# buildingMaterialPermittivity

Permittivity and conductivity of building materials

## Description

`[`

calculates the relative permittivity, conductivity, and complex relative permittivity for
the specified material at the specified frequency. The methods and equations modeled in the
`epsilon`

,`sigma`

,`complexepsilon`

] = buildingMaterialPermittivity(`material`

,`fc`

)`buildingMaterialPermittivity`

function are presented in Recommendation ITU-R P.2040
[1].

## Examples

### Calculate Permittivity of Various Building Materials

Calculate relative permittivity and conductivity at 9 GHz for various building materials as defined by textual classifications in ITU-R P.2040, Table 3.

material = ["vacuum";"concrete";"brick";"plasterboard";"wood"; ... "glass";"ceiling-board";"chipboard";"floorboard";"metal"]; fc = repmat(9e9,size(material)); % Frequency in Hz [permittivity,conductivity] = ... arrayfun(@(x,y)buildingMaterialPermittivity(x,y),material,fc);

Display the results in a table.

varNames = ["Material";"Permittivity";"Conductivity"]; table(material,permittivity,conductivity,'VariableNames',varNames)

`ans=`*10×3 table*
Material Permittivity Conductivity
_______________ ____________ ____________
"vacuum" 1 0
"concrete" 5.31 0.19305
"brick" 3.75 0.038
"plasterboard" 2.94 0.054914
"wood" 1.99 0.049528
"glass" 6.27 0.059075
"ceiling-board" 1.5 0.0064437
"chipboard" 2.58 0.12044
"floorboard" 3.66 0.085726
"metal" 1 1e+07

### Plot Permittivity and Conductivity of Concrete at Various Frequencies

Calculate the relative permittivity and conductivity for concrete at frequencies specified.

fc = ((1:1:10)*10e9); % Frequency in Hz [permittivity,conductivity] = ... arrayfun(@(y)buildingMaterialPermittivity("concrete",y),fc);

Plot the relative permittivity and conductivity of concrete across the range of frequencies.

figure yyaxis left plot(fc,permittivity) ylabel('Relative Permittivity') yyaxis right plot(fc,conductivity) ylabel('Conductivity (S/m)') xlabel('Frequency (Hz)') title('Permittivity and Conductivity of Concrete')

## Input Arguments

`material`

— Building material

`"vacuum"`

| `"concrete"`

| ` "brick"`

| `"plasterboard"`

| ...

Building material, specified as vector of strings, or an equivalent character vector or cell array of character vectors including one or more of these options:

`"vacuum"` | `"glass"` | `"very-dry-ground"` |

`"concrete"` | `"ceiling-board"` | `"medium-dry-ground"` |

`"brick"` | `"floorboard"` | `"wet-ground"` |

`"plasterboard"` | `"chipboard"` | |

`"wood"` | `"metal"` |

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

**Data Types: **`char`

| `string`

`fc`

— Carrier frequency

positive scalar

Carrier frequency in Hz, specified as a positive scalar.

**Note**

`fc`

must be in the range [1e6, 10e6] when the
`material`

is `"very-dry-ground"`

,
`"medium-dry-ground"`

or `"wet-ground"`

.

**Data Types: **`double`

## Output Arguments

`epsilon`

— Relative permittivity

nonnegative scalar | nonnegative row vector

Relative permittivity of the building material, returned as a nonnegative scalar or
row vector. The output dimension of `epsilon`

matches that of the
input argument `material`

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

`sigma`

— Conductivity

nonnegative scalar | nonnegative row vector

Conductivity, in Siemens/m, of the building material, returned as a nonnegative
scalar or row 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.2040-1 [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.2040-1 to
compute these values.

The real part of the relative permittivity is calculated as

`epsilon`

=*af*.^{b}The computation of

`epsilon`

is based on equation (58).*f*is the frequency in GHz. Values for*a*and*b*are specified in Table 3 from ITU-R P.2040-1.The conductivity in Siemens/m is calculated as

`sigma`

=*cf*.^{d}The computation of

`sigma`

is based on equation (59).*f*is the frequency in GHz. Values for*c*and*d*are specified in Table 3 from ITU-R P.2040-1.The complex permittivity is calculated as

`complexepsilon`

=`epsilon`

– 1*i*`sigma`

/ (2π*fc*ε_{0}).The computation of

`complexepsilon`

is based on Equations (59) and (9b).*f*is the frequency in GHz.*c*is the velocity of light in free space. ε_{0}= 8.854187817e-12 Farads/m, where ε_{0}is the electric constant for the permittivity of free space.

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

or `sigma`

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

The contents of Table 3 from ITU-R P.2040-1 are repeated in this table.
The values *a*, *b*, *c*, and
*d* are used to calculate 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 relative
permittivity and conductivity values for frequencies that fall outside of the noted limits.
To compute relative permittivity and conductivity for different types of ground as a
function 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 | 5.31 | 0 | 0.0326 | 0.8095 | [1, 100] |

Brick | 3.75 | 0 | 0.038 | 0 | [1, 10] |

Plasterboard | 2.94 | 0 | 0.0116 | 0.7076 | [1, 100] |

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

Glass | 6.27 | 0 | 0.0043 | 1.1925 | [0.1, 100] |

Ceiling board | 1.50 | 0 | 0.0005 | 1.1634 | [1, 100] |

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

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), the noted frequency limits cannot be exceeded. |

## References

[1] International Telecommunications Union Radiocommunication
Sector. *Effects of building materials and structures on radiowave propagation above
about 100MHz.* Recommendation P.2040-1. ITU-R, approved July 29, 2015.
https://www.itu.int/rec/R-REC-P.2040-1-201507-I/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.

**Introduced in R2020a**

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