1、 Recommendation ITU-R P.2040-1 (07/2015) Effects of building materials and structures on radiowave propagation above about 100 MHz P Series Radiowave propagation ii Rec. ITU-R P.2040-1 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical u
2、se of the radio-frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World a
3、nd Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for t
4、he submission of patent statements and licensing declarations by patent holders are available from http:/www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of
5、ITU-R Recommendations (Also available online at http:/www.itu.int/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodeterminatio
6、n, amateur and related satellite services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management SNG Satellite
7、news gathering TF Time signals and frequency standards emissions V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2015 ITU 2015 All rights reserved. No part of this publication
8、 may be reproduced, by any means whatsoever, without written permission of ITU. Rec. ITU-R P.2040-1 1 RECOMMENDATION ITU-R P.2040-1 Effects of building materials and structures on radiowave propagation above about 100 MHz (Question ITU-R 211/3) (2013-2015) Scope This Recommendation provides guidance
9、 on the effects of building materials and structures on radio-wave propagation. The ITU Radiocommunication Assembly, considering a) that electrical properties of materials and their structures strongly affect radiowave propagation; b) that it is necessary to understand the losses of radiowaves cause
10、d by building materials and structures; c) that there is a need to give guidance to engineers to avoid interference from outdoor to indoor and indoor to outdoor systems; d) that there is a need to provide users with a unified source for computing effects of building materials and structures, noting
11、a) that Recommendation ITU-R P.526 provides guidance on diffraction effects, including those due to building materials and structures; b) that Recommendation ITU-R P.527 provides information on the electrical properties of the surface of the Earth; c) that Recommendation ITU-R P.679 provides guidanc
12、e on planning broadcasting-satellite systems; d) that Recommendation ITU-R P.1238 provides guidance on indoor propagation over the frequency range 900 MHz to 100 GHz; e) that Recommendation ITU-R P.1406 provides information on various aspects of propagation relating to terrestrial land mobile and br
13、oadcasting services in the VHF and UHF bands; f) that Recommendation ITU-R P.1407 provides information on various aspects of multi-path propagation; g) that Recommendation ITU-R P.1411 provides propagation methods for short paths in outdoor situations, in the frequency range from about 300 MHz to 10
14、0 GHz; h) that Recommendation ITU-R P.1812 provides a propagation prediction method for terrestrial point-to-area services in the frequency range 30 MHz to 3 GHz, 2 Rec. ITU-R P.2040-1 recommends that the information and methods in Annex 1 and Annex 2 should be used as a guide for the assessment of
15、the effects of building material properties and structures on radiowave propagation, and in developing deterministic models of propagation involving the built environment. Annex 1 describes basic principles, and provides expressions to evaluate reflection from and transmission through building mater
16、ials and structures. It also includes a model for electrical properties as a function of frequency, and a table of parameters for relevant materials. Annex 2 gives definitions for various types of propagation loss associated with buildings, and provides guidance on measuring building entry losses. E
17、xamples of building-entry loss measurements may be found in Report ITU-R P.BEL_MEASUREMENT. Annex 1 1 Introduction This Annex provides guidance on the effects of building material electrical properties and structures on radio-wave propagation. Section 2 describes fundamental principles concerning th
18、e interaction of radio waves with building materials, defines various parameters in use for these purposes, and gives basic expressions for reflection from and transmission through single material interfaces and single and multiple layer slabs, typical of building construction. Section 3 defines a m
19、odel for electrical properties, and a table of parameters for various building materials. 2 Basic principles and theory Radio waves that interact with a building will produce losses that depend on the electrical properties of the building materials and material structure. In this section, theoretica
20、l effects of material electrical properties and structure on radio-wave propagation will be discussed. 2.1 Theory of material electrical properties 2.1.1 Introduction This section describes the development of simple frequency-dependent formulae for the permittivity and conductivity of common buildin
21、g materials. The formulae are based on curve fitting to a number of published measurement results, mainly in the frequency range 1-100 GHz. The aim is to find a simple parameterization for use in indoor-outdoor ray trace modelling. The characterization of the electrical properties of materials is pr
22、esented in a number of different ways in the literature. These are described in 2.1.2 in order that the measured data can be reduced to a common format. Rec. ITU-R P.2040-1 3 2.1.2 Method 2.1.2.1 Definitions of electrical constants The following treatment deals only with non-ionized, non-magnetic ma
23、terials, and throughout we therefore set the free charge density, f, to zero and the permeability of the material, , to the permeability of free space 0. The fundamental quantities of interest are the electrical permittivity, , and the conductivity, . There are many ways of quantifying these paramet
24、ers in the literature, so we first make explicit these different representations and the relations between them. 2.1.2.2 Derivation The starting point is the wave equation derived from Maxwells equations. Under the above assumptions, the wave equation for the electric field is: tJt EE f02202 (1) whe
25、re: : (vector) electric field intensity (V/m) Jf : current density of free charges (A/m2) : dielectric permittivity (F/m) 0 : permeability of free space (N/A2) = 4 107 by definition. In a conductor, is related to through Ohms Law by: EJf (2) where: : conductivity (S/m). Combining equations (1) and (
26、2) gives: tEt EE 02202 (3) Writing in exponential notation: rktjeEE 0 (4) where: : value of for t = = 0 (V/m) : (vector) wave number (m1) magnitude = 2/ where is the wavelength in m : angular frequency (s1) = 2f where f is the frequency in s1 : (vector) spatial distance (m). EEfJ EE0E E rk4 Rec. ITU
27、-R P.2040-1 and substituting in equation (3) gives 0 0202 jk (5) where k is the magnitude of . Equation (5) shows that the electric field intensity propagates as an attenuated sinusoidal wave. 2.1.2.3 Non-conducting dielectric In a non-conducting dielectric ( = 0) the field is unattenuated and from
28、equation (5) the velocity of propagation, v (= /k), is: (6) is conventionally written in terms of the relative permittivity and the permittivity of free space: 0 (7) where : relative dielectric permittivity of the medium concerned 0: dielectric permittivity of free space = 8.854 1012 (F/m). Thus the
29、 velocity of propagation in a medium of relative permittivity can be written: cv(8) where c is the velocity of light in free space (= ). In other words, is the refractive index of the dielectric medium. 2.1.2.4 Conducting dielectric When 0, the wave attenuates as it propagates. It is convenient in t
30、his case to define a complex relative permittivity which may be derived as follows. Equation (5) can be rearranged, with the substitution 002 /1 c , to give: 022 jc (9a) Since equation (8) gives 22c, this can be interpreted as a complex relative permittivity given by 0 j(9b) This shows that the rela
31、tive permittivity defined for a pure dielectric, becomes the real part of the more general, complex relative permittivity defined for a conducting dielectric. There are no universally accepted symbols for these terms. In this Recommendation, relative permittivity is written in the form: j (10) k01v0
32、0/1 Rec. ITU-R P.2040-1 5 where and are the real and imaginary parts. Using equation (9b), the imaginary part is given by: 0(11) Note that the sign of the imaginary part of is arbitrary, and reflects the sign convention in equation (4). In practical units, equation (11) gives a conversion from “ to
33、: GHz05563.0 f (12) Another formulation of the imaginary part of is in terms of the loss tangent, defined as: tan(13) and so: (14) From equation (10) this gives: )tan1( j (15) and in practical units: GHzt an05563.0 f (16) Another term sometimes encountered is the Q of the medium. This is defined as:
34、 (17) and is the ratio of the displacement current density to the conduction current density Jf. For non-conductors, Q . From equation (14): (18) Yet another term encountered is the complex refractive index n which is defined to be . Writing n in terms of its real and imaginary parts: njnn (19) tanQ
35、tD / tan/1Q6 Rec. ITU-R P.2040-1 , “ and are given from equations (10) and (12) by: GHz1113.022)(2)(fnnnnnn (20) 2.1.2.5 Attenuation rate A conducting dielectric will attenuate electromagnetic waves as they propagate. To quantify this, substitute equation (5) in equation (4) and simplify using equat
36、ion (14): rkjtjEE 00 t a n1e x p (21) where: : (vector) wave number (m1) in free space. The imaginary part under the square root sign leads to an exponential decrease of the electric field with distance: (22) In a practical calculation using complex variables, the attenuation distance, , at which th
37、e field amplitude falls by 1/e, can be evaluated as: 0Im 1k(23a) where the function “Im” returns the imaginary part of its argument. Analytically it can be shown that: cos1 cos210k(23b) which can be evaluated by calculating tan from and and inverting to obtain cos . More direct evaluation is possibl
38、e in the two limits of 0 (dielectric limit) and (good conductor limit). By choosing the appropriate approximation of the term under the square root sign in equation (21) these limits are: tan210kdie le c tric(24) and: t an210kc o n d u c to r(25) Equations (24) and (25) are accurate to about 3% for
39、tan 15 (conductor). conductor is usually referred to as the “skin depth”. For practical purposes the attenuation rate is a more useful quantity than the attenuation distance, and is related to it simply by 0k /exp0 rEE Rec. ITU-R P.2040-1 7 (26) where: A: attenuation rate in dB/m (with in m). Substi
40、tuting equations (24) and (25) in equation (26) and converting to practical units gives: 1636d ielectricA(27a) GHz8.545 fA c o n d u c to r (27b) 2.1.3 Frequency dependence of material properties In the literature, the real part of the dielectric constant, , is always given, but often the frequency
41、is not specified. In practice for many materials, the value of is constant from DC up to around 5-10 GHz after which it begins to fall with frequency. The value of is usually a strong function of frequency in the band of interest, increasing with frequency. This may be one reason why the imaginary p
42、art of the dielectric constant, or the loss tangent, is often specified in the literature: equations (12) and (16) show that these terms remove a linear frequency dependence compared to the frequency dependence of . For each material a simple regression model for the frequency dependence of can be o
43、btained by fitting to measured values of at a number of frequencies. 2.1.4 Models of material properties frequency dependence In order to derive the frequency dependence of material properties, the values of the electrical constants of the materials can be characterized in terms of the measurement f
44、requency, real part () and imaginary part () of the relative permittivity, loss tangent (tan ) and conductivity (). Expressions in 2.1.2.4 permit conversions between these quantities. For the conductivity, there is usually statistically significant evidence for an increase with frequency. In this ca
45、se the trend has been modelled using: dfc GHz (28) where c and d are constants characterizing the material. This is a straight line on a log()log(f) graph. The trend line is the best fit to all available data. For the relative permittivity one can assume similar frequency dependency: bfa GHz (29) wh
46、ere a and b are constants characterizing the material. However in almost all cases there is no evidence of a trend of relative permittivity with frequency. In these cases a constant value can be used at all frequencies. The constant value is the mean of all the values plotted. Some examples are give
47、n in Table 3. /686.8lo g20 10 eA8 Rec. ITU-R P.2040-1 2.2 Effects of material structure on radiowave propagation 2.2.1 Plane wave reflection and transmission at a single planar interface This section considers a plane wave incident upon a planar interface between two homogeneous and isotropic media
48、of differing electric properties. The media extend sufficiently far from the interface such that the effect of any other interface is negligible. This may not be the case with typical building geometries. For example, propagation losses due to a wall may be influenced by multiple internal reflections. Methods for calculating reflection and transmission coefficients of single-layer and multi-layer slabs are given in 2.2.2. A plane wave is useful for analysis purposes, but the concept is largely t
