Path Loss

Standard far field path loss is usually calculated using formula with different constants depending on the chosen distance units such as miles or kilometers. Each unit requires a different constant in the formula. An approach that is somewhat more insightful is to use wavelengths. In some cases this allows rough calculation to be made mentally.

The catch is that if you don't know the number of wavelengths, you will have to calculate that first. And before you do that, you have to know how long a wavelength is at your frequency of interest.

Wavelength in meters is 300/Mhz. or in feet is 984/Mhz.

Number of wavelengths, is the path distance divided by the length of your wavelength.

Now you can use the formula below.

The formula is PLdB = 22 + 20 X log (number of wavelengths)

The 22 comes from -20 X log (1/(4 pi)) which is the isotropic spreading factor,

which is actually 21.98419728..but, 22 is close enough for our purposes here.

The second part for mental calculations simplifies to:

add 6dB for double the distance or, subtract 6 dB for half the distance
add 20 dB for each power of ten increase to the number of wavelengths
subtract 20 dB for each zero removed from the number of wavelengths
add or subtract 9.5 db for three to one changes and 16.9 for 7 to 1.

Examples:

Wavelengths	Mental Process	Result in dB
1	Add 0 to 22	22
2	Add 6 to 22	28
3	Add 9.5 to 22	31.5
4	Add 12 to 22 or 6 to 28	34
5	Add 20 to 22 and sub. 6	36
6	Add 9.5 and 6 to 22	37.5
7	Add 16.9 (Formula) to 22	38.9
8	Add 18 to 22	40
9	Add 9.5 and 9.5 to 22	41
10	Add 20 to 22	42
50	Add 20 to 36 or Add 40 to 22 and sub. 6	56
2000	Add 60 and 6 to 22 or Add 60 to 28	88

The dB calculation part of this process (forget the 22) also works for voltage dB or can be modified for power calculations by using 3 instead of 6 and and 10 instead of 20 .(divide all above constants by 2)