Real-Life Math
In a wireless communications system, the path loss is defined as the loss in signal strength, or power, of the transmitted signal as it travels from the transmitter to the receiver.
When the transmitter and receiver are placed in an open environment with no obstructions between them, the path loss can be modeled using the free space path loss equation given by:
PL = -10 x log (lambda2 / ((4pi)2 x d2))where:
PL is the path loss in decibels (dB)
lambda is the wavelength of the transmitted signal in meters (m)
d is the distance between the transmitter and receiver in meters (m)
pi = approximately 3.14 (standard definition of pi)
In general, the wavelength of the transmitted signal is not explicitly specified. Typically, the frequency of the transmitted signal is known, and the wavelength must be calculated using the following equation:
lambda = c / f
lambda = wavelength of transmitted signal in meters (m)
c = 3 x 108 = speed of light in meters per second (m/s)
f = frequency of transmitted signal in Hz
Suppose that we have a transmitter and receiver placed outside with no obstructions between them. The transmitter generates a signal with a frequency of 900 MHz. One of the engineers working on this project has told us that the maximum path loss that the system can tolerate is 70 dB. If the path loss exceeds 70 dB, then the received signal will be too weak to properly detect.
Given this information, what is the maximum allowable separation between the transmitter and the receiver such that we can still properly detect the received signal?