# What is Received power value when distance value is 0 in Friis equation [closed]

The Friis equation is as follow.

$$P_r = P_tA_rA_t(\lambda/(4\pi d))^\alpha$$

where $$d$$ is distance between terminals, $$P_r$$ is received power, $$P_t$$ is transmission power, $$A_r, A_t$$ are the rx, tx antenna gains, respectively, and $$\lambda$$ is wavelength.

If $$d$$ is 0, the $$P_r$$ must be $$P_t$$. But in this equation, the $$P_r$$ is infinity.

How can I find $$P_r$$ in this situation? What formula is needed?

This equation discribes the path loss in wireless communication link between two communicated devices. While eliminating one parameters will change the condition (wireless senario here) then we will go to another scenario (wire) because of Zero Distance condition. The Pr= Pt for connected (full matched connection) using connectors.

This formula is only valid for distances $$d$$ where the antennas are in the far field of each other, which implies that $$d >> \lambda$$.

When the distance is $$d=0$$, then there is no attenuation and basically you have a wired system with $$P_r=P_t$$; no formula is necessary.