---
title: "Short note: Effective isotropic radiated power"
subject: "Propagation and Antenna"
chapter: 2
key: "semester_6/propagation_and_antenna:eirp-short-note"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/eirp-short-note
site: BCT Engineering
---

# Short note: Effective isotropic radiated power

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2080 Asoj, 3 marks; 2077 Chaitra, 4 marks; 2073 Magh, 4 marks; 2072 Magh, 3 marks (asked 4 times)
- Video: [What is EIRP? | Effective Isotropic Radiated Power Explained Simply](https://www.youtube.com/watch?v=6wix2XlZ9TQ) — WaveRes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/eirp-short-note
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Write a short note on effective isotropic radiated power (EIRP).

## Short answer

EIRP = Pt·Gt/L (or Pt+Gt-L in dB) is power an isotropic antenna would need for same maximum power density. Power flux density = EIRP/(4πd²). Used in link budgets, regulatory limits, satellite footprints. ERP referenced to half-wave dipole: EIRP = ERP + 2.15 dB.

## Answer

**Effective Isotropic Radiated Power (EIRP)** is the power that an ideal isotropic antenna would have to radiate to give the same power density, in the direction of maximum radiation, as the actual antenna.

```text
EIRP = Pt · Gt / L
EIRP (dBW) = Pt (dBW) + Gt (dBi) − L (dB)
```

where Pt = transmitter power, Gt = transmit antenna gain relative to isotropic, L = feeder/cable losses.

The power flux density at distance d is then

```text
PFD = EIRP / (4π d²)   W/m²
```

**Example:** Pt = 100 W (20 dBW), Gt = 30 dBi, feeder loss = 2 dB
EIRP = 20 + 30 − 2 = 48 dBW ≈ 63.1 kW.

Importance:
- Used in **link budget** calculations for satellite and terrestrial links.
- Lets transmitters with different powers and antennas be compared with a single number.
- Regulators set EIRP limits (e.g. for Wi-Fi), and satellite footprints are drawn as EIRP contours.
- A high-gain antenna can give a large EIRP with a small transmitter power.

**ERP** (effective radiated power) is similar but is referred to a half-wave dipole: EIRP = ERP + 2.15 dB.

## Check yourself

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

1. What is EIRP?
   A. Power fed to the antenna terminals
   B. Power an isotropic antenna would need to radiate to give the same power density in the direction of maximum radiation
   C. Power lost in feeders
   D. Receiver sensitivity
   Answer: B. EIRP is the isotropic-equivalent radiated power in the direction of maximum radiation. (Key point: Definition)

2. Which is the EIRP formula in dB?
   A. Pt (dBW) - Gt (dBi) + L (dB)
   B. Pt (dBW) + Gt (dBi) + L (dB)
   C. Pt (dBW) + Gt (dBi) - L (dB)
   D. Pt (dBW) × Gt (dBi)
   Answer: C. EIRP = Pt·Gt/L, so in dB: power plus gain minus feeder loss. (Key point: Formula in dB)

3. Pt = 20 dBW, Gt = 30 dBi, feeder loss 2 dB. What is EIRP?
   A. 52 dBW
   B. 50 dBW
   C. 88 dBW
   D. 48 dBW
   Answer: D. 20 + 30 - 2 = 48 dBW, about 63.1 kW. (Key point: Numerical example)

4. How is power flux density at distance d found from EIRP?
   A. EIRP/(4π d²)
   B. EIRP·4π d²
   C. EIRP/d
   D. EIRP/(2π d)
   Answer: A. PFD = EIRP/(4πd²) W/m². (Key point: Power flux density)

5. How are EIRP and ERP related?
   A. EIRP = ERP - 2.15 dB
   B. EIRP = ERP
   C. EIRP = ERP + 2.15 dB
   D. EIRP = 2·ERP
   Answer: C. ERP is relative to a half-wave dipole, which has 2.15 dBi gain, so EIRP = ERP + 2.15 dB. (Key point: EIRP vs ERP)

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