Shannon-Hartley Theorem formula |
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| \( C \;=\; B\; log_2 \cdot ( 1 + \dfrac{S}{N} ) \) | ||
| 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.
log2 - 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.
