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 permittivityepsilon
isepsilon
= 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 conductivitysigma
in Siemens/m issigma
= 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 permittivitycomplexepsilon
iscomplexepsilon
=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 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 | 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
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 R2020aR2024a: 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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