Just studying for the exam before it changes and looking at the official study guide page 139, it states the LdB = 20log(d) -27.55. I don't understand this formula or it derivation. My understanding is that the FSPL is a function of both distance and frequency but this only has a distance element. Is the 27.55 taking in to account the frequency element and is for a particular frequency? 27.55 is 20Log(2.385) if that is the frequency element.
OK, found the answer in the Sybex book for the previous iteration of this certification. The correct formula is
L(dB) = 20log(d) + 20log(f) -27.55
It an error in the current book.
You are correct, the equation needs to take frequency and range into account.
What you did not cite were the units, MHz or GHz, miles, kilometers, feet, or centimeters, etc. that the equation was supposedly based on. Also whether your talking about far-field or near field measurements. Regardless of the units, the equation in the book is incomplete.
The constant, 27.5 in this case, is called a "constant of proportionality" (CoP). Because decibels are involved, its value is harder to derive, and it is an additive factor as opposed to a multiplier for the same reason. You probably calculated multipliers sometime in a basic algebra class, but I doubt they involved logarithms, like dB's are based on.
The texts I have say it is 36.6 when measured in MHz and miles, or 32.4 dB where the range is expressed in kilometers.
In practice, inside of a 3x5 meter semi-anechoic RF screen room, I generally find ~34 dB to work for far-field measurements (at ~ 3m).
I don't have the gear/setup to quantitatively measure radiated power levels in the near field, but if you are extremely careful with your setup, you can make reliable A-to-B comparisons in the very near field ( < 1/10 wavelength). Expect some heated objections from purists on this last assertion.
I used a $50k+ Anritsu WLAN test set for my measurements, so don't expect to get extremely accurate numbers from lesser gear. Which you probably don't need anyway - which is one of the reasons you add a "margin" into link designs.
Hope that helps clarify some of the"numbers" involved.