Channel Capacity Calculator

Explore Shannon's Channel Capacity Theorem: C = B log₂(1 + SNR)

Channel Parameters

Channel Capacity Result

Bandwidth (B)

10 kHz

SNR (Linear)

1000.00

SNR (dB)

30.00 dB

Capacity (C)

99.66 kbps

Visualization

Formula Breakdown

Shannon-Hartley Theorem:

C = B × log₂(1 + SNR)

Where:

  • C = Channel capacity (bits per second)
  • B = Bandwidth (Hz)
  • SNR = Signal-to-Noise Ratio (linear, not dB)

Converting SNR from dB to linear:

SNRlinear = 10(SNRdB / 10)

Understanding Channel Capacity

What is Channel Capacity?

Channel capacity represents the theoretical maximum rate at which information can be transmitted over a communication channel with arbitrarily small error probability, given specific bandwidth and noise constraints.

Key Insights:

  • Bandwidth matters: Doubling bandwidth doubles capacity (linear relationship)
  • SNR has diminishing returns: The logarithmic relationship means doubling SNR doesn't double capacity
  • Fundamental limit: No coding scheme can exceed this capacity while maintaining reliable communication
  • Practical systems: Real systems operate below capacity due to practical constraints

Real-World Applications:

  • WiFi and cellular network design
  • Satellite communications
  • Fiber optic systems
  • Radio communications
  • Any digital communication system

Example:

A channel with 10 kHz bandwidth and 30 dB SNR (SNR = 1000) has a capacity of approximately 99.66 kbps. This means you can transmit up to 99,660 bits per second reliably through this channel.

SNR: dB vs Linear

Decibels (dB): A logarithmic scale commonly used in engineering

SNRdB = 10 × log₁₀(SNRlinear)

Common Conversions:

  • 0 dB = 1 (linear)
  • 10 dB = 10 (linear)
  • 20 dB = 100 (linear)
  • 30 dB = 1,000 (linear)
  • 40 dB = 10,000 (linear)

Why use dB?

  • Easier to work with very large or small numbers
  • Multiplication becomes addition (convenient for calculations)
  • Standard in telecommunications industry
Interactive Exploration Tips

Try these experiments:

  1. Double the bandwidth: Notice capacity doubles (linear relationship)
  2. Increase SNR by 10 dB: Capacity increases, but not by a factor of 10
  3. Compare visualizations: Switch between different graph modes to see relationships
  4. Low SNR scenario: Set SNR to 0-10 dB and see how capacity is severely limited
  5. High bandwidth, low SNR: See that bandwidth alone isn't enough without good SNR