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).
