Enter the bandwidth in Hertz (Hz) and the signal-to-noise ratio (SNR) into the calculator to determine the channel capacity according to the Shannon Hartley theorem. This calculator helps to estimate the maximum rate of data transmission for a communication channel.
Shannon Hartley Theorem Formula
The following formula is used to calculate the channel capacity.
C = B * log<sub>2</sub>(1 + SNR)
Variables:
- C is the channel capacity (bits per second)
- B is the bandwidth of the channel (Hz)
- SNR is the signal-to-noise ratio (dimensionless)
To calculate the channel capacity, multiply the bandwidth of the channel by the logarithm base 2 of one plus the signal-to-noise ratio.
What is the Shannon Hartley Theorem?
The Shannon Hartley theorem is a fundamental theorem in information theory that defines the maximum rate at which information can be transmitted over a communication channel of a specified bandwidth in the presence of noise. It is a cornerstone of digital communications and has implications for designing and analyzing communication systems.
How to Calculate Channel Capacity?
The following steps outline how to calculate the channel capacity using the Shannon Hartley theorem.
- First, determine the bandwidth of the channel (B) in Hertz (Hz).
- Next, determine the signal-to-noise ratio (SNR), which is dimensionless.
- Next, gather the formula from above = C = B * log2(1 + SNR).
- Finally, calculate the channel capacity (C) in bits per second.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
bandwidth of the channel (B) = 2000 Hz
signal-to-noise ratio (SNR) = 100
