Attenuation is the gradual loss or reduction in the strength (amplitude) of a signal as it travels through a transmission medium such as a cable, optical fiber, or the atmosphere.
This reduction occurs due to factors like resistance, scattering, absorption, and other dissipative effects within the medium.
Attenuation is quantitatively expressed in decibels (dB), a logarithmic unit that compares the input power to the output power of the signal.
Mathematically, attenuation \( A \) in decibels is given by:
\[
A = 10 \log_{10} \left( \frac{P_{\text{input}}}{P_{\text{output}}} \right) \, \text{dB},
\]
where \( P_{\text{input}} \) and \( P_{\text{output}} \) are the powers of the signal at the input and output ends of the transmission path, respectively.
Using decibels allows easier handling and comparison of large variations in signal power, as the logarithmic scale compresses wide-ranging values into a manageable scale.
In summary, attenuation measured in decibels indicates how much the signal weakens as it propagates through the medium.