Shannon–Hartley Theorem

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

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.

 

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 Advantages and Disadvantages
Advantages	Disadvantages
Provides an absolute upper limit for reliable data transmission over a noisy channel, serving as a benchmark for system design. Helps engineers optimize systems by understanding the trade-offs between bandwidth, signal power, and noise. Applicable to all communication systems, including wired, wireless, and optical communication, making it a versatile tool in communication theory. Encourages the development of advanced coding and modulation techniques to approach the channel capacity. Quantifies the effect of noise on data transmission and helps in designing systems resilient to interference. Helps in deciding the required bandwidth or power for a desired data rate, leading to efficient use of resources.	Assumes perfect knowledge of the channel and ideal coding schemes, which may not be practical or achievable in real-world scenarios. Practical systems often face additional constraints, such as hardware limitations, interference, and non-linearities, not accounted for in Shannon's theory. The capacity formula does not account for real-time dynamics, such as time-varying channels in wireless communication. Designing systems that operate close to the Shannon limit requires sophisticated algorithms and significant computational power. Focuses only on the maximum data rate without addressing latency or delay, which are critical for real-time applications. High SNR is often required to achieve higher capacities, which may not be feasible in environments with significant interference or limited power.