1. What is Shannon's Theorem?

Definition: Shannon's Theorem, also known as the Shannon-Hartley theorem, defines the maximum rate at which information can be transmitted over a communications channel.

Purpose: It provides a fundamental limit on channel capacity for a given bandwidth and signal-to-noise ratio, regardless of the encoding technique used.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( C \) — Channel capacity (bits per second)
• \( B \) — Bandwidth of the channel (Hertz)
• \( S \) — Signal power (Watts)
• \( N \) — Noise power (Watts)

Explanation: The formula shows that channel capacity increases with bandwidth and with the logarithm of the signal-to-noise ratio.

3. Importance of Shannon's Theorem

Details: This theorem is fundamental to information theory and forms the theoretical basis for modern communication systems, including wireless networks, fiber optics, and digital broadcasting.

4. Using the Calculator

Tips: Enter the bandwidth in Hertz, signal power in Watts, and noise power in Watts. Bandwidth must be > 0, and signal + noise must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is signal-to-noise ratio (SNR)?
A: SNR is the ratio of signal power to noise power, often expressed in decibels (dB). Higher SNR means better signal quality.

Q2: Can channel capacity be infinite?
A: No, even with infinite bandwidth, capacity is limited by noise. As bandwidth increases, noise power also increases.

Q3: How is this different from Nyquist's theorem?
A: Nyquist gives the maximum symbol rate, while Shannon gives the maximum bit rate considering noise.

Q4: What's a typical SNR for communication systems?
A: Good systems might have 20-30 dB SNR (100-1000 linear ratio), while excellent systems might reach 40 dB or more.

Q5: How does this apply to digital systems?
A: Shannon's limit determines the theoretical maximum data rate that can be achieved with arbitrarily small error probability.