

function are
presented in International Telecommunication Union Recommendation (ITU-R) P.2040-3 [1].

## Examples

### Calculate Permittivity and Conductivity of Building Materials

Calculate the real relative permittivity and conductivity of various building materials, as defined by the textual classifications in ITU-R P.2040-3, Table 3.

Specify the names of several building materials.

material = ["vacuum","concrete","brick","plasterboard","wood","glass", ... "ceiling-board","chipboard","plywood","marble","floorboard","metal"];

Specify the frequency as 9 GHz. Initialize variables for the real relative permittivity and conductivity. Then, for each building material, calculate the real relative permittivity and conductivity.

fc = 9e9; % 9 GHz epsilon = ones(size(material)); sigma = ones(size(material)); for i = 1:length(material) [epsilon(i),sigma(i)] = buildingMaterialPermittivity(material(i),fc); end

Display the results in a table.

varNames = ["Material","Real Relative Permittivity","Conductivity"]; table(material',epsilon',sigma',VariableNames=varNames)

`ans=`*12×3 table*
Material Real Relative Permittivity Conductivity
_______________ __________________________ ____________
"vacuum" 1 0
"concrete" 5.24 0.25766
"brick" 3.91 0.033826
"plasterboard" 2.73 0.066978
"wood" 1.99 0.049528
"glass" 6.31 0.068299
"ceiling-board" 1.48 0.011674
"chipboard" 2.58 0.12044
"plywood" 2.71 0.33
"marble" 7.074 0.04209
"floorboard" 3.66 0.085726
"metal" 1 1e+07

### Plot Permittivity and Conductivity of Concrete

Plot the permittivity and conductivity of concrete at multiple frequencies.

Specify frequencies between 1 GHz and 10 GHz. Initialize variables for the real relative permittivity and conductivity values. Then, for each frequency, calculate the real relative permittivity and conductivity of concrete.

fc = 10e9*linspace(1,10); epsilon = ones(size(fc)); sigma = ones(size(fc)); for i = 1:length(fc) [epsilon(i),sigma(i)] = buildingMaterialPermittivity("concrete",fc(i)); end

Plot the results on a chart with two *y*-axes.

figure yyaxis left plot(fc,epsilon) ylabel("Real Relative Permittivity") yyaxis right plot(fc,sigma) ylabel("Conductivity (S/m)") xlabel("Frequency (Hz)") title("Permittivity and Conductivity of Concrete")

## Input Arguments

`material`

— Building material

string scalar | character vector | vector of strings | cell array of character vectors

Building material, specified as a string scalar, a character vector, a vector of strings, or a cell array of character vectors that include one or more of these options:

`"vacuum"`

— Vacuum`"concrete"`

— Concrete`"brick"`

— Brick`"plasterboard"`

— Plasterboard`"wood"`

— Wood`"glass"`

— Glass`"ceiling-board"`

— Ceiling board`"floorboard"`

— Floorboard`"chipboard"`

— Chipboard`"metal"`

— Metal`"marble"`

— Marble*(since R2024a)*`"plywood"`

— Plywood*(since R2024a)*`"very-dry-ground"`

— Very dry ground`"medium-dry-ground"`

— Medium dry ground`"wet-ground"`

— Wet ground

**Example: **`["vacuum","brick"]`

**Data Types: **`char`

| `string`

| `cell`

`fc`

— Carrier frequency in Hz

positive scalar

Carrier frequency in Hz, specified as a positive scalar.

When you specify `material`

as
`"very-dry-ground"`

, `"medium-dry-ground"`

, or
`"wet-ground"`

, this argument must be in the range [1e6,
10e6].

**Data Types: **`double`

## Output Arguments

`epsilon`

— Real relative permittivity

scalar | vector

Real relative permittivity of the building material, returned as a scalar or vector.
The output dimension of `epsilon`

matches that of the input argument
`material`

. For more information about the computation for the real
relative permittivity, see ITU Building Materials.

`sigma`

— Conductivity in S/m

nonnegative scalar | nonnegative vector

Conductivity, in S/m, of the building material, returned as a nonnegative scalar or
vector. The output dimension of `sigma`

matches that of the input
argument `material`

. For more information about the computation for
the conductivity, see ITU Building Materials.

`complexepsilon`

— Complex relative permittivity

complex scalar | row vector of complex values

Complex relative permittivity of the building material, returned as a complex scalar
or row vector of complex values. The output dimension of
`complexepsilon`

matches that of the input argument
`material`

. For more information about the computation for the
complex relative permittivity, see ITU Building Materials.

## More About

### ITU Building Materials

Section 3 of ITU-R P.2040-3 [1] presents methods, equations, and values used to calculate real relative permittivity, conductivity, and complex relative permittivity at carrier frequencies up to 100 GHz for common building materials.

The `buildingMaterialPermittivity`

function uses equations from ITU-R P.2040-3 to
compute these values:

`epsilon`

— Equation (57) indicates that the real part of the relative permittivity`epsilon`

is`epsilon`

=*a**f*, where^{b}*f*is the frequency in GHz. Values for*a*and*b*are specified by Table 3 of ITU-R P.2040-3.`sigma`

— Equation (58) indicates that the conductivity`sigma`

in Siemens/m is`sigma`

=*c**f*, where^{d}*f*is the frequency in GHz. Values for*c*and*d*are specified by Table 3 of ITU-R P.2040-3.`complexepsilon`

— Based on equations (59) and (9b), the complex relative permittivity`complexepsilon`

is`complexepsilon`

=`epsilon`

–*i*·`sigma`

/ (2π*f*_{c}*ε*), where_{0}*f*is the carrier frequency in Hz and ε_{c}_{0}= 8.854187817×10^{-12}Farads/m is the dielectric permittivity of free space.

For cases where the value of *b* or *d* is 0, the
corresponding value of `epsilon`

or `sigma`

is
*a* or *c*, respectively, independent of
frequency.

This table repeats the contents of Table 3 from ITU-R P.2040-3. The
values *a*, *b*, *c*, and
*d* are used to calculate real relative permittivity and conductivity.
Except as noted for the three ground types, the frequency ranges given in the table are not
hard limits but are indicative of the measurements used to derive the models. The
`buildingMaterialPermittivity`

function interpolates or extrapolates real relative
permittivity and conductivity values for frequencies that fall outside of the noted limits.
To compute real relative permittivity and conductivity for different types of ground as a
function of carrier frequencies up to 1000 GHz, see the `earthSurfacePermittivity`

function.

Material Class | Real Part of Relative Permittivity | Conductivity (S/m) | Frequency Range (GHz) | ||
---|---|---|---|---|---|

a | b | c | d | ||

Vacuum (~ air) | 1 | 0 | 0 | 0 | [0.001, 100] |

Concrete | 5.24 | 0 | 0.0462 | 0.7822 | [1, 100] |

Brick | 3.91 | 0 | 0.0238 | 0.16 | [1, 10] |

Plasterboard | 2.73 | 0 | 0.0085 | 0.9395 | [1, 100] |

Wood | 1.99 | 0 | 0.0047 | 1.0718 | [0.001, 100] |

Glass | 6.31 | 0 | 0.0036 | 1.3394 | [0.1, 100] |

Glass | 5.79 | 0 | 0.0004 | 1.658 | [220, 450] |

Ceiling board | 1.48 | 0 | 0.0011 | 1.0750 | [1, 100] |

Ceiling board | 1.52 | 0 | 0.0029 | 1.029 | [220, 450] |

Chipboard | 2.58 | 0 | 0.0217 | 0.78 | [1, 100] |

Plywood | 2.71 | 0 | 0.33 | 0 | [1, 40] |

Marble | 7.074 | 0 | 0.0055 | 0.9262 | [1, 60] |

Floorboard | 3.66 | 0 | 0.0044 | 1.3515 | [50, 100] |

Metal | 1 | 0 | 10 | 0 | [1, 100] |

Very dry ground | 3 | 0 | 0.00015 | 2.52 | [1, 10] only |

Medium dry ground | 15 | – 0.1 | 0.035 | 1.63 | [1, 10] only |

Wet ground | 30 | – 0.4 | 0.15 | 1.30 | [1, 10] only |

Note (a): For the three ground types (very dry, medium dry, and wet), you cannot exceed the noted frequency limits. |

## References

[1] International
Telecommunications Union Radiocommunication Sector. *Effects of Building Materials and
Structures on Radiowave Propagation Above About 100MHz.* Recommendation P.2040.
ITU-R, approved August 23, 2023. https://www.itu.int/rec/R-REC-P.2040/en.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

When you specify multiple reflective materials, you must define each value as a
character vector (`char`

data type) in a cell array.

## Version History

**Introduced in R2020a**

### R2024a: Model materials using updated ITU recommendations

The `buildingMaterialPermittivity`

function models materials using the methods and
equations in ITU-R P.2040-3 [1].

In previous releases, the function used ITU-R P.2040-1. As a result of this change, the
`buildingMaterialPermittivity`

function can return different values in R2024a compared
to previous releases.

### R2024a: Model marble and plywood materials

Model marble or plywood materials by specifying `material`

as
`"marble"`

or `"plywood"`

.

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