Path loss is defined as the reduction in power with distance. Which expression represents free-space path loss?

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Multiple Choice

Path loss is defined as the reduction in power with distance. Which expression represents free-space path loss?

Explanation:
Free-space path loss is what you get when the transmitted power spreads out over the surface of a sphere as it travels to the receiver. The Friis transmission equation captures this, showing how received power depends on distance and wavelength. In linear terms, the free-space loss factor is (4πR/λ)², where R is the separation between antennas and λ is the wavelength. To express this loss in decibels, you take 10 times the log of the linear ratio. Because the linear factor is squared, the dB form becomes 20 log10(4πR/λ). This is the expression that shows the distance and wavelength relationship in a way that’s directly usable for links design: as distance increases or wavelength decreases (higher frequency), the free-space loss increases. The other forms mix the log base or the sign in ways that don’t match the actual squared relationship or invert the ratio, so they don’t reflect the correct FSPL behavior.

Free-space path loss is what you get when the transmitted power spreads out over the surface of a sphere as it travels to the receiver. The Friis transmission equation captures this, showing how received power depends on distance and wavelength. In linear terms, the free-space loss factor is (4πR/λ)², where R is the separation between antennas and λ is the wavelength.

To express this loss in decibels, you take 10 times the log of the linear ratio. Because the linear factor is squared, the dB form becomes 20 log10(4πR/λ). This is the expression that shows the distance and wavelength relationship in a way that’s directly usable for links design: as distance increases or wavelength decreases (higher frequency), the free-space loss increases.

The other forms mix the log base or the sign in ways that don’t match the actual squared relationship or invert the ratio, so they don’t reflect the correct FSPL behavior.

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