buildingMaterialPermittivity

Permittivity and conductivity of building materials

Syntax

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

Description

[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 the 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 – 1i sigma / (2πfcε₀).

  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. ε₀ = 8.854187817e-12 Farads/m, where ε₀ 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	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] ITU-R P.2040-1. "Effects of Building Materials and Structures on Radiowave Propagation Above 100MHz." International Telecommunications Union - Radiocommunications Sector (ITU-R). July 2015.

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.