Communications, Radar & Electronic Warfare (201.. - Index of

368 Communications, Radar and Electronic WarfareIn logarithmic terms, this becomes:x(dB) = 1010g(A) + 10 log (B) +2010g(C)-3010g(D)The squared and cubed terms are turned into multiplying coefficients when convertinginto the logarithmic form as10g(A X ) = x· 1010g(A)We can work through the free space loss formula to consolidate these points. The linearform of the equation is:Converting to the logarithmic form, we get:L =1010g(4n2L = 21. 984 + 20 log(d) + 20 log(J)- 16 9.542L = 20 1 og(d) + 20 1 og(J) - 147.55 8However, this formula is in the form of metres for distance and hertz for frequency.We normally work in units of km and MHz. If we express the units in the preferredformat, we can adjust the formula to a more useful form:f(MHz) = f(H::) · 1062010g[106(dB)]And similarly, converting between metres and kilometres, we get a value of 60 dB.Adding the 180 dB of the sum of both of these gives:L = 20 /og(d) + 20 log(I) + 32 .442This is the free space loss normally used.Values expressed in dB without units are ratios. Often, we will express dB valueswith reference to a particular set of units, such as dBm or dBW. Thus, we have a valueof lOOW, which is 20 dBW, or 50 dBm (dBm being 30 dB lower than dBW).