User talk:Hgfernan

=Friis law=

Friis law can be stated as:

$$P_r \ = \ P_x G_x G_r \Bigg(\frac{\lambda}{4{\pi}r}\Bigg)^2$$

where:
 * $$P_r$$ is the power received;
 * $$P_x$$ is the power transmitted;
 * $$G_x$$ is the gain of the antenna that transmits the signal;
 * $$G_r$$ is the gain of the antenna that receives the signal;
 * $$\lambda$$ is the wavelength of the signal;
 * $$r$$ is the distance between the two antennas.

The law can be restated in terms of the distance, when it becomes useful to estimate the distance a given arrange can reach:

$$r = \frac{\lambda}{4\pi}\sqrt{\frac{P_r}{P_x G_x G_r}}$$

Another form can be used to estimate the transmitted power needed for a given arrange:

$$P_x \ = \frac{P_r}{G_x G_r} \Bigg(\frac{4{\pi}r}{\lambda}\Bigg)^2$$

The form below can be used to estimate the transmission antenna needed for a given arrange:

$$G_x \ = \frac{P_r}{P_x G_r} \Bigg(\frac{4{\pi}r}{\lambda}\Bigg)^2$$

Analogously, for the receiving antenna needed for a given arrange:

$$G_r \ = \frac{P_r}{P_x G_x} \Bigg(\frac{4{\pi}r}{\lambda}\Bigg)^2$$

One last form lets one guess the value of $$\lambda$$ for a given context:

$$\lambda = 4\pi{r}\sqrt{\frac{P_x G_x G_r}{P_r}}$$