this theorem provides the information about the maximum bit rate that can be transmitted over a communication channel and the maximum available bandwidth for a communication channel. this theorem provides a formula to calculate the capacity of the channel. There is a Shannon channel capacity calculator that can be used to calculate the capacity of any communication channel.

1. Advanced communication System
Title: Shannon-Hartley theorem
& TECHNOLOGY, NAWABSHAH
QUAID-E-AWAM UNIVERSITY OF ENGINEERING, SCIENCE &
TECHNOLOGY, NAWABSHAH
Name: Shafiqa Memon
Roll Number :19ES30
Assigned By: Dr. Nadeem Naeem
Department of Electronic Engineering

2. Shannon Hartley theorem
 Introduction:
 The Shannon-Hartley theorem, also known as the
Shannon capacity or the Shannon limit, is a
fundamental result in information theory that
establishes the maximum rate at which information
can be transmitted over a noisy communication
channel without error. It was formulated by Claude
Shannon and later extended by Ralph Hartley.

3. Shannon Hartley theorem
 In reality, we cannot have a noiseless channel; the
channel is always noisy. In 1944, Claude Shannon
introduced a formula, called the Shannon capacity,
to determine the theoretical highest data rate for a
noisy channel.
 The theorem provides a mathematical formula to
determine the maximum achievable data rate,
known as the channel capacity (C), in bits per
second (bps), for a given communication channel
with a specific bandwidth and signal-to-noise ratio
(SNR).

4. Shannon Hartley theorem
 Statement:
 The Shannon-Hartley theorem states that the
channel capacity is proportional to the available
bandwidth and to the signal-to-noise ratio. In
simpler terms, the greater the bandwidth, the higher
the capacity, and the higher the signal power relative
to the noise power, the higher the capacity.

5. Shannon Hartley theorem
 The Shannon Hartley formula to find the channel
capacity is given by:
 C =B× log2 (1 + SNR)
 Where:
 C is the channel capacity in bps
 B is the available bandwidth of the channel in hertz
(Hz)
 SNR is the signal-to-noise ratio, expressed as a
linear value (SNR = signal power / noise power)

6. Shannon Hartley theorem
Example: Consider an extremely noisy channel in which the value of
the signal-to-noise ratio is almost zero. In other words, the noise is so
strong that the signal is faint. For this channel the capacity C is
calculated as:
C=B log2 (1 + SNR)
C = B log2(1 + 0)
C = B log2 (1) where log2(1)=0
C = B × 0
C = 0
 This means that the capacity of this channel is zero regardless of the
bandwidth. In other words, we cannot receive any data through this
channel.

7. Shannon Hartley theorem
Advantages and Applications:
The Shannon-Hartley theorem has been influential in
the development of digital communication systems
and serves as a benchmark for evaluating the
performance of various communication technologies,
such as wireless networks, fiber optics, and satellite
communications. It helps engineers and researchers
understand the trade-offs between bandwidth, signal
power, and noise in designing efficient and reliable
communication systems.

8. Shannon Hartley Theorem
 Channel Capacity Calculator:
 This tool calculates the channel
capacity according to the Shannon-Hartley
theorem for a given bandwidth and SNR.
 The capacity is expressed in terms of bits per
second.

9. Thank You