Main Content

buildingMaterialPermittivity

Permittivity and conductivity of building materials

Since R2020a

Description

[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].

example

Examples

collapse all

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")

Figure contains an axes object. The axes object with title Permittivity and Conductivity of Concrete, xlabel Frequency (Hz), ylabel Conductivity (S/m) contains 2 objects of type line.

Input Arguments

collapse all

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

collapse all

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.

More About

collapse all

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 = epsiloni·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.

Extended Capabilities

Version History

Introduced in R2020a

expand all