what is the relationship between antenna gain and range?
Im trying to expand the range of my wifi network, and Im not sure exactly what to expect from a +27 dbi antenna. As I understand it, this will cause the power density to increase by a factor of 2^9. Does that mean the range will increase by a factor of sqrt(2^9) from an inverse square law? If anyone knows the math behind this stuff, Id really appreciate any help. Thanks.
ok, let me preface this by warning you all: I havent taken a math or physics class in over a decade. So I apologize in advance for any logical or notational inconsistancies.
w = power density
G = initial gain
G' = final gain
P = power
r = initial distance from antenna
r' = final distance
k = proportionality constant
from this equation:
w=G*P*k / 4*pi*r^2
so if P, k, and W are constant...
G*p*k / 4*pi*r^2 = G'*p*k/4*pi*r'^2
G'/ G = r'^2 / r^2
r * sqrt(G'/ G) = r'
so, as I understand it, after a gain increase of +27 dbi, and a distance increase by a factor of sqrt(2^9), there would be an equivalent power density. Is this math correct? Does this mean that the range of my wifi network will also increase by sqrt(2^9)?