# Friis transmission equation (log scale calculation)

I am trying to understand the Friis transmission equation. My scenario: I consider transmit antennas ($$\T_x\$$) and receive antennas ($$\R_x\$$) at a distance R [km]. f [GHz], $$\G_{T_x}\$$ and $$\G_{R_x}\$$ in dBi, $$\L_a\$$ in dB ( loss) (<0). $$\G_{R_x}\$$ =0 that is why I would like to make a calculation in logarithmical scale. Friis equation: $$\P_r=P_tG_tG_r(\lambda/4\pi R)^2L_a\$$

and then I wrote in log scale:

$$\P_r(dB)=P_t(dB)+G_t(dB)+G_r(dB) + 10 log(\lambda/4\pi R)^2 + 10log(L_a)\$$

In Fundamentals of Digital Communication by Upamanyu Madhow, p 134

1. Why is G in log scale in dBi ? I thought that dBi is in log scale dB
2. $$\L_a\$$ in dB, in log scale is it also in dB?

$$G_{RX,dBi}$$
No, $$\L_a\$$ is a real number because it is converted to a decibel value by your main equation that you wrote.