1、 Rec. ITU-R P.525-2 1 RECOMMENDATION ITU-R P.525-2*CALCULATION OF FREE-SPACE ATTENUATION (1978-1982-1994) Rec. ITU-R PN.525-2 The ITU Radiocommunication Assembly, considering a) that free-space propagation is a fundamental reference for radio-engineering, recommends 1. that the methods in Annex 1 be
2、 used for the calculation of attenuation in free space. ANNEX 1 1. Introduction As free-space propagation is often used as a reference in other texts, this Annex presents relevant formulae. 2. Basic formulae for telecommunication links Free-space propagation may be calculated in two different ways,
3、each of which is adapted to a particular type of service. 2.1 Point-to-area links If there is a transmitter serving several randomly-distributed receivers (broadcasting, mobile service), the field is calculated at a point located at some appropriate distance from the transmitter by the expression: e
4、 = 30pd(1) where: e : r.m.s. field strength (V/m) (see Note 1) p : equivalent isotropically radiated power (e.i.r.p.) of the transmitter in the direction of the point in question (W) (see Note 2) d : distance from the transmitter to the point in question (m). Equation (1) is often replaced by equati
5、on (2) which uses practical units: emV/m= 173 pkWdkm(2) For antennas operating in free-space conditions the cymomotive force may be obtained by multiplying together e and d in equation (1). Its dimension is volts. _ *Radiocommunication Study Group 3 made editorial amendments to this Recommendation i
6、n 2000 in accordance with Resolution ITU-R 44. 2 Rec. ITU-R P.525-2 Note 1 If the wave is elliptically polarized and not linear, and if the electric field components along two orthogonal axes are expressed by exand ey, the left-hand term of equation (1) should be replaced by eexy22+ .exand eycan be
7、deduced only if the axial ratio is known. e should be replaced by e 2 in the case of circular polarization. Note 2 In the case of antennas located at ground level and operating on relatively low frequencies with vertical polarization, radiation is generally considered only in the upper half-space. T
8、his should be taken into account in determining the e.i.r.p. (see Recommendation ITU-R P.368). 2.2 Point-to-point links With a point-to-point link it is preferable to calculate the free-space attenuation between isotropic antennas, also known as the free-space basic transmission loss (symbols: Lbfor
9、 A0), as follows: Lbf= 20 log Ge8Ge7Ge6Gf8Gf7Gf64 dmmmmmmdB (3) where: Lbf: free-space basic transmission loss (dB) d : distance : wavelength, and d and are expressed in the same unit. Equation (3) can also be written using the frequency instead of the wavelength. Lbf= 32.4 + 20 log + 20 log dmmmmmm
10、dB (4) where: f : frequency (MHz) d : distance (km). 2.3 Relations between the characteristics of a plane wave There are also relations between the characteristics of a plane wave (or a wave which can be treated as a plane wave) at a point: 224120=rpes (5) where: s : power flux-density (W/m2) e : r.
11、m.s. field strength (V/m) pr : power (W) available from an isotropic antenna located at this point : wavelength (m). 3. The free-space basic transmission loss for a radar system (symbols: Lbror A0r) Radar systems represent a special case because the signal is subjected to a loss while propagating bo
12、th from the transmitter to the target and from the target to the receiver. For radars using a common antenna for both transmitter and receiver, a radar free-space basic transmission loss, Lbr, can be written as follows: Lbr= 103.4 + 20 log + 40 log d 10 log mmmmmmdB (6) where: : radar target cross-s
13、ection (m2) d : distance from the radar to the target (km) f : frequency of the system (MHz). Rec. ITU-R P.525-2 3 The radar target cross-section of an object is the ratio of the total isotropically equivalent scattered power to the incident power density. 4. Conversion formulae On the basis of free
14、-space propagation, the following conversion formulae may be used. Field strength for a given isotropically transmitted power: E = Pt 20 log d + 74.8 (7) Isotropically received power for a given field strength: Pr= E 20 log f 167.2 (8) Free-space basic transmission loss for a given isotropically tra
15、nsmitted power and field strength: Lbf= Pt E + 20 log f + 167.2 (9) Power flux-density for a given field strength: S = E 145.8 (10) where: Pt: isotropically transmitted power (dB(W) Pr: isotropically received power (dB(W) E : electric field strength (dB(V/m) f : frequency (GHz) d : radio path length (km) Lbf: free-space basic transmission loss (dB) S : power flux-density (dB(W/m2). Note that equations (7) and (9) can be used to derive equation (4).
