Main Content

buildingMaterialPermittivity

Permittivity and conductivity of building materials

所有的页面崩溃

Syntax

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

Description

example

[epsilon,sigma,complexepsilon] = buildingMaterialPermittivity(material,fc)calculates the relative permittivity, conductivity, and complex relative permittivity for the specified material at the specified frequency. The methods and equations modeled in thebuildingMaterialPermittivityfunction are presented in Recommendation ITU-R P.2040[1].

Examples

collapse all

Open Live Script

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表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
Open Live Script

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 yyaxisleftplot(fc,permittivity) ylabel('Relative Permittivity') yyaxisrightplot(fc,conductivity) ylabel('Conductivity (S/m)') xlabel('Frequency (Hz)') title('Permittivity and Conductivity of Concrete')

Figure contains an axes object. The axes object with title Permittivity and Conductivity of Concrete contains 2 objects of type line.

Input Arguments

collapse all

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

Carrier frequency in Hz, specified as a positive scalar.

Note

fc必须在范围(1 e6、10 e6)当吗materialis"very-dry-ground","medium-dry-ground"or"wet-ground".

Data Types:double

Output Arguments

collapse all

Relative permittivity of the building material, returned as a nonnegative scalar or row vector. The output dimension ofepsilonmatches that of the input argumentmaterial. For more information about the computation for the relative permittivity, seeITU Building Materials.

Conductivity, in Siemens/m, of the building material, returned as a nonnegative scalar or row vector. The output dimension ofsigmamatches that of the input argumentmaterial. For more information about the computation for the conductivity, seeITU Building Materials.

Complex relative permittivity of the building material, returned as a complex scalar or row vector of complex values.

The output dimension ofcomplexepsilonmatches that of the input argumentmaterial. For more information about the computation for the complex relative permittivity, seeITU Building Materials.

More About

collapse all

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.

ThebuildingMaterialPermittivityfunction uses equations from ITU-R P.2040-1 to compute these values.

  • The real part of the relative permittivity is calculated as

    epsilon=afb.

    The computation ofepsilonis based on equation (58).fis the frequency in GHz. Values foraandbare specified in Table 3 from ITU-R P.2040-1.

  • The conductivity in Siemens/m is calculated as

    sigma=cfd.

    The computation ofsigmais based on equation (59).fis the frequency in GHz. Values forcanddare specified in Table 3 from ITU-R P.2040-1.

  • The complex permittivity is calculated as

    complexepsilon=epsilon– 1isigma/ (2πfcε0).

    The computation ofcomplexepsilonis based on Equations (59) and (9b).fis the frequency in GHz.cis the velocity of light in free space. ε0= 8.854187817e-12 Farads/m, where ε0is the electric constant for the permittivity of free space.

For cases where the value ofbordis zero, the corresponding value ofepsilonorsigmaisaorc, respectively and independent of frequency.

The contents of Table 3 from ITU-R P.2040-1 are repeated in this table. The valuesa,b,c, anddare 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. ThebuildingMaterialPermittivityfunction 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 theearthSurfacePermittivityfunction.

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

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), 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

Version History

Introduced in R2020a

See Also

Functions

Objects