Free Space Path Loss (FSPL)

Free Space Path Loss (FSPL) quantifies the attenuation of signal strength that occurs when a radio wave propagates through free space—without obstacles, reflections, or interference. It represents the theoretical minimum loss due to the spreading of the wavefront over distance and is critical for estimating received power in wireless communication systems.

FSPL Formula

In linear form:

FSPL = (4πdf / c)²

In decibels (commonly used):

FSPL (dB) = 20 log₁₀(d) + 20 log₁₀(f) + 20 log₁₀(4π / c)

Or, with standard units (d in kilometers, f in MHz):

FSPL (dB) = 20 log₁₀(d) + 20 log₁₀(f) + 32.45

Where:

• d = Distance between transmitter and receiver (km)

• f = Frequency of the signal (MHz)

• c = Speed of light (~3 × 10⁸ m/s)

• 32.45 = Constant derived from unit conversion factors

Example Calculation

For a 2.4 GHz (2,400 MHz) signal transmitted over 100 meters (0.1 km), the free space path loss is:

FSPL ≈ 20 log₁₀(0.1) + 20 log₁₀(2400) + 32.45 ≈ 80 dB

This corresponds to a power ratio of 10⁻⁸, meaning that only one hundred-millionth of the transmitted power reaches the receiver—assuming ideal free-space conditions.

FSPL in Wireless System Design

FSPL is used as the baseline loss in wireless link budget calculations and is especially relevant in:

• Satellite communications

• Cellular and Wi-Fi networks

• Point-to-point microwave links

• Radar systems

• RF propagation modeling

While FSPL assumes ideal free-space conditions, it is commonly extended with additional terms to account for real-world factors such as:

• Atmospheric attenuation

• Multipath fading

• Obstructions and diffraction

• Terrain and building losses

Applications and Practical Use

Engineers use FSPL in:

• Link budget planning to ensure sufficient received power

• Antenna alignment and gain selection

• Coverage estimation for fixed and mobile radio systems

• Compliance testing involving minimum required field strength or radiated power