Lognormal shadowing + deriving pdf from normal distribution

1. May 5, 2009

JamesGoh

Im aware that for the normal distribution, the pdf is

$$f_{X}(x) = (1/$$$$\sqrt{2\pi}\sigma)$$$$exp( (x-\mu)^{2} /2\sigma^{2} )$$

and for the lognormal pdf (in the case of a faded signal) is

$$f_{f}(F) = 20/( ln(10)F\sigma_{F}\sqrt{2\pi} )$$$$exp[-(20log_{10}(F)-\mu_{dB})^{2}/2\sigma_{F}^{2}]$$

where $$x$$ is the amplitude

$$F$$ is the small scale averaged field strength

However Im having trouble trying to realise how the ln(10) and 20 could have possibly appeared in the equation, and the reasoning behind it. Can this be attributed to the fact that the power is the square of the amplitude ?

cheers