# The effect of the wavelegth on the receiving power in Friis equation

In the Friis transmission equation,

$$\frac{P_r}{P_t} = G_t G_r \left( \frac{\lambda}{4 \pi d} \right)^2,$$

it seems that if the frequency is halved while the other parameter values are fixed, the received power $$\{P_r}\$$ will quadruple since the wavelength $$\\lambda\$$ is doubled. I mean, for example, if I work on a 2 GHz system and if I switch my signal to 1 GHz, is the power level of my received signal $$\{P_r}\$$ going to become four times higher? Or do I miss something?

(I assumed the bandwidth of the antennas and other systems is suitable for both frequencies.)

• Have you ever derived Friis transmission equation by yourself? Commented Aug 27, 2023 at 11:25
• Yes with a book help
Commented Aug 28, 2023 at 15:17

That's right, but you will also have to scale your antennas by the same amount, because $$\G_{t,r}\$$ for any kind of aperture antenna is quadratic with the ratio of length of antenna to wavelength. Halving your $$\f\$$ doubled your $$\\lambda\$$ and hence divided your $$\G_t\$$ and $$\G_r\$$ by a factor of 4. So, to keep $$\G_{t,r}\$$ constant while doubling the wavelength, you need to double the sizes of your antennas as well. Often, that's not very attractive…