Received Power Calculator Formula

Received Power Formula:

\[ P_r = P_t \times G_t \times G_r \times \left(\frac{\lambda}{4 \pi d}\right)^2 \]

Transmitted Power (P_t):

Watts (W)

Transmitter Gain (G_t):

dimensionless

Receiver Gain (G_r):

dimensionless

Wavelength (λ):

meters (m)

Distance (d):

meters (m)

Received Power (P_r):

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1. What is the Received Power Calculator?

Definition: This calculator estimates the power received by an antenna based on the Friis transmission equation.

Purpose: It helps engineers and technicians in wireless communications determine signal strength at a receiver.

2. How Does the Calculator Work?

The calculator uses the Friis transmission equation:

\[ P_r = P_t \times G_t \times G_r \times \left(\frac{\lambda}{4 \pi d}\right)^2 \]

Where:

\( P_r \) — Received power (Watts, W)
\( P_t \) — Transmitted power (Watts, W)
\( G_t \) — Transmitter gain (dimensionless)
\( G_r \) — Receiver gain (dimensionless)
\( \lambda \) — Wavelength (meters, m)
\( d \) — Distance between antennas (meters, m)

Explanation: The equation calculates how much power is received given the transmission power, antenna gains, wavelength, and distance.

3. Importance of Received Power Calculation

Details: Accurate received power estimation is crucial for designing reliable wireless communication systems and determining coverage areas.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Default gains are set to 1 (isotropic antennas). Wavelength can be calculated from frequency using λ = c/f.

5. Frequently Asked Questions (FAQ)

Q1: What are typical transmitter and receiver gains?
A: Gains vary by antenna type. Dipole antennas have ~2.15 dBi gain, while directional antennas can have 10 dBi or more.

Q2: How does distance affect received power?
A: Received power decreases with the square of the distance (inverse square law).

Q3: What's the relationship between wavelength and frequency?
A: Wavelength (λ) = speed of light (c) / frequency (f). For example, 2.4 GHz has λ ≈ 0.125 m.

Q4: Does this account for real-world losses?
A: No, this is the ideal case. Real systems have additional losses from obstacles, atmospheric absorption, etc.

Q5: What if my result is extremely small?
A: Received power is often in microwatts or nanowatts for long distances. Consider using dBm for more manageable numbers.