The expression given by is: 1. Poynting vector for power flow 2. Power gain factor ...

The expression given by is:

P_r = P_t × A_et · A_er

---

r²λ²  (W)

Options:

1. Poynting vector for power flow
2. Power gain factor
3. Friis transmission formula
4. Radar received power

Correct Answer

Option (3): Friis Transmission Formula

Explanation

The given equation represents the Friis Transmission Formula expressed in terms of the effective apertures of the transmitting and receiving antennas.

P_r = P_t × A_et A_er

---

r²λ²

Where:

• P_t = Transmitted power
• P_r = Received power
• A_et = Effective aperture of the transmitting antenna
• A_er = Effective aperture of the receiving antenna
• r = Distance between antennas
• λ = Wavelength of the transmitted signal

Standard Friis Transmission Formula

The more commonly used form of the Friis equation is:

P_r = P_t G_t G_r × λ²

---

(4πr)²

or equivalently:

P_r = P_t G_t G_r \( \frac{\lambda}{4\pi r} \)^2

Relationship Between Gain and Effective Aperture

The gain of an antenna is related to its effective aperture by:

A_e = Gλ²

---

4π

Therefore:

A_et = G_tλ²

---

4π

A_er = G_rλ²

---

4π

Substituting these expressions into the aperture-based equation yields the standard Friis transmission formula:

P_r = P_t G_t G_r \( \frac{\lambda}{4\pi r} \)^2

Conclusion

The given expression is an alternative form of the Friis Transmission Formula. It predicts the received power in a free-space communication link based on transmitted power, antenna characteristics, wavelength, and separation distance.

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