Friis transmission equation (log scale calculation)

Question

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?

Answer 1

Why is G in log scale in dBi ? I thought that dBi is in log scale dB

In case you didn't know dBi means the gain of a real antenna compared to the gain of the theoretical but useful isotropic antenna. So when the formula says this: -

$$G_{RX,dBi}$$

It refers to the gain of the actual receive antenna compared to the gain of an isotropic antenna and expressed in decibels.

La in dB, in log scale is it also in dB?

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