---
title: "Received power: 0.5 km, 1 GHz circuit"
subject: "Propagation and Antenna"
chapter: 5
key: "semester_6/propagation_and_antenna:received-power-0-5km-1ghz"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/received-power-0-5km-1ghz
site: BCT Engineering
---

# Received power: 0.5 km, 1 GHz circuit

Propagation and Antenna · Chapter 5: Propagation between Antennas

- Asked in: 2075 Baisakh, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/received-power-0-5km-1ghz
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-5

## Question

Find the received power (in dBm) at a distance of 0.5 km over a free space 1 GHz circuit consisting of a transmitting antenna with 25 dB gain and a receiving antenna gain of 20 dB. The power radiated by the transmitting antenna is 150 W.

## Short answer

λ = 0.3 m. Free space loss = 20 log(4π×500/0.3) = 86.42 dB. Transmit power 150 W = 51.76 dBm. Received power Pr = 51.76 + 25 + 20 − 86.42 = 10.34 dBm (10.8 mW).

## Answer

Using the Friis transmission equation in dB form.

#### Given

- d = 0.5 km = 500 m, f = 1 GHz
- Gt = 25 dB, Gr = 20 dB, Pt = 150 W

#### Step 1: Wavelength

```text
λ = c/f = 3×10⁸ / 10⁹ = 0.3 m
```

#### Step 2: Free space loss

```text
4πd/λ = 4π × 500 / 0.3 = 2.094×10⁴
LFS   = 20 log(2.094×10⁴) = 86.42 dB

Check: 32.44 + 20 log 0.5 + 20 log 1000
     = 32.44 − 6.02 + 60 = 86.42 dB
```

#### Step 3: Transmit power in dBm

```text
Pt = 10 log(150 / 1 mW) = 10 log(1.5×10⁵) = 51.76 dBm
```

#### Step 4: Received power

```text
Pr = Pt + Gt + Gr − LFS
   = 51.76 + 25 + 20 − 86.42
   = 10.34 dBm
Pr = 10^1.034 mW ≈ 10.8 mW
```

**Answer: Received power ≈ 10.34 dBm (about 10.8 mW).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At 1 GHz the wavelength is:
   A. 0.3 m
   B. 0.03 m
   C. 30 m
   D. 3 m
   Answer: A. 3×10^8/10^9 = 0.3 m. (Key point: Wavelength)

2. LFS at 1 GHz over 0.5 km is:
   A. 86.42 dB
   B. 92.44 dB
   C. 66.42 dB
   D. 106.42 dB
   Answer: A. 32.44 − 6.02 + 60 = 86.42 dB. (Key point: Free space loss)

3. 150 W in dBm is about:
   A. 150 dBm
   B. 21.8 dBm
   C. 51.76 dBm
   D. 41.76 dBm
   Answer: C. 10 log(1.5×10^5) = 51.76 dBm. (Key point: Power in dBm)

4. The received power is about:
   A. 31.76 dBm
   B. 62.1 dBm
   C. 10.34 dBm
   D. −10.34 dBm
   Answer: C. 51.76 + 25 + 20 − 86.42 = 10.34 dBm. (Key point: Result)

## Close variants set in other exams

- [Received power: 50 km, 10 GHz link](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Areceived-power-50km-10ghz) — Propagation and Antenna, chapter 5, asked 2×

## Related in Propagation and Antenna

- [Received power: 15.5 km, 3.4 GHz, dish receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amax-received-power-15-5km) — Propagation and Antenna, chapter 5
- [Received power: 100 MHz, 0.75 km](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Areceived-power-100mhz-0-75km) — Propagation and Antenna, chapter 5
- [Free space path loss: 6 GHz, 10,500 km](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afspl-derivation-6ghz-10500km) — Propagation and Antenna, chapter 5
- [Microwave link: 90 km, 10 GHz, 40 dB antennas](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amicrowave-link-90km-10ghz) — Propagation and Antenna, chapter 5
- [Receiving antenna gain](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Areceiving-antenna-gain) — Propagation and Antenna, chapter 2
- [10 GHz LOS link loss and Friis derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alos-link-10ghz-100km-friis) — Propagation and Antenna, chapter 5

## Related in other subjects

- [Numerical: 50 W in dBm/dBW and received power](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Atransmit-power-dbm-free-space) — Wireless Communication, chapter 3
- [Numerical: free-space received power (165 W, 325 MHz)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afree-space-received-power-165w) — Wireless Communication, chapter 3
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- [Numerical: λ/4 monopole and two-ray received power](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amonopole-two-ray-received-power) — Wireless Communication, chapter 3