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Received power: 100 MHz, 0.75 km

Short answer

λ = 3 m, free space loss = 69.94 dB. Transmit power 120 W = 20.79 dBW. Pr = 20.79 + 30 + 25 − 69.94 = 5.85 dBW (3.84 W).

A 100 MHz circuit consists of a transmitting and receiving antenna of 30 dB and 25 dB gains respectively. The power radiated by the transmitting antenna is 120 W. Using Friis transmission equation find the received power at a distance of 0.75 km over a free space.

Using the Friis transmission equation Pr = Pt·Gt·Gr·(λ/4πd)².

Given

  • f = 100 MHz, d = 0.75 km = 750 m, Pt = 120 W
  • Gt = 30 dB = 1000, Gr = 25 dB = 316.23

Step 1: Wavelength

λ = c/f = 3×10⁸ / 10⁸ = 3 m

Step 2: Free space loss

4πd/λ = 4π × 750 / 3 = 3141.6
LFS   = 20 log(3141.6) = 69.94 dB

Step 3: Received power (ratio form)

Pr = 120 × 1000 × 316.23 × (1/3141.6)²
   = 3.795×10⁷ / 9.870×10⁶
   = 3.84 W

Check in dB

Pt = 10 log 120 = 20.79 dBW
Pr = 20.79 + 30 + 25 − 69.94 = 5.85 dBW = 35.85 dBm
10^0.585 = 3.84 W

Answer: Received power ≈ 3.84 W (5.85 dBW).

✓ Answer checked by Claude Opus 5.5 (high effort)

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