buildingMaterialPermittivity

Permittivity and conductivity of building materials

Since R2020a

Syntax

``[epsilon,sigma,complexepsilon] = buildingMaterialPermittivity(material,fc)``

Description

example

````[epsilon,sigma,complexepsilon] = buildingMaterialPermittivity(material,fc)` calculates the real relative permittivity, conductivity, and complex relative permittivity of the specified material at the specified frequency.The methods and equations modeled by the `buildingMaterialPermittivity` function are presented in International Telecommunication Union Recommendation (ITU-R) P.2040-3 [1].```

Examples

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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 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

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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`

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

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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.

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.

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.

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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` = afb, where 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` = cfd, where 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` / (2πfcε0), where fc is the carrier frequency in Hz and ε0 = 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 ClassReal Part of Relative PermittivityConductivity (S/m)Frequency Range (GHz)
abcd

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

107

0

[1, 100]

Very dry ground

3

0

0.00015

2.52

[1, 10] only(a)

Medium dry ground

15

– 0.1

0.035

1.63

[1, 10] only(a)

Wet ground

30

– 0.4

0.15

1.30

[1, 10] only(a)

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.

Version History

Introduced in R2020a

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