## Free Space Path Loss - Friis Equation
Note that when the distance (d) is equal to 1/4π, path loss is calculated as 0 dB, and a shorted distances the path loss is calculated as a negative number. This clearly goes against intuition, and rightly so. Therefore, this equation has practical limits. A typical rule of thumb is to not use this path loss equation for distances less than about a wavelength. At less than a wavelength, physical factors like antenna dimensions dominate and force the use of electromagnetic field equations. The Friis Equation (H.T. Friis, 1946) gives a more complete accounting for all the factors from the transmitter to the receiver:
Information in the transmitted signal is seldom concentrated at a single frequency, so the path loss will actually be different for every frequency component in the signal. Fortunately, the ratio of the bandwidth to center frequency is usually small enough to not matter. Still, a signal that is transmitted with a constant power across some bandwidth will appear at the receiver with a power slope that decreases at the upper end of the band.
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