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Shannon–Hartley Theorem

 

Shannon-Hartley Theorem formula
\( C \;=\;  B\; log_2 \cdot ( 1 + \dfrac{S}{N} )  \)
Symbol English Metric
\( C \) = Channel Capacity
 - \( bits \;/\; s \)
\( B \) = Bandwidth of the Channel - \(MHz\)
\( S \) = Average Receiver Signal (Power)
 - \(W\)
\( N \) = Average Noise (Power)
  - \(W\)
\( S/N \) = Signal-to-Noise Ratio (SNR)
 - \(dimensionless\)

Shannon-Hartley theorem, also called Shannon's law or Shannon's Theorem, defines the maximum data rate (or channel capacity) that can be achieved over a communication channel with a specified bandwidth in the presence of noise.  The Shannon-Hartley theorem calculator computes the theoretical upper limit data rate of a channel based on the bandwidth, receiver strength and channel noise.

Common Terms Related to Shannon-Hartley
Channel Capacity  -  The maximum achievable rate of information transmission over a given communication channel without errors.
Bandwidth (B)  -  The range of frequencies available for data transmission.  A wider bandwidth allows more data to pass through the channel.
Receiver Signal (Power)  -  Signal strength is the transmitter power output as received by a reference antenna at a distance from the transmitting antenna.
Noise ()  -  Any unwanted signal which can negatively impact the quality of any transmission.
Shannon's Limit  -  A theoretical limit which tells us the maximum capacity for a signal to be transmitted through a channel.
Signal-to-Noise Ratio (SNR)  -  The ratio of the signal power to the noise power in the channel.  Higher SNR indicates less noise and better transmission quality.
log⁡2  -  The logarithm to base 2 is used because the capacity is measured in bits, which is a binary unit of information.  

Key Points about Shannon-Hartley

  • The channel capacity C sets an upper limit on how much data can be transmitted without errors.
  • If the data rate exceeds C, the error rate increases, and reliable communication becomes impossible.
  • This formula assumes ideal conditions with optimal coding schemes.

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