 units. The units of power must be consistent, either in dBm or dBW. If the transmitter power is in dBW, the EIRP will be in dBW and the distant-end RSL must also be in dBW. We then algebraically add the EIRP to the free-space loss in dB (often called path loss), the result is the isotropic4 receive level (IRL). When we add the receive antenna gain to the IRL and subtract the receive transmission line losses, we get the receive signal level (RSL). This relationship of path losses and gains is illustrated in Figure 9.7. Antenna EIRP = +27.5 dBW Line loss (each end) = 2.5 dB Antenna gain (each end) = 30 dB 0 dBW Line losses Free-space path loss = 140 dB Line losses Antenna gain 7 GHZ -100 dBW Receiver input -85 dBW 20 mi Figure 9.7 LOS microwave link gains and losses (simplified). Transmitter power output is 1 W or 0 dBW. 4 An isotropic antenna is an antenna that is uniformly omnidirectional and thus, by definition, it has a 0-dB gain. It is a hypothetical reference antenna. The isotropic receive level (IRL) is the power level we would expect to achieve at that point using an isotropic antenna. 9.2 RADIO SYSTEMS Path Loss. For operating frequencies up to about 10 GHz, path loss is synonymous with free-space loss. This represents the steady decrease of power flow as the wave expands out in space in three dimensions. The formula for free-space loss is (9.4a) where L is the free-space loss between isotropic antennas, F is measured in GHz, and D is in statute miles. In the metric system Ldb = 92.4 - 20 log FGHz + 20 log Dkm, (9.4b) where D is in kilometers. Calculation of EIRP. Effective isotropically radiated power is calculated by adding decibel units: transmitter power (in dBm or dBW), the transmission line losses in dB (a negative value because it is a loss), and the antenna gain in dBi.5 EIRPdBW = trans. output powerdBW - trans. line (9.5) Figure 9.8 shows this concept graphically. Example. If a microwave transmitter has 1 W (0 dBW) of power output, the waveguide loss is 3 dB and the antenna gain is 34 dBi, what i